"We can talk to each other", taken literally, must be either hopelessly ambiguous (not a statement at all) or true and undecidable.
This is because it requires a tacit conception of truth - 'using the language properly', so to speak, and also of what counts as a language. Both of these must be reasonably reliable if the statement is to be true, but no algorithm written down in the language can demonstrate this reliability.
Also, no algorithm in a 'higher order' language would be translatable, so speculations of this sort are irrelevant (if any sense at all can be attached to them).
The reason the statement is true is not algorithmic: it's falsehood would be unitelligible, a Moorean paradox. If someone insisted on its literal falsehood, we would have to wonder what they meant (certainly not something related to the conventional uses of the words it contains). They would be doing something at the same time as seeming to claim that it was impossible. Either we'd be wrong about what they were doing, or we and they did not share an interpretation of 'impossible'. This is not an algorithmic demonstration because no explanation to such an objector would have any weight - we could never be sure that there was enough mutual understanding to articulate an explanation. We would either find a way of working out what they did mean - would find a way of continuing to talk with them which rendered their objection interpretable - or the conversation would disintegrate.
The tacitly implied predicate 'is true', here, is not grounded in Kripke's sense. But it is still a kind of basis for grounding.
Wednesday, November 20, 2013
Thursday, November 14, 2013
Diagonalisation (?), behaviour, and meaning ...
Does something like this work:
Suppose we were to give a behavioural account to of how to say things in a language - say a list of noises, and what they meant. The list could include not only 'primitive' expressions but also any complexes constructed from them. If we could describe the records in this list, then the list would be enumerable.
Notice that while one side (say the left side) of this list comprises specific physical circumstances (behaviours, or noises), the other side (the right side) is a list of contents, and so can only be identified intentionally.
If we can describe records in the list, then we can describe the contents of each left side of each element. (This means, among other things, that the descriptions of the physical behaviours must also appear as the contents of the intentional side somewhere else in the list, and so have their own describable physical counterparts.)
Everything that can be said could be somewhere in this list, linked up to a way of saying it.
Although the list is formally interminable, however, any actual statement would have to be finite. This is a barrier to the actual list containing the behaviour which counted as a description of itself, since this would require something like infinite repetition of nested representations of the list.
Also, although the list would contain statements about whether some statement was a member of the list, the number of these would be 'smaller' than the number of items in the list - otherwise the only thing the list could contain would be statements about what was in the list.
Since a description of the list would containt a complete statement of what was in the list, this description could not be in the list since there have to be some statements which do not have membership statements in the list.
Suppose we were to give a behavioural account to of how to say things in a language - say a list of noises, and what they meant. The list could include not only 'primitive' expressions but also any complexes constructed from them. If we could describe the records in this list, then the list would be enumerable.
Notice that while one side (say the left side) of this list comprises specific physical circumstances (behaviours, or noises), the other side (the right side) is a list of contents, and so can only be identified intentionally.
If we can describe records in the list, then we can describe the contents of each left side of each element. (This means, among other things, that the descriptions of the physical behaviours must also appear as the contents of the intentional side somewhere else in the list, and so have their own describable physical counterparts.)
Everything that can be said could be somewhere in this list, linked up to a way of saying it.
Although the list is formally interminable, however, any actual statement would have to be finite. This is a barrier to the actual list containing the behaviour which counted as a description of itself, since this would require something like infinite repetition of nested representations of the list.
Also, although the list would contain statements about whether some statement was a member of the list, the number of these would be 'smaller' than the number of items in the list - otherwise the only thing the list could contain would be statements about what was in the list.
Since a description of the list would containt a complete statement of what was in the list, this description could not be in the list since there have to be some statements which do not have membership statements in the list.
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