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: bud...@nyc.rr.com Subject: Re: [peirce-l] Frege against the Booleans To: PEIRCE-L@LISTSERV.IUPUI.EDU
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: 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: --------------------------------------------------------------------------------- You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU --------------------------------------------------------------------------------- You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU