Retorsion (retortion) is the philosophical procedure whereby one attempts to establish a thesis by uncovering a performative inconsistency in anyone who denies it. It is something like an ad hominem tu quoque except that the homo in question is everyman, indeed every rational being. Proofs by retortion have the following form:
Proposition p is such that anyone who denies it falls into performative inconsistency; ergo, p is true.
Suppose a person asserts that there are no assertions. That person falls into performative inconsistency: the propositional content of the speech act is 'inconsistent' with the performance. *There are no assertions* is the propositional content, or content, for short. The speech act of asserting is in this case the performance. The inconsistency is not strictly logical, which is why I employed scare quotes. Strictly logical inconsistency obtains between or among propositions, and a performance such as asserting is not a proposition. And yet it is clear that there is some sort of inconsistency here, some sort of 'contradiction.' The content asserted is falsified by the act of asserting it. The performance 'contradicts' the content.
We can put this by saying that *There are no assertions* is unassertible salva veritate. For no one can assert it without falsifying it. Its negation, *There are assertions,* has the opposite property of being such that no one can assert it without verifying it, without making it true. (Note that 'verify' has two senses.)
To be a successful metaphysical tool, a retorsive argument must establish the target proposition as true unconditionally and not merely on condition that there exist contingent beings like us who occasionally and contingently engage in such intellectual operations as affirmation and denial. Otherwise, it would have no metaphysical significance, but merely a transcendental one. Metaphysics, more precisely, metaphysica generalis, has as its task the laying bare of the most pervasive structures of being qua being. For it is one thing for the truth of a proposition to be a necessary presupposition of our intellectual operations, and quite another for that proposition to be true in itself and apart from us and our operations of sense and intellect.
To illustrate, let the target proposition be the Law of Non-Contradiction (LNC), an excellent candidate for the office of 'first principle' and a principle it would be nice to be able to establish by retorsion. (One cannot argue directly for LNC without begging the question, and to simply announce that it is self-evident smacks of an unphilosophical dogmatism.) A successful retorsive argument for LNC as a truth of metaphysics and not merely as a law of thought must demonstrate that it 'governs' reality and not merely our thoughts about reality. For if LNC were merely an unavoidable constraint on our thinking, then it might be that reality does not 'obey' it.
What worries me is the putative gap between (a) LNC is a principle without which we cannot conduct our intellectual operations and (b) LNC is a principle of being itself. (Aristotle was aware of this putative gap.) I'm not sure there is a gap, but I'm not sure there isn't either. Nor am I quite sure that we need a metaphysical, as opposed to a merely transcendental, grounding of LNC.
There are very deep questions here, and they may be above my or any mortal's 'pay grade.'
My question could be put as follows. Which propositions are such that their undeniability salva veritate entails their being true independently of of us and our intellectual operations such as denial and affirmation? In other words, in which cases is retorsion a probative procedure for the establishing of metaphysical results? Let's consider some examples.
1. There are assertions. We have seen that anyone who asserts the negation of this proposition is involved in performative inconsistency. By retorsion, then, we conclude that it is true. But is it true independently of us, independently of whether or not assertors exist? No. The unassertibility salva veritate of *There are no assertions* merely shows something about us, not about reality independently of us.
It should also be noted that although *There are no assertions* is not assertible, it is thinkable without performative inconsistency. There are times at which the negative proposition is true. And though it is false now, it (logically) might have been true now. Presumably there is no necessity that there be any assertors.
2. There are thoughts. Can I think the thought that there are no thoughts? I can, but if I do I see that the thinking falsifies the thought's content. Now does this performative inconsistency show that there are thoughts in reality apart from thinkers? No. Obviously, a thought is some thinker's thought. The unthinkability salva veritate of *There are no thoughts* does not show there are thoughts in reality apart from us.
3. I exist. The thought that I do not exist is unthinkable salva veritate. Only I can think this thought, and my thinking of the thought falsifies its content, and this is so even if 'I' picks out merely a momentary self. (I am not committed by this to a substantial self.) So we have performative inconsistency. Unfortunately, this does not show that I exist apart from my thinking.
4. There are truths. Can I think, with truth, the thought that there are no truths? No. For if there are no truths then it is true that there are no truths, in which case there are truths. What we have here, though, is not a case of performative inconsistency, but a case in which a proposition refutes itself. It is not that a performance and its content are inconsistent, but that a proposition, by itself, is self-inconsistent. It is self-inconsistent inasmuch as it entails its own negation. If there are no truths, then there are some. And if there are some, then there are some. So, necessarily, there are some truths. This necessary truth is true independently of any mind. But it is not a truth known by retorsion since no performative inconsistency is involved.
5. Some memory reports are veridical. To prove this by retorsion, we begin by negating it. Negation yields *All memory reports are non-veridical.* This is subject to the retort that one who asserts it or affirms it in thought must rely on memory, and so must presuppose the reliability of the faculty whose reliability he questions by asserting it. For if anyone is to be in a position to affirm that all memory reports are non-veridical, then he must remember that on some occasions he has misremembered. He must remember and remember correctly that some of his memories were merely apparent. He must also remember and remember correctly that he has had memories. And in executing his skeptical reasoning, he must remember and remember correctly the early phases of said reasoning. It seems obvious, then, that the truth of *All memory reports are non-veridical* is inconsistent with its being affirmed. If true, it is unaffirmable as true. But does it follow that *Some memory reports are veridical* is true apart from us and our faculties?
6. Something exists. This is a proposition that is undeniable in the sense that anyone who denies it involves himself in performative inconsistency. For if one denies that something exists , then one affirms that nothing exists. But *Nothing exists* is falsfied by the very act (performance) of affirmation.
But does this undeniability show that *Something exists* is true in itself? I don't think so. It is true in itself, but not because it is undeniable. It is true in itself because the proposition, whether true or false, entails the existence of that very proposition. In this regard, #6 is like #4.
My tentative conclusion is that retorsion has merely a transcendental significance, not a metaphysical one.