The Good Mind Project: Intolerance Toward Contradictions

Consistency is absolutely essential to reaching the truth, because without it, truth becomes a completely vacuous concept.


In the last installment of the Good Mind Project, we discussed the importance of the reductio ad absurdum as a tool for generating and exposing contradictions in our beliefs. The discussion assumed that consistency is a condition that our beliefs should always satisfy, while it insinuated that contradictions in our beliefs should always be discarded. Because it can be hard to see why a stance of intolerance toward contradictions is correct, we would like to take some space to demonstrate why consistency is imperative in order for our systems of beliefs to hold up.

To illustrate the thoroughly insidious nature of inconsistency, we’ll begin with the argument that logicians know as ex falso quodlibetSince the purpose of the ensuing argument is to act as a reductio, employing it will in some sense demonstrate the reductio’s self-justifying character.


Suppose that the (obviously contradictory) sentences “God roots for Tim Tebow” and “God does not root for Tim Tebow” are both true. Since “God roots for Tim Tebow” is true, “God roots for Tim Tebow or God roots for Charles Manson” is also true. However, “God doesn’t root for Tim Tebow” is true as well, so that “God roots for Tim Tebow” is false. This leaves only “God roots for Charles Manson” as unequivocally true. Therefore, we can validly conclude that God roots for Charles Manson.

There are a few features of ex falso quodlibet that are important to recognize. The first is that from an apparently harmless contradiction, we are able to prove that God roots for Charles Manson. The second is that instead of proving that God roots for Charles Manson, we could have proved any proposition that we like. The third is that our proof does not rely on the content of the contradictory sentences postulated at the beginning, but rather on the fact that a contradiction was postulated at all.

Therefore, the ex falso quodlibet argument is totally formal, which means that starting from any contradiction, we can prove any proposition we like. It implies that whenever we allow a single (however insignificant or innocuous) contradiction to enter into a system of facts, we open the door for anything to be demonstrably true that we please. The danger of allowing inconsistencies is no mere slippery slope, but a precipitous, frictionless cliff. Consistency is absolutely essential to reaching the truth, because without it, truth becomes a completely vacuous concept.


While up to this point we have expostulated about the dangers of allowing inconsistencies to enter into systems of facts, we still haven’t mentioned beliefs. Is there perhaps some way that facts can be constrained by the Law of Noncontradiction while beliefs are left unfettered? The answer, we believe, rests in an appraisal of the sort of thing that beliefs really are.

Simply put, beliefs are just intelligible judgments of fact. They are communicable propositions about the world accompanied by subjective endorsements of those propositions’ truth-values. A belief might be the thought that “God roots for Tim Tebow” along with the further judgment that the thought is true.

The above definition restricts what beliefs are in two ways. The first of these is an intelligibility requirement. Beliefs are mental phenomena of the sort that are possible to communicate linguistically. While some people tend to think that they possess knowledge that nobody in the world could understand even if both parties possessed perfect faculties of articulation and comprehension, those people are deluding themselves. If private knowledge exists, then the burden is on the possessor is to show it. But that is a Catch-22, because showing that you have an example of private knowledge must involve you communicating what that knowledge is, which by the assumption of its privacy is impossible. We need not account for private knowledge in a sensible ontology of beliefs, because private knowledge is a chimera.


Simplistic appeals to the authority of experience are wrong precisely because of the  intelligibility requirement. One stratagem that people often exercise in debates is to invoke personal experiences as demonstrations of the truth of their beliefs. But appeals like this are tantamount to claiming that one’s beliefs are private and noncommunicable, conditions which we have shown to be impossible. Experience might provide a solid psychological explanation for beliefs, but it provides very little in the way of valid justification. What matters in determining the legitimacy of a person’s beliefs is not a tally of their quasi-related subjective experiences, but instead the universally appreciable reasons that the person can bring to bear in support of their claims. All reasons must be able to be articulated and pass the test of logical soundness. It is just plain invalid, let alone condescending and presumptuous, to make appeals to experience when your opponent is arguing in good faith.

A futher implication of the intelligibility requirement is that moods and emotions are not beliefs, either. Even though thinking (or saying) “I am angry” constitutes a trivially true belief when you perceive yourself to be angry, the uninterpreted sensation of anger does not qualify as a belief as such. The term “belief” is thereby restricted to exclude generalized expressions of basic preferences, like “Apples are better than oranges,” which lack assignable truth-values. However, it may still include more precise expressions like “I like apples better than oranges,” which is trivially true in the same way that “I am angry” is.


At first glance, it might appear that any belief might be of the preferential sort if cleverly  restated, but such a notion ignores the function of beliefs as claims to knowledge. Claims to knowledge can be checked against logical, semantic, and empirical standards. Preferences which are completely subjective are not verifiable in that sense.

The second restriction relates to a belief’s permissible content. Not only must the propositions expressing beliefs be grammatical, but they must also pertain to objects that exist within our shared conceptual scheme or language. To think that “scrigglebugs are seven-legged” is not a belief so much as a mere fantastical assertion. The word “scrigglebug” does not exist within our language, and therefore it has no explicit meaning. However, to think that “satyrs are part weasel, part hippopotamus” constitutes a false belief because even though satyrs do not really exist, they are well-defined objects within a communicable language that lets us meaningfully talk about them.

By now, it should be evident that beliefs don’t differ in any important sense from propositions of the sort that might safely enter into a system of facts. While beliefs certainly maintain a subjective component (i.e. the agent must judge that a proposition is true), to the subject himself beliefs and facts are indistinguishable. Can a person truly believe that God roots for Tim Tebow without equivalently believing that the sentence “God roots for Tim Tebow” is true? Such a case would represent an odd type of belief indeed, and would defy our most basic notions about truth and judgment.

Because beliefs are essentially claims to knowledge, they are subject to ex falso quodlibet in the same way as facts. Thus, we see that consistency is not only a moral imperative, but a logical one as well.



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About Ben Labe

I am a PhD Economics student at The University of North Carolina, Chapel Hill. As an undergraduate, I attended The University of Pittsburgh, where I studied Math, Economics, Philosophy, and Dance. I was put on this great earth for one reason: to let others know that they were not put on this earth for any good reason, but that Ethics persists nonetheless.


  1. But do you allow for the fact that so much of reality is paradoxical? Often, we gain more control only when we surrender and let go, for example.

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