Authored by: Mitchell LeBlanc.

In this post I will be utilizing quotations from Richard Creath’s excellent article: “Carnap’s Conventionalism” Synthese 93 (1-2). The quotations will outline precisely what the conventionalist justification of logic is, and hopefully dispel some misunderstandings. I had initially posted these set of comments on a post at Choosing Hats but some emails, comments on my article regarding the TAG (those from ‘Joshua’) and other conversations with presuppositionalists have prompted me to present these explanations in a post of their own. The commenter, Joshua, has failed to engage with the bulk of my criticism against TAG stating in a Facebook comment:

“Like I said before, you are arguing against a straw man. The explanation you offered in your paper fails to account for the preconditions of intelligibility. You are simply making an attempt at showing how an atheistic/evolutionary world view accounts for the preconditions of intelligibility, but the fact that these preconditions exist demands that the Christian world view be true. ” (spelling corrections mine)

What I have tried to explain is that Joshua should simply take my arguments and run them as an internal critique in his own worldview, a sort of internal reductio. The soundness of my article, if truly sound, will not be limited to one worldview. That is to say, if my argument truly does establish its conclusion it will do so if parsed through his own worldview and if that conclusion is such that it shows that his worldview cannot account for logic, then all the worse for his worldview! He may not simply beg the question in favor of his position after seeing the outcome of my criticisms. To this suggestion he has responded:

The conclusion of your argument is based on your ignorance of the very foundation for the Christian world view. There were certain aspects of the Christian world view that you simply ignored, and the ones that you documented were misrepresented. Now, if its that important to you, I will go ahead and sift through your article one paragraph at a time and comment on the ones that are faulty.

This is a pretty heavy charge, but I look forward to his analysis. I do recommend, of course, that it take into account the following material.

With that said, in an effort to quell any further attempts at avoiding the ‘meat’ of my paper due to an “inability to account for the laws of logic,” I will present the conventionalist justification of logic. In my discussions with presuppositionalists they have seemed to largely misunderstand the system and in turn create strawmen of their own to argue against. We must be cognizant now that the TAG as I’ve outlined in the previously linked paper or the statement that only the Christian worldview can account for the laws of logic requires that no other justification be possibly true. If the presentation of conventionalism is coherent it saddens me to say that one will not even need to read my paper to show that TAG (and presuppositionalism) fails. Further, there are those who would assert that presuppositionalism is the true apologetic system in that it is the one that Christianity explicitly endorses. There are also those who say that presuppositionalism/TAG cannot possibly be false because of the guarantee given by scripture. For these people, there is much more at stake than merely the coherence of the TAG, they also risk the truthhood of Christianity.

If the TAG, and further, presuppositionalism, are the true exemplifications of Christianity it follows that their defeat is symbiotically a defeat of Christianity. We can demonstrate this with a simple modus tollens:

(1) If Christianity is true, then the TAG succeeds

(2) The TAG does not succeed

(3) Therefore, Christianity is not true

What of course needs to be shown is (2), and while I feel that I’ve shown it sufficiently in the aforementioned paper, as I’ve said there are those who wish to address my supposed “inabilities.” Let us analyze if the claim that conventionalism cannot possibly account for the laws of logic is true.

What is Conventionalism?

What follows will be a series of excerpts I’ve chosen from Creath’s article that I feel outline the conventionalist justification of logic quite well.

Carnap made a refreshing and welcome suggestion: the axioms can be construed as definitions (implicit definitions) and their assertion as commitment to a language containing the terms so defined. The axioms or postulates need no further epistemic justification because a language is neither true nor false, and one is free to choose a language in any convenient way. If someone else should choose other apparently conflicting postulates, there is in fact no disagreement because each postulate set is constitutive of the concepts it employs, and hence the one body of postulates is not denying what the other is asserting. In this manner the postulates are not even intended to reflect an antecedently and independently existing reality, but rather literally to create the claims they express.

It may be that some postulate sets are better than others. But the ‘betterness’ in question concerns their practical usefulness: some are more powerful or easier to use than others. In terms of epistemic justification or cognitive warrant they are all on a par. Indeed, they are the ‘meter sticks’ for the justification of anything else. Epistemically the choice among them is conventional, though the constraints imposed by pragmatic utility can be significant. For example, an inconsistent postulate set is not very useful. For most logicians of the period, including Carnap, every sentence as well as its negation would trivially follow from a contradiction. An inconsistent postulate set would therefore fail to draw any cognitively interesting distinctions among sentences or beliefs. Though the preference for consistent systems is treated as a pragmatic one, the pragmatic considerations are powerful indeed.

In this first excerpt we see some constant presuppositionalist claims addressed. If logic is conventional, can’t people just choose different conventions? If some people choose different conventions than others, they will be contradicting each other, so how do we know which one is true? The answers to these questions are laid quite simply in the excerpt. Each language or system of logic will have a set of definitions that require no further epistemic justification. Think about the English language, there are definitions of words but to ask why a certain word is defined as such rather than some other definition is a question that simply makes no sense for languages which are neither true nor false, they simply are. Further, if someone chooses some language different than ours (say, French), there is no contradiction because the French language cannot disagree with the English language because they are creating their claims independently of one another.

Pragmatism comes into play when want to decide which system to use. Now, keep in mind that Carnap is not proposing that people somehow “choose” their basic brain languages (the language upon which they would choose all other languages). This is as silly as suggesting that one should be able to choose their genetic makeup as to yield a certain eye-color. Our fundamental operating language, our basic logical brain language (logical because there is no such thing as non-logical languages) is not chosen by us, but rather is the precondition for all other choosing. For the systems we can choose, be it in mathematics or computer science, we use the ones that allow us to perform certain tasks. We would not choose a trivial system because anything follows from trivial systems, the answer to every proposition is “Yes,” clearly this is useless.

“This discussion of pragmatic usefulness and explication must not obscure, however, the epistemic core of Carnap’s doctrine. The choice among alternative postulate sets is epistemically arbitrary; the choice is a matter of convention. Moreover, the postulates themselves are the fundamental epistemic doctrine.”

Again, where choice is possible amongst systems the choice is arbitrary. Creath continues:

At this point it would be well to say a bit more about convention, for it is not always clear what is at stake in saying that something is a matter of convention (Quine, 1936). Plainly, when Carnap speaks of the semantic and epistemic features of our language as conventional, he does not mean to suggest that they are the products of some actual legislative assembly convened in antiquity. But shorn of such unhelpful metaphor, what does conventionality come to? The answer, in essence, is that to lay down a linguistic convention is to adopt a certain scheme of justification. This scheme involves two specific features: first, there are alternatives to certain aspects of the justificatory system; and, second, the choice among these alternatives is arbitrary in the sense that no justification is required for the choice. In particular, to say that postulates are laid down by convention commits one to the idea that there are alternative postulates that could have been chosen, but were not. It commits one likewise to the idea that no further epistemic justification for the choice of postulates is required. Conventions are not designed to reflect antecedent and independent facts; if they were thus designed one would have to show that they had done so. Rather, the postulates (together with the other conventions) create the truths that they, -the postulates, express.

So put, conventionalism is the adoption of a system of justification. Other systems could have been chosen, but weren’t and no justification is required for the choice. Further, conventionalist systems are not reflecting some external reality, they really are creating their truths. We will see a further explanation of this below.

Creath continues:

That the conventions constituting the system of justification are at bottom arbitrary poses no threat whatever to the objectivity of the postulates and their consequences. This was of particular concern to Carnap because he thought that all of logic and mathematics, insofar as the claims thereof can be assessed at all, is to be justified as are postulates and their consequences. Once a system of justification is chosen, i.e., once the various terms of the language are given a definite sense, it is a completely objective matter whether B is a consequence of A. It in no way depends on what any person may happen to imagine, think, believe, or know about these sentences. It is likewise a completely objective matter whether or not a given claim needs further justification. These things are no more subjective than the truth value of the claim “All swans are white”, given of course that the meanings of the terms are fixed. If the word ‘white’ has a sense different than it in fact does, then the truth value of the claim might be different, but this in no way impugns the objectivity of “All swans are white”.

Here we have an answer to the common presuppositionalist assertion that “if logical principles are conventional, they are not necessary.” As the quotation says, once we adopt a system of justification whether or not X is true, or Y is true is a completely objective matter. To quote myself in a previous discussion with presuppositionalist Chris Bolt:

There is a distinction between “object-level” and “meta-level”. Consider a meta-ethical circumstance, where an evolutionary account of morality may be charged with becoming eliminitivist. “if I do some good deed X just because I am programmed to, then X is not really good to do, it’s just part of my programming” But these statements are operating on different levels. Both the following propositions would be true: “X really is good to do” and “X really is just a part of my biological programing, and that’s the only reason I think X is good to do” A contradiction only occurs when both statements are taken to be expressing a proposition of the same level.

Applied to logic, “X is really necessarily true, everywhere, regardless of what anyone thinks, and regardless of anyone’s conventions. And X really is just part of a system of conventions I have adopted as part of my programming.”

Thus we can see that the common charges against conventionalism by the presuppositionalists are simply misunderstandings. Conventionalism does not entail that some logical systems will contradict others, nor does it entail that everything becomes subjective and that logical principles are no longer necessary. Now, so long as conventionalism is a possible justification of the laws of logic, the TAG (and for some people, Christianity) is simply defeated:

(1) If Christianity is true, the TAG succeeds

(2) If some system other than Christian Theism can possibly account for the laws of logic then that TAG does not succeed

(3) Conventionalism possibly accounts for the laws of logic

(4) The TAG does not succeed

(5) Therefore, Christianity is not true

Conclusion

In dispelling the myths surrounding conventionalism put forth by presuppositionalists it should be clear and evident that conventionalism is coherent. Further, given its coherence it is a possible justification of the laws of logic, showing that the TAG fails. Coupled with the criticisms in my aforementioned paper we are left with the possibility of a conventionalist justification and the impossibility of Christian Theistic justification. For certain Christians, these conclusions are nothing less than devastating. If their position is the one I’ve outlined in the syllogisms, not only can Christian Theism not account for the laws of logic, it is false altogether.