Thanks Ben. I heartily concur on dropping the thread. There is little
indication that anyone is interested in the specific H. Sluga paper or the
priority principle as put forth in that paper. Jim W
Date: Fri, 11 May 2012 22:42:12 -0400
From: [email protected]
Subject: Re: [peirce-l] Frege against the Booleans
To: [email protected]
Jim,
Sorry, I'm just getting more confused. I've actually seen "a",
"b", etc. called "constants" as opposed to "variables" such as
"x", "y", etc. Constant individuals and variable individuals, so
to speak, anyway in keeping with the way the words "constant" and
"variable" seem to be used in opposition to each other in math.
But if that's not canonical, then it's not canonical. Also, I
thought "F" was a predicate term, a "dummy letter", and at any
rate a "(unknown or veiled) constant" as I would have called it up
till a few minutes ago. I thought "~" was a functor that makes a
new predicate "~F" out of the predicate "F". If "~" and the other
functors are logical constants, then isn't the predication
relationship between "F" and "x" in "Fx" also a logical constant,
though it has no separate symbol? Really, I think the case is
hopeless. I need to read a book on the subject.
I don't see why conceptual analysis would start with the third
trichotomy of signs (rheme, dicisign, argument) and move to the
first trichotomy of signs (qualisign, sinsign, legisign). Maybe
you mean that conceptual analysis would start with Third in the
trichotomy of rheme, dicisign, argument and move to that
trichotomy's First. I.e. move from argument back to rheme. But I
don't see why the conceptual-analysis approach would prefer that
direction.
On your P.S., I don't know whether you're making a distinction
between propositions and sentences.
Thanks but this all seems hopeless! Let's drop this sub-thread
for at least 24 hours.
Best, Ben
On 5/11/2012 10:06 PM, Jim Willgoose wrote:
Ben,
I made it too complicated. Sorry. It didn't help that "/-" was
brought into the discussion. You had the basic idea earlier
with dicent and rheme. Fx and Fa have to be kept together.
So, the interpretant side of the semiotic relation has priority.
Conceptual analysis would move from the "third trichotomy" back
to the first. Synthesis would move from the first to the
third. If this is close, the priority principle would place
emphasis on the whole representation. (By the way, "F" is a
function and "a" is an individual, ~+--> are the logical
constants.)
Jim W
PS If words have meaning only in sentences (context principle),
does this mean that term, class, and propositional logics are
meaningless?
Date: Fri, 11 May 2012 20:30:53 -0400
From: [email protected]
Subject: Re: [peirce-l] Frege against the Booleans
To: [email protected]
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: [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:
---------------------------------------------------------------------------------
You are receiving this message because you are subscribed to the PEIRCE-L
listserv. To remove yourself from this list, send a message to
[email protected] with the line "SIGNOFF PEIRCE-L" in the body of the
message. To post a message to the list, send it to [email protected]
---------------------------------------------------------------------------------
You are receiving this message because you are subscribed to the PEIRCE-L
listserv. To remove yourself from this list, send a message to
[email protected] with the line "SIGNOFF PEIRCE-L" in the body of the
message. To post a message to the list, send it to [email protected]
