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

```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.
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```
On your P.S., I don't know whether you're making a distinction between propositions and sentences.
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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?
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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
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Date: Fri, 11 May 2012 16:41:32 -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>

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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