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#94 Classifying Immaterial Objects

February 02, 2009

Dear Dr Craig,

Thank you for all your work! I like many others have benefited a great deal from the time and effort you put into your areas of study. My question is regarding classification of immaterial objects. I've always been interested in this but never seen much written on it in either Christian apologetics or mainstream secular writings. I understand that one of your current areas of research is into abstract objects, which you define as entities that do not have a location in time or space but are nonetheless real things that do not stand in causal relations.

What I really want to know is how we should classify some immaterial entities that don't fit this definition. For instance, what do you make of immaterial objects that aren't causally impotent? I'm thinking specifically of scientific laws here. I remember from a young age being told that science can't explain the laws of science and thinking how funny this was. Or what about a quantity like information, which we interact with all the time. The same information can be transmitted by many different mediums yet remain unaffected by the medium itself so it seems to be immaterial but is it causally effete?

Would you classify something like beauty as an abstract object despite the fact that it seems to be both objective and subjective?

I notice that you don't define moral values as abstract objects but as part of God's character. In question 66 you say:

'In the case of the moral argument, the concept of God involved in the argument is that of a personal being, since moral values, if they exist, reside in persons, not in inanimate things, and since only a personal being can be a source of moral duty by issuing commands to us.'

It seems clear to me that moral values do posses a personal quality that other immaterial objects don't. But then so do other entities like love, loyalty and justice, so would you describe these as abstract objects or not?

How would you go about explaining your statement from question 66 to a person who doesn't believe in God but who does agree that morals are objective, believing them to exist just as abstract objects like the laws of mathematics or logic?

Yours thoughts appreciated,


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Dr. craig’s response


Thank you for your thought-provoking questions, Jon! As the reality of abstract objects and divine aseity is my current research focus, I'm glad to take this question.

First, I need to correct what you said about how I define abstract objects in distinction from concrete objects. I do not think that abstract objects, if they exist, are "entities that do not have a location in time or space." In my chapter on creatio ex nihilo and abstract objects in Creation out of Nothing (Baker: 2004), I argue that, to the contrary, some abstract objects, if they exist, do exist in both or in either time and/or space. This rather shocking conclusion seems evident from a consideration of certain kinds of abstract objects.

For example, consider propositions (the information content expressed by sentences). Propositions expressed by many declarative sentences have contingent properties, like being true or being false. Many philosophers say that propositions, unlike sentences, have no tense and so have their truth-values immutably, even if contingently. Propositions thus exist beyond space and time. But other philosophers disagree, arguing that the propositions expressed by tensed sentences can change their truth value. For example, the proposition expressed by the sentence "George W. Bush is the President of the United States" was true during December of 2008 but became false in January of 2009 at Obama's inauguration. Such propositions are therefore not immutable and must exist in time, if not in space.

Or again, consider properties. Properties raise the age-old dispute concerning what medieval thinkers called universals. For unlike particulars, properties do not seem to be confined to a specific place. For example, if we have two particular balls existing at the same time, they each occupy a distinct spatial location. If they occupied exactly the same space-time points, then we'd have, not two balls, but one ball. But properties seem to be different. For suppose the two balls have the same shape. In that case they each have the same property, namely, being spherical. They cannot be said to have different properties in this respect, or they would differ in shape, which ex hypothesi they do not. Thus, the same property exists at the same time in two distinct spatial locations. Moreover, the property exists wholly in those two places simultaneously. That is precisely why properties are called universals. If they really exist, they have, at least on the usual account, the bizarre property of existing wholly in two distinct places at the same time. But in that case, properties do seem to exist in space and time.

Even if we try to avoid this conclusion by saying that properties themselves are non-spatio-temporal, but that their instantiations or instances are in space and time, we still seem saddled with saying that properties can acquire and lose the property of being exemplified. In other words, they are mutable with respect to exemplification, just as propositions can be with respect to truth-value. Thus, properties also seem to be temporal entities.

What I have come to realize since writing that chapter is that, even more shockingly, some abstract objects, if they exist, exist not merely in time and space but also exist contingently! Consider, for example, the equator or the center of mass of the solar system. The equator has properties like a certain length and yet is clearly not a physical object. If there is such a thing as the equator it is an abstract entity. Yet it exists in both time and space. You can actually cross the equator! You can step over this abstract object! The center of mass of the solar system is a point which is moving about in space and is therefore spatio-temporal. Here is an abstract object which you could literally enclose in the hollow of your hand—though only momentarily, since it would quickly pass right through your hand as it moves about! If neither the earth nor the solar system existed, then neither the equator nor the center of mass of the solar system would exist, so that these abstract objects exist merely contingently.

Or take fictional characters or musical compositions. As explained in Question #9 in the Q & A Archive, if these exist as abstract objects and yet are products of human creation, as some philosophers think, they also exist contingently and temporally, since they begin to exist.

So we can't plausibly include in our definition of abstract objects their being non-spatio-temporal. Rather, as I explained in Creation out of Nothing, what differentiates abstract from concrete objects is that abstract objects, if they exist, are essentially causally impotent, that is to say, they cannot stand in causal relations. Their essential causal impotence serves to distinguish abstract objects from entities which just happen to be causally isolated in our world, but which could have had effects, and from God, who could have refrained from creating and so have stood in no causal relations, had He so wished.

Thus, in answer to your question, immaterial objects which are not causally effete are concrete objects. God, angels, and the soul would be premier examples. But I would not classify scientific laws as causally potent and therefore as concrete. Scientific laws themselves don't cause anything. If they really exist, they are propositions of some sort, which as such are abstract objects. They describe causes in the universe but are not themselves causes. Similarly, information seems to be identical to propositions.

Beauty seems to be a property and therefore an abstract object (if such objects exist).

On the ethical theory which I have defended moral values are not abstract objects, but God Himself is the paradigm of the Good (see Question #59 in the Q & A Archive). Analogously, a meter was traditionally defined not as an abstract length but as the length of the meter bar in the Bureau of Weights and Measures in Paris. The meter bar served as the concrete paradigm of a meter. Lest you reply that the length of the Parisian meter bar is a property and therefore an abstract object, I should say that I presuppose some nominalistic account of properties, according to which, while God is loving, there is no abstract object Lovingness to which God stands in the strange relation of exemplification. Similarly, while God is just and loyal, there are no objects Justice and Loyalty to which God stands in some exemplification relation.

What would I say to "a person who doesn't believe in God but who does agree that morals are objective, believing them to exist just as abstract objects like the laws of mathematics or logic?" In my Reasonable Faith, 3rd ed. (Crossway, 2008), I call this view Atheistic Moral Platonism and raise three objections to it.

First, it's difficult even to comprehend this view. What does it mean to say, for example, that the moral value Justice just exists? It's hard to know what to make of this. It is clear what is meant when it is said that a person is just; but it is bewildering when it is said that in the absence of any people, Justice itself exists. Moral values seem to exist as properties of persons, not as mere abstractions—or at any rate, it is hard to know what it is for a moral value to exist as a mere abstraction. Curiously, since the abstract object Justice is not itself just (just as Quickness is not quick or Laziness lazy), it would seem to follow that in the absence of any people justice does not exist—which seems to contradict the hypothesis! Atheistic moral Platonists seem to lack any adequate foundation in reality for moral values but just leave them floating in an unintelligible way.

Second, the nature of moral duty or obligation seems incompatible with Atheistic Moral Platonism. Let's suppose for the sake of argument that moral values do exist independently of God. Suppose that values like Mercy, Justice, Love, Forbearance, and the like just exist. How does that result in any moral obligations for me? Why would I have a moral duty, say, to be merciful? Who or what lays such an obligation on me? On this view moral vices such as Greed, Hatred, and Selfishness also presumably exist as abstract objects. Why am I obligated to align my life with one set of these abstractly existing objects rather than any other? Theism, by contrast, provides a plausible basis for moral duty in the divine commands or will.

Thirdly, it is fantastically improbable that just that sort of creatures would emerge from the blind evolutionary process who correspond to the abstractly existing realm of moral values. This seems to be an utterly incredible coincidence when one thinks about it. It's almost as though the moral realm knew that we were coming. It is far more plausible to regard both the natural realm and the moral realm as under the hegemony of a divine Creator and Lawgiver than to think that these two entirely independent orders of reality just happened to mesh.

For these reasons, I find a divine command theory of ethics to be a more adequate moral theory.

- William Lane Craig