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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