# Re: [peirce-l] Frege against the Booleans

```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: bud...@nyc.rr.com
Subject: Re: [peirce-l] Frege against the Booleans
To: PEIRCE-L@LISTSERV.IUPUI.EDU```
```

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

Subject: Re: [peirce-l] Frege against the Booleans

To: 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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