Hi, Jim,
Sorry, I'm not following you here. "F" and "a" look like logical
constants in the analysis. I don't know how you're using "v", and so
on. I don't know why there's a question raised about taking the
judgment as everything that implies it, or as everything that it
implies. Beyond those things, maybe you're suggesting, that Frege didn't
take judgments as mere fragments of inferences, because he wasn't aware
of some confusion that would be clarified by taking judgments as mere
fragments of inferences? But I'm afraid we're just going to have to
admit that I'm in over my head.
Best, Ben
On 5/11/2012 7:36 PM, Jim Willgoose wrote:
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
/- ExFx
Fa x=a
ExFx
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 W
------------------------------------------------------------------------
Date: Fri, 11 May 2012 16:41:32 -0400
From: bud...@nyc.rr.com
Subject: Re: [peirce-l] Frege against the Booleans
To: PEIRCE-L@LISTSERV.IUPUI.EDU
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: bud...@nyc.rr.com <mailto:bud...@nyc.rr.com>
Subject: Re: [peirce-l] Frege against the Booleans
To: PEIRCE-L@LISTSERV.IUPUI.EDU <mailto:PEIRCE-L@LISTSERV.IUPUI.EDU>
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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