[Inquiry] Re: Peirce Through The Looking Glass

[Jon Awbrey]

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PLG.  Vortextual Note 1

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| Mathematics and logic, historically speaking, have been entirely
| distinct studies.  Mathematics has been connected with science,
| logic with Greek.  But both have developed in modern times:
| logic has become more mathematical and mathematics has
| become more logical.  The consequence is that it has
| now become wholly impossible to draw a line between
| the two;  in fact, the two are one.  They differ as
| boy and man:  logic is the youth of mathematics and
| mathematics is the manhood of logic.  This view is
| resented by logicians who, having spent their time
| in the study of classical texts, are incapable of
| following a piece of symbolic reasoning, and by
| mathematicians who have learnt a technique
| without troubling to inquire into its
| meaning or justification.  Both types
| are now fortunately growing rarer.
| So much of modern mathematical work
| is obviously on the border-line of
| logic, so much of modern logic is
| symbolic and formal, that the very
| close relationship of logic and
| mathematics has become obvious
| to every instructed student.
| The proof of their identity is,
| of course, a matter of detail:
| starting with premisses which
| would be universally admitted
| to belong to logic, and arriving
| by deduction at results which as
| obviously belong to mathematics,
| we find that there is no point
| at which a sharp line can be drawn,
| with logic to the left and mathematics
| to the right.  If there are still those
| who do not admit the identity of logic and
| mathematics, we may challenge them to indicate
| at what point, in the successive definitions and
| deductions of 'Principia Mathematica', they consider
| that logic ends and mathematics begins.  It will then
| be obvious that any answer must be quite arbitrary.
|
| Russell, IMP, pages 194-195.
|
| Bertrand Russell, 'Introduction to Mathematical Philosophy',
| Routledge, London, UK, 2000.  Originally published in 1919.

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