Tony Flood e-mails:
Bill, when you distinguish retorsive arguments that work from those that don't, I'm not clear about what you mean by "working." You haven't said that some retorsive arguments are fallacies, but if they're not, then what is their defect? A "performative contradiction," e.g., "I cannot write a sentence in English," may not be, as you noted, a contradiction between propositions, but to expose its untenability is certainly effective and therefore "works." Do you exclude performative contradictions from the class of retorsive arguments? If you do and if you're right, my celebration of that "point of connection" was misplaced. (I've modified that paragraph to include the link to your post.)
I will try to answer Tony's question by giving an example of a retorsive argument that does not 'work.' In Retortion and the Existence of Truth I gave an example that did seem to 'work.'
As I understand it, retortion is of interest to the metaphysicians who employ it, Transcendental Thomists in particular, as a method of establishing fundamental propositions ('first principles') without infinite regress, circularity, or dogmatism, thereby evading the dreaded Muenchhausen Trilemma. Retortion is the procedure whereby one attempts to establish a thesis by uncovering a performative inconsistency in anyone who attempts to deny it. It is something like an ad hominem tu quoque except that the homo in question is everyman, indeed every rational being. To be successful, to 'work,' a retorsive argument must establish the target proposition as true unconditionally and not merely on condition that there exist contingent beings like us. Otherwise, it would have no metaphysical significance, but merely a transcendental one. Let the target proposition be the Law of Non-Contradiction (LNC), an excellent candidate for the office of 'first principle.' A successful retorsive argument for LNC 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.
To illustrate, suppose someone wishes to prove by retortion that
1. Some statements are negative.
He does this by considering whether the negation of (1),
~1. No statements are negative
is affirmable. Surely it is not. For anyone who states or asserts or affirms (~1) is involved in a performative inconsistency. In the very act of making the negative statement that no statements are negative, the person produces a negative statement, thereby contradicting his claim that no statements are negative. His performance 'contradicts' the content of his assertion. (The sneer quotes signal that this is not a logical contradiction strictu dictu.) It cannot be true both that the content of the assertion is true and that the assertion is made. The content, if true, is unassertible without performative inconsistency. More generally, it is unaffirmable in thought or in overt speech. By uncovering this performative inconsistency, we presumably establish (1) by retortion. It is therefore the undeniability or ineluctability of (1) that is supposed to prove its truth.
But have we really established by retortion that some statements are negative? Have we proven this to be the case in itself? Or have we proven merely that affirming the negation -- No statements are negative -- is impossible for us? How can we show that reality in itself is governed by what we must affirm and what we cannot deny? Here is the nub of the difficulty. The proposition expressed by (~1) cannot be stated or asserted on pain of performative inconsistency. But it could be true for all that. Consider a world W in which there are statements, but all of them are affirmative. In W, (~1) is true but unassertible. For if anyone were to assert it, he would falsify it by doing so. Therefore, the unassertibility of (~1) does not prove the truth of (1).
In this case, then, it appears that retortion does not 'work.' That is, we cannot prove by retortion that some statements are negative. All we succeed in proving is that No statements are negative cannot be denied by us. Now if all retorsive arguments were like this, then retorsion would have at best a transcendental, but not a metaphysical significance. My present view, however, is that some retorsive arguments work and some do not. It depends on the subject matter.
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