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Language, proof and logic
What do the fields of astronomy, economics, finance, law, mathematics, medicine,
physics, and sociology have in common? Not much in the way of subject
matter, that's for sure. And not all that much in the way of methodology.
What they do have in common, with each other and with many other ¯elds, is
their dependence on a certain standard of rationality. In each of these ¯elds,
it is assumed that the participants can di®erentiate between rational argumentation
based on assumed principles or evidence, and wild speculation or
nonsequiturs, claims that in no way follow from the assumptions. In other
words, these fields all presuppose an underlying acceptance of basic principles
of logic.
For that matter, all rational inquiry depends on logic, on the ability of
people to reason correctly most of the time, and, when they fail to reason
correctly, on the ability of others to point out the gaps in their reasoning.
While people may not all agree on a whole lot, they do seem to be able to agree
on what can legitimately be concluded from given information. Acceptance of
these commonly held principles of rationality is what di®erentiates rational
inquiry from other forms of human activity.
Just what are the principles of rationality presupposed by these disciplines?
And what are the techniques by which we can distinguish correct or \valid"
reasoning from incorrect or \invalid" reasoning? More basically, what is it
that makes one claim \follow logically" from some given information, while
some other claim does not?
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