Atheism and the Laws of Logic

Daniel (@DarwinToJesus) recently tweeted the following:

#1. The laws of logic: There are three basic foundational laws of logic.
1. The law of identity (A* is A*)
2. The law of non contradiction (A* is not/cannot be B* in the same place and time)
3. The law of the excluded middle (every proposition is either true, or false)

These…

— Daniel (@darwintojesus) April 23, 2023

Transcendental Arguments

Philosophers trace transcendental arguments back to the philosopher Immanuel Kant. In his Critique of Pure Reason, Kant used the word “transcendental” to refer to our a priori knowledge of objects.

I entitle transcendental all knowledge which is occupied not so much with objects as with the mode of our knowledge of objects insofar as this mode of knowledge is to be possible a priori.

Critique of Pure Reason, Introduction, VII

The late philosopher Anthony Brueckner explained reconstructs the ontological version of Kant’s argument as having two stages.

Kant’s goal was to refute extreme Cartesian skepticism; he wanted to do that by showing that there are permanently existing objects located in space. His ontologically-oriented argument had two stages.

Stage 1: Knowledge of the objective time-order of one’s experiences (one’s subject time-order) only if one has knowledge of a permanent.

Stage 2: Nothing permanent is given in intuition if all we are given is representations. 

The reasoning behind Stage 1 is invalid. Given the supposition that P entails Q, it does not follow that one knows that P only if one knows that Q (that would follow, many would say, only if one knew that P entails Q).[1]

The Christian philosopher James Anderson provides a helpful description of the link between Kant’s transcendental arguments and what contemporary Christian apologists like Bahnsen call the transcendental argument for God’s existence.

Brought to prominence by Kant, transcendental arguments purport to uncover what must be the case (or alternatively, what we must take to be the case) in order for various kinds of intentional operation (e.g., individuating, predicating, perceiving, knowing) to be possible….. 

Transcendental arguments are commonly thought of as anti-skeptical arguments: the idea being to show that whatever it is that the skeptic doubts or denies turns out to be a necessary precondition of some other principle or experience that the skeptic takes for granted. In the case of a theistic transcendental argument, it is skepticism about the existence of God that comes under scrutiny.[2]

As Dr. Anderson alludes to in the passage above, a key concept in transcendental arguments is a special kind of necessary condition, which contemporary proponents sometimes call a “precondition.” 

X is a precondition for the possibility of Y, in the sense that Y cannot obtain without X. But what we do mean by the word “cannot”? The claim, “X is a precondition for the possibility of Y,” is metaphysical and a priori, not natural and a posteriori. Why does this matter? As Stern points out, the basis for claiming, “X is a precondition for the possibility of Y” is 

not just because certain natural laws governing the actual world and discoverable by the empirical sciences make this impossible (in the way that, for example, life cannot exist without oxygen), but because certain metaphysical constraints that can be established by reflection make X a condition for Y in every possible world (for example, existence is a condition for thought, as the former is metaphysically required in order to do or be anything at all).[3]

Commenting on that Stern quotation, Christian philosopher Sean Choi reconstructs the general form of Transcendental Arguments as follows:

(TA1) q. 

(TA2) It is necessary that: if not-p, then not-q. 

(TA3) So, p.[4]

Exposition

I personally happen to agree with the way Choi puts transcendental arguments in standard form, but philosophers are divided on the best way to do that. Since Daniel doesn't put his argument from logic in standard form, I'm going to steelman his argument and put it in the form given by Choi. This yields the following.

(TA1') There is a rational justification for the laws of logic.

(TA2') It is necessary that: if Christian theism is false, then there is no rational justification for the laws of logic.

(TA3') So, Christian theism is true.[5]

As written, this argument is valid: if (1) and (2) are true, then (3) must be true. But what is Daniel's supporting argument for (2)? Here, again, is what he wrote in his tweet.

These laws are eternal, they are necessary, universal, immaterial, and conceptual* in nature. All concepts require a mind in order to exist, so because the laws of logic are CONCEPTUAL, they must exist in an eternal mind that is also universal. The mind of God if it exists makes this possible. Therefore God (an eternal all present mind) must exist for the laws of logic to exist. 

This suggests the following supporting argument:

(1) All concepts require a mind in order to exist. 

(2) The laws of logic are conceptual.

(3) Therefore, the laws of logic must exist in an eternal mind that is also universal.

Assessment 

Daniel doesn't explicitly define what he means by "conceptual," so my definition might be different than his. Depending on how he defines it, I might reject (1), (2), or both. In any case, this argument implicitly raises what we might call the "ontology of logic." He believes, as I do, that the laws of logic are discovered, not invented, by humans. Where we disagree is God's relationship to logic, if God exists. Daniel appears to hold the view known as "divine conceptualism," which says that the laws of logic are ideas in the divine mind. But another view is what I will call "logical aseity": the laws of logic are propositions which exist as ontologically independent abstract objects. If logical aseity is true, then the laws of logic do not require a divine mind to think them. 

Why prefer divine conceptualism over and against logical aseity? I think I understand the theological motivation, but I think it is ultimately misguided. Even if I were a Christian, I would reject it. On divine conceptualism, there is no deeper reason why God is the way He is. More to the point, there is no deeper reason why God thinks logical laws at all or the logical laws he thinks; God's thoughts about logical laws are a brute fact. If God's thoughts about logical laws are a brute fact, rather than based on reasons, then God's thoughts are literally unreasonable. But surely reasonableness is a great-making property (albeit one not typically identified as such in the literature on perfect being theology). Thus, it would seem that divine conceptualism preserves one great-making property, divine aseity, only by sacrificing another apparent great-making property, divine reasonableness. When the point is put this way, the "greatest possible being" of perfect being theology no longer sounds as great. If I were a theist (and a proponent of perfect being theology), I would say that a God whose reasons are logical (by reasoning in accordance with ontologically independent, a se laws of logic) is greater than a God whose reasons are brute facts.

Of course, if logical aseity is true, then it also the case that the laws of logic are a brute fact, albeit a necessarily true brute fact or set of facts. The atheistic Platonist rejects the divine conceptualist's claim that a divine mind is required to think logical laws (or any other necessarily true propositions).

 

Notes

[1] Anthony Brueckner, Essays on Skepticism (New York: Oxford University Press, 2010), p. 57 n. 22.

[2] James Anderson, “If Knowledge Then God: The Epistemological Theistic Arguments of Plantinga and Van Til” Calvin Theological Journal (April 2005). 

[3] Robert Stern, Transcendental Arguments: Problems and Prospects (New York: Oxford University Press, 1999), p. 3.

[4] Sean Choi, “The Transcendental Argument.” In Reasons for Faith: Making a Case for the Christian Faith: Essays in Honor of Bob Passantino and Gretchen Passantino (ed. Norman L. Geisler, Chad V. Meister, Coburn-Crossway, 2007).

[5] Choi 2007.