What’s the big deal with consistency?

(Cross-posted at M-Phi)

It is no news to anyone that the concept of consistency is a hotly debated topic in philosophy of logic and epistemology (as well as elsewhere). Indeed, a number of philosophers throughout history have defended the view that consistency, in particular in the form of the principle of non-contradiction (PNC), is the most fundamental principle governing human rationality – so much so that rational debate about PNC itself wouldn’t even be possible, as famously stated by David Lewis. It is also the presumed privileged status of consistency that seems to motivate the philosophical obsession with paradoxes across time; to be caught entertaining inconsistent beliefs/concepts is really bad, so blocking the emergence of paradoxes is top-priority. Moreover, in classical as well as other logical systems, inconsistency entails triviality, and that of course amounts to complete disaster.

 

Since the advent of dialetheism, and in particular under the powerful assaults of karateka Graham Priest, PNC has been under pressure. Priest is right to point out that there are very few arguments in favor of the principle of non-contradiction in the history of philosophy, and many of them are in fact rather unconvincing. According to him, this holds in particular of Aristotle’s elenctic argument in Metaphysics gamma. (I agree with him that the argument there does not go through, but we disagree on its exact structure. At any rate, it is worth noticing that, unlike David Lewis, Aristotle did think it was possible to debate with the opponent of PNC about PNC itself.) But despite the best efforts of dialetheists, the principle of non-contradiction and consistency are still widely viewed as cornerstones of the very concept of rationality.

 

However, in the spirit of my genealogical approach to philosophical issues, I believe that an important question to be asked is: What’s the big deal with consistency in the first place? What does it do for us? Why do we want consistency so badly to start with? When and why did we start thinking that consistency was a good norm to be had for rational discourse? And this of course takes me back to the Greeks, and in particular the Greeks before Aristotle.

 

 Variations of PNC can be found stated in a few authors before Aristotle, Plato in particular, but also Gorgias (I owe these passages to Benoît Castelnerac; emphasis mine in both):

 

You have accused me in the indictment we have heard of two most contradictory things, wisdom and madness, things which cannot exist in the same man. When you claim that I am artful and clever and resourceful, you are accusing me of wisdom, while when you claim that I betrayed Greece, you accused me of madness. For it is madness to attempt actions which are impossible, disadvantageous and disgraceful, the results of which would be such as to harm one’s friends, benefit one’s enemies and render one’s own life contemptible and precarious. And yet how can one have confidence in a man who in the course of the same speech to the same audience makes the most contradictory assertions about the same subjects? (Gorgias, Defence of Palamedes)

You cannot be believed, Meletus, even, I think, by yourself. The man appears to me, men of Athens, highly insolent and uncontrolled. He seems to have made his deposition out of insolence, violence and youthful zeal. He is like one who composed a riddle and is trying it out: “Will the wise Socrates realize that I am jesting and contradicting myself, or shall I deceive him and others?” I think he contradicts himself in the affidavit, as if he said: “Socrates is guilty of not believing in gods but believing in gods”, and surely that is the part of a jester. Examine with me, gentlemen, how he appears to contradict himself, and you, Meletus, answer us. (Plato, Apology 26e- 27b)

What is particularly important for my purposes here is that these are dialectical contexts of debate; indeed, it seems that originally, PNC was to a great extent a dialectical principle. To lure the opponent into granting contradictory claims, and exposing him/her as such, is the very goal of dialectical disputations; granting contradictory claims would entail the opponent being discredited as a credible interlocutor. In this sense, consistency would be a derived norm for discourse: the ultimate goal of discourse is persuasion; now, to be able to persuade one must be credible; a person who makes inconsistent claims is not credible, and thus not persuasive.

As argued in a recent draft paper by my post-doc Matthew Duncombe, this general principle applies also to discursive thinking for Plato, not only for situations of debates with actual opponents. Indeed, Plato’s model of discursive thinking (dianoia) is of an internal dialogue with an imaginary opponent, as it were (as to be found in the Theaetetus and the Philebus). Here too, consistency will be related to persuasion: the agent herself will not be persuaded to hold beliefs which turn out to be contradictory, but realizing that they are contradictory may well come about only as a result of the process of discursive thinking (much as in the case of the actual refutations performed by Socrates on his opponents).

Now, as also argued by Matt in his paper, the status of consistency and PNC for Aristotle is very different: PNC is grounded ontologically, and then generalizes to doxastic as well as dialogical/discursive cases (although one of the main arguments offered by Aristotle in favor of PNC is essentially dialectical in nature, namely the so-called elenctic argument). But because Aristotle postulates the ontological version of PNC -- a thing a cannot both be F and not be F at the same time, in the same way -- it is difficult to see how a fruitful debate can be had between him and the modern dialethists, who maintain precisely that such a thing is after all possible in reality.

Instead, I find Plato’s motivation for adopting something like PNC much more plausible, and philosophically interesting in that it provides an answer to the genealogical questions I stated earlier on. What consistency does for us is to serve the ultimate goal of persuasion: an inconsistent discourse is prima facie implausible (or less plausible). And so, the idea that the importance of consistency is subsumed to another, more primitive dialogical norm (the norm of persuasion) somehow deflates the degree of importance typically attributed to consistency in the philosophical literature, as a norm an sich.

Besides dialetheists, other contemporary philosophical theories might benefit from the short ‘genealogy of consistency’ I’ve just outlined [thanks, comment #4!]. I am now thinking in particular of work done in formal epistemology by e.g. Branden Fitelson, Kenny Easwaran (e.g. here), among others, contrasting the significance of consistency vs. accuracy. It seems to me that much of what is going on there is also a deflation of the significance of consistency as a norm for rational thought; their conclusion is thus quite similar to the one of the historically-inspired analysis I’ve presented here, namely: consistency is over-rated.