Abstract
We consider dialogues over both specific and general Kripke structures where individuals convey and acquire knowledge through statements. We show that conventional ‘proofs’ of the existence of knowledge actually correspond to optimal strategies (which may not occur when real individuals talk). Sometimes these optimal, (and hence all) strategies need to be transfinite in that knowledge can only be acquired at some infinite ordinal. However, the situation changes sharply when we consider dialogues geared not to acquiring knowledge but to taking a justified risk.
Article Note
“But how does he know where and how he is to look up the word ‘red’ and what he is to do with the word ‘five’ ?” Well, I assume he acts as I have described. Explanations come to an end somewhere. Ludwig Wittgenstein
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© 1992 Springer-Verlag New York, Inc
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Parikh, R. (1992). Finite and Infinite Dialogues. In: Moschovakis, Y.N. (eds) Logic from Computer Science. Mathematical Sciences Research Institute Publications, vol 21. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2822-6_18
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DOI: https://doi.org/10.1007/978-1-4612-2822-6_18
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