Why would one would consider contradictory speech to be philosophically appropriate? Given that contradictions can be meaningful, why would one use them? First, it may be that one believes that all systems are going to be inconsistent at some point anyhow. If this is true, then there is relatively little value in ironing out all of the wrinkles of discourse instead of simply investigating what one can. Also, if I have doubts about any given chain of reasoning or system, I have much less reason to follow it through consistently. It may be far better to pursue many lines of reasoning, even if they are mutually inconsistent, since then I may hit the truth on a couple points at least.
Second, one may be strongly convinced by both the arguments for x and the arguments for not-x. The contradiction does not mean that there isn't some y which is coherent with x but which is semantically and practically similar to not-x. This is the problem with some ad hominem attacks: showing that a given person is inconsistent shows nothing about whether a better version of their views could succeed, entailing that they really were close to being right in the first place. In the meantime, holding on to the contradiction may be the most intellectually responsible choice, while pursuing a research program of eventually resolving the contradiction while keeping the insights.
Third, it may be that certain mystical views can only be couched in contradictory terms. If there is some reality utterly responsible for absolutely anything, then language which can only look at certain things at any given time will encounter difficulties. Contradiction shows language's (and thought's) breaking points, and it is the fact of breaking which points to what is to be communicated.
Fourth, one may be holding to a dialectical tension. This I think is closest to what I am talking about with skepticism. On the one hand, I think that everything is doubtable (and once this is realized, also already doubted, for those familiar with what I've said before on this blog). But I also think that we should continue investigating the truth. Should I throw one side or the other away because I can't unite them at one time? No; I continue in a constant back-and-forth, which seems to accomplish a number of aims (including understanding) better than any single idea or system.
But if nothing else, saying that someone is being contradictory is a paltry criticism. It contributes nothing to discussion; it merely wins points in debate. It is therefore sophistry and not philosophy, unless it is accompanied by substantial interaction. Show how some premise is wrong, show how my understanding is off, show some alternative, but show something of value.
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