# [FOM] ARISTOTLE, BOOLE, AND PEIRCE ON "SOME ECKS IS NOT A WYE".

Hartley Slater slaterbh at cyllene.uwa.edu.au
Mon Dec 13 21:04:36 EST 2004

```At 5:54 PM -0500 13/12/04, John Corcoran wrote:
>  I would
>never have noticed this if I had not been inspired to go looking for it
>by reading Peirce's brilliant 1865 Harvard Lecture "Boole's Calculus of
>Logic" in which he points out that the equation Boole uses in the 1854
>LAWS OF THOUGHT  for  "Some Xs are not Ys" yields the corresponding one
>for "Some Ys are not Xs". Thus, although Boole made changes for the 1854
>work, he did not correct this problem: Boole's 1854 "translation" is
>inadequate or his logic is unsound. [POINT 3] ...
>
>Q3 Has anyone any explanation for point 3?

Boole's translation of 'Some Y is not-X' in The Laws of Thought is
'vy=v(1-x)', see Boole's Collected Logical Works Vol. 2, Open Court
1916, p69 - for the complete list of Aristotelian translations
including this, see p241.  What Peirce seems to have overloooked is
that the 'v' symbol is explained on p69 to be context relative:
'Putting, then, y for "men," x for "wise," i.e. "wise beings," and
introducing v as the symbol of a class indefinite in all respects but
this, that it contains some individuals of the class to whose
expression it is prefixed, we have  vy=v(1-x).'   Thus we might also
write it '(Ez)(Et)[-(zy=0).-(t(1-x)=0).zy=t(1-x)]' (or '-(y(1-x)=0)')
and this does not convert to 'vx=v(1-y)'.  So however 'brilliant'
Peirce's lecture was, he had misinterpreted Boole at this point.
--
Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, M207 School of Humanities
University of Western Australia
35 Stirling Highway
Crawley WA 6009, Australia
Ph: (08) 6488 1246 (W), 9386 4812 (H)
Fax: (08) 6488 1057
Url: http://www.philosophy.uwa.edu.au/staff/slater

```