05 / 06

Van Inwagen On Uncreated Beings

William Lane Craig


Peter van Inwagen argues that (1) there are uncreated abstract objects like properties and (2) the affirmation of the existence of uncreated abstract objects is consistent with the affirmation of the Nicene Creed that God is the creator of all things. I dispute both of these contentions. An examination of ante-Nicene and Nicene theology reveals that the Church Fathers opposed the postulation of any uncreated entity apart from God Himself, including such entities as properties and numbers, which they identified as ideas in the mind of God. Moreover, a detailed examination of van Inwagen’s argument for properties reveals a variety of nominalistic responses of which van Inwagen takes scant cognizance, thereby undermining his claim that one can’t get away with nominalism.


In the opening paragraph of his provocative article “God and Other Uncreated Things,” Peter van Inwagen asks two questions: (1) Is there anything (other than Himself) that God has not created? and (2) Must a Christian take the statement of the Nicene Creed “I believe in one God, the Father Almighty, Maker of heaven and earth and of all things visible and invisible” to mean that God has created “everything, everything tout court, everything simpliciter, everything full stop, everything period?” [1]

Van Inwagen’s reiteration of synonymous qualifiers shows how exercised he is by this second question. For van Inwagen is a Christian philosopher who takes very seriously the constraints laid by the orthodox faith upon philosophical speculation and the conclusions reached thereby. He is clearly troubled by the fact that he feels forced philosophically to answer “Yes” to the first question despite the seemingly clear statement of the first article of the Creed to the contrary. He acknowledges,

I am happy to admit that I am uneasy about believing in the existence of ‘causally irrelevant’ objects. The fact that abstract objects, if they exist, can be neither causes or [sic] effects is one of the many features of abstract objects that make nominalism so attractive. I should very much like to be a nominalist, but I don’t see how to be one . . . . [2]

Van Inwagen tells us that when he recites the Nicene Creed, therefore,

I must regard the phrase ‘creator of all things visible and invisible’ as containing a tacitly restricted quantifier . . . . I commit myself only to the proposition that God is the creator of all things (besides himself) that can in some sense be either causes or effects. [3]

This is what he, as a realist about uncreated abstract objects, must do; but can he justifiably do so? That is the import of question (2) above. In van Inwagen’s words, “Is it permissible for the Christian to regard the range of the quantifier ‘everything’ in the sentence ‘God has created everything’ as restricted to a certain class of objects . . . .?” [4] The degree to which van Inwagen is conflicted about this issue is evident in the timorousness of his answer: “It is by no means prima facie absurd to suppose that this might be so.” [5] This answer, taken at face value, is so hedged (“might be,” “suppose,” “absurd,” “prima facie”) as to cease to be interesting or important. (Imagine being told, “It is by no means prima facie absurd to suppose that his threats of murder might be meant as a joke.”) What the interpreter wants to know is what the likely meaning of a text is, especially when it is orthodoxy that is at stake.

Van Inwagen states that his purpose is not to convince us that abstract objects—in particular, abstract objects that are free of concrete objects—exist. “My purpose is rather to defend the proposition that my belief is consistent with the creedal statement that God has created everything.” [6] Ostensibly, then, pride of place is being given to question (2) over question (1). It is surprising, then, how little effort and attention is actually given in his paper to a defense of van Inwagen’s answer to this question. So far as I can tell, all that we are given by way of a defense of a negative answer to question (2) is the plausibility of taking Jesus’ logion “With God all things are possible” (Mt. 19:26) as tacitly involving a restricted quantifier. Van Inwagen concludes, “This example . . . shows that it is at least not beyond dispute that in the creedal statement ‘God is the creator of all things,’ ‘all things’ must be understood as an unrestricted quantifier.” [7]

Van Inwagen’s conclusion seems to me, however, both a non sequitur and an irrelevancy. Jesus’ saying provides at best an illustration of a tacitly restricted universal quantifier. But it sheds no light at all upon the meaning of the first article of the Nicene Creed. We could just as well have illustrated van Inwagen’s point by the statement, “There’s nothing in the refrigerator.” Question (2) is a question about the meaning of the Nicene Creed, and no responsible answer to such a question can be given without serious engagement in exegesis and historical theology. [8] In any case, van Inwagen’s conclusion, taken at face value, is framed in such extreme terms that it ceases to be relevant. If his illustration actually does suffice to show that it is “not beyond dispute” that panton should be understood as an unrestricted quantifier, then the same is true with respect to any universally quantified statement and so is no longer interesting. What the Christian who is concerned to stay within the bounds of orthodoxy wants to know is how likely it is that the domain of the quantifier in the first article of the Creed is intended to be unrestricted or tacitly restricted in some way. [9]

Van Inwagen thinks that the domain of the quantifier in the opening article is tacitly restricted to objects that can enter into causal relations. But whereas he provides grounds for thinking that the quantifier in Jesus’ saying was intended to be restricted to matters of practical interest to people, van Inwagen provides no evidence at all to show that the formulators of Nicaea understood the domain of their quantifier to be in any way restricted. On the contrary, I think we have convincing evidence that they assumed the quantifier to be unrestricted in its scope. In the next section I explore some of that evidence.

Ante-Nicene Theology

At the heart of the Arian controversy which occasioned the convening of the Council of Nicaea lay a pair of terminological distinctions prevalent among the Church Fathers: agenetos/genetos and agennetos/gennetos. Most of us are familiar with the famous “i” which marked the difference between Christ as homoousios with the Father versus homoiousios with the Father, so that the difference between heresy and orthodoxy could rightly be said to hang on a single iota. But a similar world of difference lay in the single “n” by means of which Christ could be said to be agenetos but gennetos, in contrast to the Father, who is both agenetos and agennetos. The word pair agenetos/genetos derives from the verb “ginomai,” which means to become or to come into being. “Agenetos” means unoriginated or uncreated, in contrast to “genetos,” that which is created or originated. It (in the plural) is precisely the Greek equivalent of the word featured in the title of van Inwagen’s paper: “God and other ageneta.” The second word pair agennetos/gennetos derives from the verb “ginnao,” which means to beget. That which is agennetos is unbegotten, while that which is gennetos is begotten.

Being homonyms as well as so close in spelling, these terms were not always clearly distinguished by the early Church Fathers. [10] For example, Justin Martyr asserts, “God alone is agennetos and incorruptible, and therefore He is God, but all other things after Him are genneta and corruptible” (Dialogue with Trypho a Jew [Dialogus cum Tryphoni] 5.30-33). Here the contrast is evidently intended to be between the uncreated and the created, since inanimate things are not properly said to be begotten. As G. L. Prestige notes, so long as reference was being made to God the Father, no harm was done in failing to distinguish between the agenetos and the agennetos, since the Father is both. Athenagoras, Irenaeus, Hippolytus, and Origen will sometimes mix terms, contrasting the agenetos and the gennetos. Again, little harm is done, so long as one is contrasting non-divine beings, even though inanimate objects would be more appropriately called geneta than genneta. But with the rise of the Arian threat, greater precision became necessary.

As Athanasius, that great champion of Nicene orthodoxy, explains, Arians had borrowed the term “agenetos” from Greek philosophy and applied it exclusively to God the Father (Defense of the Nicene Definition [De decretis] 7: “On the Arian symbol ‘Agenetos’;” cf. Discourses against the Arians [Orationes contra Arianos IV] 1.9.30; On the Councils of Ariminum and Seleucia [De synodis]46-47). The relevant meaning of the term, he notes, is “what exists but was neither originated nor had origin of being, but is everlasting and indestructible.” He complains with obvious indignation that the Arian strategy was to ask the unsuspecting whether the agenetos is one or two. When the person replied that the agenetos is one, the Arians would spring the trap by exclaiming, “Then the Son is genetos!” and thus a creature. Not surprisingly, then, Athanasius says that he prefers to use the term “Father” rather than “agenetos,” though he recognizes that the latter term has a proper and religious use (Defense 7.31-32; Discourses 1.9.33-34).

On Athanasius’ view, although God is agenetos, the Father alone is self-existent, the Son having his existence from the Father by being begotten eternally of the Father and all else being in turn created by the Son. He writes,

We do not regard God the Creator of all, the Son of God, as a creature, or thing made, or as made out of nothing, for He is truly existent from Him who exists, alone existing from Him who alone exists, in as much as the like glory and power was eternally and conjointly begotten of the Father. . . . All things to wit were made through the Son; but He Himself is not a creature, as Paul says of the Lord: ‘In Him were all things created, and He is before all’ (Col. 1.16). Now He says not, ‘was created’ before all things, but ‘is’ before all things. To be created, namely, is applicable to all things, but ‘is before all’ applies to the Son only (Statement of Faith [Expositio fidei] 3).

According to Athanasius, then, God alone is agenetos; but the Father is agennetos while the Son is gennetos; everything else is genetos. So in his own statement of faith, Athanasius confesses, “We believe in one Unbegotten God, Father Almighty, maker of all things both visible and invisible, that hath His being from Himself. And in one Only-begotten Word, Wisdom, Son, begotten of the Father without beginning and eternally” (Statement of Faith 1).

Like the Arian heretics, the ante-Nicene and Nicene Church Fathers rejected any suggestion that there might exist ageneta apart from God alone:

there is not a plurality of agenneta: for if there were some difference between them, you would not discover the cause of the difference, though you searched for it; but after letting the mind ever wander to infinity, you would at length, wearied out, stop at one agenneton, and say that this is the Cause of all things (Justin Dialogue 5).

it is impossible for two ageneta to exist together (Methodius On Free Will [Peri tou autexousiou] 5)

in all things God has the pre-eminence, who alone is uncreated, the first of all things, and the primary cause of the existence of all, while all other things remain under God’s subjection (Irenaeus Against heresies [Adversus haeresis] 4.38.3)

For before all things God was alone, himself his own world and location and everything—alone however because there was nothing external beside him (Tertullian Against Praxeas [Contra Praxeum] 5.13-15).

God, subsisting alone, and having nothing contemporaneous with Himself, determined to create the world. And conceiving the world in mind, and willing and uttering the Word, He made it; and straightaway it appeared formed as it had pleased Him. For us, then, it is sufficient simply to know that there was nothing contemporaneous with God. Beside Him there was nothing (Hippolytus Against Noetus [Contra Noetum] 10.1; cf. Refutation of All Heresies 10.28).

the Father is the one agennetos (Epiphanius Panarion [Adversus haeresis 33.7.6]

It would be flawed exegesis, I think, to suggest that the quantifiers in these statements are not intended to be unrestricted. According to patristic scholar Harry Austryn Wolfson, [11] the Church Fathers all accepted the following three principles:

1. God alone is uncreated.

2. Nothing is co-eternal with God.

3. Eternality implies deity.

Each of these principles implies that there are no ageneta apart from God alone.

But lest it be suggested that abstracta were somehow exempted from these principles, we shall see that the ante-Nicene Church Fathers explicitly rejected the view, championed by van Inwagen, that entities such as properties and numbers are ageneta. The Fathers were familiar with the metaphysical worldviews of Plato and Pythagoras and agreed with them that there is one agenetos from which all reality derives; but the Fathers identified this agenetos, not with an impersonal form or number, but with the Hebrew God, who has created all things (other than Himself) ex nihilo.

Although the primary target in their defense of creatio ex nihilo was the doctrine of the independence and eternality of matter, [12] the Fathers did not countenance the idea that although matter might be originated, properties might nonetheless be beginningless and uncreated. Athenagoras characterizes Christians as those who “distinguish and separate the uncreated (agennetos) and the created (genetos)” (Plea for the Christians 15). Although Athenagoras assumed that the latter realm was the material world (including material spirits), that is not because he considered properties to be agenneta but rather because he considered properties to lack any existence independent of concrete objects. His conviction is evident in his comment on how Satan is opposed to God’s goodness:

. . . to the good that is in God, which belongs of necessity to Him and co-exists with Him, as colour with body, without which it has no existence (not as being part of it, but as an attendant property co-existing with it, united and blended, just as it is natural for fire to be yellow and the ether dark blue)—to the good that is in God, I say, the spirit which is about matter. . . is opposed” (Plea 24, my emphasis).

Athenagoras here clearly rejects the idea that properties have some sort of independent existence apart from concrete objects.

His fellow Apologist Tatian affirms that God alone is without beginning and attributes to Him the creation of both matter and form:

Our God did not begin to be in time; He alone is without beginning, and He Himself is the beginning of all things. God is a Spirit, not pervading matter, but the Maker of material spirits and of the forms [schematon] that are in matter; He is invisible, impalpable, being Himself the Father of both sensible and invisible things (Address to the Greeks [Oratio ad Graecos] 4.10-14).

Tatian rejected the notion that there is besides God any eternal, uncreated thing, even pure forms. Instantiated forms he would presumably take to belong to the realm of things invisible.

Methodius in his dialogue Concerning Free Will [Peri tou autexousiou], after declaring that there cannot be two ageneta, defends creatio ex nihilo by having Orthodoxus say to Valentinian:

ORTHODOXUS: Do you say then, that there co-exists with God matter without qualities out of which He formed the beginning of this world?
ORTHODOXUS. If, then, matter had no qualities, and the world were produced by God, and qualities exist in the world, then God is the maker of qualities?
ORTHODOXUS. Now, as I heard you say some time ago that it is impossible for anything to come into being out of that which has no existence, answer my question: Do you think that the qualities of the world were not produced out of any existing qualities?
ORTHODOXUS. And that they are something distinct from substances?
ORTHODOXUS. If, then, qualities were neither made by God out of any ready at hand, nor derive their existence from substances, because they are not substances, we must say that they were produced by God out of what had no existence. Wherefore I thought you spoke extravagantly in saying that it was impossible to suppose that anything was produced by God out of what did not exist.

Here Orthodoxus, who obviously speaks for the orthodox faith, will not allow that even properties are uncreated by God. For God alone is uncreated.

Neither were numbers thought to exist independently of God as ageneta. Thus, Hippolytus traces the heresy of Valentinian Gnosticism to the systems of Plato and Pythagoras and ultimately to the Egyptians (Refutation 6.16). The latter asserted that ultimate reality is an agennetos unit and that the other numbers are generated from it (Refutation 4.43). “Pythagoras, then, declared the originating principle of the universe to be the unbegotten monad, and the generated duad, and the rest of the numbers” (Refutation 6.18). The material world was thought to be in turn generated from these incorporeal principles. “There are, then, according to Pythagoras, two worlds: one intelligible, which has the monad for an originating principle; and the other sensible. . . . Nothing, he says, of intelligibles can be known to us from sense. For he says neither has eye seen, nor ear heard, nor whatsoever any of the senses known that (which is cognized by mind)” (Refutation 6.19; cf. Clement of Alexandria Stromata 5.14). Hippolytus then makes the connection with Valentinus: “And from this (system), not from the Gospels, Valentinus . . . has collected the (materials of) heresy—and may (therefore) justly be reckoned a Pythagorean and Platonist, not a Christian” (Refutation 6.24). Hippolytus charges that “Valentinus. . . and the entire school of these (heretics), as disciples of Pythagoras and Plato, (and) following these guides, have laid down as the fundamental principle of their doctrine the arithmetical system. For, likewise, according to these (Valentinians), the originating cause of the universe is a Monad, agennetos, imperishable, incomprehensible, inconceivable, productive, and a cause of the generation of all existent things” (Ibid.).

The Logos doctrine of the Greek Apologists provided the key for grounding the intelligible realm in God rather than in some independent realm of self-subsisting entities like numbers or forms. [13]Combining the Gospel of John’s presentation of Christ as the pre-existent Logos who was with God and was God and through whom all things came into being (John 1.1-3) with Philo of Alexandria’s conception of the Logos as the immanent mind of God in which the Platonic realm of ideas subsists (On the Creation of the World according to Moses [De opificio mundi] 4.16-25), Tatian offers one of the earliest expositions of this doctrine:

God was in the beginning; but the beginning, we have been taught, is the power of the Logos. For the Lord of the universe, who is Himself the necessary ground of all being, inasmuch as no creature was yet in existence, was alone; but inasmuch as He was all power, Himself the necessary ground of things visible and invisible, with Him were all things; with Him by Logos-power, the Logos himself also, who was in Him, subsists. And by His simple will, the Logos springs forth; and the Logos, not coming forth in vain, becomes the first-begotten work of the Father. Him (the Logos) we know to be the beginning of the world (Address to the Greeks 5.1-9). [14]

The invisible, intelligible realm of exemplar ideas exists in the immanent Logos, who, proceeding out from God the Father (whether eternally or at the moment of creation), is begotten as God the Son. He then creates the sensible world of things that we experience.

Hippolytus, in language that would later echo at Nicaea, exults in the fact that even the opponents of orthodoxy must finally concede that there is but one agenetos which is the source of all reality:

God, subsisting alone, and having nothing contemporaneous with Himself, determined to create the world. And conceiving the world in mind, and willing and uttering the Word, He made it; and straightaway it appeared, formed as it has pleased Him. For us, then, it is sufficient simply to know that there was nothing contemporaneous with God. Beside Him there was nothing; but He, while existing alone, yet existed in plurality. For He was neither without reason, nor wisdom, nor power, nor counsel. And all things were in Him, and He was the All. . . . He begat the Word; . . . and thus there appeared another beside Himself. But when I say another, I do not mean that there are two Gods, but that it is only as light of light. . . . Who then adduces a multitude of gods brought in, time after time? For all are shut up, however unwillingly, to admit this fact, that the all runs up into One. If, then, all things run up into One, even according to Valentinus, and Marcion, and Cerinthus, and all their fooleries, they are also reduced, however unwillingly, to this position, that they must acknowledge that the One is the cause of all things. Thus, then, these too, though they wish it not, fall in with the truth, and admit that one God made all things according to His good pleasure (Against Noetus 10-11; cf. Refutation 10.28-29).

It is ironic, in view of the present debate, that even the heretics against whom the Church Fathers contended did not think to postulate a plurality of ageneta. Whether Gnostic, Arian, or Christian, all were committed to there being a single agenetos[15] The challenge facing the framers of Nicaea was how to preserve the deity and distinctness of the Son while acknowledging that there cannot exist a plurality of ageneta.

Recurring, then, to the Nicene formula, we can see in light of its historical background that when God the Father is said to be the Maker (poieten) of all things (panton) visible and invisible, the domain of quantification is intended to be unlimited. There is a state of affairs in the actual world which consists of God existing alone in absolute solitude. Even numbers and properties do not exist outside Him, much less independently of Him, for He is the ground of all being, and nothing is co-eternal with Him. The tradition of the Logos Christology of the Greek Apologists comes to expression in the Nicene affirmation that the Son of God is begotten, not made (gennethenta ou poiethenta). Echos of the prologue to the fourth Gospel are heard in the affirmation that it is the Son through whom all things came to be (di’ ou ta panta egeneto). Since he himself is unmade and everything else is genetos, the Son must be agenetos and is therefore God, even though as the Son he is gennetos from the Father.

In one of the earliest commentaries on the Creed promulgated at Nicaea, Theodore of Mopsuestia lays special emphasis on the Creed’s distinguishing God as Father and as Creator:

He is the Father of the Son and the Creator of the creatures. The creatures were created later while the Son was from the beginning with Him and from Him. This is the difference between Father and Creator. He is called the Father of the one who was born of Him, and the Creator of all the natures which are outside Him and which were created from nothing by His will.

He is called and He is the Father of the Son, because He is of the same nature as the one who is said to be His Son, but He is the Creator of everything because everything was created from nothing; and although the natures of the visible and invisible things differ among themselves yet all these created things, whether visible or invisible, came into existence by the will of their Maker. The fact that they were made from nothing is common to all of them, as all were created from nothing by the will of their Maker. Because everything was created by Him and is sustained by His will, everything whether visible or not owes praise to the Creator (Commentary on the Nicene Creed).

There is no tertium quid: the Son alone is begotten of the Father, and everything outside God is created ex nihilo. The idea that there could be things co-eternal with God and unmade by Him is excluded.

Now it might be said that since God’s ideas are not identical with God Himself—God is not, after all, an idea—, His ideas must be ageneta in their own right. Thus, in spite of themselves, the Church Fathers, by identifying Platonic objects with the divine ideas, are committed the reality of eternal, uncreated things other than God. Later medieval theologians like Thomas Aquinas would avoid the problem by denying a plurality of divine ideas in favor of a strong doctrine of divine simplicity; but so strong a doctrine of simplicity is unlikely to have characterized the Ante-Nicene and Nicene Fathers. But if there is a plurality of divine ideas conceived by the Logos, then there is a multitude of uncreated things.

The objection presupposes, however, that the Fathers accorded to the divine ideas a substantial existence as things or objects. This assumption is dubious. The Fathers did not seem to think that there was a conflict between their belief in a single, all-originating agenetos and their Logos doctrine. Their unrelenting insistence on there being but one agenetos from which all else derives requires that they would not have accorded to the divine ideas the status of things or objects. There is some tantalizing evidence for this conclusion in a creed formulated by the Eastern bishops in the aftermath of Nicaea. As all students of church history know, the Eastern churches were deeply opposed to the Nicene Creed’s affirmation that the Son is homoousios with the Father because the affirmation that the Father and the Son are the same substance would collapse the distinction between the members of the Trinity. So the Eastern bishops formulated a number of alternative creeds in which they sought to make clear their full commitment to the deity of the Son without employing the term homoousios. Following the Council of Sardica in 343, the Eastern bishops sent to the church in Italy a lengthy credal statement dealing with the relation between the Father and the Son. In it they affirm that “there is one unbegotten principle without beginning, the Father of Christ” and advise that “it must not be thought that the Son is co-inoriginate (συνάναρχον) or co-unbegotten (συναγέννητον) with the Father,” for “there is but one God perfect in himself, unbegotten, inoriginate, and invisible, the God and Father of the only-begotten, who alone has existence from himself, and alone affords existence abundantly to all other things.” [16] Then comes this intriguing anathema:

Moreover we execrate and anathematize those who falsely style him the mere unsubstantial word of God, having existence only in another, either as the word to which utterance is given, or as the word conceived in the mind. [17]

Here the existence of the Son or Word is contrasted with the existence of word-types or concepts in the divine mind. These, in contrast to the Son, have an existence which is “unsubstantial” and merely “in another.” By contrast

we know him to be not simply the word of God by utterance or mental conception, but God the living Word subsisting of himself; . . . who did, not by presence only, co-exist . . . with his Father before the ages, and ministered to him at the creation of all things, whether visible or invisible, but was the substantial Word of the Father, and God of God. [18]

The Son has substantial existence, subsisting of himself (though, as we have seen, begotten), not merely present in another, and he created everything else. It seems clear that the Fathers did not consider linguistic types or mental concepts in the divine mind to be real things. Accordingly, the divine ideas are not, in fact, uncreated things.

So if confronted with an ontology which included abstract objects which were ageneta and so co-eternal with God, the Church Fathers would have rejected such an account as blasphemous, since such an account would impugn God’s aseity by denying its uniqueness and undermine creatio ex nihilo by denying that God is the universal ground of being. The Fathers could not therefore exempt them from God’s creative power, since He is the sole and all-originating agenetos.

Indeed, the very fact that abstract objects such as are countenanced by van Inwagen are causally unrelated to anything, even God, is precisely what would make such an account so objectionable. Orthodoxy could not countenance such a metaphysical pluralism. The Fathers would have been bewildered by van Inwagen’s parting shot: “whether there are objects to which the concept of causation has no application is a question that theology should regard as no business of hers.” [19] The framers of Nicaea could not, as the heirs and protectors of the orthodox faith, have looked upon such a question with indifference. Indeed, in affirming that God the Father is the Maker of all things, that all things are geneta through God the Son, they did not, we may be thankful, ignore this question but answered it in the negative.

Are There Other Uncreated Beings?

If we take van Inwagen’s purpose statement seriously, we must say, therefore, that he has failed to establish the central thesis of his paper. He writes,

Now I will affirm something I believe. It will not be my purpose to try to convince you that belief of mine is true. My purpose is rather to defend the proposition that my belief is consistent with the creedal statement that God has created everything. The belief, as you will no doubt have guessed, is that there are free abstract objects [i.e., abstract objects which exist independently of particular concrete objects]. [20]

Here the belief that free abstract objects exist is merely affirmed without argument. The ostensible purpose for which van Inwagen has written his paper is to defend the compatibility of his belief in abstracta with Nicene orthodoxy. But, in fact, van Inwagen has devoted a mere two paragraphs to that defense and fallen terribly short. [21]

But then what purpose is the remainder of his paper supposed to serve? It seems to be an answer to van Inwagen’s original question (1): Is there anything that God has not created? Specifically, it seems devoted to a defense of the following argument: [22]

1. There are free abstract objects.

2. Free abstract objects cannot enter into causal relations.

3. Creation is a causal relation.

4. Therefore, there are uncreated abstract objects.

Van Inwagen then says that “A theist might dispute my thesis that there are uncreated abstract objects, and the argument I have given for this thesis, in either of two ways:” nominalism or Aristotelianism. So he proceeds to criticize those positions.

Now nominalists and Aristotelians reject (1), the premise the defense of which van Inwagen eschewed. Notwithstanding his disclaimer, the rest of the paper does, indeed, seem to be a defense of this belief against defeaters, principally Aristotelianism and, in the latter part of the paper, yet a third alternative, conceptualism. We are referred to another paper for van Inwagen’s defense of (1) against nominalism. [23]

Despite his statement to the contrary, then, it seems clear that van Inwagen’s paper is not about the compatibility of (4) with Nicene orthodoxy but is almost entirely devoted to a defense of (1), his professed belief in the existence of free abstract objects. Indeed, by rejecting all the alternative accounts, he in effect offers a positive case for accepting the truth of (1). The argument above is intended, in turn, to justify an affirmative answer to his first question.

There is, however, in addition to nominalism, Aristotelianism, and conceptualism a fourth potential defeater of his thesis that there are uncreated abstract objects which van Inwagen does not mention but which deserves a place at the table, namely, absolute creationism, the view that free abstract objects exist and that God has created them, in contradiction to (2). [24] One problem for absolute creationism from a biblical perspective is that creation is an inherently temporal concept implying a temporal beginning of existence for any created thing; yet it is plausible that many types of abstract objects, if they exist, exist necessarily and so have no beginning of existence. Since they would be co-eternal with God, they could not be properly said to have been created. Some other category would have to be chosen to express their ontological dependence on God, for example, their being sustained by God. Alternatively, the absolute creationist might broaden the concept of creation to encompass anything brought into or sustained in being by God. Van Inwagen opines, “I am myself inclined to think that ‘x exists necessarily’ does entail ‘x is uncreated’, but I will not use this thesis as a premise because it is controversial and I know of no very interesting argument for it.” [25]  This remark suggests that while he would not be sympathetic to absolute creationism due to the incompatibility of being created with being necessary, van Inwagen has no substantive argument against it.

A second and more serious problem with absolute creationism is not so easy to evade: the bootstrapping objection. [26] Simply stated, the problem is that the creation of certain abstract objects presupposes that those objects already exist, so that a vicious explanatory circle is formed. For example, God cannot create the property of being powerful unless He already has the property of being powerful. The challenge facing absolute creationists is to find a way out of this explanatory circle. Indeed, I should say that the problem posed by the existence of abstract objects to classical theism stems not from their necessary existence but from, in certain cases, their uncreatability. It is not the existence of abstract objects as such, or even of free abstract objects, that poses a serious challenge to divine aseity but rather the putative existence of uncreatables.

It is puzzling that van Inwagen takes no cognizance of this problem in his treatment of uncreated beings. Indeed, he says that creationists “could, of course, simply insist that—however hard it may be to see what the creation of ante res universals might consist in—God nevertheless does perform this act of creation. And there is no way to refute this position.” [27] This is a stunning concession. Absolute creationism would offer the means of reconciling van Inwagen’s belief in free abstract objects with Nicene orthodoxy. So why in the absence of any compelling reason to reject it does van Inwagen not eagerly embrace this solution? I am baffled by his failure to explore this alternative. Those who are not so sanguine as van Inwagen about the prospects of absolute creationism, however, will be motivated to look elsewhere for a way out.

A Nominalist Way Out?

So, we might ask, what are the prospects for a nominalistic solution to the problem of uncreatables? Contemporary nominalism is a diverse and rich cornucopia of views united by their anti-realism concerning abstract objects. Why does van Inwagen think that none of these is a viable alternative to the platonism he reluctantly embraces? What forces him, an unwilling lover, into platonism’s arms? He drops hints along the way—such as his denial that there is any suffering in the world or that there is a crack in the Liberty Bell, lest there be things in the world uncreated by God—, but it is not until the paper’s close that he becomes explicit:

I should very much like to be a nominalist, but I don’t see how to be one—since (having been exposed to Philosophical Investigations at an impressionable age) I think that most of the things we human beings believe must be true, and (having come in more mature years to accept Quine’s theses on ontological commitment, and having come to believe that many of the things we all believe involve ineliminable quantification over abstract objects) I think that a very significant proportion of the things we believe entail the existence of abstract objects. [28]

The first belief—that most of the things we believe are true—precludes Fictionalism, while the second belief—that a significant proportion of the things we believe entails the existence of abstract objects—precludes nominalistic theories of quantification and reference according to which true statements involving reference, or apparent reference, to or quantification over abstract objects are not, in fact, ontologically committing. Since van Inwagen accepts a version of Quine’s Criterion of Ontological Commitment and since he thinks abstract object talk cannot be entirely paraphrased away (“many of the things we all believe involve ineliminable quantification over abstract objects”), he considers us committed by the things we believe to the reality of abstract objects. These two beliefs—that most of what we believe is true and that much of what we believe commits us to the reality of abstract objects—are so deeply held by van Inwagen that his resistance to platonism is overcome.

Just how deeply committed to those two beliefs van Inwagen is becomes evident in his critique of nominalism. For wholly apart from considerations of Christian orthodoxy, he explains, “It would better not to believe in abstract objects if we could get away with it.” [29] Van Inwagen thinks that we should reject platonism if we can. For it is very puzzling that objects should fall into two so radically different and exclusive categories as abstract and concrete. [30] It would be much more appealing to suppose that one of the categories is empty. But concrete objects are indisputably real and well-understood, in contrast to abstract objects. So we should presume that abstract objects do not exist. Nominalism of some sort is thus the default position. Indeed, van Inwagen believes, “one should not believe in abstract objects unless one feels rationally compelled by some weighty consideration or argument. . . . my conclusion is that a philosopher should wish not to be a platonist if it’s rationally possible for the informed philosopher not to be a platonist.” [31]

This seems to set an almost impossibly high standard for adopting platonism. Overcoming the presumption of nominalism is said to require a rationally compelling argument. It looks as if Van Inwagen esteems his subsequent argument for platonism to be rationally compelling for any informed philosopher. But van Inwagen surely does not think that informed philosophers like Azzouni, Balaguer, Båve, Chihara, Field, Hellman, Leng, Maddy, Routley, Yablo, and so on, who resist van Inwagen’s argument and remain nominalists are irrational in doing so. [32] At the same time, Van Inwagen does not think that his argument is just person relative. Not being a subjectivist, he must think that anybody who knows what he knows is rationally compelled to embrace his conclusion (otherwise, he would not be rationally compelled to embrace it). Those who fail to agree with his conclusion must not believe something which he thinks he knows. So what does he know that makes it rationally impossible to get away with nominalism?

That takes us to his argument and the support for its premises. [33] Van Inwagen argues that we cannot get away with denying platonism because we cannot get away with denying the existence of properties. Van Inwagen thinks it fair to say that there are apparently such things as properties. For example, there is apparently such a thing as humanity, which the members of the class of human beings have in common. There is something, then, that the members of the human race have in common, and what could it be but the property humanity? That is apparently an existential claim, so that it follows that properties exist.

Van Inwagen observes that nominalists will say that despite appearances, there are no properties. I should think that so saying concedes too much on the part of the imagined nominalist interlocutor. For it is doubtful that properties even apparently exist. [34] Certainly there are brown dogs and big elephants, but the average man would not think that there exist in addition to these things the brownness of the dog and the bigness of the elephant (especially were he told that brownness is a timeless, spaceless object which is not even brown). [35] When told that there is such a thing as humanity, he would take one to be talking about the human race, to be speaking of all the people in the world. Thinking that there are objects called properties requires a degree of metaphysical abstraction that rises far above the ordinary world of appearance. It is far from apparent that there are properties; it requires a philosopher to isolate them as distinct entities.

In any case, van Inwagen proposes to settle the dispute by appeal to Quine’s ontological method. Quine says we should examine the beliefs we already have and see what they commit us to. This method for resolving disputes over ontology presupposes those aforementioned theses on ontological commitment of Quinean provenance which van Inwagen has come to accept in his mature years. What are these theses? In a more recent piece van Inwagen spells out exactly what he understands by “Quine’s theses on ontological commitment”:

The parties to such a dispute should examine, or be willing in principle to examine, the ontological implications of everything they want to affirm. And this examination should consist in various attempts to render the things they want to affirm into the quantifier-variable idiom (in sufficient depth that all the inferences they want to make from the things they want to affirm are logically valid). The ‘ontological implications’ of the things they affirm will be precisely the class of closed sentences starting with an existential-quantifier phrase (whose scope is the remainder of the sentence) that are logical consequences of the renderings into the quantifier-variable idiom of those things they want to affirm. Parties to the dispute who are unwilling to accept some ontological implication of a rendering of some thesis they have affirmed into the quantifier-variable idiom must find some other way of rendering that thesis into the quantifier-variable idiom (must find a paraphrase) that they are willing to accept and which does not have the unwanted implication. [36]

Van Inwagen characterizes Quine’s theses as a set of rules or a strategy for settling ontological disputes. As such they are neither true nor false, anymore than are rules for the arbitration of labor disputes. This raises the question why the nominalist should buy into Quine’s metaontological method for settling ontological disputes. Van Inwagen elsewhere says it is the “most profitable strategy to follow to get people to make their ontological commitments clear.” [37] Profitable in what sense? The nominalist is not apt to see it as profitable in view of the strange entities to which we may find ourselves committed simply for want of a paraphrase and in view of the subjectivity of its commitments due to the creativity permitted by paraphrase; and the adherent to Nicene orthodoxy who is not an absolute creationist will find it extremely unprofitable because it may well commit us to the reality of objects which he knows do not exist.

Van Inwagen seeks to motivate adoption of Quine’s metaontology by appeal to its application in the case of the ontological status of holes. In order to avoid quantifying over holes, he says, the materialist has to put forward symbolizations of key sentences that are “bizarre.” “Certain untoward consequences of a strict nominalistic materialism thus become evident only when one adopts Quine’s strategy for clarifying ontological disputes—and it is unlikely that they would otherwise have been noticed.” [38] The general lesson to be drawn from this, he says, is that “If Quine’s ‘rules’ for conducting ontological disputes are not followed, then, . . . it is almost certain that many untoward consequences of the disputed positions will be obscured by imprecision and wishful thinking.” [39]What van Inwagen does not seem to appreciate is that these untoward consequences only result precisely as a consequence of adopting Quine’s procedure. If one shuns the need of a paraphrase, one will not be forced to bizarre symbolizations; if one denies that one is ontologically committed to the values of bound variables, one will not be troubled in the first place by quantifying over holes and other dubious entities. The nominalist who rejects Quine’s metaontological method will thus not be saddled with the untoward consequences that Quine’s procedure would force upon him. The exposure of such consequences thus provides no reason at all for adoption of Quine’s procedure. Indeed, Quine’s procedure, the nominalist will insist, has the decided drawback that it could force us to embrace all sorts of spurious reifications like holes, Wednesdays, Sherlock Holmes,—and properties.

But let us follow van Inwagen’s argument to its conclusion. He invites us to suppose that we find that we hold the belief that “Spiders share some of the anatomical features of insects.” If we examine the meaning of this sentence, we find that what it says is this: “There are anatomical features that insects have and spiders also have,” or in the canonical language of quantification, “It is true of at least one thing that it is such that it is an anatomical feature and insects have it and spiders also have it.” [40] Now if there are anatomical features that insects have and spiders have, then there are anatomical features that insects have; and if there are anatomical features that insects have, then there are anatomical features—period. An anatomical feature seems to be a property. It follows that properties exist. [41]

Van Inwagen says that there are four possible ways in which the nominalist might respond to this argument:

(1) Become a platonist.

(2) Abandon the belief that spiders share some of the anatomical features of insects.

(3) Show that it does not follow that there are anatomical features.

(4) Admit the apparent inconsistency of one’s beliefs, affirm one’s nominalistic faith that this inconsistency is apparent rather than real, and confess that one doesn’t know at present where the fault in the argument lies.

In what follows I propose to explore these various options. My purpose will not be to endorse or argue for any of the particular nominalistic alternatives I shall sketch but, more modestly, to argue that van Inwagen has not, in his cited works, shown them to be untenable, so that one is forced to embrace option (1).

Option (1)

Van Inwagen favors option (1), which is also the option preferred by the absolute creationist. But van Inwagen never really tries to justify the adoption of (1) over its rivals. In fact, all he claims is, “A plausible case can be made for the thesis that this belief [viz., that spiders share some of the anatomical features of insects] commits us to the existence of properties.” [42] But given the presumption of nominalism, a merely plausible case is far from adequate to warrant adoption of (1). For, one will recall, van Inwagen requires a rationally compelling argument in order to overcome the strong presumption of nominalism with which he came to this inquiry. That he does not even try to provide.

Option (4)

Consider now option (4). Van Inwagen grants that “(4) is always an option, but no philosopher is likely to embrace it except as a last resort.” [43] This retort is far too quick. For it forgets once more the presumption of nominalism with which we come to this inquiry. In van Inwagen’s view, we approach the argument with very good grounds already for thinking nominalism to be true. Like Zeno’s Paradoxes or McTaggart’s Paradox, the present argument may strike us as a recalcitrant brainteaser whose conclusion we have excellent reason to think is false. It must not be forgotten that in van Inwagen’s view, these four options are not on a level playing field, for we come to the argument with very strong reason already in hand for thinking (1) to be false. [44] Given the difficulty of the issues before us and the contemporary debate raging over them, (4) remains a very reasonable option, indeed, in which case the adoption of (1) has not been justified.

Moreover, (4) becomes even more viable an option when we recall that Nicene orthodoxy implies either absolute creationism or the falsity of (1). The Christian philosopher does not consider the present argument in a vacuum. Adopting (1) will require either embracing absolute creationism or else endorsing an ad hoc exegesis of the Nicene Creed that violates the canons of the historical-grammatical method. If the objection to absolute creationism strikes us as more compelling than the objections to nominalism, then faithfulness to Christian orthodoxy makes (4) an attractive and reasonable alternative.

It seems to me therefore that even if van Inwagen’s objections to options (2) and (3) should prove to be persuasive, he has not thereby eliminated nominalism as a defeater of his argument for uncreated abstract objects. But are his reasons for rejecting options (2) and (3) persuasive?

Option (2)

Option (2) represents a Fictionalist alternative: we hold that it is not true that spiders share some of the anatomical features of insects. Now it needs to be carefully understood what it is that the Fictionalist is here denying. He is not denying, for example, that spiders have legs and insects have legs. What he denies is that the similarity of spiders to insects is to be parsed in metaphysical terms of their having properties, since properties, understood as abstract objects, do not exist. Outside the philosophy seminar, as van Inwagen puts it, the statement that spiders share some of the anatomical features of insects is unobjectionable and harmless. It is only when a metaphysician like van Inwagen starts pressing the statement as a piece of serious metaphysics that the Fictionalist protests that taken as an assertion implying the existence of abstracta like properties the statement is not true. The Fictionalist may or may not think that there are suitable paraphrases of the assertion which are free of platonistic commitments. If there are not, then the Fictionalist will regard such statements as simply false, so that the metaphysical commitments of our discourse in general will not extend beyond the nominalistic content of that discourse. Although property-talk is deeply embedded in our language and may even be indispensable for describing how the physical world is, such talk neither commits us to the existence of abstract objects nor adds to our knowledge of how the world really is.

Van Inwagen thinks that option (2) “is not very attractive” for at least two reasons. First, it is a simple fact of biology that spiders share some of the anatomical features of insects. This retort, however, misrepresents the Fictionalist position. It is just as misleading as the assertion, which van Inwagen vigorously protests, that “Peter van Inwagen believes that there are no chairs.” [45] The Fictionalist is not claiming, for example, that a person examining an insect will discover that it has no legs, eyes, mouth, and so forth, as a spider does. Rather his claim is that biology has no stake in the existence of causally irrelevant, abstract objects, which, were they magically to vanish overnight, would have absolutely no effect upon the organisms studied by biologists. The nominalistic content of biology is quite independent of the platonistic implications of sentences used in biological discussions and is all that matters to biologists. It is not a simple fact of biology that spiders have properties; this is pure metaphysics.

Second, there are great many “simple facts” that could have been used as a premiss in an essentially identical argument for the conclusion that there properties. This, I think, is the crucial objection and serves to recall van Inwagen’s deeply held belief that most of the things we believe are true. If we must regard all sentences implying the existence of properties as false, then it may no longer be the case that most of what we believe is true.

One cannot resist the ad hominem observation that this is an odd objection from a metaphysician who believes that scarcely any of the perceived objects about us exist. On van Inwagen’s view, the sentence “There are two very valuable chairs in the next room” seems to have much the same status as sentences quantifying over properties have for the Fictionalist. Van Inwagen says that his philosophy of language permits him to affirm that people who make such claims often say something literally true, so that he does not, like the Fictionalist, ascribe falsity to such sentences. But van Inwagen admits, “If. . . I accepted this austere philosophy of language, then . . . I should not be willing to say that people who uttered things like ‘There are two very valuable chairs in the next room’ very often said what was true. I should be willing to say only that they very often said what might be treated as a truth for all practical purposes.” [46] But this is precisely what the Fictionalist says with respect to properties. He is simply more austere in his philosophy of language in granting that sentences quantifying over or referring to properties are literally false, though they may be taken as truths for all practical purposes.

Van Inwagen is sensitive to the objection that his own metaphysical view implies that many of our commonly accepted beliefs turn out to be false. He asks,

Is the existence of chairs—or, at any rate, of things suitable for sitting on, like stones and stumps—a matter of Universal Belief? If it were, this would count strongly against my position, for any philosopher who denies what practically everyone believes is, so far as I can see, adopting a position according to which the human capacity for knowing the truth about things is radically defective. And why should he think that his own capacities are the exception to the rule? [47]

So van Inwagen essays to prove that his view of material objects “does not contradict our ordinary beliefs.” [48] His defense is:

It is far from obvious, however, that it is a matter of Universal Belief that there are chairs. In fact, to say that any particular proposition that would be of interest to philosophers belongs to the body of Universal Belief is to put forward a philosophical thesis and no trivial one. It is difficult to settle such questions, in part because there are lots of things that one might express by uttering ‘philosophical’ sentences like ‘There are chairs’, and some of them might be things that are irrelevant to the concerns of ordinary life. It may be that the intellectual training provided by dealing with ordinary matters ill equips one to appreciate them. [49]

This defense strikes me as inadequate. I think it is indisputable that the vast majority of people believe that there are objects that one can sit on like chairs and stones and stumps. So saying is not to put forward a philosophical thesis but a sociological thesis. What is a philosophical thesis is the thesis that there are objects like chairs, and the average person accepts that thesis almost unthinkingly. Certainly there are many things that the philosopher might regard as the propositional content expressed by utterances like “There are chairs” other than that there are chairs, and it is likely that the common man believes none of them. [50]

The concern here is not merely ad hominem. The real question raised by this Auseinandersetzung is why we should invest commonly held beliefs with such authority as van Inwagen lodges in them. For as he says, the intellectual training provided by dealing with ordinary matters ill equips the average person to handle such recondite metaphysical matters. So why accept the average man’s beliefs about the existence of physical objects like chairs—or whether spiders share properties with insects? Indeed, the Fictionalist enjoys the advantage that the average person does not, in fact, believe that in addition to objects like chairs, there also exist (abstract) objects like having four legs or being made of wood. The average man would be quite surprised to learn that his belief, say, that the chair and the couch have the same number of legs entails that numbers exist. We can paraphrase away such an ontological commitment by saying that the chair and the couch each has four legs, but why not just say that the common man’s belief is strictly false?

Van Inwagen’s answer to that question is, as we have seen, that so saying impugns the human capacity for knowing the truth about things as being radically defective. Such a concern strikes me as unduly alarmist. The Fictionalist espouses what van Inwagen calls an austere philosophy of language, such as is useful for the seminar room; but like van Inwagen he can distinguish useful fictions from outrageous falsehoods like “Spiders are mammals” by ascribing to useful fictions terms of alethic commendation like “being a falsehood that may for all practical purposes be treated as a truth.” [51]  His claim that the common man’s beliefs are often false is merely to say what van Inwagen himself affirms: that a good deal of intellectual training may be required in order to get at the deep metaphysical truth about things. The reason that the philosopher should think that his own capacities are the exception to the rule is that he has received such training and so has developed the capacity to discern the deeper questions which escape the common man because they are practically irrelevant. The positivist philosophers of a bygone generation may have impugned the human capacity to know the deep truth about things, but the serious metaphysician in plying his craft is affirming that we do have such a capacity. It just needs to be honed and strengthened by intellectual training.

It seems to me, therefore, that van Inwagen’s rejection of option (2) is too facile. If Fictionalism is an unreasonable option for the adherent of Nicene orthodoxy, then we need more substantive objections than those van Inwagen has proffered in his present critique of nominalism.

Option (3)

That brings us to option (3), which is to show that it does not follow from our true belief that “Spiders share some of the anatomical features of insects” that there are anatomical features. The goal is to show that one’s belief, though true, does not in fact commit one to platonism. Because Van Inwagen presupposes a Quinean metaontology for settling ontological disputes, he interprets this option to be the adoption of a paraphrastic strategy which attempts to find a paraphrase of the target sentence which could be used instead of it and which does not even appear to have the conclusion “There are anatomical features” as one of its logical consequences. If successful, such a strategy would show that the apparent existence of properties is due merely to certain forms of words that we use but need not use.

Van Inwagen just assumes that the nominalist who opts for (3) accepts, as van Inwagen does, Quine’s theses on ontological commitment, including his Criterion of Ontological Commitment and its legitimate application to ordinary language. But while Fictionalists accept Quine’s theses, this is not the case for most nominalists who adopt the third option. Granted, paraphrastic strategies are pursued by some important contemporary nominalists, especially in the philosophy of mathematics, in order to avoid ontological commitment to various abstract objects. Moreover, such strategies have been remarkably successful in their aim. One thinks, for example, of Charles Chihara’s constructibilism or Geoffrey Hellman’s modal structuralism, which offer algorithms for formulating paraphrases of arithmetical sentences which are fully adequate for classical mathematics. [52] But most nominalists who embrace (3) are not trying to find paraphrases in order to avoid a conclusion of the form “There is/are x.”

Rather the resort to paraphrase is typically a device employed by devotees of Quine’s Criterion of Ontological Commitment (especially platonists!) who want to avoid the bizarre ontological commitments which such a criterion would foist upon us as a result of its application to ordinary language. [53] According to that criterion, we are ontologically committed to the value of any variable bound by the existential quantifier in a first-order symbolization of a canonically formulated statement which we take to be true. Everyone realizes that “there is/are” or “some,” which the existential quantifier symbolizes, is not ontologically committing in ordinary language. We say such things as “There are deep differences between Republicans and Democrats” or “There is a lack of integrity in his behavior” or “Some of your misgivings about the new boss seem quite justified” without thinking that we thereby commit ourselves to including such things as differences, lacks, and misgivings in our ontology. [54] Quine recognized that the application of his criterion to ordinary language would bring with it all sorts of fantastic and unwanted ontological commitments, and so he limited its legitimate application only to an artificial, canonical language involving the formulation in first order logic of appropriate paraphrases of the sentences of our best scientific theories. The problem with this restriction, as Chihara emphasizes, is that Quine provided no clue as to how such paraphrases are, in general, to be carried out nor any argument at all that so doing will rid them of all unwanted commitments of ordinary language nor any guarantee that our best scientific theories can be successfully put into first-order logical notation. [55]

Van Inwagen is much more radical than Quine in that he sanctions the unrestricted use of Quine’s criterion even with regard to ordinary language and so is prepared to accept the ontological commitments which the want of acceptable nominalistic paraphrases brings with it. [56] But then he faces a two-fold challenge: first, since he wants to avoid the most bizarre commitments, he needs to provide a general, universally applicable way of paraphrasing ordinary sentences which carry unwanted ontological commitments and, second, he needs to show that nominalistic paraphrases cannot similarly be found for ordinary sentences involving commitment to properties. And van Inwagen admits at least with respect to the latter task, “I cannot hope to provide an adequate defense of this position, for an adequate defense of this position would have to take the form of an examination of all possible candidates for nominalistically acceptable paraphrases of such sentences, and I cannot hope to do that. . . . My statement ‘We can’t get away with it’ must be regarded as a promissory note.” [57] But a mere promissory note is plainly inadequate to overcome the strong presumption of nominalism which he brought to this inquiry. It hardly provides a rationally compelling argument for platonism. Moreover, we are still left with no guarantee that paraphrases will shield us from the unwanted ontological commitments of ordinary language.

Nominalists who are not Fictionalists typically do not seek such paraphrases and even delight in the want of acceptable paraphrases for what they take to be truths of ordinary language which would by the application of Quine’s criterion issue in implausible ontological commitments. [58] For this situation helps to motivate a more fundamental challenge to platonism, namely, a rejection of Quine’s metaontology and the theories of reference that result in such implausible commitments. Nominalists who embrace option (3) thus do not in general understand it in the way in which van Inwagen characterizes it. Rather than search for acceptable paraphrases of sentences involving platonistic ontological commitments, they challenge the criterion which bears the fruit of such commitments. Whereas Fictionalists accept Quine’s criterion but differ from platonists in regarding the sentences having platonistic commitments as false, nominalists who embrace option (3) reject Quine’s criterion and so see the truth of such sentences as not involving such commitments. Thus, because van Inwagen presupposes that the dispute is being adjudicated according to the rules of Quine’s metaontology, he does not directly engage the main versions of contemporary nominalism of the sort that adopts option (3), which for one reason or another repudiate that strategy.

Unlike van Inwagen, nominalists who opt for (3) do not see the “there is/are” of ordinary language and/or the so-called existential quantifier “∃” as ontologically committing. So the fact that “In the end one can avoid quantifying over properties only by quantifying over other sorts of abstract object” [59] is just irrelevant. There is no need to paraphrase away any ontological commitments which the platonist would take to attend true sentences represented formally as existential quantifications. I shall mention briefly some of the nominalistic theories which van Inwagen needs to engage if he is to sustain his claim that option (3) is not a tenable means of avoiding platonism.

Meinongianism. The most radical would be Meinongianism, which is enjoying something of a renaissance in our day. [60] Many of us were taught that Alexius Meinong was, frankly, something of a kook who was blind to the obvious contradiction involved in affirming that “There exist things that do not exist.” But neo-Meinongians emphasize that for Meinong es gibt (“there is/are”) is not, as Richard Routley puts it, “existentially loaded.” [61] It does not imply that something exists. It seems to me that this is almost indisputable with respect to ordinary language. Ask the common man whether there are things that do not exist, and he will answer that, of course, there are things that do not exist—unicorns, centaurs, the aether, the Tooth Fairy, and so forth. He would not imagine that he is thereby asserting that these non-existent things exist.

Routley takes the quantifiers of classical logic to be existentially loaded and therefore proposes a reform of classical logic by replacing it with a neutral quantified logic. [62] The central truths of logic, Routley insists, should be prior to and independent of theses of particular metaphysical theories. For since those truths are applied in deducing consequences from and thereby assessing those theories, they should not depend for their correctness on those very theories. Classical logic suffers two significant limitations: (1) its inability to express subject-predicate assertions and truths where the subject item does not exist and (2) its inability to formalize quantificational claims about what does not exist. Routley places the fault principally on the scheme of Existential Generalization Fa ⊃ (∃x) Fx. The correct scheme of Existential Generalization will involve the use of an existence predicate E: Fa & Ea ⊃ (∃x) Fx. In neutral quantification logic the existential quantifier will be replaced by a quantifier of particularization P to be interpreted as “for some item.” So “Some things do not exist” is symbolized (Px) (¬Ex). Existential Generalization (Fa ⊃ (∃x) Fx) will be replaced by a Principle of Particularization Fa ⊃ (Px) Fx, that is, for some item, Fx. Routley, in contrast to Meinong who thought that abstract objects subsist, takes abstract objects to be items that do not exist and so discourse about them to be properly formalized by a neutral quantification logic. This allows us to affirm, in contrast to the Fictionalist, that it is true that “3 = √9” without committing ourselves to the reality of mathematical objects.

Van Inwagen touches briefly on Routley’s neo-Meinongianism in his paper, complaining,

neo-Meinongians have never explained what they mean by ‘exist’. We anti-Meinongians and they mean the same thing by ‘be.’ We anti-Meinongians say that ‘exists’ and ‘be’ mean the same thing; the neo-Meinongians say that this is wrong and ‘exists’ means something else, something other than ‘be’. . . . But, so far as I can see, there is nothing for ‘exists’ to mean but ‘be’. In the absence of further explanation, I am therefore inclined to reject their theory as meaningless. [63]

I think that these allegations are inaccurate. Routley states that the rejection of classical logic’s scheme of Existential Generalization is the result of the neo-Meinongian rejection of what he calls the Ontological Assumption, to wit, the assumption that a statement has the value true and is about something only if the subject of the statement refers to an existent object. [64] Once we give up the Ontological Assumption, he says,

We can foresake [sic] the easy platonism that even nominalists sometimes slip into over mathematics; for we have nothing to lose (in the way of discourse) by taking a hard, commonsense line on what exists, e.g., that to exist is to be, and be locatable now, in the actual world. We are no longer forced to distinguish between being or existence from actuality or to extend ‘exists’ beyond this sense, e.g., to numbers and to ideal items of theoretical sciences, simply in order to cope with the fact that apparently nonexistent items figure fruitfully in many calculations and in much theory, for we may retain the (perhaps redrafted) theory while admitting that the items do not exist. [65]

It is clear that Routley does explain what he means by “exist,” namely, to be locatable now in the actual world, and, moreover, that he equates existence and being. Where he differs from van Inwagen is in his replacing classical logic along with its existentially loaded quantifiers with a neutral logic featuring a quantifier of particularization. [66] Neo- and anti-Meinongians thus differ with respect to their understanding of the commitments made by the use of “there is/are.” If neo-Meinongianism is untenable, we need to hear more than van Inwagen has offered in his paper.

Neutral Logic. Less radical nominalistic versions of option (3) are also available. For example, the appeal to neutral logic is independent of Meinongianism. Advocates of neutralism like Jody Azzouni do not advocate a reform of classical logic to replace the existential quantifier but challenge the assumption that the quantifier of classical logic is ontologically committing. The purpose of the existential quantifier is simply to facilitate logical inferences. [67] It can carry out that function without making ontological commitments to objects existent or non-existent. Why, Azzouni asks, should we think that this quantifier has any different meaning or carries any more ontological force than “there is/are” in ordinary language, which is clearly non-committing? [68]

Azzouni observes that philosophers typically discriminate between two interpretations of the existential quantifier: the objectual (or referential) and the substitutional. The objectual interpretation of the quantifier conceives it as ranging over a domain of objects and picking out some of those objects as the values of the variable bound by it. The substitutional interpretation takes the variable to be a sort of place-holder for particular linguistic expressions which can be substituted for it to form sentences. The substitutional interpretation is generally recognized not to be ontologically committing. But Azzouni maintains that even the objectual interpretation of the quantifier is not ontologically committing until one so stipulates. [69] The claim that it must be ontologically committing overlooks the fact that the quantifiers of the metalanguage used to establish the domain of the object language quantifiers are similarly ambiguous. Whether the items in the domain D of the object language quantifier actually exist will depend on how one construes the “there is” of the metalanguage establishing D. Even referential use of the quantifier in the object language need not be ontologically committing if the quantifiers in the metalanguage are not ontologically committing. If, when we say that there is an element in D, we are using ordinary language, then we are not committed to the reality of the objects in D which we quantify over.

Saul Kripke observes that the “weird notation” of the existential quantifier was explained to us by our teachers by means of such ordinary language expressions as “there is an x which is a rabbit.” He proceeds to say:

And the quantifiers will be said to range over a non-empty domain D, where the technical term ‘non-empty’ is explained by saying that D is non-empty iff there is an element in D, or the equivalent. If the interpretation of the English ‘there are’ is completely in doubt, the interpretation of the formal referential quantifier, which depends on such explanations, must be in doubt also; perhaps the explanation the teacher used when he taught it to us was couched in a substitutional language, and we spoke such a language when we learned his interpretation! . . . Nonsense: we speak English, and the whole interpretation of the referential quantifier was defined by reference to ‘there are’ in its standard employments. [70]

Kripke does not think that the meaning of “there is/are” in ordinary English is in doubt; but he himself admits that there are [N.B.!] English uses which are not ontologically committing, as in “there is a good chance” or “there are three feet in a yard.” Kripke’s overriding point, however, remains: the existential quantifier is defined in terms of the ordinary English “there is/are”, so that if the latter is neutral in its ontological commitments, so is the former. [71] There is no reason to think that one cannot set up as one’s domain of quantification a wholly imaginary realm of objects. D is then non-empty, but objectual quantification in the object language of the domain will not be ontologically committing.

All van Inwagen really offers for thinking that we are ontologically committed to the values of variables bound by the existential quantifier is the synonymy in ordinary language of “there is/are” and “there exist(s).” Synonymy is really beside the point, however, for it is indisputable that ordinary language is very loose in its use of these expressions, so that neither expression is always ontologically committing in ordinary language. It will be contextual factors that will tip us off to whether the locutions are being used in ontologically committing ways. [72]

Free Logic. Yet another alternative is provided by Free Logic. Free Logics are logics whose quantifiers remain existentially loaded but which are devoid of existence assumptions with respect to general and singular terms. Karel Lambert, a champion of Free logic, complains that modern logic still retains existence assumptions that ought not to characterize a purely formal discipline. These surface in that according to standard modern logic, identity statements presuppose existence assumptions. [73] That is to say, their truth requires the existence of the objects referred to in the identity statement. This is evident in the fact that from t = t, where t is some singular term, it follows that ∃x (x = t). For if we substitute the predicate “ = t” for “P” in Pt ⊃ ∃x (Px), a theorem of modern logic,we have t = t ⊃ ∃x (x = t). But, then, absurdly, it would follow from “Vulcan = Vulcan” that there is some object identical with Vulcan, that is to say, that Vulcan exists. Standard logic avoids this untoward result by restricting the terms in true identity statements to those designating existing objects. As a result standard logic becomes limited in its application to certain inferences and does not permit us to discriminate between inferences where the referentiality of the terms is crucial and those where it is not.

Proponents of Free Logic like Lambert therefore propose to rid logic of all existence assumptions with respect to both general and singular terms. According to Lambert, Free Logic has become almost synonymous with the logic of irreferential (or non-denoting, vacuous, empty) singular terms. It thus does not presuppose that the referents of such terms are non-existent objects; there just are no referents. Because Free Logic retains the existential force of the quantifiers of standard logic, it is consistent with Quine’s Criterion of Ontological Commitment. Indeed, if we invoke an existence predicate E!, in Free Logic E!a = def.x (x = a), which just is Quine’s criterion. But Free Logic avoids gratuitous commitments by modifying Existential Generalization and Universal Instantiation. EG now becomes ∃x (x = t) ⊃ (Pt ⊃ ∃x (Px)), and UI is replaced by ∀y (∀x (Px) ⊃ Py).

The relevance of Free Logic to our concern is that the Free Logician who does not accept the reality of properties may object that van Inwagen’s argument must rely crucially on Existential Generalization if it is not to be question-begging. Van Inwagen takes as his starting point the belief that “Spiders share some of the anatomical features of insects,” which he takes to mean or say, “There are anatomical features that insects have and spiders also have.” But that belief is a generalization of particular beliefs about anatomical features like “a is shared by spiders and insects.” The Free Logician will insist that we shall not be ontologically committed to a unless we can infer “Therefore, there is something that is shared by spiders and insects.” But in Free Logic that existential generalization is not valid. We should also need to know that E!a, which to assert is question-begging. If a is an irreferential term, as the nominalist believes, then the truth of “a is shared by spiders and insects” does not commit us to the reality of features. Of course, van Inwagen could simply begin with his premiss “There are anatomical features shared by spiders and insects.” But an argument based on this premiss will not be impressive, since it will simply beg the question. The nominalist Free Logician will, like the Fictionalist, regard this statement as false, however harmless it may be outside the seminar room.

Substitutional Quantification. Still another option: the Nominalist may adopt substitutional interpretation of the existential quantifier when quantifying over abstract objects like properties. Rather than construe the variables bound by the quantifier as ranging over a domain of objects, we take the variables as dummy letters which may be replaced by linguistic expressions in order to form sentences. A universally quantified statement is true just in case the substitution of any term for the variable bound by the quantifier yields a true sentence. An existentially quantified statement is true just in case the substitution of at least one term for the bound variable yields a true sentence. If I assert (∃x) Px, where “P” represents the predicate “is a property,” then I can say that this sentence is true because “malleability” can be substituted for x to yield the true sentence “Malleability is a property” without thereby committing myself ontologically to the reality of malleability or properties. Whether properties exist will have to be decided by extra-logical arguments and can be explicitly expressed by means of an existence predicate.

Dale Gottlieb maintains that in the case of concrete objects the objectual interpretation of the existential quantifier may be used without difficulty. But when it comes to abstract objects, we should interpret the quantifier substitutionally, so as not to prejudge the question of there being such objects over which to quantify. Such a selective use of substitutional quantification may be justified in the special case of quantification over abstract objects not only, as Gottlieb argues, in view of the almost magical ontological consequences that are said to ensue from the objectual interpretation of existentially loaded quantifiers, [74] but also by the strong presumption of nominalism which van Inwagen brings to this inquiry. Moreover, we have compelling theological grounds for rejecting the existence of uncreated objects and, hence, any interpretation of the existential quantifier which would commit us ontologically to their reality. Thus, for van Inwagen’s argument to succeed, one would have to show that the quantifier cannot be taken substitutionally, which is, in Gottlieb’s judgement, “almost impossible to establish.” [75]

Van Inwagen grants that “My argument fails if there is such a thing as substitutional quantification.” [76] But he maintains that substitutional quantification is, in fact, meaningless.

Substitutional quantification is meaningless unless it is a kind of shorthand for objectual quantification over linguistic items, taken together with some semantic predicates like ‘x is true’ or ‘something satisfies z’. But substitutional quantification, so understood, is of no use to the nominalist; for, so understood, every existential substitutional quantification implies the existence of linguistic items (words and sentences) and those are abstract objects. [77]

Van Inwagen refers to an earlier article for a defense of these claims. [78] His original objection was analogous to his problem with Meinongianism: Substitutional quantification is meaningless unless it is understood as objectual quantification over linguistic items; but that is not how its proponents understand it; so it is meaningless. Here he modifies the objection by adding that if we do take the substitutional quantifier to range over a domain of linguistic items, then it implies the reality of abstract objects, presumably word and sentence types.

Now while this last conclusion would, indeed, make substitutional quantification of no use to the nominalist, our interest, it will be recalled, is not in defending nominalism as such but Nicene orthodoxy. And the elimination of properties by substitutional quantification in favor of linguistic types may well suffice to allow the orthodox Christian to meet the challenge before us. For as we have seen, the challenge is posed, not by the reality of abstract objects as such, but rather by the reality of uncreatables. And it is not at all evident that any boot-strapping objection could be raised to God’s being the creator of the linguistic items allegedly required by substitutional quantification. For it is hard to see how in order for God to create any particular word or sentence type that type must already exist. So if van Inwagen’s objection to substitutional quantification were no more than that it implies the reality of linguistic types, he seems to have a way out of the original difficulty he posed.

Unfortunately, as he realizes, the substitutional quantifier does not range over a domain of linguistic items. Rather one simply eschews altogether objects in a domain and instead substitutes linguistic expressions for the variables bound by the quantifier. In that way one is not committed by the use of the quantifier to any objects, existent or non-existent. Van Inwagen’s objection then is that he simply does not understand what, for example, the sentence “(∃x) x is a dog” means, where the quantifier is understood to be substitutional rather than objectual. His bewilderment strikes me as odd. I should have thought this sentence means exactly what it means when the quantifier is understood objectually. The sentence’s meaning does not change with the interpretation of the quantifier, but rather its truth conditions[79] (In that sense it may be misleading to speak of different interpretations of the quantifier.) The difference between objectual and substitutional quantification lies not in the meaning of the quantifier but the truth conditions of the relevant proposition. Only on the objectual interpretation must there be a (non-empty) domain of objects over which the quantifier ranges.

The general proposition van Inwagen specifies can be variously expressed in English: “There is a dog,” “Something is a dog,” etc. Now such a sentence normally implies the existence of a concrete object, namely, a dog. But, on the substitutional interpretation, it does so, not because some domain of objects which includes dogs is ranged over by the quantifier, but because this is how such a sentence is normally used. By contrast, when we assert, “There is a prime number between 2 and 4,” we have good reason to think that no object is thereby implicated because we have good independent reasons for rejecting the existence of abstract objects. Nor can it be said that we are committed to there being some such object due to the domain of the quantifier’s being non-empty, for our quantifier does not range over a domain. An existentially quantified sentence, then, may on the substitutional interpretation of the quantifier commit its user to the existence of some object if, pace Gottlieb, we do not restrict its employment to cases of abstract objects; but an existentially quantified sentence is not automatically ontologically committing in virtue of its logical form. Given the neutrality of the ordinary language expression “there is/are,” one cannot be sure whether a statement commits its user to the existence of an object until one knows the context of its use.

In a sense, then, van Inwagen’s estimation of the incompatibility of substitutional quantification with his argument is exaggerated. For van Inwagen’s argument does not rest on whether there is domain of objects over with the quantifier ranges or whether one forms singular propositions by substituting linguistic expressions for the bound variable, but rather on the meaning of “there is.” But then the weakness of his case lies in the fact that this expression is not inherently ontologically committing in ordinary language.

Figuralism. Finally, one more nominalistic version of option (3) deserves mention: Figuralism. Stephen Yablo has moved through Fictionalism to what he calls Figuralism so as to be able to preserve the truth of abstract object talk without ontological commitment. [80] Yablo is impressed with the similarities between abstract object talk and figurative talk such as we find in understatement, hyperbole, metonymy, and metaphor. An assertion like “It’s raining cats and dogs!” is literally false, but to stop there is to miss the whole point of such language. When a speaker uses figurative language, the literal content is not what the speaker is asserting. There is what Yablo calls a “real content” to figurative statements which may well be true. This is not to say that figurative statements can always be successfully paraphrased into expressions of their real content. Numbers, for example, may be indispensable as representational aids for the expression of the real content of mathematical language. The real content of mathematical statements are logical truths, which is why mathematics seems necessary and a priori.For example, the real content of “2+3 = 5” is the logical truth employing numerical quantifiers:

(∃2x (Fx) & ∃3y (Gy) & ¬∃z (Fz & Gz)) ⊃ ∃5u (FuGu).

Yablo extends his analysis to include other sorts of abstract object talk as well, including talk about properties. For example


The truth value of: is held to turn on:
Argument A is valid the existence of counter-models
It is possible that B the existence of worlds
There are as many Cs as Ds the existence of 1-1 functions
There are over five Es the number of Es
He did it F-ly the event of his doing it’s being F
There are Gs which ___ there being a set of Gs which ___
She is H her relation to the property H-ness

The entities on the right hand side are not what the expressions on the left are really about. We simulate belief, perhaps quite unconsciously, that the entities on the right exist, but they are mere figures of speech which are vehicles of the real content. [81] Figurative speech may be true—herein lies the difference between Figuralism and Fictionalism—but the representational aids it employs are not ontologically committing. Contra Quine’s criterion, then, some uses of the quantifier are figurative. Yablo concludes, “A consistent Quinean should therefore want us to ferret out all traces of non-literality in our theories before we turn to them for ontological guidance. To the extent that there is no sensible project of doing that, there is no sensible project of Quinean ontology.” [82]

Van Inwagen does not comment directly on Figuralism, but he does interact with a similar suggestion that a purported nominalistic paraphrase like “Spiders are like insects in some anatomically relevant ways” should not be understood as “∃z (z is a way in which a thing can be like a thing, and z is anatomical, and spiders are like insects in z,” which would commit us to abstract objects called “ways.” Rather it is more like the statement “There’s more than one way to skin a cat,” which should not be understood as “∃xy (x is way of skinning a cat, and y is a way of skinning a cat, and xy).” Van Inwagen construes the nominalist defender of this metaphorical truth to be asserting that there is no internal logical structure to his sentence. But then he challenges the nominalist to explain the evident logical relations between similar sentences or to account for obviously valid inferences involving such sentences. [83]

Such a criticism does not touch Yablo’s Figuralism, however, because he does not mean to deny that once one chooses to adopt that manner of speaking which features in the right hand column above, there is an internal logical structure of such discourse. Obviously, the sentences of number theory and set theory are characterized by such structure. One simply is not committed to the entities referred to in such discourse because, though speaking truly, one is not speaking literally. Of course, one will have to be sensitive to the question of whether one is operating within the same figurative universe of discourse, lest one draw fallacious inferences by “mixing metaphors,” so to speak. But that should not be an insuperable problem for native speakers.

With respect to option (3) at least, the disagreement between van Inwagen and the nominalist is not primarily ontological, a disagreement about what there is, but more fundamentally metaontological, a disagreement about how to settle disputes about what there is. Since van Inwagen presupposes that the parties to the ontological dispute are operating with the same metaontology, when in fact they are on quite different playing fields, he fails to connect with some of the most important forms of contemporary nominalism.


I think it is clear, then, that van Inwagen has not shown that the nominalist “can’t get away with it.” Of the four originally stated options available to the nominalist, van Inwagen did not show that adopting platonism is the only viable course, nor did he show that the orthodox Christian could not rationally simply remain in tension on this issue. Moreover, we have seen that there are a good number of nominalistic views unrefuted by van Inwagen, which we may represent by their respective positions on existential quantification:

Fictionalism bears the closest resemblance to van Inwagen’s Quineanism in that it treats the existential quantifier as having existential force and takes Existential Generalization to be valid. Moreover, Fictionalism is very close to van Inwagen’s own position when it comes to our beliefs about material objects. Only his confidence about the availability of paraphrases in the one case but not the other serves to distinguish them; but that confidence had but a promissory note to support it. That hardly serves to overcome the presumption of nominalism with which he began. Fictionalism should therefore seem to him a congenial option.

For those of us who are more sceptical of Quine’s criterion, the field is wide open. Ordinary language is very loose in its use of “there is/are” and “there exist(s),” so that neither expression is inherently ontologically committing in the vernacular. Quine himself realized this and so limited the application of his criterion to an imaginary, artificial language; but van Inwagen’s rejection of nominalism depends upon a more sweeping and, I think, unrealistic use of the criterion. We may well find the entities we discover ourselves to be saddled with as a result of Quine’s criterion sufficiently implausible that the criterion which sanctioned them comes to appear unprofitable and so unworthy of retaining.

One final point is worth making: although van Inwagen states that “my argument is an argument for the existence of properties,” he says that he does not suppose that the indispensability of quantification over properties is “any sort of evidence for the existence of properties.” [84] His point seems to be that, in virtue of his preferred paraphrases, we just find ourselves stuck with properties because of their indispensability in our discourse. Van Inwagen says that his general methodological principle is that “if one doesn’t believe that things of a certain sort exist, one shouldn’t say anything that demonstrably implies that things of that sort do exist.” [85] He qualifies this by commenting, “Or, at any rate, one may say such things only if one is in a position to contend, and plausibly, that saying these things is a mere manner of speaking—that, however convenient it may be, it could, in principle be dispensed with.” [86] Van Inwagen thinks that this methodological principle should not be controversial. But it assumes that we could not find ourselves in a situation in which the limitations of language compel us to use locutions which we know to be merely useful fictions. We recognize that such locutions are merely a manner of speaking, but we find them indispensable. It does not seem to me at all inconceivable or implausible that we might find ourselves in such a situation. [87] If we do not take the indispensability of property-talk to be evidence of the reality of properties, and we have good reason to think that properties do not exist, then it seems not at all unreasonable to take the indispensability of property-talk to provide no insight into the nature of reality.

And Van Inwagen himself rehearses what seems to me to be an extraordinarily powerful argument to think that properties, at least as van Inwagen conceives them, do not exist. He takes properties to be what he calls “assertibles,” things that can in principle be said of things or can be true of things. For example, “that it is white” can be said, and said truly, of the White House. But it cannot be truly said of the assertible “that it is white” that it is white, for it is an abstract object. So one of the things we can say truly of “that it is white” is that it cannot be said truly of itself. So there is an assertible “that it cannot be truly said of itself.” But the existence of such a property leads immediately to the analogue of Russell’s familiar set theoretical paradox. Van Inwagen concludes, “If, therefore, we accept the conditional ‘If there are things that can be said of things, one of them must be “that it can’t be said truly of itself”,’ we can only conclude that there are no things that can be said of things,” that is, that there are no properties. [88] Van Inwagen admits that this conditional “seems self-evident.” [89] His response: “Well, I choose to deny the conditional.” [90] His so choosing does nothing to show that the nominalist is not entirely within his rational rights in declining to follow him in that choice. If we do not take ourselves to have evidence that properties exist and we do have a very powerful argument that they do not, but we find ourselves committed to properties as a result of van Inwagen’s general methodological principle, then why not give up that principle? Could anyone pretend that that principle is more evidently true than the conditional which van Inwagen chooses to deny? Why not regard property-talk as a mere manner of speaking which we find ourselves stuck with? At the very least, we have to grant the nominalist the rational right to this position.


The stated purpose of van Inwagen’s paper was to ask whether an orthodox Christian could espouse the position that there are besides God other uncreated beings. Unfortunately, van Inwagen did very little to defend his affirmative answer to the question. His defense consisted wholly of illustrating the way in which universal quantifiers can have restricted domains. But he engaged in no serious attempt to show that the quantifiers in the Nicene Creed are so restricted. We saw to the contrary that the history of theology leading up to the council drew a fundamental distinction between what is agenetos and what is genetos and that heretics and orthodox alike were agreed that there is a single agenetos which is God Himself. The Church Fathers explicitly rejected the view proffered by van Inwagen that there might be things, such as properties and numbers, which are causally unrelated to God as their Creator. Abstract objects have at most an insubstantial existence in the mind of the Logos.

If a Christian theist is to be a platonist, then, he must, it seems, embrace absolute creationism, the view that God has created all the abstract objects there are. Van Inwagen says that he has no argument against such a position. He should therefore avail himself of this option if he finds himself unable to shed his platonism. Those of us who find the boot-strapping problem compelling, however, must look elsewhere to find some solution to the problem posed by the existence of uncreatables. In recent decades there has been a proliferation of nominalistic treatments of abstract objects which has served to make nominalism an attractive alternative for the orthodox theist. Van Inwagen himself holds that there is rightly a strong presumption of nominalism’s truth which only a rationally compelling argument for platonism can overcome. Even if we do not hold to such a presumption, the orthodox Christian who is not an absolute creationist has grounds for thinking that platonism is false and therefore has powerful reasons for entertaining nominalism. Unless all forms of nominalism can be shown to be untenable, the orthodox Christian can on theological grounds rationally embrace nominalism as a viable alternative to platonism. Van Inwagen’s rejection of nominalism on the grounds of the existence of properties is predicated upon the controversial assumptions that most human beliefs are true and that Quine’s metaontology is not only the correct method for settling ontological disputes but that his Criterion of Ontological Commitment is applicable to ordinary language. Van Inwagen does not, at least in the articles which he references, substantively engage the most important forms of contemporary nominalism, which challenge these presuppositions. He has not therefore shown that uncreated abstract objects exist, much less that such an affirmation is permissible for the confessor of orthodox Christianity. [91]



  • [1]

    Peter van Inwagen, “God and Other Uncreated Things,” in Metaphysics and God, ed. Kevin Timpe (London: Routledge, 2009), p. 3.

  • [2]

    Ibid., p. 19.

  • [3]


  • [4]

    Ibid., p. 3.

  • [5]


  • [6]

    Ibid., p. 7.

  • [7]

    Ibid., p. 4.

  • [8]

    This is worth emphasizing. Van Inwagen takes his paper to be a defense of the consistency of his belief in uncreated abstract objects with the first article of the Nicene Creed, and his defense of that position depends crucially upon what the Creed means. That is an exegetical, not a philosophical, question. It is easy to give an interpretation of the Creed which is consistent with one’s philosophical beliefs; but texts have objective meanings, and not every interpretation is consistent with the meaning of a given text. Van Inwagen is explicit about his claim that his beliefs about abstract objects are consistent with the meaning of the Creed.

  • [9]

    It should not, but probably does, need to be said that the question here is not whether the framers of Nicaea intended abstract objects to be included in the domain of their quantifiers, anymore than the question is whether they intended automobiles, quarks, and black holes to be included in the domain; rather, as Van Inwagen rightly sees, the question is whether they intended the domain of their quantifiers to include everything other than God, whatever such an inventory might include.

  • [10]

    For a survey of texts see the nice discussion by George L. Prestige, God in Patristic Thought (London: SPCK, 1964), pp. 37-55, which I follow here. See also the references in J. B. Lightfoot’s “Excursus on the Words gennethenta ou poiethenta” reprinted in Nicene and Post-Nicene Fathers, 2d series, vol. 14: Seven Ecumenical Councils, ed. Philip Schaff and Henry Wace (rep. ed.: Peabody, Mass.: Hendrickson,1994), pp.4-7.

  • [11]

    Harry A. Wolfson, “Plato’s Pre-existent Matter in Patristic Philosophy,” in The Classical Tradition, ed. Luitpold Wallach (Ithaca, NY: Cornell University Press, 1966), p. 414.

  • [12]

    See the discussion in Paul Copan and William Lane Craig, Creation out of Nothing (Grand Rapids, Mich.: Baker, 2004), pp. 119-145.

  • [13]

    For a discussion of texts taken from pseudo-Justin, Irenaeus, Tertullian, Clement of Alexandria, Origen, and Augustine, see Harry Austryn Wolfson, The Philosophy of the Church Fathers, vol.: I: Faith, Trinity, and Incarnation, 3rd ed . rev. (Cambridge, Mass.: Harvard University Press, 1970), chap. XIII: “The Logos and the Platonic Ideas.” According to Wolfson, every Church Father who addressed the issue rejected the view that the ideas were self-subsisting entities but instead located the intelligible world in the Logos and, hence, in the mind of God.

  • [14]

    Similarly, Athenagoras declares that “our doctrine acknowledges one God, the Maker of this universe, who is Himself uncreated. . . but has made all things by the Logos which is from Him” (Plea for the Christians 4). The patterns after which all created things are made (Ibid. 8) are to be found in the Logos, who is the mind of the Father: “The Son of God is the Logos of the Father, in idea and in operation; for after the pattern of him and by him were all things made, the Father and the Son being one. And the Son being in the Father and the Father in the Son. . . , the understanding and reason of the Father is the Son of God” (Ibid. 10. Cf. Theophilus To Autolycus 2.22; Eusebius Demonstratio evangelica 4.13).

  • [15]

    Certain Marcionite advocates of metaphysical dualism were the exception that proved the rule.

  • [16]

    Socrates Ecclesiastical History 2.19. The creed concludes, “Thus do we devoutly trace up all things by the Son to one source of all things who is without beginning.”

  • [17]


  • [18]


  • [19]

    Van Inwagen, “Uncreated Things,” p. 19.

  • [20]

    Ibid., p. 7.

  • [21]

    Indeed, we have seen that it is likely that van Inwagen’s interpretation is actually inconsistent with the meaning of the creed.

  • [22]

    I take the argument to be a sympathetic reconstruction based on these words:

    “I appeal only to my conviction that there are free abstract objects.
    If there are, as I suppose, free abstract objects, then they must be uncreated—since (I affirm this thesis as well) creation is a causal relation and free abstract objects cannot enter into causal relations” (Ibid., p. 8).

    One might think that (1) should be introduced as a premise for a conditional proof of

    4′. If there are free abstract objects, then there are uncreated abstract objects.

    But van Inwagen speaks of “my thesis” as the categorical statement that there are uncreated abstract objects, and the conditional conclusion is hardly one that nominalists and Aristotelians would care to dispute.

  • [23]

    Viz., Peter van Inwagen, “A Theory of Properties,” in Oxford Studies in Metaphysics, vol. 1, ed. Dean Zimmerman (Oxford: Clarendon Press, 2004), pp. 107-38.

  • [24]

    Thomas V. Morris and Christopher Menzel, “Absolute Creation,” in Thomas V. Morris, Anselmian Explorations (Notre Dame, Ind.: University of Notre Dame Press, 1987), pp. 161-78.

  • [25]

    Van Inwagen, “Uncreated Things,” p. 5.

  • [26]

    Michael Bergmann and Jeffrey E. Brower, “A Theistic Argument against Platonism (and in Support of Truthmakers and Divine Simplicity),” in Oxford Studies in Metaphysics, vol.2, ed. Dean Zimmerman (Oxford: Clarendon Press, 2006), pp. 357-86.

  • [27]

    Van Inwagen, “Uncreated Things,” p. 11.

  • [28]

    Ibid., p. 19.

  • [29]

    Van Inwagen, “Theory of Properties,” p. 107.

  • [30]

    Elsewhere he affirms that only the difference between Creator and creature is greater than the difference between abstract and concrete things (Peter van Inwagen, “Being, Existence, and Ontological Commitment,” in Metametaphysics: New Essays on the Foundations of Ontology, ed. David Chalmers, David Manley, and Ryan Wasserman [Oxford: Clarendon, 2009], p. 477).

  • [31]

    Van Inwagen, “Theory of Properties,” p. 107.

  • [32]

    See note 42.

  • [33]

    Van Inwagen, “Theory of Properties,” pp. 113-15.

  • [34]

    On the distinction between appearance and reality, see Peter van Inwagen and Dean Zimmerman, “Introduction: What Is Metaphysics?” in Metaphysics: The Big Questions, ed. Peter van Inwagen and Dean Zimmerman, Philosophy: The Big Questions (Oxford: Blackwell, 2008), p. 2. I should deny that properties are part of the realm of appearance.

  • [35]

    Elsewhere van Inwagen tries to justify his claim by appeal to the ubiquity of property talk in the sciences and everyday life. “The fact that such talk is ubiquitous in science and in the ordinary business of life suggests that it is at least apparently true that features are one of the ‘sorts of thing the World contains’” (Peter van Inwagen, Metaphysics, 3d ed. [Boulder, Col.: Westview Press, 2009], p. 289). I demur. Van Inwagen assumes that such talk is taken by its users with ontological seriousness, which it is not. Compare number talk. When it is said that the number of people in Africa dying of AIDS is increasing every year, people do not imagine that numbers are apparently one of the sorts of thing the world contains. This is especially evident in locutions like “The number of people in Africa dying of AIDS is horrifying,” which would be inept if one were intending to talk about numerical objects.

  • [36]

    Van Inwagen, “Being, Existence, and Ontological Commitment,” p. 506.

  • [37]

    Peter van Inwagen, “Metaontology,” in Ontology, Identity, and Modality, Cambridge Studies in Philosophy (Cambridge: Cambridge University Press, 2001), p. 28; similarly, van Inwagen, “Being, Existence, and Ontological Commitment,” p. 506.

  • [38]

    Van Inwagen, “Metaontology,” p. 31.

  • [39]


  • [40]

    Is this really what the sentence says? One might think it to be a universally quantified statement, in which case it is no more ontologically committing than “Wizards share some of the magical powers of sorcerers.” Interestingly, in the version of the argument in his Metaphysics, pp. 299-300, van Inwagen himself takes a similar sentence to be a universally quantified statement. This raises the very interesting and important question of exactly what is required to put a sentence acceptably into the canonical language of quantification. In a fascinating discussion of this problem, van Inwagen points out that there is no such thing as the unique translation of some sentence(s) into what he calls the quantifier-variable idiom, and that for two reasons: (i) that idiom is present in different degrees in various translations of the original sentence, and (ii) there are alternative ways open to the creative theorist of translating the sentence into the idiom (Van Inwagen, “Metaontology,” pp. 23-4). With respect to (i) van Inwagen gives the example of rendering the sentence “Every planet is at any time at some distance from every star” into quantifier-variable idiom of increasing complexity in four successive steps, beginning with “∀x if x is a planet, x is at any time at some distance from every star” and finishing with “∀x (x is a planet → ∀y (y is a star → ∀t (t is a time → ∃z (z is a distance & x is at t separated from y by z)))). How much of the original sentence is transformed into the idiom, says van Inwagen, will depend on the purposes of the person who is introducing the notation. This raises the question why the nominalist should not be content to render van Inwagen’s original sentence in quantifier-variable idiom as “∀x if x is a spider, then x shares some of the anatomical features of insects,” which is ontologically non-committing. Even if we suppose that a is a spider, so that we may infer that a shares some of the anatomical features of insects, we are not committed to features by a’s being truly ascribed the predicate “shares some of the anatomical features of insects.” The nominalist might prescind from quantifying over features. Van Inwagen himself confronts a similar situation with regard to quantifying over distances in the above astronomical example. Since he cannot give a coherent account of such an object as a distance, and the original sentence is intelligible without such objects, van Inwagen says that he is inclined to reject the final proffered translation. So why not just draw up short of quantifying over such entities in order to avoid dubious ontological commitments?

    The answer, as we have seen, is that van Inwagen holds that our rendering into the canonical idiom must proceed “in sufficient depth that all the inferences we want to make from the things we want to affirm are logically valid.” So if we do not like the entity to be quantified over, rather than draw up short, we must come up with a paraphrase which avoids quantifying over the dubious entity. So in the above example, van Inwagen invents an ingenious paraphrase that avoids distances but preserves the inferences he wants to make. Here is where the philosophical creativity mentioned in (ii) comes into play, for there is no one right way to paraphrase the relevant sentence. Different paraphrases will leave us with different ontological commitments, and which we adopt will depend on personal philosophical and even aesthetic preferences. In this van Inwagen shows himself to be heir to Quine’s ontological relativity.

    It seems to me that the nominalist might justifiably look at this whole procedure with a good deal of scepticism. Seeing the dubious entities, like distances, to which the procedure is leading, he might well deny that the quantifier is ontologically committing after all or say that if it is, then he does not want to make the inferences from things that he wants to affirm, since so doing would involve dubious reification. Or he might question why ontological commitment should hang so crucially on the availability of a paraphrase, especially given the lack of objectivity of the commitments of the paraphrases and the dubiousness of some of those commitments. Van Inwagen’s paraphrase for distances, for example, quantifies over numbers, so that the original statement, which made no mention whatsoever of numbers, winds up committing us to the reality of not just stars and planets but an infinity of numbers! Is ontology really that easy?

    Moreover, the relativity of one’s ontological commitments on van Inwagen’s view seems subversive of his metaontology. For if ontological commitment means that one is committed to those entities which must exist if the sentences of a certain class are to be true (see Peter Simons, “Ontological Commitment,” in Handbook of Metaphysics and Ontology, ed. Hans Burkhardt and Barry Smith, 2 vols. [Munich: Philosophia Verlag, 1991]), then it follows that we have no ontological commitments, since, given the creativity of paraphrase, none of the postulated entities must exist.

  • [41]

    One might quibble about van Inwagen’s specific example. One might think that an anatomical feature of an organism is something that can be seen and touched, a part of an organism, not a property. So to say that “Spiders share some of the anatomical features of insects” is, indeed, just a way of saying, “There are anatomical features that insects have and spiders also have,” i.e., insects have eyes and legs and mouths, etc., and spiders also have eyes and legs and mouths, etc. They obviously do not have the very same parts, but the relevant part of an insect is like the corresponding part of a spider. In this case the canonical statement misrepresents what was said. But for van Inwagen “feature” is a technical term for what he calls an assertible, which is what he takes properties to be (Van Inwagen, Metaphysics, p. 282). Still, nominalists who are content to remain on the ontological level, rather than taking the dispute to a metaontological level, could argue that features are not abstract objects, but tropes, property instances, or some other nominalistically acceptable entities. The more interesting and important debate, however, is in my opinion metaontological.

  • [42]

    Van Inwagen, “Theory of Properties,” p. 113. There is a striking difference in the degree of weight ascribed to this argument in van Inwagen’s more recent exposition of the argument in the coda “Being” added to the third edition of his Metaphysics, pp. 297-309. Whereas in “Theory of Properties” he boldly asserts that “we can’t get away with” nominalism (p. 121), in the coda he emphasizes that what he offers is not a refutation but simply a reply (p. 297). His conclusion is merely that “it is very difficult to be a consistent nominalist. And this statement obviously does not entail that nominalism is false” (p. 298, cf. p. 300). In response to the Fictionalist claim that the existence of features is a useful, even indispensable, illusion, van Inwagen replies, “No one is in a position to be confident about the answers to these questions. But the possibility that the apparent existence of features is a useful illusion is consistent with the only thesis we have affirmed: that it is difficult to be a consistent nominalist” (p. 304). This modest thesis, if true, is obviously inadequate to overcome the weight of the presumption of nominalism, which to do, it will be recalled, required a rationally compelling argument—not to mention the theological predisposition against platonism.

  • [43]

    Van Inwagen, “Theory of Properties,” p. 116.

  • [44]

    If I understand him correctly, van Inwagen himself adopts a position very much like option (4) with respect to libertarian freedom. He admits the apparent inconsistency of his belief in metaphysical freedom, affirms his libertarian faith that this inconsistency is apparent rather than real, and confesses that he doesn’t know at present where the fault in the argument lies (Peter van Inwagen, “The Mystery of Metaphysical Freedom,” in Free Will, ed. Robert Kane, Blackwell Readings in Philosophy [Oxford: Blackwell, 2002], pp. 189-95). Just as we cannot believe that metaphysical freedom is contradictory, so we cannot believe that reality is contradictory, and so there must be something wrong with one of the arguments at issue, even if we are clueless as to where the fallacy lies and so find ourselves condemned to embrace a mystery.

  • [45]

    Van Inwagen believes that chairs do not exist but merely particles arranged chair-wise; the particles so arranged do not constitute an object in its own right. But he protests,

    If you were to tell the ordinary man that I thought that there were no chairs, he would probably think that I was mad. But you would have misled him about my thesis. He would understand you to be saying—given his education and interests, what else could he understand you to be saying?—something that implied that whenever anyone uttered a sentence like ‘There are two valuable chairs in the next room’, that person was under an illusion of some sort” (Peter van Inwagen, Material Beings [Ithaca, NY: Cornell University Press, 1990], p. 107).

    Van Inwagen’s first objection to Fictionalism misleads in the same way. Both van Inwagen and the Fictionalist are making high level metaphysical claims that are easily misrepresented to the man on the street.

  • [46]

    Van Inwagen, Material Beings, p. 103.

  • [47]


  • [48]

     Ibid., p. 98.

  • [49]

    Ibid., p. 103.

  • [50]

    Van Inwagen holds that “Any of the propositions that an English speaker might express by uttering, ‘There are two very valuable chairs in the next room’ on a particular occasion . . . is, I would argue, consistent with the proposition that I, as a metaphysician, express by writing the words, ‘There are no chairs’” (Material Beings, p. 101). That is clearly wrong, for van Inwagen’s denial is not consistent with the proposition that there are chairs. What van Inwagen must mean is that any proposition which his theory of objects allows is expressed by an English speaker’s utterance, etc. But those propositions are obviously not the content of the common man’s beliefs. For example, van Inwagen would say that one of the propositions expressed by the sentence in question is more accurately captured by a paraphrase like

    There are xs and there are ys such that [the xs are not the ys and both the xs and the ys are arranged chairwise and both the xs and the ys are in room 103 of the Morris Inn and both the xs and the ys are collectively very valuable and, for any zs, if those zs are arranged chairwise and are in room 103 of the Morris Inn and are collectively very valuable, then those zs are the xs or those zs are the ys] (personal communication, 27 Jan., 2010).

    Additional caveats need to be added concerning how “chairwise” and “collectively valuable” are to be understood. It goes without saying that the average person believes nothing of this sort. Recall that we are not discussing whether sentences like “There are chairs” express some truth but rather whether van Inwagen’s metaphysical claim that there are no chairs contradicts widely held beliefs. Van Inwagen seems to think that average people do not hold metaphysical beliefs about the existence of objects, which seems to me clearly wrong. The average person believes that there are objects like chairs, just as he believes that the external world is real or that time is tensed.

  • [51]

    Van Inwagen, Material Beings, pp. 102-03.

  • [52]

    Charles S. Chihara, Constructibility and Mathematical Existence (Oxford: Clarendon Press, 1990); idem, A Structural Account of Mathematics (Oxford: Clarendon Press 2004); idem, “Nominalism,” in The Oxford Handbook of Philosophy of Mathematics and Logic, ed. Stewart Shapiro (Oxford: Oxford University Press, 2005), pp. 483-514; Geoffrey Hellman, Mathematics without Numbers: Towards a Modal-Structural Interpretation (Oxford: Oxford University Press, 1989); idem, “Three Varieties of Mathematical Structuralism,” Philosophia Mathematica 3 (2001): 129-57; idem, “Structuralism,” in The Oxford Handbook of Philosophy of Mathematics and Logic, pp. 536-62, ed. Stewart Shapiro (Oxford: Oxford University Press, 2005), pp. 536-62.

  • [53]

    For example, an argument parallel to van Inwagen’s for an unwanted ontological commitment to prerogatives might run: The Vice-President shares some of the prerogatives of the President; therefore, there are prerogatives that the Vice-President has and the President also has; or in the canonical language of quantification, it is true of at least one thing that it is such that it is a prerogative and the Vice-President has it and the President also has it.

  • [54]

    For a nice statement of this point along with a persuasive critique of what he calls the “quantification argument” see Gerald Vision, “Reference and the Ghost of Parmenides,” in Non-Existence and Predication, ed. Rudolf Haller, Grazer Philosophische Studien 25-26 (Amsterdam: Rodopi, 1986), pp. 297-36. We say there are, e.g., shades of grey, differences in height, angles from which something can be seen, principles, hostilities, prospects for success, primes between 2 and 12, hours before dawn, dangerous excesses, drawbacks to the plan, etc. Cf. Thomas Hofweber, “Ontology and Objectivity” (Ph.D. dissertation, Stanford University, 1999), pp. 1-2.

  • [55]

    See Chihara’s trenchant critique of Quine’s project in Charles S. Chihara, Ontology and the Vicious Circle Principle (Ithaca, N.Y.: Cornell University Press, 1973), chap. 3; idem, Constructibility and Mathematical Existence, chap. 2. Van Inwagen finds himself confronted with a similar problem. He says that he would like to be able to show that it is always possible to provide a paraphrase of target sentences about supposed material objects, but “to do that, I think, it would be necessary to discover a general, universally applicable way of paraphrasing ordinary sentences of the kind we are interested in,” which he admits he cannot do (Van Inwagen, Material Beings, p. 108).

  • [56]

    To see how his Quineanism leads him to the bold, if nuanced, affirmation, for example, that fictional characters exist, see Peter van Inwagen, “Quantification and Fictional Discourse,” in Empty Names, Fiction, and the Puzzles of Non-Existence, ed. Anthony Everett and Thomas Hofweber (Stanford: Center for the Study of Language and Information, 2000), pp. 235-47.

  • [57]

    Van Inwagen, “Theory of Properties,” pp. 118-19.

  • [58]

    See, e.g., the nice examples furnished by Ruth Barcan Marcus, “Quantification and Ontology,” Noûs 6 (1972): 240-50.

  • [59]

    Van Inwagen’s summarizing conclusion in “Theory of Properties,” p. 121.

  • [60]

    See, e.g., Richard Routley [Sylvan], Exploring Meinong’s Jungle and Beyond: An Investigation of Noneism and the Theory of Items (Canberra: Australian National University Research School of Social Sciences, 1979); Terence Parsons, Non-Existent Objects (New Haven: Yale University Press, 1980; Ken Perszyk, Nonexistent Objects: Meinong and Contemporary Philosophy, Nijhoff International Philosophy Series 49 (Dordrecht: Kluwer, 1993); Graham Priest, Towards Non-Being: The Logic and Metaphysics of Intentionality (Oxford: Oxford University Press, 2005). What makes neo-Meinongianism radical, I think, is not its rejection of what Routley calls the Ontological Assumption (viz., the assumption that a statement has the value true and is about something only if the subject of the statement refers to an existent object), but its espousal of what Routley calls the Independence Thesis, the claim that an item may fail to exist and yet have properties. It is very hard to understand how something that does not exist can have properties. See Routley’s discussion in Exploring Meinong’s Jungle and Beyond, pp. 433-4.

  • [61]

    Routley, Exploring Meinong’s Jungle, p. 76.

  • [62]

    See, e.g., ibid., 73-117.

  • [63]

    Van Inwagen, “Theory of Properties,” pp. 128-9. Van Inwagen consistently interprets the Meinongian claim that there are things that do not exist to signal a difference in meaning between “being” and “existence” (see, e.g., Van Inwagen, “Being, Existence, and Ontological Commitment,” p. 480). This seems to me a misinterpretation.

  • [64]

    Routley, Exploring Meinong’s Jungle, p. 44; cf. pp.17, 22.

  • [65]

    Ibid., p. 45. Cf. Graham priest’s statement: “what is most naturally called the particular quantifier (being the dual of the universal quantifier) should not be read as ‘there exists’ – or even ‘there is’, there being no real difference between being and existence; it should simply be read as some, leaving it open whether the some in question exists or not” (Graham Priest, “The Closing of the Mind: How the Particular Quantifier Became Existentially Loaded behind Our Backs,” Review of Symbolic Logic 1 [2008]: 42).

  • [66]

    So when van Inwagen charges,

    “of course, if there is no distinction in meaning between ‘be’ and ‘exist’, then neo-Meinongianism cannot be stated without contradiction. If ‘be’ and ‘exist’ mean the same thing, then the open sentence ‘x exists’ is equivalent to ‘∃y x = y’. And, if that is so, ‘There are objects that do not exist’ is logically equivalent to ‘Something is not identical with itself’”(Van Inwagen, “Theory of Properties,” p. 129),

    he errs in thinking that for the neo-Meinongian “There are objects that do not exist” is logically equivalent to “Something is not identical with itself,” since the former sentence is correctly symbolized, not by the existential quantifier, as van Inwagen assumes, but by the quantifier of particularization.

  • [67]

    J. Azzouni, “On ‘On what There Is’,” Pacific Philosophical Quarterly 79 (1998): 1-18.

  • [68]

    It is worth noting, in view of van Inwagen’s insistence that “existence” is not only synonymous with “being” but univocal as well (see, e.g., “Being, Existence, and Ontological Commitment,” pp. 482-92), that the non-committing character of “there is/are” and “there exists” in ordinary language is not, on neutralism, due to a lack of univocity of meaning of such expressions, as though there were one meaning which is ontologically committing and another which is not. Rather, as Azzouni emphasizes, these expressions in the vernacular just do not force ontological commitments (Jody Azzouni, “Ontological Commitment in the Vernacular,” Nous 41 [2007]: 204-226). Azzouni contrasts his neutral view with the position that the quantifier is ambiguous and has two meanings. This is relevant to van Inwagen’s comments in Metaphysics, p. 304. Azzouni would agree that “∃” is always used with the same sense and that number words always have the same sense but insist that “there is” and “the number of . . . is” are not ontologically committing in ordinary language. On Azzouni’s view ontological commitment is person-relative and context-dependent; hence, “there are no words or phrases in the vernacular that—in virtue of their standard usage—convey ontic commitment” (Idem, “Ontology and the Word ‘Exist’: Uneasy Relations,” Philosophia Mathematica 18 [2010]: 81-2). Hence, van Inwagen’s arguments about the intimate connection between existence statements and number statements do not phase the neutralist, since number statements in the vernacular are also ontologically non-committing, whether of the form, e.g., “He had one goal in mind” or “The number of obstacles to success remains three.” N.B. that if van Inwagen is right that to say that “Horses exist” is to say that “The number of horses is one or more,” and that this is ontologically committing, then we are committed not only to horses by such a statement but also to numbers, a bizarre consequence. I presume that he would paraphrase away such a commitment by saying that there is at least one horse; but then we are back to using “there is.” Moreover, the intimate connection between existence statements and number statements may hold for statements involving count nouns, but it is hard to see its applicability to statements like “Water exists,” “John exists, “Bad weather exists,” “Intemperance exists,” etc.

  • [69]

    Jody Azzouni, Deflating Existential Consequence: A Case for Nominalism (Oxford: Oxford University Press, 2004), p. 54.

  • [70]

    Saul Kripke, “Is There a Problem about Substitutional Quantification?” in Truth and Meaning: Essays in Semantics, ed. Gareth Evans and John McDowell (Oxford: Clarendon Press, 1976), p. 379. Van Inwagen concurs, commenting, “The meaning of the quantifiers is given by the phrases of English. . . that they abbreviate. The existential quantifier therefore expresses the sense of ‘there is’ in ordinary English” (Peter van Inwagen, “Quantification and Fictional Discourse,” in Empty Names, Fiction, and the Puzzles of Non-Existence, ed. Anthony Everett and Thomas Hofweber [Stanford: Center for the Study of Language and Information, 2000], p. 239). But if the quantifier has no different meaning than “there is/are” in ordinary English, a criterion of ontological commitment based on existential quantification seems hopeless.

  • [71]

    For a good discussion, see Hofweber, “Ontology and Objectivity,” chap. 2, “Quantification.” Moreover, for what it is worth, I do not find at all implausible the claim which Kripke dismisses that when our teacher taught us logic, he may have been using the quantifier substitutionally. I must confess that when I first became acquainted with Quine’s Criterion of Ontological Commitment, it astonished me to think that anyone, much less so many people, could make such enormous metaphysical commitments on the basis of the slender reed of logical notation! Symbolic logic seemed to me from the start to be a sort of notational game involving expressions, not reference to real objects.

  • [72]

    It is worth noting, in view of van Inwagen’s insistence that “existence” is not only synonymous with “being” but univocal as well (see, e.g., “Being, Existence, and Ontological Commitment,” pp. 482-92), that the non-committing character of “there is/are” and “there exists” in ordinary language is not, on Neutralism, due to a lack of univocity of meaning of such expressions, as though there were one meaning which is ontologically committing and another which is not. Rather, as Azzouni emphasizes, these expressions in the vernacular just do not force ontological commitments (Jody Azzouni, “Ontological Commitment in the Vernacular,” Nous 41 [2007]: 204-226). On Azzouni’s view ontological commitment is person-relative and context-dependent; hence, “there are no words or phrases in the vernacular that—in virtue of their standard usage—convey ontic commitment” (Idem, “Ontology and the Word ‘Exist’: Uneasy Relations,” Philosophia Mathematica 18 [2010]: 81-2). Hence, van Inwagen’s arguments about the intimate connection between existence statements and number statements do not phase the Neutralist, since number statements in the vernacular are also ontologically non-committing, whether of the form, e.g., “He had one goal in mind” or “The number of obstacles to success remains three.” N.B. that if van Inwagen is right that to say that “Horses exist” is to say that “The number of horses is one or more,” and that this is ontologically committing, then we are committed not only to horses by such a statement but also to numbers, a bizarre consequence. I presume that he would paraphrase away such a commitment by saying that there is at least one horse; but then we are back to using “there is.” Moreover, the intimate connection between existence statements and number statements may hold for statements involving count nouns, but it is hard to see its applicability to statements like “Water exists,” “John exists, “Bad weather exists,” “Intemperance exists,” etc.

  • [73]

    A point repeatedly emphasized by a champion of free logic Karel Lambert in, e.g., “Existential Import Revisited,” Notre Dame Journal of Formal Logic 4 (1963): 288-92; Meinong and the Principle of Independence (Cambridge: Cambridge University Press, 1983); “The Nature of Free Logic,” in Philosophical Applications of Free Logic, ed. Karel Lambert (Oxford: Oxford University Press, 1991), pp. 3-27; Free Logic (Cambridge: Cambridge University Press, 2003). Van Inwagen endorses standard logic on this head. He holds, “For a thing to be or to exist is simply for it to be something (for to be some thing, for it to be one and the same thing as something). And that is to say that for a thing to be or to exist is for it to be itself, for the only way for a thing to be something is for it to be itself” (Van Inwagen, Metaphysics, p. 289). Thus, Van Inwagen cannot distinguish the truth value of “Zeus = Zeus” and “Zeus = Allah.” Nor can he affirm the truth of “Aristotle = Aristotle,” since Aristotle no longer exists and so there is no thing with which he can be identified. Significantly, van Inwagen merely expounds but does not argue for his view of being, commenting, “We assumed. . . that ‘being’ and ‘existence’ were two names for a certain feature that everything has: being self-identical” (ibid., p. 292).

  • [74]

    Dale Gottlieb, Ontological Economy: Substitutional Quantification and Mathematics (Oxford: Oxford University Press, 1980), pp. 53-4.

  • [75]

    Ibid., p. 50.

  • [76]

    Van Inwagen, “Theory of Properties,” p. 123.

  • [77]

    Ibid., p. 124.

  • [78]

    Peter van Inwagen, “Why I Don’t Understand Substitutional Quantification,” Philosophical Studies 39 (1981): 281-5.

  • [79]

    Compare sentences comprising indexical expressions. The sentence “I wish you were here” uttered by different persons at different places has the same linguistic meaning but involves different referents on different occasions of use and therefore different truth conditions (see discussion and literature in my The Tensed Theory of Time: A Critical Examination, Synthese Library 293 [Dordrecht: Kluwer Academic Publishers, 2000], chap. 4). Similarly, quantified sentences may have the same linguistic meaning but differ in reference because the objectual semantics requires there be objects to serve as values of the variables whereas the substitutional semantics has no such requirement. So, for example, a sentence like “There are gods in the Babylonian pantheon who have no counterparts in the Greek pantheon” has the same linguistic meaning under either interpretation but is plausibly true given a substitutional semantics though false given an objectual semantics. The objectual semantics in this case gives the wrong truth conditions.

  • [80]

    See, e.g., Stephen Yablo, “A Paradox of Existence,” in Empty Names, Fiction, and the Puzzles of Non-Existence, ed. Anthony Everett and Thomas Hofweber (Stanford: Center for the Study of Language and Information, 2000), pp. 275-312.

  • [81]

    For an intriguing use of such figurative language on van Inwagen’s own part, see his analysis of existence in Metaphysics, chap. 13. He asserts that to say that Fs exist is to say that the number of Fs is not zero. So “Unicorns do not exist” means “The number of unicorns is zero,” and “Sherlock Holmes does not exist” is to be understood as “The number of things that are Sherlock Holmes is zero” (ibid, pp. 285, 295). Van Inwagen seems oblivious to the fact that in asserting that unicorns and Sherlock Holmes do not exist, we have, then, just committed ourselves ontologically to the reality of numbers! That van Inwagen does not take such language seriously is evident when he reduces the property “that the number of things that it is is not zero” to “that it is identical with itself.” He says that “The number of things identical with the Taj Mahal is not zero” and “The Taj Mahal is identical with itself” are alternative formulations of the same assertion about the Taj Mahal, the latter being the simpler formulation (ibid., p. 308). But unless he is using language figuratively, these are clearly not merely alternative formulations of the same assertion, for the first commits us ontologically to numbers, while the latter does not.

  • [82]

    Yablo, “Paradox of Existence,” pp. 304-5.

  • [83]

    Van Inwagen, “Theory of Properties,” p. 120; cf. idem, “Quantification and Fictional Discourse,” pp. 244-5.

  • [84]

    Van Inwagen, “Theory of Properties,” p. 122.

  • [85]


  • [86]


  • [87]

    See further Joseph Melia’s argument that “Sometimes, without abstracta, we may lack the linguistic resources for expressing what we want to say about concrete objects” (Joseph Melia, “On What There’s Not,” Analysis 55 [1995]: 228; cf. van Inwagen, Metaphysics, p. 304). If van Inwagen insists that his principle requires merely that such talk must be dispensable in principle, then it may be asked how we could ever be sure that such talk is not, indeed, dispensable, however resistant to paraphrase it may seem?

  • [88]

    Van Inwagen, “Theory of Properties,” p. 133. Compare the interesting comment by Quine and Goodman during Quine’s nominalist phase:

    “Why do we refuse to admit the abstract objects that mathematics needs? Fundamentally this refusal is based on a philosophical intuition that cannot be justified by appeal to anything more ultimate [N. B. Quine and Goodman, of course, lacked the theological grounds which the Christian philosopher enjoys]. It is fortified, however, by certain a posteriori considerations. What seems to be the most natural principle for abstracting classes or properties leads to paradoxes. Escape from these paradoxes can be apparently effected only by recourse to alternative rules whose artificiality and arbitrariness arouse suspicion that we are lost in a world of make-believe” (Nelson Goodman and W. V. Quine, “Steps toward a Constructive Nominalism,” Journal of Symbolic Logic 12 [1947]: 105).

    Unfortunately, Quine already labored under the presupposition of his metaontology that later led him to platonism.

  • [89]

    Van Inwagen, “Theory of Properties,” p. 133. Indeed, he asks, “What could be more evident than that this is one of the things that can be said (whether truly or falsely) of something?” (Ibid.) Van Inwagen must think that the principles that underlie his commitment to platonism, such as Quine’s Criterion of Ontological Commitment, the belief that most of what human beings believe is true, and so on, are more evidently true, which seems fantastic.

  • [90]

    Van Inwagen, “Theory of Properties,” p. 133.

  • [91]

    I am grateful to Peter van Inwagen as well as to Thomas Crisp, Ross Inman, Joshua Rasmussen, Michael Rea, Peter Simons, Edward Wierenga, and Dean Zimmerman for comments on portions or all of this paper.