Edwina,
Thank you for your continued patience and admonitions. I take it that if I can convince you, I can convince others. So, you say that I *ought not* to state the following frame because it’s wrong: *“If p then q. = “But if A were true, C would be a matter of course”* * p. = “The surprising fact C is observed”* * Ergo, q. = “Hence there is reason to suspect that A is true”* *The difference I see here is that p = A in the first line but p = C in line 2.* Reminder of modus ponens: *If p then q. p, ergo q.* Since you stated in the chain above that CP 5.189 *is* modus ponens (“First, I agree with your description of the 5.189 as a 'modus ponens'..”), the alternative, then, is the following: *If p then q. = “But if A were true, C would be a matter of course”* * p. = “Hence there is reason to suspect that A is true” * *Ergo, q. = “The surprising fact C is observed”* *Because in the first line: p = A, q = C* * Second line: p = A* * Third line: q = C* Now the incongruity in this second frame would be that the suspicion comes before the surprising fact, which I take to be a bit odd since the reason to suspect A is true comes before there is even a surprise presented. Even if we flip the order, “Ergo” is separated from “Hence there is reason to…”, whereas in the previous form, they were together. A third possibility is if we reassign equivalence of the first line *so that * *If p then q = If C then A, * but that’s a problem, too, because “if” conjoins p and A and because “then” and “would be a matter of course” conjoins Q and C. So, since there can be no clear correspondence between CP 5.189 and modus ponens, which equivalence is most consistent or are they all different enough to say that CP 5.189 is not modus ponens, either? If not modus ponens, and not syllogism, then what is it? Should we invent a new word for it or apply a very general term like “schema”, which is so general so as to not be terribly informative? Best, Jerry R On Tue, Apr 26, 2016 at 4:03 PM, Jeffrey Brian Downard < [email protected]> wrote: > Hi Ben, List, > > > You have fastened on my last, somewhat undeveloped remark and question: > > (JD) This, I think, is a rather remarkable hypothesis about the source of > our ideas concerning the validity of arguments--such as an argument to an > explanatory hypothesis. What obligations, if any, follow from the > supposition that is formed as the conclusion of this abductive argument > about the logical validity of abduction? > > You say: (BU) One way to test Peirce's idea is to do some inventory of > the abstractions which power cenoscopy and mathematics, and look for how > they could, or ought to, be abstracted from perceptual judgments, > especially in "tough" cases, most especially such cases as have been > adduced as evidence that not all that is in the intellect has entered by > way of the senses." > > > Yes, that is the route I would go in trying to answer that kind of > question. > > > After trying to sketch an account of what such a hypothesis might amount > to and what such a related set of obligations might require, you then say: > "But I'm pretty rusty on that sort of thing, and don't remember such > claimed evidences." > > > Here is one place I see Peirce exploring such evidences: > > > At the time I was originally puzzling over the enigma of the nature of the > logical > interpretant, and had reached about the stage where the discussion now is, > being > in a quandary, it occurred to me that if I only could find a moderate > number of concepts which should be at once highly abstract and abstruse, > and yet the whole nature of whose meanings should be quite > unquestionable, a study of them would go far toward showing me how and > why the logical interpretant should in all cases be a conditional future. > I had no sooner framed a definite wish for such concepts, than I perceived > that in mathematics they are as plenty as blackberries. I at once began > running > through the explications of them, which I found all took the following > form: Proceed according to such and such a general rule. Then, if such > and such a concept is applicable to such and such an object, the > operation will have such and such a general result; and conversely. Thus, > to take an extremely simple case, if two geometrical figures of > dimensionality N should be equal in all their parts, an easy rule of > construction > would determine, in a space of dimensionality N containing both figures, an > axis of rotation,.... Here was certainly a stride toward the solution of > the enigma. (CP, 5.483) > > Does this passage fit the line of interpretation I am suggesting--at least > as one fruitful approach for reading his remarks about the nature > of abduction and its role in philosophical theorizing about the principles > of logic at CP 5.189-94? > > > --Jeff > > > Jeffrey Downard > Associate Professor > Department of Philosophy > Northern Arizona University > (o) 928 523-8354 > > > ------------------------------ > *From:* Benjamin Udell <[email protected]> > *Sent:* Tuesday, April 26, 2016 11:45 AM > *To:* [email protected] > > *Subject:* Re: [PEIRCE-L] Is CP 5.189 a syllogism? > > > Jeff D., list, > > You wrote in conclusion, > > This, I think, is a rather remarkable hypothesis about the source of our > ideas concerning the validity of arguments--such as an argument to an > explanatory hypothesis. What obligations, if any, follow from the > supposition that is formed as the conclusion of this abductive argument > about the logical validity of abduction? > > I'll give it a try. > > The generic obligation would be to deduce conceivable practical > implications testable at least in principle. In cenoscopy (as opposed to > the special sciences), these would not be tests by special experiments or > special experiences, with special classes of concrete objects; in other > words, we wouldn't be doing physics or psychology or the like. Cenoscopic > tests seem to be chiefly by phaneroscopic consideration, critical > reflection, etc., and sometimes some applied math. > > What are conceivable practical implications of finding, embedded so to > speak in perception, or perceptual judgments, such generals and logical > relations as "or", "if...then", and "therefore"? As I recall, Peirce > includes as perception the observation of individual diagrams. One way to > test Peirce's idea is to do some inventory of the abstractions which power > cenoscopy and mathematics, and look for how they could, or ought to, be > abstracted from perceptual judgments, especially in "tough" cases, most > especially such cases as have been adduced as evidence that not all that is > in the intellect has entered by way of the senses. But I'm pretty rusty on > that sort of thing, and don't remember such claimed evidences. > > Best, Ben > > On 4/25/2016 5:32 PM, Jeffrey Brian Downard wrote: > > List, > > For those who (like me) might like or need to brush up on their > understanding of the development of the Aristotelian approach in logic, in > which great weight is placed on the notion of the canonical forms of > inference, see the very nice and relatively short explanations of > Aristotle's work on the syllogism and the development of those ideas in the > medieval tradition in the Stanford Encyclopedia of philosophy. > > Aristotle's logic: http://plato.stanford.edu/entries/aristotle-logic/ > > Medieval theories of the syllogistic forms: > <http://plato.stanford.edu/entries/medieval-syllogism/> > http://plato.stanford.edu/entries/medieval-syllogism/ > > For the sake of understanding the influences that Peirce was drawing on as > he formulated his explanations of synthetic inference--and set up > the examples of inductive and abductive arguments the way he did--it might > be helpful to consider the Medieval account of supposition and logical > consequence. This approach in logic differs in a number of respects from a > logical theory that is built around the idea of canonical forms of > inference. On this approach, the idea of a logical consequence is modeled > on the relationship found in the conditional (and vice versa)--which is an > approach that Peirce found to be quite illuminating. > > Medieval account of logical consequence: > <http://plato.stanford.edu/entries/consequence-medieval/> > http://plato.stanford.edu/entries/consequence-medieval/ > > The author of this entry (Catarina Dutilh Novaes) on the theory of logical > consequence makes the following remark: It is important to note that, in > the 14th century, rules of consequence were often discussed against the > background of the genre of oral disputation known as *obligationes* (see > entry on *obligationes* of this encyclopedia). It is common to encounter > formulations of rules of consequence in obligational terms, for example: if > you have conceded the consequence and its antecedent, then you must concede > the consequent. Thus, interesting reflections on consequence are also to be > found in *obligationes* treatises (and vice-versa). > > In light of that remark, we can see that the theory of logical consequence > might provide an interesting way of thinking about the character of the > conclusion in the example of abductive inference that is offered at CP > 5.189. What, if anything, is a reasonable person obligated to do in > drawing the consequence? Peirce says: "Hence, there is reason to suspect > that A is true. " If we affirm that having a reason to suspect that > something is true involves an obligation to form a supposition (but not > necessarily an assertion) that A is true, then what should on do on the > basis of such a supposition? In order to answer that question, we would > need to consider the mode of the supposition. Here is what Buridan says > about the mode of the different suppositions one might form: In the > present context, the way in which we here speak of matter and form, we > understand by the “matter” of the proposition or *consequentia* the > purely categorematic terms, i.e. subjects and predicates, omitting the > syncategorematic terms that enclose them and through which they are > conjoined or negated or distributed or forced to a certain mode of > supposition. All the rest, we say, pertains to the form. (Buridan, TC, 30) > > To answer the question I posed above, I suspect that the obligation that > follows is a duty to engage in further inquiry for the sake of putting the > matter to the test before making any assertions about what, really, is the > truth of the matter (or something of that sort). In his discussion of > Peirce's logical theory in Reading Peirce Reading, Richard Smyth draws out > these sorts of points in quite interesting ways. In the remarks that > follow the quote from Buridan, Novaes says that part of Buridan's point > lives on in the modern discussion of what is necessary in order properly to > set up the constants in a logical theory (see > http://plato.stanford.edu/entries/logical-constants/) > <http://plato.stanford.edu/entries/logical-constants/>. > > In what sense might the first cotary proposition that Peirce is arguing > for in this essay on perception and abduction be a matter of setting out > something akin to a set of "constants" that govern the proper application > of the leading principle that guides us in abductive reasoning? Notice the > manner in which Peirce draws the conclusion in the essay when he moves from > a claim about the logical form to one about the matter of thought. > > But as to the logical *form*, it would be, at any rate, extremely > difficult to dispose of it in the same way. ... Where do the conceptions of > deductive necessity, of inductive probability, of abductive expectability > come from? Where does the conception of inference itself come from? ... Now > when an inference is thought of *as* an inference, the conception of > inference becomes a part of the *matter* of thought. Therefore, the same > argument which we used in regard to matter in general applies to the > conception of inference. 5.194 > > This, I think, is a rather remarkable hypothesis about the source of our > ideas concerning the validity of arguments--such as an argument to an > explanatory hypothesis. What obligations, if any, follow from the > supposition that is formed as the conclusion of this abductive argument > about the logical validity of abduction? > > Jeffrey Downard > Associate Professor > Department of Philosophy > Northern Arizona University > (o) 928 523-8354 > > *From:* Jon Alan Schmidt <[email protected]> > <[email protected]> > *Sent:* Monday, April 25, 2016 1:50 PM > *To:* Edwina Taborsky > *Cc:* Benjamin Udell; [email protected] > *Subject:* Re: [PEIRCE-L] Is CP 5.189 a syllogism? > > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to > [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L > but to [email protected] with the line "UNSubscribe PEIRCE-L" in the > BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm > . > > > > > >
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