Necessary Paradoxes

We experiment with how to talk - we find out what works.  Sometimes we can write down rules from our experiments, that can be used to predict what will work and what will not.  Some of these rules will be provisional, and some will be derived (and so hypothetical on their derivations).  All these rules tell us what will be true.  Some (provisional and hypothetical) rules are just statements like 'P is true'.  Some of these rules seem to be hypothetical only on the possibility that there are any rules like this at all - the possibility of intelligibility, of language itself - but there will always be an interpretive (a semantic) step in any demonstration of this.  To those who accept this step - we might call them those to whom we can speak - the rules which can be demonstrated in this way will seem to be absolutely true.

We need 'is true' to talk about all these kinds of rules.  We cannot ('in principle') write down all the rules - we never reach the end of experiment.

'Semantically closed' languages must be 'empirically' open.  It is the paradoxes that give us science.