I feel as though I'm crisscrossing a familiar landscape, now, but perhaps revisiting it is worthwhile ...
Demonstrating the truth of 'It is a fact that A' is exactly the same as demonstrating that 'It is not a fact that A' is unintelligible. The two cases are methodologically indistinguishable.
We want to believe that an 'unintelligible' statement is unintelligible because it breaks some specific (explicit) rule - perhaps it is self-contradictory. This has led us astray. I have identified (in previous posts) three different ways in which a statement can be unintelligible:
(1) The familiar one (above), which is that it contains or entails an explicit contradiction.
(2) One in which it entails an implicit contradiction, so that any 'conventional' semantic interpretation makes the 'content' of the 'statement' inconsistent with its being a statement at all. Examples are Moore's paradox, and other more general cases such as 'we are unable to converse' (as in Stroud's 'privileged class').
(3) One in which we simply fail to be able to talk to one another, where we do not know 'how to go on'. This would happen if, for instance, we were unable to agree on some immediate empirical facts.
We can find ourselves uncertain about which of these applies to any particular case, of course, because the boundaries of intelligibility are also the boundaries of definite meaning. A contradiction or a Moorean paradox can only be demonstrated on the grounds of definite meanings, and meaning begins to evaporate quite quickly if we cannot agree on facts.
And, of course, the sense of 'demonstrating' in the second paragraph is also quite hard to pin down. We can only 'demonstrate' the truth of something if we can agree that something counts as a demonstration; can give specific examples and answer questions about why they work.
The bounds of this process are, of course, exactly the bounds of intelligibility - and this is what saves us from incoherent relativism or scepticism. Without the possibility of some valid demonstrations we have no language - no possible way of distinguishing truth from falsehood, and so no 'meanings'.
No way of asking questions, never mind answering them ...
Experimenting with intelligibility and experimenting with reality are, ultimately, the same activity.
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