FOM: Dawson on Aristotle
Fred Johnson
johnsonf at lamar.ColoState.EDU
Fri Jan 23 12:43:50 EST 1998
No doubt Dawson's *Logical Dilemmas* deserves the praise it
has been given, but there are problems. Unfortunately, his
sketch of Aristotelian logic perpetuates the common myth
that Aristotle's thoughts about logic were very primitive.
Evidence that Dawson has not read the *Prior Analytics* comes
from his claim (p. 38) that Aristotle recognized fourteen
patterns of valid deductions. For Darapti, which is not one
of the fourteen, Aristotle gives a valid ecthetic deduction
that uses principles that are now commonly named UI and EG.
The reader of *PrAn* will recognize that for Aristotle there
are *infinitely many* valid deductions.
Dawson's claims about the lack of relevance of Aristotle's work
to "the mathemical logic of today" are irritating. After all,
Aristotle was clear about the distinction between syntax and
semantics. He separated deducibility (proof theory) from
entailment (model theory) and had his eye on soundness and
completeness results.
Aristotle uses second-order logic in his discussion of
circular reasoning. He embeds the fragmentary system
Dawson alludes to in a developed system of modal logic that
distinguishes two notions of possibility such that one is
not reducible to the other. (According to one notion, that
it is possible that all A are B implies that it is possible
that no A are B.)
There is no question that modern-day relevance logicians
have made good use of Aristotle's principles.
Fred Johnson
More information about the FOM
mailing list