Many distinguished philosophers have attached great importance to logical deduction as the preferred route to certain knowledge.
This includes Descartes,
Leibniz,
and Hobbes.
These philosophers did not benefit from as good an understanding of the limits of logic as is possible now, and their practice fell short of their ideals.
The empiricist philosophers were at pains, au contraire, to emphasise the importance of sensory experience as a source of knowledge.
They nevertheless, with the exception of David Hume, had a rather woolly sense of where the line lay between those trivial propositions which are independent of our senses and the general morass which are not.
|
|
Hume, though an empiricist, recognised that mathematics is (though other sciences are not) demonstratively true.
Considered a skeptic, his skepticism consisted in drawing the line as well as it has ever been drawn before this century, between those propositions which can be established demonstratively (by which it seems likely that he meant something like what we would now call deductively) and those which cannot.
This is the line between analytic and synthetic truths.
Until this century, though philosophers could aspire to mathematical (and hence logical) standards of rigour in their demonstrations, they did not have the technical resources to realise their aspirations, and often failed to appreciate the limits in principle of deductive methods.
|
|
This century began with the emergence of analytic philosophy, at least partly inspired by Bertrand Russell's work in mathematical logic.
The logical positivists later placed great emphasis on the importance of logic.
The other main element of analytic philosophy came through the commonsense philosophy of G.E.Moore and through the influence of Wittgenstein's work became a major trend in Western academic philosophy.
This trend emphasised the resolution of philosophical problems through the study of ordinary language, and contributed to an underexploitation of modern logic in philosophy.
|
|