It’s easy to “make” a new truth. I can define the term busy* thusly:
For any x, x is busy* iff it contains more than five items.
Given this definition it is true that the room I am currently in is busy*. I can define another term busy** thusly:
For any x,
(1) x is busy** if it contains five items or more, and
(2) it is not the case that x is busy** if it contains seven items or fewer.
Now consider a room containing six items; it is both true and false that the room is busy**. Clearly the concept of busyness** is inconsistent, yet the sentence ‘This room is busy**’ seems to express a proposition—inconsistent claims are not unintelligible in virtue of their inconsistency. Since the claim expresses a proposition it has a truth value, and in cases where ‘this room’ designates a room containing six items, the claim will be both true and false.
Now, we might not be too worried about inconsistencies of this sort, since they involve no worldly contradiction—there is nothing inconsistent or incoherent about a room containing six items—only the deployment of inconsistent concepts. Yet, so long as some sentence or proposition is both true and false—regardless of whether this involve a worldly contradiction)—then, in classical logic, by the misnomed (yes, that is a word) ex falso quodlibet, it follows that every sentence or proposition is true, which is absurd. As such, cheap dialetheism of this sort is sufficient to show that we must reject classical logic in favour of a relevance logic.
It seems to me something must be wrong with this argument, but I’m not sure what.
Nice piece. But isn't the problem here merely definitional? If I say, for example, that greal is that color which is closest to teal and you say that greal is that color which is closest to green, isn't the issue here one that involves a lack of clarity concerning the definition of greal? So sure, greal does express something, but we aren't exactly sure what it expresses. Buzy** does seem to express some sort of proposition, but it's not clear exactly what it expresses (given (1) and (2)).
ReplyDeleteYes, one way of blocking the argument is to deny that inconsistent claims really express propositions. I wondered about this. We have a grip on the meaning of a claim to the extent that we know how to use it in inferences. Since, given ex falso quodlibet, *everything* follows from an inconsistent claim, you might think that it is inferentially degenerate and so not properly meaningful. My worry about this line of thought is (i) that it seems to beg the question against dialetheists, who will reject ex falso quodlibet anyway, (ii) that we do seem to be able to grasp inconsistent claims, otherwise things like reductio proofs would just be meaningless or incomprehensible. Also (1) and (2) both express meaningful propositions, so, on the face of it, so should the conjunction of (1) and (2).
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