[FOM] Mill on Aristotle and Euclid

Robert Black Mongre at gmx.de
Sat Mar 27 03:58:09 EST 2004

It's a bit later than MIll  and I don't have it with me to check the 
details, but you'll find versions of euclidean proofs in syllogisms 
in Ueberweg's 'System der Logik und Geschichte der Logischen Lehren 
'of 1857. The technique used to create the illusion of having done 
this is basically one which was once explained to me by a Dominican 
friar who used to conduct performances of medieval disputationes. In 
his words: 'You can get anything into Barbara'.


>Subject: Mill on Aristotle and Euclid
>FORMALIZING EUCLID'S DEDUCTIONS: The whole of Euclid, for example, might
>be thrown without difficulty into a series of syllogisms, regular in
>mood and figure. MILL 1843:I,191
>Q1. Who commented on this absurdity? De Morgan? Boole? Hamilton? Frege?
>Q2. Who took the brilliant J.S. Mill up on this? Who tried to do it? If
>your standards were low enough, you could develop the illusion of
>Q3. Where did Mill get this? He could not have been the first person to
>clearly understand the ultimate goal of Aristotle's syllogistic and
>misunderstand how far Aristotle was from reaching it?
>Q4. Which contemporary historians have quoted this? Where have you seen
>it before? Q5. Did Mill conceive of this on the basis of reading
>Aristotle? Or did Mill get the idea from one of his predecessors, e.g.
>Descartes, or one of the Port Royalists? Q6. Who realized the absurdity
>of Mill's claim, but instead of simply ridiculing Mill, went on to
>propose that logic be improved and strengthened to the point where it is
>capable of "reproducing" all geometric demonstrations?
>John Corcoran
>University of Buffalo
>Buffalo, NY  14260-4150
>FOM mailing list
>FOM at cs.nyu.edu

PS I'm sending this from my gmx address because I'm currently in 
Berlin, but you can reply to my usual <Robert.Black at nottingham.ac.uk>

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