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 <baud...@gmail.com> Sent: Tuesday, April 26, 2016 11:45 AM To: peirce-l@list.iupui.edu 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 <jonalanschm...@gmail.com><mailto:jonalanschm...@gmail.com> Sent: Monday, April 25, 2016 1:50 PM To: Edwina Taborsky Cc: Benjamin Udell; peirce-l@list.iupui.edu<mailto:peirce-l@list.iupui.edu> Subject: Re: [PEIRCE-L] Is CP 5.189 a syllogism?
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