[FOM] Book on the history of logic

Sara L. Uckelman S.L.Uckelman at uva.nl
Wed Mar 2 10:40:10 EST 2011

Sam Sanders wrote:
>> A good compliment to Kneale and Kneale (which despite its extremely
>> narrow view of what counts as "logic" is still an invaluable resource)
> Can someone explain to me why Kneale & Kneale's account of logic is 
> "extremely narrow"?
> If their account is indeed of such nature, what else should have been included?

Since I was the one who called Kneale & Kneale's view of logic narrow,
it's incumbent upon me to defend this view; my apologies for taking so
long in doing so.

The clearest statement about the scope of 'logic' in Kneale & Kneale's
view actually comes very nearly at the end of the book:

   When the word 'logic' has no agreed definition, the question whether
   the theory of sets or any other branch of _a priori_ knowledge
   should be accounted part of logic is one that can be settled only by
   linguistic legislation.  But such legislation may be well- or ill-
   advised.  For it is desirable that any new rules we adopt deliberately
   for old words should depart little, if at all, from previously
   established customs, and that the distinctions on which they depend
   should be distinctions important to the organization of knowledge.
   Thus, if we think that the logic of tradition has been concerned
   primarily with principles of inference valid for all possible subject-
   matters, we must reject as unprofitable an extension of usage which
   allows such phrases as 'the logic of "God"'.  And if we think that the
   theory of sets is closely connected with some topics of traditional
   logic but are nevertheless puzzled by the devices needed to free it
   from paradox, we must consider carefully the structure of the science
   of logic as it is presented by those who wish to make it include the
   theory of sets...[Logic] is best defined as the pure theory of
   involution, that is to say, the theory of the general form of
   principles of involution without regard to the special natures of the
   propositions contained in the classes between which the relation
   holds [Development of Logic, pp. 741-742]

They further argue on p 742 that even the concept of 'identity' should
not be included in what is properly called logic.

By rejecting such things as 'the logic of "God"', the Kneales dispense
with much of the developments in logic in the medieval period (both in
the West and in the Arabic tradition).  One of the most illustrious
logicians of the 11th century, St. Anselm of Canterbury, is only
mentioned in passing, and only in reference to the so-called ontological
argument.  Of the four primary innovations of medieval logic
(supposition theory, analyses of sophismata and insolubilia, the
development of various types of obligationes, and the theory of
consequentiae), the first three merit only a page or two a piece.

I discuss the Kneales' narrow view of logic, and the consequences it,
and similar views, have on the study of logic in the medieval period
from the modern perspective, in the first chapter of my dissertation --

Best wishes,

Dr. Sara L. Uckelman
Institute for Logic, Language, & Computation
Universiteit van Amsterdam

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