[FOM] Re: Foundations and Frege

William Ewald wewald at law.upenn.edu
Wed Oct 15 16:46:31 EDT 2003

Dear Bill,

Many thanks for your email, and also for the other FOM comments.  Let me 
briefly try to clarify a few points.

[1]  My own starting point is a pair of claims (to be found in many 
philosophers).  The first is the claim that the boundary-line separating 
modern from pre-modern logic is to be identified with the line 
separating propositional logic from first-order quantification theory; 
the second, that Frege created the apparatus of modern quantification 
theory *ex nihilo.*  In fact, several logicians (at a minimum, Peirce 
and Peano, and possibly a couple of others) independently introduced 
quantifiers at about the same time.  This should cast doubt upon the *ex 
nihilo* claim; but that’s a relative triviality.  More importantly it 
raises the question: Why did these various discoveries occur at this 
time (and not, say, in the time of Aristotle)?  Once one starts to 
address that question in earnest, one must begin to wonder about the 
first claim; and it seems to me that the current understanding of the 
importance of the quantifiers is quite different from the understanding 
that prevailed *circa* 1900. So that leaves us with a second important 
question: When, precisely, did logicians begin to write the history of 
the subject in the now-standard way, and why?

[2]  The issues of intellectual history here are quite delicate.  One 
must distinguish, for various values of X and Y, between:
(1)  What Logician X discovered;
(2)  What Logician X thought he discovered;
(3)  What Logician X thought was an important discovery;
(4)  What Logician X published;
(5)  What Logician Y knew (or could have known) about the work of 
Logician X;
(6)  What Logician Y thought Logician X discovered; and,
(7)  What we now standardly think of the work of Logicians X and Y.  And 
one has to take these various questions in proper chronological 
sequence: what Russell thought of Frege in 1898 is quite different from 
what he thought of him in 1903, for instance.

[3]  I agree with the helpful points made by Alasdair Urquhart and 
Michael Kremer, which persuasively refute things that they seem to 
suspect me to have said.  I haven’t seen the Whitehead manuscripts, and 
am grateful to learn about them; but the dates are critical.  Already in 
1898 Whitehead had referred in print to the papers of Peirce and his 
students on quantification; and already in early 1901 (at the latest) 
Russell had shown him Peano’s notation for the existential quantifier.

[4]  Of course Frege influenced modern logic, and of course he had a 
“pretty good insight” into modern logic.  But the point is to be precise 
about what those insights and influences in fact were.  Many modern *ex 
nihilo* accounts ascribe to Frege a near miraculous understanding of the 
entire modern apparatus of first-order quantification theory.  But when 
those standard accounts fail to observe e.g. that Peirce, too, 
introduced quantifiers (and gave them their name), then perhaps a 
careful examination of (1)-(6) is in order.  The story appears to me to 
be quite complex, and untidy, and at many points frustratingly unclear; 
it also does not lend itself to a quick summary.

[5]  I now find myself saddled with an inordinately long manuscript, 
with a lot of loose ends.  I am in the process of trimming and 
tightening, but hope to have the thing finished by the end of the 
semester.  Perhaps it would be best to wait until that job is finished, 
and then to send you a draft (and also to anybody else who is interested).

Best wishes,


William Tait wrote:

> I did not note that Charles Stewart's message (10/14/03, 9:19 AM) was to FOM as well as to me and sent a reply only to him. Here it is:
> Thank you. I heard a talk by Bill Ewald on this topic some years ago and wish dearly that he would publish some version of it. The view (Dummett's) of Frege's creation of logic ex nihilo never seemed very plausible; but it would be nice to have a detailed investigation.
>>1. Frege was the first of several independent discoverers of the quantifiers; the
>> discovery of quantification was in many respects waiting to happen.
> Aside from Pierce,who else did he mention? I remember a student here years ago, Geraldine Brady, who raise some question about Pierce's independence from Frege.
>> 4. Frege's technical work in fact had close to no impact, both Peano and Pierce were
>> far more influential.
> Was Peano's use of quantifiers independent of Frege? I had thought not (but don't really know).I believe that Hilbert referred to Frege for the ground-work in codifying logic(?)
>> 5. The crucial importance of the quantifier was not commented upon until far later,
>> by Quine.
> I would like to see the argument for this, to me, outrageous claim.
> Bill Tait

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