The argument for God from logic

https://www.proginosko.com/tag/argument-for-god-from-logic/

The argument from logic

https://www.proginosko.com/2020/01/a-conversation-with-tom-jump/

The Lord of logic

If, on the one hand you think that God is (necessarily?) logical, while, on the other hand, you think the source of logic is not God, but is independent of God, then that makes divine rationality contingent on something that's not God, that's independent of God, and more ultimate than God. If God isn't the source of things like logic, numbers, and possible worlds, then that's a smaller God, a less impressive God. Not the greatest conceivable being. 

"Why you can't use logic to prove God"

I'm going to comment on this post:

http://brianhuffling.com/2018/05/01/from-whence-does-logic-come-and-why-you-cant-use-it-to-prove-god/

There is much talk about logic today. It is obviously used significantly in discussions with philosophers and mathematicians. It has also been a tool of some (particularly presuppositional) apologists to argue for God. They insist that atheists cannot account for logic since it is immaterial and universal. Since logic undeniably exists, then something else immaterial and “universal” must also exist to account for it, namely God. 

There's a lot more to the argument than: since universal, immaterial logic undeniably exists, then something else immaterial and “universal” must also exist to account for it, namely God. 

This understanding of logic is taught as if it is some ephemeral abstract notion or set of principles of reason that “exists” only in the mind with no basis in physical reality. 

The position is that logic primarily or fundamentally subsists in the infinite and timeless mind of God. God's mind is the exemplar. Logic has its "basis" in God's mind. However, math and logic are exemplified in time and space. 

That is, according to this argumentation physical reality cannot account for the principles of logic. Nothing could be further from the truth. The principles of logic, such as the principles of identity, excluded middle, and non-contradiction are not just principles of rationality. They are principles of being. Let’s look to see what they are and why they must be grounded in reality and not thought.

It's important to distinguish between divine and human thought. The position is not that logic is reducible to human psychology. It's not intuitionism (e.g. Brouwer). God's thought and God's being are conterminous. 

Yes, you could say logic is grounded in "being", but not just any kind of being will do. Physical existence won't suffice. 

The law of identity states that something is identical with itself. If a thing is “A” then it is “A”. If something is a tree, then it is a tree. This seems rather mundane and uninformative; however, try imagining reality if this were not the case. The principle of excluded middle says that something is either “A” or “non-A”. It is either a tree or a non-tree. There is no middle ground (the middle ground is excluded). The law of non-contradiction says something can’t both be “A” and “not-A” at the same time in the same sense. That is, it can’t be a tree and a non-tree simultaneously.

That confuses logic with concrete exemplifications (or property instances) of abstract objects. A tree approximates the law of identity. Ideally, logical and mathematical truths map onto static, timeless relations or objects with discrete boundaries. 

But physical objects undergo continuous incremental change. Physical objects have fuzzy boundaries in space and time. They have degrees of solidity. They exchange atoms with the surrounding environment. They blend into each other. So that comparison is counterproductive. There's never an exact match between a tree and the law of identity. 

We get our understanding of these principles from the world around us. They are not just principles of thought, but of being. The law of non-contradiction is not just that a statement can’t be both true and false. The law of non-contradiction is that something in existence can’t be and not be simultaneously in the same way. In other words, a tree can’t be a tree and not a tree at the same time in the same sense. These laws are thus grounded in being and abstracted via our knowing process. We have experience of reality and then induce said principles of being and know that they apply to all thought and experience…While these laws are undeniable and are self-evident, the source of our knowledge of them is still physical reality. 

He operates with an epistemology according to which all knowledge of universals is based on a psychological process of abstraction from particulars. 

Now, I have no problem with sense knowledge or induction. Yes, we often generalize on the basis of samples. Fine. 

But that can't be the basis of knowledge all the way down. You can't derive a concept of numbers from observing physical objects, for unless you already have numerical concepts to work with, you can't group physical objects numerically. Numbering objects requires a numerical preconception. 

You can't bootstrap logical or mathematical knowledge from sensory perception. You can't group five apples by number unless you recognize that they comprise five apples, and you're not going to arrive at that classification by staring at some apples with a blank slate mind. 

It takes knowledge to learn. It takes some prior knowledge to acquire additional knowledge. An initially empty mind has no frame of reference to evaluate sensory input. The mind of the percipient must have a logical structure which enables it to organize or reorganize sensory input. An inbuilt classification-system. 

Another way we know the laws of logic is that they are undeniable. One cannot deny something like the law of non-contradiction without using it. If one attempted to do this, he would be forced into saying that his position is true and not false, and that the opposite opinion would be false and not true. We don’t argue from more foundational principles to arrive at these principles of logic. They are first principles of thought and being. The are first because they are foundational and self-evident. They can’t be denied. Further, they don’t require, nor could they require, antecedent proof. Such proof would have to use the laws of logic.

But necessary truths of logic can't derive from contingent truths of the physical world. In many respects, the physical world might have been different. Causation is a weaker principle than logical entailment.  

Physical reality is known directly and is evident to our senses. 

Actually, physical reality is known indirectly. Physical reality is mediated to the mind via sensory perception. A process of encoded and decoded information. 

Note I said “evident” not “self-evident.” Propositions are self-evident when we know their meaning. “Bachelors are unmarried men” is a self-evident proposition because as soon as we know the meaning of the terms and the proposition as a whole, we know it is true. 

But that's different from logic. That's stipulative. True by definition. 

However, things are evident to our senses. I do not need an argument that there is a tree outside of my window. I simply see it. Thus, things are evident and the laws of logic are self-evident and undeniable. (I realize I am skipping over a veritable wonderland of skepticism and rationalism which I have no desire to deal with here. I simply don’t think I need to “justify” the existence of something I just ran my car into. If someone honestly doubts the existence of external reality, I would submit that his problem is not philosophical but psychological and he needs to seek medical treatment immediately.)

That confounds the metaphysics of math and logic with the psychology of sensory perception. 

Of course, such principles can be applied to thoughts and propositions that don’t say things about reality. Logic can be applied to fictitious beings and propositions that say something like, “All monsters live in London.” However, such fictitious beings and propositions are still based in being—that is, things that exist extra-mentally. While a fictitious being doesn’t exist in reality (by definition), we get the concepts of things like monsters from reality. In other words, following the great empirical maxim, “All knowledge is grounded in reality,” we don’t have any new ideas, even of fictitious monsters, that are not tethered to or grounded in reality.

i) Fictions, hypotheticals, and counterfactuals have their source in God's power and imagination. Something is ultimately possible because God can enact that scenario. And God's infinite imagination is the repository of all concepts. God has created rational agents with some knowledge and power. 

ii) I'd add that fictions are ideas, and therefore have a discrete identity lacking in physical objections. 

This is why the presuppositional argument for the existence of God from logic fails. A common argument from them is that atheists cannot account for logic. Logic is immaterial and universal, they say, and as such, atheists can’t account for anything that is immaterial and universal. But if what I am arguing for is true, the presuppositionalist’s argument is not successful. This is because atheists can account for logic, because logic is grounded in reality and being. Yes, God is being as such, and as “being” the laws of logic are tethered to God. (God is God, God cannot be non-God, etc.) That is, in a sense they are antecedently grounded in God because they would be the case even if the physical realm did not exist.

But that means an atheist can't account for the laws of logic inasmuch as these are essentially independent of the physical world. To be sure, some atheists are Platonic realists, but that's different from Brian's paradigm. Moreover, Platonic realism is arguably ad hoc. 

Another important note is that the laws of logic are not really immaterial. Sure the abstracted propositional form of being such as “A tree can’t be a tree and not a tree simultaneously” can be immaterial. But if logic is not merely a rational enterprise and is a second order based on the first order of physical reality, then the basis for logic is not immaterial. 

God's rationality is not a second-order exercise based on God's first-order being. That's a false dichotomy. God's mind and God's being are both first-order realities, which underlie physical reality. 

Our abstractions of the principles are mental, such as numbers, but many, if not most, philosophers do not think that numbers are real. 

That's an illicit argument from authority. Moreover, it's not coincidental that mathematicians like Quine, Gödel, and Penrose subscribe to mathematical realism. 

They like logical principles are abstracted from the real world. The number 2 does not exist. But I can say there are two trees. The two-ness is simply the addition of one more tree than the first. Math then is like logic in that the numbers are abstracted from the material world and then one can perform mental operations. But these numbers do not exist (unless one holds an extreme Platonic view). And as such, the atheist can account for logic by its foundation in sensible objects—just like he can account for numbers. Thus, the presuppositional argument for logic is going to reduce to some cosmological argument that says the universe needs a grounding in something other than itself.

If Big Ben strikes three o'clock, what do I actually hear? Do I hear three tones? No. I only hear a succession of discrete tones. I hear one tone, followed by another tone, followed by another tone. My mind apprehends three tones. That's not given in the raw stimulus, but requires an act of intellectual recognition. The mind isn't just a passive recipient of auditory input, but makes a contribution by its ability to classify the auditory input using innate mathematical categories. 

Compare a human percipient to a canine percipient. Both hear the same sounds, but only the human has the additional understanding to discern the numerical significance of the tonal sequence. A dog doesn't register "three o'clock". It lacks the intelligence to group particulars. There must be something prior in the mind to interpret what was heard as three of something.   

Van Tilian Old Calendarists

In this post I’m going to comment on some recent criticisms of James Anderson and Greg Welty by Nate Shannon and Vern Poythress.

In recent years, James Anderson, David Reiter, and other scholars have shown interest specifically in TAG, the transcendental argument for the existence of God. This philosophically rigorous discussion overlooks the fact that in the context of van Til’s apologetic, the transcendental argument amounts to the claim that Christianity is true, and everything contrary to it false. There is no indication in van Til’s writing that he had any interest in formal transcendental argumentation apart from positive Reformed, Christian presuppositions. I think Lane Tipton is correct when he says, “van Til never viewed his transcendental method as operating outside of a trinitarian theology and a corresponding ‘revelational epistemology.’ To construe van Til’s approach as attempting to establish his theology on the basis of philosophical argumentation is simply to misunderstand his approach at a very basic level. This would be to grant a priority to philosophy that van Til’s system in principle prohibits” (Lane G. Tipton, “The Triune Personal God: Trinitarian Theology in the Thought of Cornelius van Til” [Ph.D. diss., Westminster Theological Seminary, 2004], 170).

N. Shannon, “Christianity and Evidentialism: Van Til and Locke on Facts and Evidence,” WTJ 74 (2012).

i) So philosophical argumentation is, by definition, non-Christian? Whatever happened to “taking every thought captive”?

ii) Didn’t Van Til say things like: “there is an absolutely valid argument for the existence of God and for the truth of Christian theism,” “the argument may be poorly stated, and may never be adequately stated. But in itself the argument is absolutely sound”?

Doesn’t this suggest Van Til was convinced that there was, in principle, a rigorously formulatable version of TAG? Doesn’t he present this as a hypothetical ideal which Christian apologists should aim for, even if they fall short? 

iii) Does TAG merely “claim that Christianity is true, and everything contrary to it false”? A claim in contrast to a reasoned argument? So it just comes down to competing claims? What about the claim that atheism, Buddhism, Mormonism, Islam, Scientology, or Hare Krishna (fill in the blank) is true, and everything contrary to it is false? 

iv) Likewise, suppose Tipton and Shannon are correct in their interpretation of Van Til. So what? Is the purpose of apologetics to stay faithful to Van Til, or to defend the faith? The attitude of Tipton and Shannon reminds me of the Old Calendarists, who felt it was impious to deviate even slightly from Russian Orthodox tradition. Apologetics is not an end in itself, but a means to an end. The objective of apologetics is not to defend Van Til’s methodology, but to defend Christian theology.  Van Til is not the object of faith.

v) They haven’t learned the lesson of the Peter Enns affair. His claims can’t be allowed to go unchallenged. They need to be directly rebutted. How well did the Tipton/Shannon/Oliphint strategy work at out at WTS? How would invoking “covenantal apologetics” be effective?

vi) I skimmed Shannon’s blog (the entries from 10/11-2/13). From my admittedly cursory review, Shannon appears to be preoccupied with methodological purity. In that respect he falls into a trap all-to-common among Van Tilians: he devotes nearly all his time to talking about how to do apologetics rather than doing what he talks about. Leaves without fruit (Lk 13:6-9).

It’s like designing the perfect racecar, when you have no intention of ever racing the car. The car is always in the garage, as you keep refining your technology. Something to look at rather than drive. Something to admire. Buff and polish. But heaven forbid you should ever do anything with it.

v) Van Til talked about the metaphysics of knowledge. James and Greg are turning that programmatic claim into an actual, full-fledged argument. Redeeming the IOUs. That makes a significant advance in Van Tilian apologetics.

They are rewarded for their efforts by aghast expressions. How could they be so presumptuous as to stray beyond Van Tilian flash cards to unpack the claim and furnish supporting arguments!

Now I’m going to comment on Shannon’s recent “Necessity, Univocism, and the Triune God: A Response to Anderson and Welty.” (I simply copy/pasted excerpts from a PDF. This resulted in some transcriptional infelicities, but I won’t take the time to tidy that up.)

To put it another way, a proposition is essentially 'about' something, as AW note; propositions are essentially intentional (333-5). (This quality of intentionality or 'aboutness' serves AW as the link between propositions and personal minds.) So a proposition is essentially parasitic on whatever it is about. Apart from the thing it is about, a proposition has no referent and no meaning and thus cannot bear truth-value.6 The law of identity is an attribution, a de dicto sort of thing, of de re necessity to the state of affairs A=A, but the attribution itself—the law, the proposition—can have only de dicto necessity.

In an attempt to make them more like the sorts of objects that can have necessity, AW affirm that the laws of logic exist; but this is irrelevant. Real existence, particularly mental, intentional real existence, does not change the fact that the modality of propositions, just like their truth-value, is derivative and dependent upon a state of affairs distinct from any proposition 'about' that state of affairs. Quite the contrary. Affirming the mental existence of propositions in fact emphasizes the intentional and thus derivative nature of propositions and confirms that the modality of a proposition is merely de dicto.

Suppose God thinks to himself, “I am omnipotent,” or “I am the Son of the Father.”

Are divinely self-referential and/or intratrinitarian propositions derivative, parasitic, de dicto entities? Do they lack de re necessity?

If there is no possible world in which the law of noncontradiction is false, it does not follow necessarily that the LNC is true in all possible worlds. For to not be false, a proposition does not have to exist; a proposition might not exist at all and still be not false. But to not fail to be true, it must exist.

What does it even mean to say “a proposition might not exist at all”?

According to the doctrines of divine simplicity and aseity, God's mind and thoughts are identical to his being; the only necessarily existing thing, because God did not have to create…

Actually, isn’t the theory of divine simplicity in tension with divine freedom? Doesn’t divine simplicity make it difficult to finesse a principled distinction between necessary truths and contingent truths? Between intrinsic and extrinsic relations? Between what God is and what he wills?

…is God himself; thus God does not necessarily think anything other than himself. No thought content can be imputed to God essentially, in the possible world which is only God, short of implying that the thought content is identifiable with the being of God. Neither the proposition in question, nor any of the laws of logic, are part of the essential being of God: they are not God.

But that’s a false dichotomy, for possible worlds can be a subset of God’s self-knowledge. God knows what God can do. Possible worlds are variations on divine omnipotence.

Univocal mind. Univocal terms imply unitarian ontology.

How does that implication follow? Does the Father have a univocal concept of the Son? If so, does that imply unitarianism rather than Trinitarianism?

Wouldn’t it make more sense for Shannon to claim that univocal terms imply a pantheistic ontology? Of course, I don’t think that’s correct, but if he’s saying univocity blurs the Creator/creature distinction, wouldn’t pantheism be the corresponding category, rather than unitarianism?

 AW use  “mind,” “thought,” and “proposition” univocally. In their argument, all of these terms, familiar to us in the created realm, in the context of our knowledge and familiarity, are applied univocally to the mind and being of the uncreated God. When we say “a thought requires a mind,” what do we mean by mind? If no distinction appears, the use of the term suggests that there is one kind of mind; and of that kind, AW argue, there must be at least one which exists in all possible worlds, but that 'necessarily existing' mind is essentially of a kind with minds that exist in only some possible worlds.

He’s committing the word-concept fallacy. The fact that the same word is used doesn’t mean one can’t draw conceptual distinctions between the nature of God’s mind and the nature of man’s mind. At the same time, they share some things in common–which makes them both mental.

The problem with couching possible worlds in terms of logical necessity should be obvious: it is tautologous to say that the laws of logic are true in all possible worlds, and it is pure stipulation. It clearly indicates that we have reached the explanatory limits of this explanatory category.

i) To begin with, what’s wrong with reaching explanatory bedrock? Isn’t that inevitable at some point in the analysis? The only question is whether we stop prematurely.

ii) Moreover, it’s not tautologous, but linear. It’s not saying the same thing in different words, but explicating and grounding one thing by reference to something else.

In other words, possible worlds delineate, by pure stipulation, the boundaries for metaphysical speculation. We who use them for that purpose endorse this surrender to the laws of logic as the most basic and non-negotiable principles of intelligibility; we agree to play by those rules because we can neither find nor imagine any less controversial ones.

James and Greg aren’t treating the laws of logic as the most basic and non-negotiable principles of intelligibility. Rather, they are nesting the laws of logic in the mind of God. So there is an underlying explanation. Again, we need to distinguish between the metaphysical level at which the laws of logic subsist and the explanatory level.

The problem of a univocal notion of necessity comes to the fore in of apparent paradox. In 2 Kings 6 an axehead floats; it rises to the surface of the waters of the Jordan river.

i) First of all, that would be a contingent fact, not a necessary truth.

ii) Second, how is that paradoxical? The miracle involves changing the natural, normal conditions in some way or another. Could involve changing the properties of water into something that’s not water, or changing the composition of the axehead, or changing the relationship between water and a heavier object by interfering with gravity at that particular time and place. We could speculate on how it happens. But I don’t think it’s paradoxical.

iii) How can he even use that example if he rejects univocity? In that event, what do the terms refer to? What’s an axehead?

In John 2 Jesus changes water to wine.

i) A contingent fact, not a necessary truth.

ii) How is that paradoxical? It’s not saying water has the properties of wine. It’s not simultaneously ascribing contradictory properties of the same object. Rather, one kind of thing is changed into another kind of thing. Where’s the paradox? Unless we say change itself is paradoxical, a la Zeno, McTaggart, et al. but that wouldn’t be confined to miracles.

 On a larger scale, there are the problems of freedom and election and of providence and evil. All of these are thought to be at least apparently paradoxical. And the reason for this perception, and for the tremendous efforts it evokes toward resolution, is that it is assumed that notions of logical relations and of logical necessity operate univocally; it is assumed that they apply equally to man and to God.

The alleged problem of freedom and election or providence and evil isn’t logical, but moral or metaphysical. We’re not denying the God unconditionally elects some while reprobating others. We’re not denying that God providentially governs all events. The terms are not ambiguous.

It is assumed that the laws of logic, as we articulate them and have come to understand them, obtain identically or are equally true in all possible worlds, even in eternity past, before creation. If, however, we confess first the unique ontological self-sufficiency of the triune creator God, and, indeed, the (moral) authority and (epistemological and soteriological) necessity of divine self-disclosure in Scripture, then we always have ready in hand the derivative, dependent, and partial nature of the laws of logic. There is no possible world in which an iron axehead floats; This one did.

Why is there no possible world in which an iron axehead floats? Where’s the argument? What makes his assertion even prima facie plausible?

This is a true or even only an apparent contradiction only if it is assumed that our logical tools exist independently of God, and apply equally to creator and creature.10

i) Who said a floating axehead was an apparent (much less true) contradiction? At best, it would only be contradictory if ordinary conditions obtain. But the miracle presupposes a new and additional factor: God doing something that alters the usual conditions.

ii) He also fails to distinguish between a logical proposition and a concrete object.

It's likely that the incentive for positing these second order thoughts in the divine mind, distinct from content rich first order thoughts, is largely the preservation of the purely formal nature of the laws of logic, which is crucial to their existing (or being true) necessarily. God must think the laws of logic because the laws of logic exist necessarily. So this much is clear: AW are theologizing by the sheer force of logical necessity alone.

In an attempt to maintain pure formality and sustain the notion of necessity they've built their argument upon, AW claim that on some level distinct from his first order thoughts, God thinks exclusively about the form of his first order thoughts. That claim depends on the separability of form and content in God's first order thoughts, which is to lean on a broken reed. For second order thoughts to be purely formal, they must have as their content only the abstracted logical relations of God's first order thoughts. And if the content of first and second order thoughts is distinct, isn't the obvious implication that there are distinct first and second order divine minds?13 In that case the second order thoughts and the second order mind, rather than the first order, are more properly said to exist necessarily, as they only are purely formal.

And so why not say that God essentially thinks only the laws of logic, and these give form to his other thoughts, should he have any other thoughts? What is God at this point anyway—is he not merely logic thinking itself? Or, put it this way: what now of God's first order thoughts? What are those thoughts about? What is the stuff that God subtracts from his thoughts in order to think about them qua thoughts? And if only thoughts about thoughts qua thoughts are necessary, why suppose that God has first order thoughts at all? Aren't these thoughts contingent? The notion of thoughts about thoughts as thoughts in the divine mind is incoherent.

Doesn’t Trinitarianism imply second-order thoughts? What about this thought: “I am the Son of the Father”?

It is also pure fiction, forced upon AW by their commitment to a univocal notion of necessity, and standing in the place where AW should have been led to consult the riches of historical theology in which one finds orthodox protestantism consistently denying that God thinks discursively, infers one thing from another, or has propositional knowledge.14

i) Really? Orthodox Protestantism denies that God has propositional knowledge? How did he pull that out of the hat?

ii) There is no process of inference in the divine mind. No temporal succession. But God timelessly understands timeless implications.

iii) The standard Reformed position is that God doesn’t learn about the world from the world. God is not dependent on the world for anything he knows. Indeed, God has nothing to learn in the first place. God knows the world indirectly by knowing his plan for the world. In that sense, God lacks inferential knowledge of the world.

But I don’t think James and Greg deny that in their paper.

However, God's self-knowledge involves God's timeless knowledge of all logical relations.

This leads to a third theological concern. According to the doctrine of divine simplicity, God's thoughts are identical to his being. Indeed, AW think this much is true of any mind: “. . . thoughts belong essentially to the minds that produce them” (336 n.31). So if we think thoughts that are essential to God's being—exactly those thoughts that God thinks about his own thoughts as thoughts—are we not participating in the divine essence? The same thoughts—univocal thoughts—belong essentially to our minds and to God's mind. Given simplicity, in other words, unless we deny that our thoughts are ever identical to God's, we flirt with pantheism or apotheosis.

That confuses knowing the same truths with being what you know. Must I be a tree to know something about trees?

Or, hoping to maintain simplicity and the ontological distinction between God and creation, we may say that the laws of logic are abstract objects existing independently of both God and man.15 In that case, perhaps God knows the laws of logic in all possible worlds because he is omniscient in all possible worlds and the laws of logic exist in all possible worlds, not because he essentially thinks the laws of logic.

Of course, James and Greg expressly reject that model.

Even more troubling is this question: would we be able to affirm in this case that God's Word is essentially—necessarily, in all possible worlds—self-consistent and trustworthy?

If anything, it’s it harder to maintain the trustworthy, self-consistent character of God’s word when he rejects univocity. Doesn’t that mean the Bible is just partially logical, partially true? What we have in Scripture isn’t verity, but verisimilitude.

Traditionally there are three choices in terms of the meaning of theological language: equivocal, univocal, and analogical. AW implicitly reject the thesis that language and concepts are equivocal and say nothing intelligible about God. For readers of this journal, this is uncontroversial. Enjoying equally broad consensus in the history of Christian theology is a rejection of univocism: when we say “God is good” and “John is good,” it is clear that the predicates are not identical.16  Orthodox protestant thought takes theological language analogically and grounded in verbal divine self-revelation.

Analogy and univocity aren’t necessarily opposed. You can have a theory of analogical predication which allows for univocity if you compare two things at the relevant level of generality or abstraction.

On the basis of the voluntary self-revelation of God, we have true knowledge, and yet, since God is incomprehensible to the creature, our knowledge is never exhaustive. Add to this the metaphysics of the Creator-creature relationship: the creation is a contingent image of the Creator. All things are from him, to him, and through him (Rom 11:36, indicating aseity); and everything that was created was created by and through the Word (Col 1:6, John 1:3, indicating the triune economy of the act of creation). So we understand our theological knowledge and categories as applying to God truly but incompletely, imitatively and derivatively. So our concepts are analogical.  Not only the nature of the relation as analogical, but the order figures in as well: God is the original or the archetype, and we—and our knowledge—are the analogue, or the ectype. As in any analogy, there is an original and there is an analogue, and the order is irreversible—in the Creator-creature analogy more than in any other. God is the original; we and the created order are derivative. In sum, the irreducible ontological distinction between Creator and creature, and precisely this archtypal-ectypcal or original-analogue order, give us revelationally grounded, analogical theological predication. We have true knowledge, so we reject equivocism; but because of the 'ontological distance' between the Creator and the creature, our knowledge is ever partial; so we reject univocism.

There’s a sense in which I can agree with this. However, Shannon is simply using buzzwords like “ectypal” and “analogical.” He’s not giving the reader a model of analogical predication or ectypal knowledge. He’s not fleshing out the concepts. And he’s skating over the complexities and difficulties of articulating a satisfactory theory of analogy. He attacks James and Greg on philosophical grounds, but he doesn’t present a philosophically rigorous alternative. Instead, he just retreats into pious formulas. These don’t solve any problems. They are merely verbal placeholders. All the hard work remains to be done–assuming it can be done.

So in Christian thought, triunity is more basic than either threeness or oneness…

That’s modalistic. That makes Trinitarian oneness and threeness secondary to something more primary. A projection or epiphenomenon of something more basic.

Now I’m going to comment on some statements by Vern Pothress, in his forthcoming book on Logic: A God-Centered Approach to the Foundation of Western Thought.

Before I comment, I’d like to say that to his credit, Poythress isn’t one of those Van Tilians who spends all his time talking about apologetic method. Poythress does practice apologetics in books like Redeeming Science, Redeeming Sociology, Inerrancy and Worldview, Inerrancy and the Gospels.

Something similar to this argument can be found in James N. Anderson and Greg Welty, “The Lord of Non-Contradiction: An Argument for God from Logic,” Philosophia Christi 13:2 (2011): 321–338. But it appears to me that this article does not take into account the presence of analogy and the Creator-creature distinction in logical reasoning about God (see chapter 24 below).

If he’s saying the Trinitarian relations are merely analogous to logical relations, that’s a problem, for that would generate three layers of reality: Trinitarian relations, logical relations (which are somehow distinct from Trinitarian relations), and concreta. If logical relations are analogous to Trinitarian relations, then they have a realty that’s distinct from God, without being creatures. Entities which are analogous to Trinitarian relations, but not identical. So what's their metaphysical status?

The problem, in relation to the ontology of logic, is that theological analogy usually involves a contrast between transcendent reality and mundane reality. And, presumably, logical relations would be on the transcendent (=divine) side of the distinction–although they’d have concrete analogates. If, however, logical relations are merely analogous to the Trinity, then what are they? What’s their ontological status? Are they transcendent, but different from God? Are they a tertium quid? Not quite divine and not quite mundane?

If any concrete piece of reasoning is, by theological definition, an imperfect creaturely representation of uncreated logic.

Isn’t the claim that “any concrete piece of reasoning is, by theological definition, an imperfect creaturely representation of uncreated logic” itself an imperfect creaturely representation of uncreated logic? So is that claim an imperfect representation of a truth?

We need to distinguish between logical arguments, and arguments for the ontology of logic. Needless to say, Greg and James are using ectypal logical arguments, in the sense that their arguments reflect their human understanding of logic; but that's distinct from what they are arguing for or arguing about. They are arguing for or about the archetypal logical truths or logical relations constituted by God’s mind.

Can we have one term, father, that applies both to God and to human creatures who are biological fathers? Clearly we can. But God’s fatherhood and human fatherhood are not on the same level. So the relation between the two is one of analogy rather than strict identity.

One problem with this comparison is that formal logic is fact free (“topic neutral”). A formal system of entailment relations that doesn’t make constantive claims. Rather, it provides an abstract framework into which you can plug factual premises or truth-claims. Formal logic isn’t comparing one thing with another, is it? We need to distinguish logic from what we do with logic. James and Greg aren’t talking about the content which we plug into logical syllogisms, but the necessary metaphysical system of entailments.

He seems to be confusing whether logic is worldview neutral with whether logic is content neutral? There’s an obvious sense in which the ontology of logic is worldview sensitive, viz. conceptualism, constructivism, fictionalism, platonic realism. These go with different views of reality. And you have the whole effort at a naturalized logic, to match a naturalistic or materialistic worldview.

In that sense, logic is not neutral. But of course, James and Greg weren’t arguing for neutrality at that level. Just the opposite. They were presenting a theistic foundation for logic.

Conversely, that kind of “neutrality” is very different from topic neutrality.

Truths, Propositions, and the Argument for God from Logic

http://www.proginosko.com/2012/06/truths-propositions-and-the-argument-for-god-from-logic/

HT: Patrick Chan

Are the Laws of Logic Propositions?

http://www.proginosko.com/2012/02/are-the-laws-of-logic-propositions/

Tuggy's pseudo-logic

DALE SAID:

Steve, as you want to read those chapters, the prophet's points are about *divinity* (godhood, deity) - the property of being a god. He is, I think, making a point about true godhood (vs. the old, polytheistic conception), but as you summarize things, he's left the door wide open to others also being divine - so long as they have the sort of deity he spells out. (all provident creator, able to predict future, etc.) But this is an odd reading, for he roundly insists that Yahweh is the only deity, so defined! So, the reader infers, no one other than YHWH is also a deity. You can call that a facile appeal, and you'd like to think there's some undue philosophizing going on there, but that's just common sense. You just refuse to yield, because you're wedded to a theory with three deities - and of course, logically, none of them can be the only true God.

Tuggy fancies himself a logician, but he keeps fudging on the logic. One of his problems is that Tuggy has a bad habit of bundling two objections into one. From my exchanges, he’s really raising two different objections to the Trinity, but he conflates them.

Objection #1

Isaian monotheism contradicts the Trinity

Objection #2

The Trinity is self-contradictory.

#1 posits a logical contradiction between the Trinity and Isaian monotheism.

#2 posits an internal contradiction involving traditional (e.g. credal) theological and/or philosophical formulations of the Trinity.

From a Protestant standpoint, #1 is the primary issue. The duty of a theological formulation is not to be internally consistent, but to be consistent with revealed truth. Of course, it’s preferable to have a theological formulation that is, or appears to be, internally consistent, but that’s secondary. The ultimate duty of a theological formulation is to faithfully summarize revealed truth.

To make good on #1, Tuggy needs to demonstrate that Isaiah’s terms and comparisons entail the falsity of the Trinity. If he’s going to insist that the Trinity violates the law of identity in reference to his unitarian prooftexts, then he has to show how that’s a necessary implication of his unitarian prooftexts. Does that follow by strict implication?

Notice that in his response to me, he doesn’t do that. He doesn’t even come close. This is all he says: “Yahweh is the only deity, so defined! So, the reader infers, no one other than YHWH is also a deity.”

How does that contradict the Trinity? Do Trinitarians claim someone other than Yahweh is the only deity? Do Trinitarians deny that Jesus is Yahweh?

When is Tuggy going to stop issuing promissory notes and begin to pay the overdue bills? Unfortunately, Tuggy doesn’t even seem to be aware of the issue. He subconsciously reads his position back into Isaiah.

God and logic

Many people treat logic as a worldview-invariant criterion. A standard that transcends any worldview in particular. An umpire that adjudicates between one worldview and another.

In light of that, it’s striking to read some of Quine’s statements on the status of logic. After all, Quine was the most distinguished logician of his generation. Yet here are two of his statements on logical necessity:

The modal logic of necessity–necessary truth and necessary consequence–is an extravagant departure from extensionality.  Necessity itself can instead be clearly and usefully construed in one and another relativistic way.

 

I have not been sold on the notion of necessity, the distinction between necessity and contingency, which is what modal logic in its standard interpretation and primary motivation is about.

W. V. Quine, Confessions of a Confirmed Extensionalist and Other Essays (Harvard 2008), 191, 444.

Why does Quine say that? He doesn’t explicitly give his reason, but I assume it’s bound up with his naturalized epistemology. Indeed, the very same essay from which I took the former, he makes naturalistic evolution his point of departure.

On this view, logic is merely the grammar of human thought. Ideas bouncing around the brain. Logic is an emergent property. The laws of logic actually evolve.

But if logic is just a description of how the brain thinks, then logical truths are contingent truths rather than necessary truths. Logic is reducible to human psychology, or higher animals.

Of course, one might say that’s self-refuting. But it only seems that way to our little simian brains. If logic is just a notion in our noggins­–the firing of C-fibers or whatever–then when we intuit a logical contradiction, we’re just staring back at ourselves in the mirror of our minds–the way a cat is deluded by its own reflection. There’s nothing on the other side of the silver.

Necessary truths require some metaphysical underpinnings. Logic alone is not a sovereign god who can dispatch every claimant, for we must also take into account the ontology of logic. As Quine vividly illustrates, logic without firm foundations will sink back into the quicksands of psychologism.

Theology and logic enjoy a symbiotic relationship. If theology can’t do without logic, logic can’t do without theology.

Logicality and Triadology

Unitarians typically reject the Trinity because they claim it’s illogical. However, one can turn this objection around. If God is a Trinity, then that’s a necessary truth. That’s as much a necessary truth as modus ponens.

The Trinity is not a contingent truth, but a necessary truth–just like other divine attributes. Take the unicity of God. If there is only one true God, that’s a necessary truth. There is one and the same God in every possible world. A truth of reason rather than a truth of fact.

But the same holds true for the Trinity. If the ontological Trinity is real, then that’s the case in every possible world.

You could only attack the Trinity on logical grounds if you beg the question by assuming in advance that logical truths are necessary truths, while the Trinity is not a necessary truth.

Carrier's Argument for Miracles

In critiquing Victor Reppert's AFR, Richard Carrier writes:

"For logical laws are just like physical laws, because physical laws describe the way the universe works, and logical laws describe the way reason works — or, to avoid begging the question, logical laws describe the way a truth-finding machine works, in the very same way that the laws of aerodynamics describe the way a flying-machine works, or the laws of ballistics describe the way guns shoot their targets. The only difference between logical laws and physical laws is the fact that physical laws describe physics and logical laws describe logic. But that is a difference both trivial and obvious."

Among the less obvious problems with this quote is this:

Logical laws are supposedly species of physical laws, just like laws of aerodynamics are.

Now, several atheists have defined miracles as violations of laws of nature. And, many atheists have scoffed at the Bible for reporting supposed violations of such laws.

Furthermore, atheists like Carrier and Richard Price find belief in miracles unwarranted, in part, because we don't see them happening today. We don't see laws of nature being violated, ever.

However, if logical laws are species of physical laws, and "the only difference" between the two is that laws of physics describe physics and laws of logic describe how logic works, then since we see hundreds of thousands of violations of logical laws during our life, what is the big deal with believing the paltry few violations of physical laws called 'miracles'?

If laws of aerodynamics describe how flying things work, then laws of logic describe how thinking things work. But does anything fly that violates laws of aerodynamics? Does anything think or argue that violates laws of logic? Sure they do. If laws of logic can be violated then why can't aerodynamic laws? Especially since "the only difference" between the two is the physical domain the describe. So for those who think Jesus' post-resurrection ascension is nonsense, since it violates laws of aerodynamics, think again. According to Carrier, we live in a strange universe where supposedly inviolable laws are actually violated.

This argument will be known in the literature as CAM (Carrier's Argument for Miracles). Atheists who want to mock talking animals and resurrected men had better deal with CAM.