I agree that this is too dreamy and programmatic, and it would have been better if I had presented a concrete plan.
The idea that logic can be an ultimate foundation seems difficult to justify.
Well, the foundation are the axioms, not the logic. The philosophical position of logicism (i.e. "mathematics can be reduced to logic") is accepted as untenable, let alone for science.
Since we're talking about formalizing empirical science, then these axioms don't even need to be "self-evident", general or anything like that.
Is it possible to have a non-logical "foundation" for something? (and what would that mean?)
One problem is the problem of infinite regress: when is one justified taking things as axioms? Still, "foundations" can be nice because they may be the simplest way of unifying disparate pieces of knowledge... foundations give us links through which we get explanatory unification.
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The idea that logic can be an ultimate foundation seems difficult to justify.
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The idea that logic can be an ultimate foundation seems difficult to justify.
Well, the foundation are the axioms, not the logic. The philosophical position of logicism (i.e. "mathematics can be reduced to logic") is accepted as untenable, let alone for science.
Since we're talking about formalizing empirical science, then these axioms don't even need to be "self-evident", general or anything like that.
Is it possible to have a non-logical "foundation" for something? (and what would that mean?)
Reply
Reply
One problem is the problem of infinite regress: when is one justified taking things as axioms? Still, "foundations" can be nice because they may be the simplest way of unifying disparate pieces of knowledge... foundations give us links through which we get explanatory unification.
Reply
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