William

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Abstract objects and the aseity of God
« on: June 06, 2007, 07:15:57 pm »
Is anyone familiar with the problem of abstract objects and the aseity of God?

    The problem is that if abstract objects like logical truths, numbers propositions, properties, exist necessarily, then in what sense are they dependent on God. It is a fact that there is a truth (a) 2+2=4. a is true wether or not God wants it to be and there is nothing he can do to change it.
   So does the existence of logical truths and other necessarily extant entities challenge the aseity of God, and if not, then why?

   A good and concise book outlining the problem is "Does GOd have a Nature", by Alvin Plantinga.

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Harvey

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Abstract objects and the aseity of God
« Reply #1 on: June 06, 2007, 09:59:07 pm »

William  wrote:    Is anyone familiar with the problem of abstract objects and the aseity of God? The problem is that if abstract objects like logical truths, numbers propositions, properties, exist necessarily, then in what sense are they dependent on God. It is a fact that there is a truth (a) 2+2=4. a is true wether or not God wants it to be and there is nothing he can do to change it. So does the existence of logical truths and other necessarily extant entities challenge the aseity of God, and if not, then why?  A good and concise book outlining the problem is "Does GOd have a Nature", by Alvin Plantinga.

I'll try to buy that book in the future, it sounds interesting...

I think that God is anterior to mathematical propositions. So, just like axiomatic propositions of arithmetic are anterior to 2+2=4, so it is that God is anterior to any proposition. Propositions require a mind to comprehend from gibberish, and in fact it is the comprehended meaning that makes propositions what they are. Since God exists anterior to all propositions, it is God that decides their truth value. I think that God does this by constructing worlds that verify the truth of the proposition. If the world is consistent with the proposition, then the world remains. If that world is inconsistent with the proposition, then that world is blotted out of existence ("as if it had never been"). If the proposition is inconsistent altogether (e.g., bad math), then the proposition is completely discarded.

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William

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Abstract objects and the aseity of God
« Reply #2 on: June 07, 2007, 01:37:54 pm »
That is one solution. And you are in god company. Descartes held this view. But to be clear, you are comitted to complete conventionalism about logic and modalities. So you must say, for instance, that the sentence 'necessarily 2+2=4' is false (when the nec operator is read in the broadly logical sense). Or again the sentence 'It is possible for God to creat a round square' is true. ANd also 'IT is possible for God to exist and not exist at the same time and in the same sense' must be true.
   Also, there is the problem of 'explosion'. Any traditional system of logic alows you to prove anything from a contradiciton. HEnce the old adage, 'from a contradiction everything follows'. Heres the proof.
 (1) A & -A (Assumption)
 (2) A (simplification 1)
 (3) -A
 (4) -A v B (addition 3)
 (5) B (disjunctive syllogism 3 and 4)

were & means and, v means or, and A and B are any propositions. Simplification addition and disjunctive syllogism are all pretty basic and intuitive rules. Notice that addition on line 4 allows you to put in anything C, D F, -F, -D, etc. This view, the view that everything is both true and false is sometimes called trivialism. ANd most want to reject it.
   IN order to avoid it you must adopt a system of logic that does not permit the above inferences. There are several methods for acompolishing this. These systems are called paraconsistent systems. A rather famous advocate of these systems is Graham Priest. You might look him up.
    But I am rather skeptical of these systems, and am also unable to bring myself to a complete conventionalism. Seems to me like God is bound by the laws of logic, and that the theist needs this just as much as the atheist for various reasons-not the least of which is being able to have a sensible  argument about it.


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Harvey

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« Reply #3 on: June 07, 2007, 02:02:32 pm »
William wrote: That is one solution. And you are in god company. Descartes held this view. But to be clear, you are comitted to complete conventionalism about logic and modalities. So you must say, for instance, that the sentence 'necessarily 2+2=4' is false (when the nec operator is read in the broadly logical sense). Or again the sentence 'It is possible for God to creat a round square' is true. ANd also 'IT is possible for God to exist and not exist at the same time and in the same sense' must be true.


I don't think that I need to commit to conventionalism about logic and modalities. As I said, all propositions (e.g., logic, modality, mathematics) depend upon Mind to be distinguishable from gibberish. This position does not sacrifice the necessity of logico-mathematical statements since they obtain their necessity on God's existence. They are quidditative statements about God as well as the modalities that God can infer are true as a result. They are not contingent in this case since they draw their existence from God.

William wrote: These systems are called paraconsistent systems. A rather famous advocate of these systems is Graham Priest. You might look him up.
But I am rather skeptical of these systems, and am also unable to bring myself to a complete conventionalism.


He's one of my list of favorite philosophers. I think that there are other branches of worlds that utilize different logics. Although, as far as I understand, we haven't identified the logic that our universe behaves (assuming that different levels within the universe all follow the exact same logic).

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William

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Abstract objects and the aseity of God
« Reply #4 on: June 07, 2007, 02:55:15 pm »


I don't think that I need to commit to conventionalism about logic and modalities. As I said, all propositions (e.g., logic, modality, mathematics) depend upon Mind to be distinguishable from gibberish. This position does not sacrifice the necessity of logico-mathematical statements since they obtain their necessity on God's existence. They are quidditative statements about God as well as the modalities that God can infer are true as a result. They are not contingent in this case since they draw their existence from God.

What do you mean when you say that other branches of worlds utilize diferent logics. What are branches of worlds and what does it mean to utilize a different logic.
I don't know exactly what you mean by God giving meanings to propositions. Striclty speaking propositions don't have meanings. They are the meanings. So a sentence is a linguistic item that expresses a proposition. THe proposition is the meaning of a sentence.
    'Snow is white' and 'Nieve es blanco' are two completely different sentences that pick out or express the same proposition. But that proposition does not have a meaning-this is a category error.
   Why do you think that propositions are mind dependent?
 PLantinga suggests that there is some way to understand logical propositions as being dependant upon God without his being able to change them. PErhaps you also are making this suggestion.
   Perhaps you can explain your position better to me. In particular, what I want to know is can God make contraditions true?

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Harvey

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« Reply #5 on: June 07, 2007, 03:23:20 pm »

William  wrote: What do you mean when you say that other branches of worlds utilize diferent logics. What are branches of worlds and what does it mean to utilize a different logic.

Just as an example, the quantum world may utilize a quantum logic that is limited to that scale. As an aside, perhaps other worlds outside our own don't utilize the principle of bivalence. I'm not committed to the notion that there are other logics that better describe how things happen in other worlds (assuming they exist), but I see no reason to restrict this possibility. (Of course, I think that there are general logical principles that are true for all worlds.)

William wrote: I don't know exactly what you mean by God giving meanings to propositions. Striclty speaking propositions don't have meanings. They are the meanings. So a sentence is a linguistic item that expresses a proposition. THe proposition is the meaning of a sentence.


You're forgetting the interpreter. A "proposition has meaning" actually means that a "proposition has meaning for all of X." X must be an entity or entities possessing comprehension. If X is a rock, then the proposition is gibberish since presumably rocks are not capable of any kind of comprehension.

William wrote: 'Snow is white' and 'Nieve es blanco' are two completely different sentences that pick out or express the same proposition. But that proposition does not have a meaning-this is a category error.


If it were the case that no humans ever existed, then this proposition would not be a meaningful proposition since there would be no interpreter to comprehend it from gibberish.

William wrote: In particular, what I want to know is can God make contraditions true?


Sorry, maybe I wasn't clear: God cannot make contradictions true within a formal system that violates the axioms of that formal system.

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William

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Abstract objects and the aseity of God
« Reply #6 on: June 07, 2007, 04:40:35 pm »
Lets get a couple of things straight.I think it will make our conversations more clear.
  First -it is not correct to say that something is "true within a system". Propostitions are just true simpliciter. Briefly, something is true if and only if it coresponds to reality.
    Truth is a corespondence from a proposition to a state of affairs in the actual world. If the state of affairs 'described' by the proposition coresponds to the actual world, then we say that that proposition is true.
    A proposition is the meaning of a sentence. It is that which is expressed by a sentence. The sentence is the linguistic item-just a combination of words. The proposition is what that sentence means. It is what the sentence picks out.
    Propositions do not have meanings-they just are meanings.
     Sentences are not true or false within a system (formal or informal). Sentences (the linguistic item) are true if and only if the proposition they express corresponds to reality. This is what is called diquotational truth value. WE often make the distinction  between use and mention. (We can talk about 'cat' the word-ie the word 'cat' has three letters-, or I can use the word cat to denote an animal). SO the sentence 'Fluffy is a cat' is true if and only if fluffy is a cat.'
     Now inferences can be valid or invalid within a system. ANd that means that the systems rules do not permit you to make that inference. A sentence can be valid in a system (as some people use the term)-meaning that the sentence is a theorem of the system.
     When philosophers talk about worlds they mean possible worlds. They do not mean other universes (as physicists mean when they talk about pluriverses and what not). So when we talk about the semantics for modal logics, we bring in possible worlds. To say that x is possible-means that there is some possible world in which x is true. To say that x is necessary means that x is true in every possible world. THis is what I mean when I use the phrase possible world. If I mean 'possible' in a different sense (as there are many senses of the world) I will make that explicit.
    Now about logic.
There is no dispute about propositional logic. It is sound, complete and decidable. There is not really any dispute about first order predicate logic, it is complete and sound, but not decidable. I think second order logic is incomplete. This is like basic arithmatic.
   There is dispute about modal logic-the logics of possibiloty and necessity-the analogue is geometry- where what you have is a number of consistent systems.
    Part of the need for modal logics was to understand logical entailment. SO we understand by x entails y, 'it is not possible that x and not y' or that in every possible world 'if x then y'.
     So it would not be the case that different logics obtain in different worlds. Whatever the facts are about modal logics-whatever system one might accept-it would not be something that varies from world to world. The same goes with traditional logics.
   IN other words take an inference from the propositional calc
(1) A
(2) A>B
(3) B
 Modus ponens. What it means for this to be a valid inference is that the sentence (4) [A & (A>B)]>B (where > is read as the material implication)
is true in every possible world. We say that (4) is necessarily true.
  Logic is not something that will vary from world to world. There is only one correct system of logic. ANd this makes sense right-because logic does not depend on physical law or any other contingent features of a universe.
     So let me put my quetion again in a diferent way. Is the following sentence true.
   'It is possible for God to create round squares'

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Harvey

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« Reply #7 on: June 07, 2007, 05:14:03 pm »

William wrote: Propositions do not have meanings-they just are meanings.

I don't want to trip over words, but propositions have an everyday meaning and a more metaphysical meaning. For example, if I said "that proposition you just said is false," what I mean is that what you meant is false--the facts in the world do not obtain to correspond with . I agree that propositions in this sense do not have meaning, they are what is meant. However, when a philosopher states that "propositions exist," they mean there are entities (e.g., physical laws) that exist independent of that which obtains, and often they mean the proposition has something to do with the reason why something obtained. So, for example, some quantum cosmologists postulate that quantum laws exist and as a result, the universe came into existence from a vacuum (i.e., "nothing"). This is an example of propositions as a structure possessing meaning (e.g., quantum rules)--as a result something happens in the world. When I talk about propositions existing and being dependent on God, I am talking in the latter sense. If you'd like to use a different term, e.g., law, then I'll oblige to make things more clear.

William wrote: So it would not be the case that different logics obtain in different worlds.


It's better to skip this issue for now. It's not essential to anything I'm saying.

William wrote: So let me put my quetion again in a diferent way. Is the following sentence true. 'It is possible for God to create round squares'


No, this is not true.

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Cole

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Abstract objects and the aseity of God
« Reply #8 on: June 10, 2007, 03:59:58 pm »
The existence of truth pressuposes the existence of minds. The object of knowledge is a proposition, a meaning, a significance, it is a thought.

Truth is mental. Using your mind to deny or show that it's true or that it's true that it's possible that truth is not mental shows that it's mental. It's self-stultifying to deny the mental nature of truth.

Truth is eternal and truth is mental. So, truth must exist in an Eternal Mind. God is truth.

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Cole

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Abstract objects and the aseity of God
« Reply #9 on: June 10, 2007, 10:16:33 pm »
Any form of materialism is incompadible with the existence of truth. Conciousness is an effect and not a cause. Thoughts become the result of bodily changes. Thinking is the result of mechanical necessity. But bodily changes can be neither true or false. So, if there is no mind, there can be no truth; and if there is no truth materialism can't be true. Any denial of the mental nature of truth is self-stultifying.

Truth is eternal and mental. So, truth must exist within an eternal mind.

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Cole

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Abstract objects and the aseity of God
« Reply #10 on: June 12, 2007, 03:48:45 am »

Coming to believe with your mind the truth - "truth is not mental" shows that truth is mental.


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Cole

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Abstract objects and the aseity of God
« Reply #11 on: June 12, 2007, 04:12:07 am »
Coming to believe with your mind the truth - "truth is not mental" shows that truth is mental. The fact that you believe it's true that truth is not mental or that it's true that it's possible truth is not mental shows that truth is mental.

Truth exists
Truth is eternal
Truth is mental

Truth must exist in an Eternal Mind. God is truth. Deny this and you deny the truth.

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Cole

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Abstract objects and the aseity of God
« Reply #12 on: June 13, 2007, 03:30:45 am »
Also,

If the eternaly true proposition "triangles have three sides" existed and nothing else existed including God it wouldn't really mean anything.

Or if the eternaly true proposition George Bush is president of the Uninted States in the year 2007 existed and the world including God didn't exist it wouldn't make any sense. The proposition seems to have known that George Bush was comming. Information pressuposes intelligence. Truths are eternal so truths exists in an infinite intelligence.

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Harvey

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« Reply #13 on: June 13, 2007, 06:53:07 am »

Cole wrote: The proposition seems to have known that George Bush was comming. Information pressuposes intelligence. Truths are eternal so truths exists in an infinite intelligence.

A dreadful fact that God must have lived all eternity with knowing...

However, I disagree that contingent propositions have an eternal truth about them. In my view, the proposition "George Bush is coming" was not true about the George Bush we all know and love (cough, cough) until certain fact of matters fell into place. I believe that once those facts fell into place (i.e., in a weak Molinist sense--not the strong Molinist sense argued by WLC), then I think the proposition about GWB went from "probably true" to "true."

Necessary propositions, such as those from logic and mathematics, in my view are true prior to Creation (i.e., prior to temporal becoming), and therefore I think those propositions became true at the same metaphysical time as their axioms. However, there is an "analytical time" to even these necessary propositions in that there is an analytical dependence that the theorems possess to their axioms and prior theorems needed to derive the other theorem.

This, I suspect, is what led God to creation. A very advanced theorem of decision theory perhaps...? Ramanujan might have agreed.

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Cole

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Abstract objects and the aseity of God
« Reply #14 on: June 13, 2007, 08:43:38 am »
Well the eternaly true proposition "triangles have three sides" has always existed. Triangles have always existed.  It existed before human minds existed. Information presupposes intelligence.

"George Bush is president of the U.S. in the year 2007" is a true statement. It is true today, it will be true tomorrow, it will be true when you die, it will be true when I die, It will always be true. It will be true when everybody dies. It is eternally true. Information pressuposes intelligence. There must be an infinite intelligent mind.