[Inquiry] Re: Simple Meanings In Limnal Expressions

[Jon Awbrey]

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

SMILE.  Note 3

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| 3.1.  The Essence of Mathematics (cont.)
|
| It does not seem to me that mathematics depends in any way upon logic.
| It reasons, of course.  But if the mathematician ever hesitates or
| errs in his reasoning, logic cannot come to his aid.  He would be
| far more liable to commit similar as well as other errors there.
| On the contrary, I am persuaded that logic cannot possibly attain
| the solution of its problems without great use of mathematics.
| Indeed all formal logic is merely mathematics applied to logic.
|
| It was Benjamin Peirce, whose son I boast myself,
| that in 1870 first defined mathematics as "the
| science which draws necessary conclusions".
| This was a hard saying at the time;  but
| today, students of the philosophy of
| mathematics generally acknowledge
| its substantial correctness.
|
| C.S. Peirce, 'Collected Papers', CP 4.228-229
|
| C.S. Peirce, 'Collected Papers of Charles Sanders Peirce, Volume 4,
| The Simplest Mathematics', Charles Hartshorne and Paul Weiss (eds.),
| Belknap Press of Harvard University Press, Cambridge, MA, 1933, 1961.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
inquiry e-lab: http://stderr.org/pipermail/inquiry/
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o