Hi Ben; My interest was historical (and philosophical) in the sense of what did
they say about the developing work of symbolic logic in their time. The period
is roughly 1879-1884. The anchor was two references by Irving (the historian of
logic) to Van Heijenhoort and Sluga as worthy start points. But the issue of
simply language/calculus(?) need not be the end. This is not a Frege or Logic
forum per se, but I wanted to keep the thread alive and focused on symbolic
logic because I get curious how the (darn) textbook came about periodically.
The "priority principle," as extracted by Sluga, with Frege following Kant,
takes the judgment as ontologically, epistemologically, and methodologically
primary. Concepts are not. I will suppose, for now, that the content of a
judgment is obscured in a couple of ways. First, if you treat the concept as
the extension of classes, and then treat the class as a unity class or use the
Boolean quantifier "v" for a part of a class, you end up with an abstract logic
that shows only the logical relations of the propositional fragment.
(especially if the extensions of classes are truth values) Frege might say that
this obscures the content of the judgment. Thus, I would say that the
propositional fragment is not primary at all for Frege, and is just a special
case. You are on to something with the rheme and dicisign. But in 1879, the
systems of symbolic logic did not appreciate the propositional function, the
unrestricted nature of the quantifier, and the confusion that results from a
lack of analysis of a judgment and the poverty of symbolism for expressing the
results of the analysis. Jim W Date: Fri, 11 May 2012 12:24:33 -0400
From: [email protected]
Subject: Re: [peirce-l] Frege against the Booleans
To: [email protected]
Jim, Jon, list,
I'm following this with some interest but I know little of Frege
or the history of logic. Peirce readers should note that this
question of priority regarding concept vs. judgment is, in
Peirce's terms, also a question regarding rheme vs. dicisign and,
more generally, First vs. Second (in the rheme-dicisign-argument
trichotomy).
Is the standard placement of propositional logic as prior to term
logic, predicate calculus, etc., an example of the Fregean
prioritization?
Why didn't Frege regard a judgment as a 'mere' segment of an
inference and thus put inference as prior to judgment?
I suppose that one could restate an inference such as 'p ergo q'
as a judgment 'p proves q' such that the word 'proves' is
stipulated to connote soundness (hence 'falsehood proves
falsehood' would be false), thus rephrasing the inference as a
judgment; then one could claim that judgment is prior to
inference, by having phrased inference as a particular kind of
judgment. Some how I don't picture Frege going to that sort of
trouble.
Anyway it would be at the cost of not expressing, but leaving as
implicit (i.e., use but don't mention), the movement of the
reasoner from premiss to conclusion, which cost is actually
accepted when calculations are expressed as equalities ("3+5 = 8")
rather than as some sort of term inference ('3+5, ergo
equivalently, 8').
If either of you can clarify these issues, please do.
Best, Ben
On 5/11/2012 11:41 AM, Jim Willgoose wrote:
John,
I followed up on two paper suggestions by Irving (Sluga and Van
Heijenoort) in the context of the languge or calculus topic.
With Sluga, I detect the idea that the Begriffsshrift is a
universal language because it is meaningful in a way
that the Boolean logic is not.
Sluga sees his paper as an "extension and adjustment" of Van
Heijenoort's paper on logic as language or calculus. He
places great emphasis on the "priority principle." He quotes
from Frege, "I begin with judgments and their contents and not
with concepts...The formation of concepts I let proceed from
judgments. (Posthumous writings) Sluga says, "This principle of
priority, in fact, constitutes the true center of his critique
of Boolean logic. That logic is a mere calculus for him because
of its inattention to that principle, while his own
logic approximates a characteristic language because of its
reliance on it."
(Sluga, Frege against the Booleans)
The Frege quote above is from around 1879 and the material focus
is on 1884 or earlier; especially "Boole's calculating logic and
the Begriffsshrift." ( a response to Schroder's criticism) There
is a lot more to this article, including linking the priority
principle to the better known "context principle." (words have
meaning only in sentences)
What I am doing is reading these two papers concurrently with
Mitchell and Ladd-Franklin from Studies in Logic. (1883)
Jim W.
ps I like the way you diagram a thread on your site.
> Date: Fri, 11 May 2012 08:16:14 -0400
> From: [email protected]
> Subject: Re: [peirce-l] Frege against the Booleans
> To: [email protected]
>
> Re: Jim Willgoose
> At: http://thread.gmane.org/gmane.science.philosophy.peirce/8141
>
> JA = Jon Awbrey
> JW = Jim Willgoose
>
> JA: Just to be sure we start out with the same thing in
mind, are you talking about
> the notion of judgment that was represented by the
"judgment stroke" in Frege's
> “Begriffsschrift” and that supposedly got turned into the
turnstile symbol ( ⊦ )
> or “assertion symbol” in later systems of notation?
>
> JW: Sluga ties the priority of judgement in Frege to
Kant's favoring judgements
> over concepts in the Critique of Pure Reason. The article
is open source.
> I can see a connection with the judgement stroke /- since
one asserts the
> truth; a trick that is hard to do with only concepts or
objects. Sluga
> includes a quote from Frege where he says something to
the effect that
> he (Frege) never "segments the signs" of even an
incomplete expression
> in any of his work. (ie. "x" is never separated from "F"
as in Fx.)
>
> Jim,
>
> With this token and this turnstile then we enter on a
recurring issue,
> revolving on the role of assertion, evaluation, or
judgment of truth,
> in contradistinction to “mere contemplation”, as some of
my teachers
> taught me to bracket it, of a “proposition”, whatever
that might be.
>
> If I have not made it clear before, this is one of the
points where
> I see the so-called “Fregean Revolution”, more French
than American,
> if you catch my drift, begin to take a downward turn. But
I cannot
> decide yet whether to assign that to Frege's account,
taken in full
> view of his work as a whole, or whether it is due to the
particular
> shards that his self-styled disciples tore off and took
to extremes.
>
> Regards,
>
> Jon
>
> --
>
> academia: http://independent.academia.edu/JonAwbrey
> my word press blog: http://inquiryintoinquiry.com/
> inquiry list: http://stderr.org/pipermail/inquiry/
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>
>
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