Logic and Interpretation

Here are two compound expressions:

~(P&~P)

    P&~P

Conventionally, the first is a tautology and the second a contradiction.  However, we might introduce a 'rule of interpretation' here:

When an expression appears on the left of an ampersand, it means the contrary of what it would mean if it appeared on the right.

Applying this rule, we make the first expression a contradiction, and the second a tautology.

Since it is always possible to distinguish expressions that are sentences, and to distinguish whether they are on one side of an ampersand or the other, it seem likely that this rule would not render the notation inconsistent.  By putting '~( ... )' round all sentential expressions on one side of an ampersand we could 'encode' and 'decode' our normal propositional logic.

If this was a rule that a reader might mistakenly apply when doing logical calculations, we would have to warn against it.  On the other hand, such a warning would sound mad to a reader who had never thought of such a rule.  It would say 'Remember to treat an expression on one side of the ampersand as meaning the same thing as when it appears on the other side'.  But this, of course, is another rule of interpretation, just like the first one.

Neither rule is more fundamental than the other.  Each resolves an ambiguity which, if we did not see it, would not need resolving.

Not only is it absurd to consider ourselves to be applying a myriad of interpretational rules in order to eliminate unimagined ambiguities, it is also incoherent.  In order to say 'I am applying rule X', we need to articulate rule X, and so also interpret it.  Not only would every rule, itself, require interpretation; but there would be rules whose correct interpretation would depend upon their own application.

Constructive Semantics

We can be confused by the fact that breaking some rules (e.g. non-contradiction) destroys semantic content.  We can't conclude from this that there is a set of rules which, if followed, guarantees semantic content.

In fact, the OQ argument would suggest otherwise - because we would need to know what these rules meant.

A constructive semantics could be quite rough and ready, and contain many unresolved ambiguities, and still do the work that is required of it (i.e. make semantic determination tractable).  What would also be required would be a method for resolving the ambiguities and cleaning up any loose ends that became problems, and this method could be (I think would need to be) experimental.

What we can't tell, however, is whether there are some things that we resolve by experiment that could be worked out from some set of rules that we are (unknowingly?) following.  For this to make sense, the rules would have to be discoverable - but the OQ problem doesn't rule this out.  It just rules out the discovery of a complete set of rules.

Some Intentional Facts

That I know how to do arithmetic is a fact about the world.

Does this make either epistemology or mathematics empirical?

We test whether I know by making experiments.  Does the verb 'to know' mean something beyond the quality of these tests?

Yes, but this is because we don't understand what an 'experiment' is - specifically, we don't understand that whether an experiment has taken place, and what it's outcomes are, depend upon semantic considerations that cannot be eliminated, cannot be exchanged for something which looks more mechanical.

Language games

Suppose we simplify our picture of language so that we can fit 'saying things' into a game analysis grid - with 'statements' or 'utterances' as strategies and a dimension for each player.  We could count each utterance opportunity as a sub-game.

We would need some way of ranking outcomes for players, in order to analyse the game.

If we wanted to retain our conception of the game as a language game, the 'moves' would have to translatable into the language we use to describe the game (the one we're using now) as intelligible utterances - as moves in 'the language game' we are now playing.  There could be more than one way of doing this, and perhaps no clear way to select between translation schemas.

Describing the rules of the game would not be a possible move in the game.  (Although describing the rules of some sub-games would be).

Given a translation schema, we could attach a value to 'truth-telling' - i.e. maintaining general intelligibility and individual credibility.  Perhaps.

But our selection of a schema would depend on assuming that players already attached a value to intelligibility?

(Davidson and decision theory?)