Re: [PEIRCE-L] Re: [biosemiotics:8549] Re: Natural Propositions,
Dear Frederik, lists, Frederik: Something like that. P seldom used the word empiricist. Sometimes he refers to the British empiricists, sometimes to James' radical empiricism which he equated with pragmatism. I do not remember seeing him using it about himself. Of course the later version of empiricism a la Vienna (sense data + tautological logic) had not seen the light of day at the time so he could not refer to that (and he was definitely not an empiricist in that narrow sense) … Franklin: Well, I can't really agree to that; it seems to me that he is certainly an empiricist. But what you have to say is food for thought, and I'll try to keep it in mind when reading Peirce. Frederik: I suggest P gave up the Kandinskys graphical experiment because he realized it led nowhere in its present shape - in that sense it was a red herring. I guess he realized that in order to address real kinds, such figures would have to be made up of graphical properties with formal dependency relations between them - which was not the case in the graphical formalism he was experimenting with in that case. But if that is the case, that was no small result, and I think the whole development of the notion of icon, diagram, and of theorematic reasoning comes out of that train of thought in P Franklin: That's interesting. I hadn't quite taken away the idea from Ch.9 that the Kandinsky's were a failed graphical experiment, and that the diagrammatic reasoning represents an advance beyond that failure in terms of graphical representation. Now that's insightful. I wish you had made that point clearer in the conclusions drawn at the end of the chapter, but it's good to see it that way now. Not that I necessarily agree, but nevertheless that is possibly a much more fruitful idea to consider. Frederik: Frankly, I am away in a summer house right now so I cannot consult my Writings copies either. The ref. in ch. 9 is to W 1, 418 and the year is given there as 1866, is it not? As far as I can find on the internet, this ref. is correct, and the text referred to is not the OLEC, but the fourth Lowell lecture. So the error is not in that reference, but rather in the sentence you quote where I ascribe that position to MS. 725 as well. Frankliln: Ah, I see that now, p.236 of NP. Thank you for that clarification! Frederik: You are indeed right, that is Peirce's position. I do not claim it is not. But I claim I cannot see that position is consistent. Franklin: Well, I can't see what is inconsistent about it, so I suppose we'll just have to agree to disagree about that one. Frederik: Certainly, but his idea is to go to beyond term-symbols to proposition-symbols where b and d are independent - Franklin: My guess is that you mean in a proposition-symbol, the breadth and depth are distinguished from each other as subject and predicate, which is not true in the case of a term-symbol. At least, that's the only way I can understand your statement as reasonable. I'm not sure what that has to do with what I said about analytic term-symbols involving an inverse relation of increase and decrease in logical quantity. Frederik: I think you here again confuse procedural necessity of reasoning with logical necessity of the result. Peirce knew very well that theorematic reasoning was not algorithmic and required the creative selection of additional elements - but still he stably classified it as deduction, because of the logical necessity of the conclusion. Franklin: Okay, I see your point about the logical necessity of the conclusion. But still, if I were to consider how abductive, deductive, and inductive inference work together in inquiry, it's not as if the inquiry as a whole is an inference (contra IBE). Instead, it's different inferences drawing conclusions that contribute to the inquiry as a whole. In the case of theorematic reasoning, it seems to me that both abductive and deductive inferences are at work, so the reasoning as a whole is not simply deductive, but constitutes an inquiry that involves more than one kind of inference. It is recognizing the inclusion of abductive inference that to me shows why the conclusions of mathematics can only concern hypotheses. The difference between corollarial and theorematic then would be whether, during a series of deductive inferences, another abductive inference occurred, rather than before the deductive reasoning altogether. Yes, the conclusion is logically necessary. But there is still an abduction conducted during the reasoning process, and I find it misleading to call the whole thing overall deductive. Well, that's what I think, but I recognize that I am in disagreement with both you and Peirce on this one, which makes me leery of my thoughts on it. Frederik: Getting to natural kinds are among the main purposes of all the different disciplines of the sciences - so all of the machinery of observation, experiment, epistemology, logic, ontology etc. etc. are involved in their discovery. My
Re: [PEIRCE-L] Re: [biosemiotics:8549] Re: Natural Propositions,
Dear Franklin, lists, Many important questions indeed! I concur with Gary that Frederik's post was a very informative post, particularly the last part of it. Depends upon how you define empiricist. I do not deny that Peirce strongly emphasized the role of empirical knowledge! And what definition of empiricist do you think would apply to Peirce? Simply someone who strongly emphasized the role of empirical knowledge, while nevertheless advocating non-empirical knowledge as well? Something like that. P seldom used the word empiricist. Sometimes he refers to the British empiricists, sometimes to James' radical empiricism which he equated with pragmatism. I do not remember seeing him using it about himself. Of course the later version of empiricism a la Vienna (sense data + tautological logic) had not seen the light of day at the time so he could not refer to that (and he was definitely not an empiricist in that narrow sense) … I would not say it was the entire point. The initial point was simply to find out what in the world those Kandinskys were really about ... In a post in the Ch.9 thread, I noted that I agreed with you about the Kandinskys, that they should have been included in publication of the Ms. However, after going through the chapter, you ended up saying that it was all a red herring, and ultimately led to theorematic reasoning as the way to take instead towards hidden properties and natural kinds. In the context of the book as a whole, which is explicitly aimed at introducing and defending the dicisign idea in order to advance your work from Diagrammatology, I think it clear that the overall take-away point of the chapter is its significance for diagrammatic reasoning, and theorematic reasoning in particular. But yes, I overstated it when I said that it was the entire point. I apologize for overstating my case. I suggest P gave up the Kandinskys graphical experiment because he realized it led nowhere in its present shape - in that sense it was a red herring. I guess he realized that in order to address real kinds, such figures would have to be made up of graphical properties with formal dependency relations between them - which was not the case in the graphical formalism he was experimenting with in that case. But if that is the case, that was no small result, and I think the whole development of the notion of icon, diagram, and of theorematic reasoning comes out of that train of thought in P I had said: In the thread for Ch. 9, I already noted that I couldn't find in the quoted passage from Peirce where he says that a definition of natural kinds is that they are classes which have more properties than their definition (NP, p.255). You replied: It is in the OLEC - Writings vol. 1, page 418. I think there is an error in the ref. saying 419, sorry for that. This is really confusing. Unfortunately, I don't have a copy of the Writings. What I do have is your book and the online copy of ULEC at cspeirce.comhttp://cspeirce.com/. In your book (p.234, 2nd fn), you noted that OLEC is published as ULEC in Writings vol. 2, not vol.1, and the pages are 70-86; so they do not include 418 or 419. As to any mention of Writings vol. 1 and p.419, I do not see that anywhere in Ch.9. Is there a different version published in W 1 as well, which includes discussion of natural kinds? The ULEC copy at cspeirce.comhttp://cspeirce.com/ contains no such reference to natural kinds. Furthermore, you say on p.255 the following: In the brief paragraph preceding the graphical experiments of Ms. 725, Peirce proposes no less than three different definitions of natural classes, two of them negative: they are 1) classes which are not mere intersections of simpler natural classes, 2) classes which have more properties than their definition, 3) classes without [sic] an Area. As to the brief paragraph you quote in full that is an addendum discussing natural kinds, I can find no reference regarding classes which have more properties than their definition. Please help me out here? Frankly, I am away in a summer house right now so I cannot consult my Writings copies either. The ref. in ch. 9 is to W 1, 418 and the year is given there as 1866, is it not? As far as I can find on the internet, this ref. is correct, and the text referred to is not the OLEC, but the fourth Lowell lecture. So the error is not in that reference, but rather in the sentence you quote where I ascribe that position to MS. 725 as well. But analytic quantities are also quantities - so you can also multiply them to give an area? Looking at paragraph 6 of the ULEC at cspeirce.comhttp://cspeirce.com/, we can see that Peirce would say we cannot. Introducing the multiplication of breadth and depth is preceded by this statement in the text: By breadth and depth, without an adjective, I shall hereafter mean the informed breadth and depth. This will of course include the breadth and depth mentioned in
[PEIRCE-L] Re: [biosemiotics:8549] Re: Natural Propositions,
Frederik, Gary F, lists, I concur with Gary that Frederik's post was a very informative post, particularly the last part of it. Depends upon how you define empiricist. I do not deny that Peirce strongly emphasized the role of empirical knowledge! And what definition of empiricist do you think would apply to Peirce? Simply someone who strongly emphasized the role of empirical knowledge, while nevertheless advocating non-empirical knowledge as well? I would not say it was the entire point. The initial point was simply to find out what in the world those Kandinskys were really about ... In a post in the Ch.9 thread, I noted that I agreed with you about the Kandinskys, that they should have been included in publication of the Ms. However, after going through the chapter, you ended up saying that it was all a red herring, and ultimately led to theorematic reasoning as the way to take instead towards hidden properties and natural kinds. In the context of the book as a whole, which is explicitly aimed at introducing and defending the dicisign idea in order to advance your work from Diagrammatology, I think it clear that the overall take-away point of the chapter is its significance for diagrammatic reasoning, and theorematic reasoning in particular. But yes, I overstated it when I said that it was the entire point. I apologize for overstating my case. I had said: In the thread for Ch. 9, I already noted that I couldn't find in the quoted passage from Peirce where he says that a definition of natural kinds is that they are classes which have more properties than their definition (NP, p.255). You replied: It is in the OLEC - Writings vol. 1, page 418. I think there is an error in the ref. saying 419, sorry for that. This is really confusing. Unfortunately, I don't have a copy of the Writings. What I do have is your book and the online copy of ULEC at cspeirce.com. In your book (p.234, 2nd fn), you noted that OLEC is published as ULEC in Writings vol. 2, not vol.1, and the pages are 70-86; so they do not include 418 or 419. As to any mention of Writings vol. 1 and p.419, I do not see that anywhere in Ch.9. Is there a different version published in W 1 as well, which includes discussion of natural kinds? The ULEC copy at cspeirce.com contains no such reference to natural kinds. Furthermore, you say on p.255 the following: In the brief paragraph preceding the graphical experiments of Ms. 725, Peirce proposes no less than three different definitions of natural classes, two of them negative: they are 1) classes which are not mere intersections of simpler natural classes, 2) classes which have more properties than their definition, 3) classes without [sic] an Area. As to the brief paragraph you quote in full that is an addendum discussing natural kinds, I can find no reference regarding classes which have more properties than their definition. Please help me out here? But analytic quantities are also quantities - so you can also multiply them to give an area? Looking at paragraph 6 of the ULEC at cspeirce.com, we can see that Peirce would say we cannot. Introducing the multiplication of breadth and depth is preceded by this statement in the text: By breadth and depth, without an adjective, I shall hereafter mean the informed breadth and depth. This will of course include the breadth and depth mentioned in the multiplication. The analytic quantities, as I called them, would be referred to by Peirce as essential breadth and essential depth, as shown in paragraph 5 that they encompass what is given in a definition. Of course, this doesn't stop you from disagreeing with Peirce. I suppose he would say that when we manipulate the breadth and depth of analytic term-symbols, it's always an inverse relation, so that an increase in depth means a decrease in breadth, and vice versa, as per the traditional doctrine of the logical quantities that he discusses earlier in the paper. Information allows us to get past the inverse relation with term-symbols, but, given that he distinguishes natural from artificial kinds by the use of area, I suppose that only natural classes can involve the synthetic propositions that inform the term-symbol. To me, this makes intuitive sense. If induction worked for artificial kinds, they wouldn't seem to be so artificial anymore. Peirce's point in theorematic reasoning is that there are deductive reasonings which are not analytic - in the sense that they give access to theorems which do not lie directly (as corollaries) in the definition of terms (cf. the example with Euclid's proof of the angle sum of the triangle which can not be conceptually deduced from the triangle definition)...Here are some important consequences. One is that the theorematic type of deductive reasoning process involves an abductive trial-and-error phase (in order to find the right new elements to add or manipulations to make with your diagram). This admission that abduction plays a role counts against theorematic
[PEIRCE-L] RE: [biosemiotics:8549] Re: Natural Propositions,
Frederik, Franklin, lists, This is a very helpful post (as usual for Frederik!) and does clarify the nature of theorematic reasoning, but I still have to admit that the chapter about the “Kandinskys” and the follow-up to it strike me as more of an appendix to the book than an integral part of its argument. I know Franklin is working on the question of how Chapter 10 relates to the book, so I’m looking forward to that (and to Frederik’s response) as a good way of bringing our seminar to a close. I think I can speak for others who haven’t posted much lately in saying that this latter part of the seminar has been very fruitful. Gary f. From: Frederik Stjernfelt [mailto:stj...@hum.ku.dk] Sent: May 1, 2015 5:50 AM To: biosemiot...@lists.ut.ee Cc: Peirce-L 1 Subject: [biosemiotics:8549] Re: Natural Propositions, Dear Franklin, lists, : Frederik, thank you for sending this off-list exchange to the lists. I think Tommi explicated more fully my own concerns regarding abduction and the a priori, and your response is very helpful for understanding your view. I can hardly believe that you deny Peirce is an empiricist, but I suppose I will have to accept it and let it go at that. Depends upon how you define empiricist. I do not deny that Peirce strongly emphasized the role of empirical knowledge! I too share Tommi's concerns. It seems to me that most folks here don't understand that you view theorematic reasoning as the road to identifying natural kinds, although it is clear from your concluding paragraphs in Ch. 9 that this is exactly what you believe; indeed, that was the entire point of writing that chapter, was it not? I would not say it was the entire point. The initial point was simply to find out what in the world those Kandinskys were really about ... But in the realm of such forms, we are back to diagrams and diagrammatical reasoning. And here, again, it remains central to Peirce that such diagrams may give occasion of 'theorematic reasoning' whose aim it is exactly to discover properties of their objects which were not mentioned in the explicit construction of the diagram--corresponding to the definition of the class. So the idea of the additional, hidden properties to be deduced kept their place in Peirce's doctrine, so that the 'system of forms' of the 'Minute Logic' may give rise to natural classes for the same reasons sketchily outlined in MS. 725. So, the strange drawings at the end of that Ms. may have put him on an important track, realizing that the fascinating diagrammatic experiments with Cows and Red Cows were originally motivated by a red herring. (NP, p.257) In the thread for Ch. 9, I already noted that I couldn't find in the quoted passage from Peirce where he says that a definition of natural kinds is that they are classes which have more properties than their definition (NP, p.255). It is in the OLEC - Writings vol. 1, page 418. I think there is an error in the ref. saying 419, sorry for that. I also gave in that post a response to a statement made on the same page, It is hard to see why Red Cows should not have an Area in the simple b x d sense defined in the OLEC; as defined in the OLEC, it makes perfect sense because artificial classes cannot involve synthetic propositions, only analytic logical quantity of breadth and depth. But analytic quantities are also quantities - so you can also multiply them to give an area? The position that natural kinds must have an area, or information, is still important, as is the point that area or information has to do with synthetic propositions, and not merely the analytical ones found in deductive reasoning, including theorematic diagrammatic reasoning. Theorematic reasoning cannot be the way we get to natural kinds. Peirce's point in theorematic reasoning is that there are deductive reasonings which are not analytic - in the sense that they give access to theorems which do not lie directly (as corollaries) in the definition of terms (cf. the example with Euclid's proof of the angle sum of the triangle which can not be conceptually deduced from the triangle definition). So actually I find the corollarial/theorematic disctinction is a good bid of where to find the analytic/synthetic distinction in Peirce. I discussed this in ch. 8 of Diagrammatology (2007); as far as I remember, Sun-Joo Shin made that point earlier. Here are some important consequences. One is that the theorematic type of deductive reasoning process involves an abductive trial-and-error phase (in order to find the right new elements to add or manipulations to make with your diagram). This points to the distinction - blurred in Kantian notions of the a priori - between the necessity of deductive procedure and the logical necessity of the results of that procedure. These are not at all the same thing (and I believe it is the same distinction which is addressed in
