The Trinity and the Laws of Logic

logic-poythressI started to make my way through Dr. Vern S. Poythress‘ book Logic: A God-Centered Approach to the Foundations of Western ThinkingIt saddens me to say this, but I am very unimpressed with the book. Apologist Steve Hayes from Triablogue expressed some of my same criticisms of Dr. Poythress’ book on his blog some time ago. Here are the relevant quotations:

…my preliminary impression of the book is that it’s a huge missed opportunity. A basic problem is his target audience. He tries very hard to pitch his new book on logic to the average Christian layman. I think that’s a fundamental misstep. On the one hand, I seriously doubt most non-philosophy majors are going to slog through a 708-page monograph on logic, even if Poythress bends over backwards to make it user-friendly.
…The book has lots of juicy chapter titles, but when you dip into the chapters, the actual treatment is very sketchy. His basic style of writing is almost sermonic. I’m struck by the very loose quality of reasoning. He will take a Biblical prooftext, then assert that this relates to something in logic. And that’s about it. There’s very little intensive argumentation. It’s largely reverent claims with illustrative prooftexts.
…This is disappointing, if not entirely unexpected. I’m sure he’s capable of operating at a much higher level. He’s a Caltech grad with a doctorate in math from Harvard. He studied logic under Hilary Putnam and Saul Kripke. And he’s clearly been researching and ruminating on these issues for many years.
…I think his Van Tilian view of divine incomprehensibility severely limits how far he thinks we can or ought to explicate the theistic foundations of logic. Analogy is the glass ceiling, and the ceiling is low. Doesn’t take much to bump your head against the glass ceiling of the Creator/creature distinction, or the immanence/transcendence distinction. I think that’s the basic reason his analysis tends to peter out so soon.
For him, analogy is almost like a natural, impenetrable barrier. It conceals as much as it reveals.

On these points, I find myself agreeing with Hayes for the most part.

I am currently writing on the Trinity and the laws of logic. I am aiming to correct a misapprehension that has been perpetrated by those who promote the idea that logic is created.

Here is the rough draft of what I’m currently working on.

I. The Trinity and the Laws of Logic

In Ch 2 Art. 3 of the 1689 London Baptist Confession of Faith, we are taught that in the one Being of God

. . . there are three subsistences, the Father, the Word or Son, and Holy Spirit, of one substance, power, and eternity, each having the whole divine essence, yet the essence undivided: the Father is of none, neither begotten nor proceeding; the Son is eternally begotten of the Father; the Holy Spirit proceeding from the Father and the Son; all infinite, without beginning, therefore but one God, who is not to be divided in nature and being, but distinguished by several peculiar relative properties and personal relations; which doctrine of the Trinity is the foundation of all our communion with God, and comfortable dependence on him.

The confession teaches us the following about God.

He is one in essence.

He is Father, Son, and Holy Spirit.

The Father is neither begotten nor proceeding.

The Son is eternally begotten of the Father.

The Holy Spirit proceeds from the Father and the Son.

The implications for logic will become clear as we consider that, firstly, in God there is an eternal distinction between essence and subsistences. God is eternally One, in one sense ( i.e. with respect to His essence), and He is eternally Three, in another sense (i.e. with respect to His trinality). Secondly, each Divine Person is eternally distinct from the Other. The Father is neither the Son nor the Spirit; the Son is neither the Father nor the Spirit; and the Spirit is neither the Father nor the Son. Lastly, we must add that God knows that He is Himself (this is the law of identity, A:A). God also knows that His essence and subsistences are not identical to one another (this is the law of non-contradiction, ~[A: ~A]). Father, Son, and Holy Spirit, moreover, know

One Another perfectly, which implies that Father, Son, and Holy Spirit eternally know their “peculiar relative properties and personal relations,” as the 1689 LBC phrases it, further implying that each Divine Person eternally thinks that the laws of logic.

II. The Creator/Creature Distinction & The Created Order

In Genesis 1-2, we learn that God creates all things by His Word. This implies that God conceived of what did not exist, then brought it into existence. What He brought into existence, moreover, was understood by Him to be other than Himself (i.e. God knows all things, we are not pantheists). It may seem tedious to mention this, but for the sake of our current undertaking it is necessary. For if God conceived of creation prior to creating it, then God thought the laws of identity and non-contradiction prior to creating all things. The phrase “all things,” as we know, includes time. Therefore, before there was time, God thought the laws of identity and non-contradiction in conceiving of what He would create.

IIa. Workdays and Sabbaths

Additionally, there are two kinds of days which God identifies, viz the workdays (i.e. Sunday through Friday) and the days of rest (i.e. the first Sabbath and all Sabbaths subsequent to it). Sunday through Friday are workdays (this is the law of identity, A:A), not Sabbaths (this is the law of non-contradiction, ~[A:~A]); likewise, Saturdays are Sabbaths (this is the law of identity, A:A), not workdays (this is the law of non-contradiction, ~[A:~A]). What is important to note here is that God, not man, is the One who has declared these things to be the case. Consequently, it is God who, prior to, and during, the creation of all things is thinking the laws of logic.

IIb. The Creation of Man

In Genesis 1:26, we are told prior to God creating man he communed within Himself and said:

“Let Us make man in Our image, after our likeness. And let them have dominion over the fish of the sea and over the birds of the heavens and over the livestock and over all the earth and over every creeping thing that creeps on the earth.”

Note that God is thinking the laws of logic in that He identifies man as distinct from the animals and vegetation in the following ways. Firstly, man is not identified as an animal. Secondly, man, unlike the plants and animals, is made in the image and likeness of God. Thirdly, man has dominion over all of the animals and vegetation. Man, God says, will be different from the rest of creation. In other words, there are two broad categories implied here: (a.)non-angelic, non-human creatures, and (b.)human creatures. God’s purpose in creating man as distinct from the animals and plants and inanimate minerals, therefore, shows us that logic is how He thinks.

III. Concluding Remarks

To reiterate: Firstly, because God is eternally self-conscious of Himself as One in essence and Three in person, He is eternally thinking the laws of identity and non-contradiction. Secondly, because Father, Son, and Holy Spirit eternally know their own “several peculiar relative properties and personal relations,” it follows that each Divine person knows Himself as Himself and distinct from each other Divine person; and this means that each Divine person eternally thinks the laws of identity and non-contradiction. Thirdly, because God conceived of creating what did not exist, it follows that He thought the laws of identity and non-contradiction prior to making anything, including time. Fourthly, because it is God who differentiates the kinds of days from one another, it follows that it is He who thinks the laws of identity and non-contradiction. Lastly, because it is God who declares that man will be (a.)distinct from the rest of the living creatures and from the vegetation, and (b.)will bear His image and likeness, it follows that God thinks the laws of identity and non-contradiction.

-h.

p.s.

This is a rough draft, so I’m still working out the kinks….

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5 thoughts on “The Trinity and the Laws of Logic

  1. Deontic Scorekeeper says:

    Hi,

    I was recently thinking again about whether logic is created or discovered, and it seems if logic is discovered then God must think several other laws of inference, axioms, and derivation systems other than the law of non-contradiction, and the law of excluded middle.

    If he doesn’t then there follow worrying consequences about God’s ignorance of, or inability to think/derive certain logics, and logical systems.

    Consider this:

    Suppose God only thinks i> the law of identity, and ii> the law of non-contradiction with respect to logic, then it follows that God is unable to think any axiomatic systems of propositional logic, Aristotle’s syllogistic, and Classical first order logic. Assuming that God also thinks the rule of Modus Ponens, He still wouldn’t fare much better. This is because i> and ii> along with Modus Ponens simply don’t suffice to specify an axiomatic derivation system for propositional logic; one still needs to assume one of many possible (mutually incompatible) sets of axiom schemata to specify an axiomatic derivation system for propositional logic. Furthermore, using only i>, ii> and Modus Ponens God would also fail to think/derive rules for quantifiers, and so could derive niether Aristotle’s syllogistic nor Classical First Order Logic. Therefore, either God thinks much more than i> the law of identity, ii> the law of non-contradiction, and Modus Ponens, with respect to logic or God is unable to think any axiomatic systems of propositional logic, Aristotle’s syllogistic, and Classical first order logic. [I suspect, you’ll agree] God can think all possible axiomatic systems of propositional logic, Aristotle’s syllogistic, and Classical first order logic [and all other logics besides]. So, by Modus Tollens, God thinks much more with respect to logic than merely i> the law of identity, ii> the law of non-contradiction, and Modus Ponens.

    Like

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