Ben, I suppose you could take the judgment as everything which implies it. (or
is implied by it) In this way, you could play around with the "judgment stroke"
and treat meaning as inferential. But, using a rule of substitution and
instantiation, I could show the content of the following judgment without any
logical constants /- ExFxFa x=aExFx But if I say vx, is v "a" or is it another
class "G?" Further, "vx" is a logical product. The above analysis has no
logical constants. I guess the point is that once you segment Fx and then talk
of two interpretations; boolean classes or propositions, you create some
confusion which Frege (according to Sluga) traces back to favoring concepts
over judgments with resulting totalities such as m+n+o+p that are not rich
enough, lacking in meaning and content. But this is in 1882. Jim WDate: Fri, 11
May 2012 16:41:32 -0400
From: [email protected]
Subject: Re: [peirce-l] Frege against the Booleans
To: [email protected]
Hi, Jim
Thanks, but I'm afraid that a lot of this is over my head.
Boolean quantifier 'v' ? Is that basically the backward E? A
'unity' class? Is that a class with just one element? Well, be
that as it may, since I'm floundering here, still I take it that
Frege did not view a judgment as basically fragment of an
inference, while Peirce viewed judgments as parts of inferences;
he didn't think that there was judgment except by inference (no
'intuition' devoid of determination by inference).
Best, Ben
On 5/11/2012 3:08 PM, Jim Willgoose wrote:
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:
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