Re: [peirce-l] Frege against the Booleans
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
Re: [peirce-l] Frege against the Booleans
Re: Jim Willgoose At: http://thread.gmane.org/gmane.science.philosophy.peirce/8141 JA = Jon Awbrey JW = Jim Willgoose JA: Just to be sure we start out with the same thing in mind, are you talking about the notion of judgment that was represented by the judgment stroke in Frege's “Begriffsschrift” and that supposedly got turned into the turnstile symbol ( ⊦ ) or “assertion symbol” in later systems of notation? JW: Sluga ties the priority of judgement in Frege to Kant's favoring judgements over concepts in the Critique of Pure Reason. The article is open source. I can see a connection with the judgement stroke /- since one asserts the truth; a trick that is hard to do with only concepts or objects. Sluga includes a quote from Frege where he says something to the effect that he (Frege) never segments the signs of even an incomplete expression in any of his work. (ie. x is never separated from F as in Fx.) Jim, With this token and this turnstile then we enter on a recurring issue, revolving on the role of assertion, evaluation, or judgment of truth, in contradistinction to “mere contemplation”, as some of my teachers taught me to bracket it, of a “proposition”, whatever that might be. If I have not made it clear before, this is one of the points where I see the so-called “Fregean Revolution”, more French than American, if you catch my drift, begin to take a downward turn. But I cannot decide yet whether to assign that to Frege's account, taken in full view of his work as a whole, or whether it is due to the particular shards that his self-styled disciples tore off and took to extremes. Regards, Jon -- academia: http://independent.academia.edu/JonAwbrey my word press blog: http://inquiryintoinquiry.com/ inquiry list: http://stderr.org/pipermail/inquiry/ mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey facebook page: https://www.facebook.com/JonnyCache - 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
Re: [peirce-l] Frege against the Booleans
John, I followed up on two paper suggestions by Irving (Sluga and Van Heijenoort) in the context of the languge or calculus topic. With Sluga, I detect the idea that the Begriffsshrift is a universal language because it is meaningful in a way that the Boolean logic is not. Sluga sees his paper as an extension and adjustment of Van Heijenoort's paper on logic as language or calculus. He places great emphasis on the priority principle. He quotes from Frege, I begin with judgments and their contents and not with concepts...The formation of concepts I let proceed from judgments. (Posthumous writings) Sluga says, This principle of priority, in fact, constitutes the true center of his critique of Boolean logic. That logic is a mere calculus for him because of its inattention to that principle, while his own logic approximates a characteristic language because of its reliance on it.(Sluga, Frege against the Booleans) The Frege quote above is from around 1879 and the material focus is on 1884 or earlier; especially Boole's calculating logic and the Begriffsshrift. ( a response to Schroder's criticism) There is a lot more to this article, including linking the priority principle to the better known context principle. (words have meaning only in sentences) What I am doing is reading these two papers concurrently with Mitchell and Ladd-Franklin from Studies in Logic. (1883) Jim W.ps I like the way you diagram a thread on your site. Date: Fri, 11 May 2012 08:16:14 -0400 From: jawb...@att.net Subject: Re: [peirce-l] Frege against the Booleans To: PEIRCE-L@LISTSERV.IUPUI.EDU Re: Jim Willgoose At: http://thread.gmane.org/gmane.science.philosophy.peirce/8141 JA = Jon Awbrey JW = Jim Willgoose JA: Just to be sure we start out with the same thing in mind, are you talking about the notion of judgment that was represented by the judgment stroke in Frege's “Begriffsschrift” and that supposedly got turned into the turnstile symbol ( ⊦ ) or “assertion symbol” in later systems of notation? JW: Sluga ties the priority of judgement in Frege to Kant's favoring judgements over concepts in the Critique of Pure Reason. The article is open source. I can see a connection with the judgement stroke /- since one asserts the truth; a trick that is hard to do with only concepts or objects. Sluga includes a quote from Frege where he says something to the effect that he (Frege) never segments the signs of even an incomplete expression in any of his work. (ie. x is never separated from F as in Fx.) Jim, With this token and this turnstile then we enter on a recurring issue, revolving on the role of assertion, evaluation, or judgment of truth, in contradistinction to “mere contemplation”, as some of my teachers taught me to bracket it, of a “proposition”, whatever that might be. If I have not made it clear before, this is one of the points where I see the so-called “Fregean Revolution”, more French than American, if you catch my drift, begin to take a downward turn. But I cannot decide yet whether to assign that to Frege's account, taken in full view of his work as a whole, or whether it is due to the particular shards that his self-styled disciples tore off and took to extremes. Regards, Jon -- academia: http://independent.academia.edu/JonAwbrey my word press blog: http://inquiryintoinquiry.com/ inquiry list: http://stderr.org/pipermail/inquiry/ mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey facebook page: https://www.facebook.com/JonnyCache - 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
Re: [peirce-l] Frege against the Booleans
JW = Jim Willgoose JW: I followed up on two paper suggestions by Irving (Sluga and Van Heijenoort) in the context of the language or calculus topic. With Sluga, I detect the idea that the Begriffsshrift is a universal language because it is meaningful in a way that the Boolean logic is not. Sluga sees his paper as an extension and adjustment of Van Heijenoort's paper on logic as language or calculus. He places great emphasis on the priority principle. He quotes from Frege, I begin with judgments and their contents and not with concepts ... The formation of concepts I let proceed from judgments. (Posthumous writings) Sluga says, This principle of priority, in fact, constitutes the true center of his critique of Boolean logic. That logic is a mere calculus for him because of its inattention to that principle, while his own logic approximates a characteristic language because of its reliance on it. (Sluga, Frege against the Booleans) The Frege quote above is from around 1879 and the material focus is on 1884 or earlier; especially Boole's calculating logic and the Begriffsshrift. (a response to Schroder's criticism). There is a lot more to this article, including linking the priority principle to the better known context principle. (words have meaning only in sentences) What I am doing is reading these two papers concurrently with Mitchell and Ladd-Franklin from Studies in Logic. (1883) JW: ps. I like the way you diagram a thread on your site. Jim, Sorry, I was away on several excursions and missed that part of the context. My main concern, here and elsewhere, resides with the potential contribution of Peirce to our understanding of inquiry. If I were starting a new project today, instead of trying to dig my way out of unfinished business, it would get a title like The Unrealized Potential of Peirce's Thought or maybe The Unmet Challenge of Peirce's Work. My feeling is that only a small fraction of Peirce's potential contribution to our understanding has yet been realized and that something critical has been lost in the years between Peirce and Russell. Consequently, my concern is less with Boole and Frege than with the clues their work provides to what was found and what was lost. It has long been my experience that we cannot grasp the full import of Peirce's work from the shadows that are cast on the analytic, atomistic, logistic, reductive plain. I prefer looking at the work of what came after from Peirce's conceptual perspective, instead of the other way around. I think that affords a much clearer view of things. Regards, Jon -- academia: http://independent.academia.edu/JonAwbrey my word press blog: http://inquiryintoinquiry.com/ inquiry list: http://stderr.org/pipermail/inquiry/ mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey facebook page: https://www.facebook.com/JonnyCache - 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
Re: [peirce-l] Frege against the Booleans
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:
John,
I followed up on two paper suggestions by Irving (Sluga and Van
Heijenoort) in the context of the languge or calculus topic.
With Sluga, I detect the idea that the Begriffsshrift is a
universal language because it is meaningful in a way
that the Boolean logic is not.
Sluga sees his paper as an extension and adjustment of Van
Heijenoort's paper on logic as language or calculus. He
places great emphasis on the priority principle. He quotes
from Frege, I begin with judgments and their contents and not
with concepts...The formation of concepts I let proceed from
judgments. (Posthumous writings) Sluga says, This principle of
priority, in fact, constitutes the true center of his critique
of Boolean logic. That logic is a mere calculus for him because
of its inattention to that principle, while his own
logic approximates a characteristic language because of its
reliance on it.
(Sluga, Frege against the Booleans)
The Frege quote above is from around 1879 and the material focus
is on 1884 or earlier; especially Boole's calculating logic and
the Begriffsshrift. ( a response to Schroder's criticism) There
is a lot more to this article, including linking the priority
principle to the better known context principle. (words have
Re: [peirce-l] Frege against the Booleans
Jon, The way I learned it, (formal) implication is not the /assertion/ but the /validity/ of the (material) conditional, so it's a difference between 1st-order and 2nd-order logic, a difference that Peirce recognized in some form. If the schemata involving p and q are considered to expose all relevant logical structure (as usually in propositional logic), then a claim like p formally implies q is false. On the other hand, a proposition /à la/ if p then q (or p materially implies q) is contingent, neither automatically true nor automatically false. I agree that you can see it as the same relationship on two different levels. That seems the natural way to look at it. Another kind of implication is expressed by rewriting a proposition like Ax(Gx--Hx) as G=H. In other words All G is H gets expressed G implies H. In first-order logic, at least, it actually comes down to a material conditional compound of two terms in a universal proposition. If in addition to logical rules one has postulated or generally granted other rules, say scientific or mathematical rules, then these lead to scientific or mathematical implications, the associated conditionals being true by the scientific or mathematical rules, not just contingently on a case-by-case basis. Anyway, all these kinds of implication do seem like the same thing in various forms. It's not clear to me how any of this figures into the concept-vs.-judgment question. The only connection that I've been able to make out in my haze is that when we say something like p formally implies p, we're thinking of the proposition p as if it were a concept rather than a judgment; our concern is limited to validity. If we say 'p, ergo p' or, in a kindred sense, p proves p, we're thinking of p as a judgment, and our concern includes soundness as well as validity. Best, Ben On 5/11/2012 2:25 PM, Jon Awbrey wrote: Ben, Just to give a prototypical example, one of the ways that the distinction between concepts and judgments worked its way through analytic philosophy and into the logic textbooks that I knew in the 60s was in the distinction between a conditional ( → or - ) and an implication ( ⇒ or = ). The first was conceived as a function (from a pair of truth values to a single truth value) and the second was conceived as a relation (between two truth values). The relationship between them was Just So Storied by saying that asserting the conditional or judging it to be true gave you the implication. I think it took me a decade or more to clear my head of the dogmatic slumbers that this sort of doctrine laid on my mind, mostly because the investiture of two distinct symbols for what is really one and the same notion viewed in two different ways so obscured the natural unity of the function and the relation. Cf. http://mywikibiz.com/Logical_implication Regards, Jon - 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
Re: [peirce-l] Frege against the Booleans
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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list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Frege against the Booleans
Sorry, corrections in bold: Jon, The way I learned it, (formal) implication is not the /assertion/ but the /validity/ of the (material) conditional, so it's a difference between 1st-order and 2nd-order logic, a difference that Peirce recognized in some form. If the schemata involving p and q are considered to expose all relevant logical structure (as usually in propositional logic), then a claim like p formally implies q is false. On the other hand, a proposition /à la/ if p then q (or p materially implies q) is contingent, neither automatically true nor automatically false. I agree that you can see it as the same relationship on two different levels. That seems the natural way to look at it. Another kind of implication is expressed by rewriting a proposition like Ax(Gx--Hx) as G=H. In other words All G is H gets expressed G implies H. In first-order logic, at least, it actually comes down to a material conditional compound of two terms in a universal proposition. If in addition to logical rules one has postulated or generally granted other rules, say scientific or mathematical rules, then these lead to scientific or mathematical implications, the associated conditionals being true by the scientific or mathematical rules, not just contingently on a case-by-case basis. Anyway, all these kinds of implication do seem like the same thing in various forms. It's not clear to me how any of this figures into the concept-vs.-judgment question. The only connection that I've been able to make out in my haze is that when we say something like p formally implies p, we're thinking of the proposition p as if it were a concept rather than a judgment; our concern is limited to validity *as of an argument* p ergo p. If we *_/say/_* 'p, ergo p' or, in a kindred sense, p proves p, we're thinking of p as a judgment, and our concern includes the soundness as well as validity *of the argument p ergo p*. Best, Ben On 5/11/2012 2:25 PM, Jon Awbrey wrote: Ben, Just to give a prototypical example, one of the ways that the distinction between concepts and judgments worked its way through analytic philosophy and into the logic textbooks that I knew in the 60s was in the distinction between a conditional ( → or - ) and an implication ( ⇒ or = ). The first was conceived as a function (from a pair of truth values to a single truth value) and the second was conceived as a relation (between two truth values). The relationship between them was Just So Storied by saying that asserting the conditional or judging it to be true gave you the implication. I think it took me a decade or more to clear my head of the dogmatic slumbers that this sort of doctrine laid on my mind, mostly because the investiture of two distinct symbols for what is really one and the same notion viewed in two different ways so obscured the natural unity of the function and the relation. Cf. http://mywikibiz.com/Logical_implication Regards, Jon - 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
Re: [peirce-l] Frege against the Booleans
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 /- ExFxFa x=aExFx 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 WDate: 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
Re: [peirce-l] Frege against the Booleans
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
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. 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 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
Re: [peirce-l] Frege against the Booleans
JW = Jim Willgoose JW: List, Irving, John et. al., Sluga (Frege against the Booleans; Notre Dame Journal of Formal logic 1987)) places great emphasis upon the priority principle in Frege, which stresses that the judgement is epistemically, ontologically, and methodologically primary. He tries to show that Frege thought that Schroder's view exhibited a bias towards the methodological primacy of concepts by drawing on Schroder's Introductory parts of the Algebra of Logic. I think the central claim of the Sluga paper is that this supposed bias of the Booleans towards abstraction and the treatment of concepts as extensions of classes leads to a confusion over the relation between abstract or pure logic and predicate logic. How this is, is not always easy to see, but the segmenting of the judgement relation does seem to lead to a problem in seeing the abstract logic as a special case of predicate logic. How serious any of this is I don't know. For instance, Mitchell took issue with a Mr. Peirce for speaking of a universe of relation instead of a universe of class terms. (Studies in Logic; Johns Hopkins 1883). Maybe Peirce was vaguely aware of something which the products of analysis would end up obscuring. Jim, Just to be sure we start out with the same thing in mind, are you talking about the notion of judgment that was represented by the judgment stroke in Frege's “Begriffsschrift” and that supposedly got turned into the turnstile symbol ( ⊦ ) or “assertion symbol” in later systems of notation? Jon -- academia: http://independent.academia.edu/JonAwbrey my word press blog: http://inquiryintoinquiry.com/ inquiry list: http://stderr.org/pipermail/inquiry/ mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey facebook page: https://www.facebook.com/JonnyCache - 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
Re: [peirce-l] Frege against the Booleans
John, Sluga ties the priority of judgement in Frege to Kant's favoring judgements over concepts in the Critique of Pure Reason. The article is open source. I can see a connection with the judgement stroke /- since one asserts the truth; a trick that is hard to do with only concepts or objects. Sluga includes a quote from Frege where he says something to the effect that he (Frege) never segments the signs of even an incomplete expression in any of his work. (ie. x is never separated from F as in Fx.) Date: Thu, 10 May 2012 23:50:09 -0400 From: jawb...@att.net Subject: Re: [peirce-l] Frege against the Booleans To: PEIRCE-L@LISTSERV.IUPUI.EDU JW = Jim Willgoose JW: List, Irving, John et. al., Sluga (Frege against the Booleans; Notre Dame Journal of Formal logic 1987)) places great emphasis upon the priority principle in Frege, which stresses that the judgement is epistemically, ontologically, and methodologically primary. He tries to show that Frege thought that Schroder's view exhibited a bias towards the methodological primacy of concepts by drawing on Schroder's Introductory parts of the Algebra of Logic. I think the central claim of the Sluga paper is that this supposed bias of the Booleans towards abstraction and the treatment of concepts as extensions of classes leads to a confusion over the relation between abstract or pure logic and predicate logic. How this is, is not always easy to see, but the segmenting of the judgement relation does seem to lead to a problem in seeing the abstract logic as a special case of predicate logic. How serious any of this is I don't know. For instance, Mitchell took issue with a Mr. Peirce for speaking of a universe of relation instead of a universe of class terms. (Studies in Logic; Johns Hopkins 1883). Maybe Peirce was vaguely aware of something which the products of analysis would end up obscuring. Jim, Just to be sure we start out with the same thing in mind, are you talking about the notion of judgment that was represented by the judgment stroke in Frege's “Begriffsschrift” and that supposedly got turned into the turnstile symbol ( ⊦ ) or “assertion symbol” in later systems of notation? Jon -- academia: http://independent.academia.edu/JonAwbrey my word press blog: http://inquiryintoinquiry.com/ inquiry list: http://stderr.org/pipermail/inquiry/ mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey facebook page: https://www.facebook.com/JonnyCache - 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
