Syntax and Paradoxes

Syntactical rules may appear to set minimal standards of intelligibility, but they don't guarantee intelligibility.

We shouldn't be deceived by the 'obviousness' of some of these rules - finding them obvious is really just the condition of being able to talk. In other words, we wouldn't be able to to talk if we didn't find quite a few of them obvious.

For Kripkean reasons, we cannot render a syntactical rule mechanically: any potential mechanical isomorph could be unreliable. We cannot say 'to find the consequence of the non-contradiction rule, press this button', because we would have to use the non-contradiction rule to test the reliability of the button.

We can only state syntactical rules if we have a working semantic context: if we can speak.

So while they might represent boundaries of intelligibity they cannot exist independently of it. They cannot conceptually precede it. We can't make sense of a syntactical rule outside of a semantic context.

So: incompleteness/inconsistency theorems, which seem to be purely syntactical, can only be constructed in a semantic context within which the normative syntactical rules can be stated unequivocally. It is within this semantic context that the rules have the correct scope, and can stand as tests for any potential mechancial isomorph.

It is because we can describe a logic gate functionally that it counts as a logic gate.

(But also: we describe the world this way as well. It is only because we can describe the world functionally that we can describe it at all - Goodman's paradox is constructed the same way as Kripke's).

Godel's paradoxes, then, become semantic paradoxes because we can say whether it is true that certain syntactical rules have been observed.

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