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

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