[ The Types Forum, http://lists.seas.upenn.edu/mailman/listinfo/types-list ]
On 05/03/13 23:28, Mark Janssen wrote:
[ The Types Forum, http://lists.seas.upenn.edu/mailman/listinfo/types-list ]
To me, that sounds like a total and unconditional rejection.
No, what I meant is that the classical logic represents a stage in the
development of logic. It cannot be taken as the final answer. In fact, we
cannot accept that we have a final answer until the entire natural language
has been formalized, which might take a very very long time indeed! (The
view I take, following Quine, is that logic is a regimentation of natural
language. We can perfectly well circumscribe various regimens for various
purposes.)
But if we're going to be in the Computer Science department, can we
get away from the idea of "logic as a regimentation of natural
language" (which is fine for the Philosophy department) and move to
the idea of logic as equations of Binary Artihmetic and Boolean
Algebra?
We must do no such thing! Booleans are not especially fundamental to
computing, however much they are part of our hardware implementations.
To talk about how things map onto binary arithmetic and boolean algebra,
we must talk about the things we are mapping onto them: this means
accepting that some logics talk about other objects of study.
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