It is easy to see that thoroughgoing skepticism devours itself. If we can’t know the truth, then we can’t know that we can’t know the truth.
Postmodernism, likewise, obviously. If all texts are tendentious, then the texts that propagate postmodernism are tendentious.
But here’s a question: do all false propositions devour themselves? Are they autophagous? I.e., is it the case that if any false proposition were true, it would under the force of some necessity or other – logical, causal, historical, etc. – be false, or meaningless?
I think it may be.
There are two sorts of truths: those pertaining to contingent facts, and those pertaining to necessary facts. But with respect to both sorts of fact, the whole set of truths is necessarily coherent. There can be in it no contradiction whatever; no truth can contradict another. A contradiction of one truth contradicts the whole of truth.
Take the necessary truths, as of math, logic, or metaphysics.
No proposition about necessary facts can be expressed except under terms that purport to pertain properly to the whole of truth – of, i.e., all the necessary truths. The definitions of the terms themselves must be correct in order for true theorems to follow. Get the definition of a single term wrong, and you will generate false theorems, that will work havoc throughout your doctrinal stack. You’ll be forced either to abandon your false proposition, or redo the entire system of theorems and their instantiations.
The necessary truths constitute a seamless interdependent web of mutual implication. They must all be true, or none of them can be true. Change one, and you must change the rest to go along with it, so that they all fit together without contradiction.
False propositions are very expensive to believe.
Let’s drill down a bit.
False propositions in mathematics cannot but be expressed in terms whose definitions entail theorems. We can’t say that 2 + 2 = 5, e.g., except by the implicit invocation of terms from number theory. From the definitions of those terms, the theorems of number theory logically follow, together with the whole network of their implications for other fields of mathematics. The instantiations of those theorems in arithmetical operations then implicitly presuppose those theorems; the operations could not proceed as they do, were the theorems other than they are.
If it is true that 2 + 2 = 5, then what we had been meaning by 2 and 5 must be incorrect. So then logically are all the theorems that derive from the terms as they had been defined. In that case, the statement that 2 + 2 = 5 will remain simply meaningless, until we arrive at some other meanings for 2 and 5 – and by an inescapable logical necessity, all the other numbers, and ergo numbers as such – that will endow it with intelligible meaning. But when we had done that (supposing we could), we would then discover that our modifications to the meanings of numerical terms logically entailed a different set of theorems than had formerly been instantiated in our previous arithmetical operations.
All those operations would then be falsified, or rendered incoherent. And among those operations would be 2 + 2 = 5. To express 2 + 2 = 5, you can’t do without addition. But under the new numerical paradigm, addition would be a different operation than it had been under the old. To make 2 + 2 = 5 meaningful under the new paradigm, you’d need something other than +, or perhaps than =. Under those new operations, the operations employed in 2 + 2 = 5 would be inapposite. 2 + 2 = 5 presupposes and invokes definitions, theorems and operations that its truth renders nonsensical.
Any false proposition in mathematics must somehow eventually contradict one or another of those definitions or axioms or theorems that it implicitly presupposes are proper or true, and from which therefore its own meaning derives.
2 + 2 = 5, then, is autophagous. If it is true, it must be incoherent. So it is necessarily false.
The autophagy of falsehood may be easier to see in the case of contingent truths – causal truths – especially historical truths. E.g.: we cannot state that the sun exploded yesterday unless it is false that the sun exploded yesterday. The truth of the statement would render the statement itself impossible. The statement presupposes its own falsity.
This is somewhat harder to discern in respect to false statements about less imposing facts than the explosion of the sun. But, explosion of Sol : baby’s spilt milk :: galactic collision : explosion of Sol. At any scale, an assertion of a historical falsehood can occur only in a world that in its historical outworking has rendered that falsehood a statement about a different world than the world in which it is uttered. That different world to which the false statement of historical fact refers is false to fact; it is not the true world. It is not the factual world that has given rise to the false statement, and made it possible for the false statement to take its place coherently in the causal nexus of true facts.
Like the logical truths, the historical truths are a seamless web. You can’t change one of them without changing the whole shooting match. But if you change the whole shooting match, you delete the world in which the false statement factually exists, and replace it with some other world. So doing, you delete the statement itself.
A false statement of historical fact then is an assertion that we live in a different world than the one in which the statement itself exists. It is a statement that the world in which the statement exists does not exist. It is therefore a statement that the statement itself does not exist.
So, yes, it appears that all falsehoods respecting either contingent or necessary facts are autophagous.