Aristotle's Cat: An Argument against Dialetheism

Aristotle’s Cat: An Argument against Dialetheism Bryan W. Van Norden (first draft: 23 October 2015) 5 Introduction According to dialetheists, there are some contradictions that we ought to believe. In other words, there are some sentences that are simultaneously true and false. For example, dialetheists claim that the sentence, “This sentence is false” is both true and false. Contemporary dialetheists (like Graham Priest) have plausible rebuttals to the “standard” 10 arguments we were all taught for why contradictions cannot be true.1 For instance, a common objection to rational belief in contradictions is that a contradiction entails that every sentence is true. Dialetheists like Priest agree that not all sentences are true (and certainly not all sentences are both true and false). However, there are non-classical, paraconsistent logics in which a contradiction does not entail everything. Moreover, even 15 if one is not a dialetheist, there are independent reasons for accepting paraconsistent logics. (In other words, paraconsistent logics are not simply an ad hoc way of defending dialetheism.) Some other classic arguments against contradictions turn out to be essentially question-begging. Speaking for myself, I see the appeal of dialetheism; however, I have a stubborn intuition that there is a problem with contradictions that 20 dialetheists (and also their critics) have failed to see. In this essay, I shall present a new argument that we cannot rationally believe that a sentence is both true and false. My 1 Graham Priest, “What Is So Bad about Contradictions?” Journal of Philosophy Vol. 95, No. 8 (Aug., 1998), pp. 410-426. 2 Erwin Schrödinger, “The Present Situation in Quantum Mechanics,” (1935), trans. John D. Trimmer, http://www.tuhh.de/rzt/rzt/it/QM/cat.html#sect5, accessed 23 October 2015. argument is based on a thought experiment, which I have labeled “Aristotle’s Cat” (with a tip of the hat to Schrödinger’s Cat). 25 Aristotle’s Cat Imagine that Aristotle has been arguing with one of his students at the Lyceum over the sentence, “This sentence is false.” Neither Aristotle nor his student are dialetheists, and suppose they agree that the sentence in question is either true or false (but not both). Aristotle says that the sentence is false, while his student says that it is true. After hours 30 of arguing, the two are unable to convince one another. In a moment of frustration, Aristotle picks up his beloved cat, Ailuros, and says, “If it is true that ‘this sentence is false,’ let Zeus strike Ailuros dead with a bolt of lightening. However, if it is false that ‘this sentence is false,’ let Zeus spare Ailuros.” What will Zeus do? 35 If dialetheists are right, “this sentence is false” is true, so Zeus will incinerate poor Ailuros with lightening. However, if dialetheists are right, “this sentence is false” is also false, so Zeus will let Ailuros live (i.e., not incinerate Ailuros). Now we have a problem, because Zeus cannot both incinerate Ailuros and not incinerate Ailuros, but he will do both if dialetheism is true. (Notice that you can generate the same result with any 40 sentence that is taken to be both true and not true, not just “this sentence is false.”) So dialetheism cannot be true. Some Objections (A) I can imagine a dialetheist arguing that I am begging the question against her. After 45 all, why do I think it is impossible that Ailuros both is and is not incinerated? Isn’t this itself just an application of the law of non-contradiction, which is precisely the principle at issue? I think my thought experiment is not question-begging. Even without assuming the law of non-contradiction, we have an extremely strong intuition that one cannot accept the truth of both “Ailuros was incinerated by a bolt of lightening” and “Ailuros 50 was not incinerated by a bolt of lightening.” Ailuros is (or was) a concrete physical object, and being incinerated by lightening is a specific physical event. We simply do not know how to conceptualize what it means for it to be the case that she was and was not incinerated. (Try it! What do you visualize happening?) 55 (B) Perhaps a dialetheist will raise the following objection: Admittedly, Ailuros cannot both be incinerated and not be incinerated, but this just shows that not all contradictions can be accepted. Dialetheists do not claim that all sentences are simultaneously true and false, or that we should, like the Red Queen in Through the Looking Glass, believe “as many as six impossible things before breakfast.” Consequently, the dialetheist will 60 happily accept that Ailuros cannot be both incinerated and not incinerated. Unfortunately, this rebuttal quite misses the force of the argument. The problem is that, if dialetheism is true, then (under the conditions specified by the thought experiment) Zeus will incinerate Ailuros and will not incinerate Ailuros. Since we all agree that it cannot be true that Ailuros both is and is not incinerated, dialetheism must be false. 65 (C) A third sort of objection might turn on the apparent role of volition in my thought experiment. Aristotle has made an appeal to Zeus. Zeus must choose whether to act on Aristotle’s plea, and (if he acts at all) what form his response should take. Zeus’s choices are not necessitated, or at least his decision whether to answer a plea from a mortal is not 70 necessitated. For example, Zeus, understanding that Aristotle’s request was based on a mistaken understanding of logic, might simply ignore the request. Ignoring Aristotle’s request would have the practical consequence that Ailuros would live, but this would not be the same as Zeus taking the request seriously and deciding to spare Ailuros. Alternatively, Zeus might decide that the best response would be to materialize before 75 Aristotle and gently explain dialetheism to him, so that Aristotle could withdraw his request. Because of the role of Zeus’s volition in the example, there is no necessary connection between dialetheism and the conjunction of “Ailuros was incinerated” and “Ailuros was not incinerated.” 80 The preceding objection fails to grasp that the problem is not about Zeus’s practical reasoning. More precisely, any problems that involve Zeus’s practical reasoning are not problems with his reasoning, but problems created for his reasoning by dialetheism. Let us stipulate that Zeus has taken a vow to fulfill Aristotle’s next request. (Perhaps that last time Zeus turned into a swan, Hera asked Aristotle where Zeus was, and Aristotle 85 covered for him, so Zeus now “owes Aristotle a solid.”) Since Zeus is bound to honor Aristotle’s request, he cannot ignore it, nor can he attempt to talk Aristotle out of it. I agree that Zeus now faces a problem in practical reasoning, but the problem is not generated by anything internal to practical reasoning. The problem Zeus faces is generated by taking seriously the notion that a sentence can be both true and not true. 90 Conclusion In general, we are less bothered by counterintuitive claims when they are in realms far removed from our ordinary experience. The Copenhagen Interpretation of Quantum Mechanics claims that reality at the atomic level is genuinely indeterminate until an 95 observation on it is performed. Initially, these indeterminacies appeared to be isolated at the atomic level. However, the thought experiment of Schrödinger’s Cat was intended to show that “an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy.”2 Just as Schrödinger’s Cat suggests that quantum indeterminacy might bleed over into the everyday world, Aristotle’s Cat 100 motivates the intuition that we cannot be sanguine about contradictions simply because they appear harmlessly isolated from the world of everyday experiences. 2 Erwin Schrödinger, “The Present Situation in Quantum Mechanics,” (1935), trans. John D. Trimmer, http://www.tuhh.de/rzt/rzt/it/QM/cat.html#sect5, accessed 23 October 2015.