Jeff, I think this is a very astute analysis of what Peirce is doing in the latter Lowell lectures. Certainly they focus on the classification of arguments, which is in a sense the climax of speculative grammar; and what stands out to me lately is the overlapping of the three main divisions of arguments (abduction, induction, deduction). When Peirce lays out in detail the steps in a Euclidean argument, for instance, we see that there’s an element of induction (quasi-experimentation), and of abduction (ingenuity), within a process which is in the main deductive. Peirce repeatedly rethought his analysis of signs, I think, because that was the inductive part of the investigation he called speculative grammar (or later Stechiology): once you have the main divisions a priori, then you have to keep adjusting and refining them as you look at more and more specific examples of reasoning processes. Peirce was not the type to be satisfied that he had come to the end of such an investigation, one that would give him a final and definitive taxonomy. Rather we approach a complete understanding of semiosis by reiterating our examination of it, with each iteration looking at the semiosic phenomena from a slightly different angle of observation. And we as Peirceans go through the same reiterative process in developing our understanding of Peirce, as we try to follow the various texts now coming to light (some of which had been dismembered by the CP editors).
But I guess I’m rambling here and I’d better get back to the investigation instead of talking about it … Gary f. From: Jeffrey Brian Downard <jeffrey.down...@nau.edu> Sent: 17-Jul-18 19:59 To: 'Peirce List' <peirce-l@list.iupui.edu> Subject: Re: [PEIRCE-L] Lowell Lecture 7 Hi Gary F, List, Thank you for making and sharing the transcription of Lecture 7. I've been reading the latter lectures in manuscript form, and it is much easier for me to search through the contents, construct outlines what appears to be going on and comprehend the structure of the arguments when reading them in the transcribed format.` Looking at the account of induction that he is developing--and the refinements he is making with respect to prior statements of his accounts of the three main classes of induction, it does now appear clearer how lectures 5 and 6 support the clarifications and amendments he appears to be making. He express aims in those lectures were to make further clarifications of the conceptions of multitude and probability for the sake of providing a better account of the nature and validity of the three main classes of inductive reasoning. Drawing on the points made about the alpha, beta and gamma graphs in the earlier lectures, it looks to me like he is trying to make good on his promise of drawing on these mathematical systems of deductive logic for the sake of inquiry in critical logic concerning synthetic forms of inference. As such, I imagine that Peirce is drawing on the EG as he reflects on the points he has made about multitude and probability drawing. In turn, the logical diagrams are informing his inquiries--especially about the differences that he is articulating between the second and third classes of induction. In this first part of Lecture 7, he provides and explanation of how the three forms of inference fit together in the cycle of inquiry. Having compared the more analytic and the synthetic forms of inference, he says that the more analytic form is the least important of the three: You will see from what I have said that Deduction is decidedly the least important of the three. Deduction is merely a link by which the result of Abduction,— that is to say the proposed explanatory hypothesis,— is put into a form in which Induction can be applied to it; and it only consists in making thought distinct as to what the Supposition that the Abduction suggests really supposes. Having made this point, he goes on to say that deduction has a special role to play in critical logic--including the study of synthetic forms of inference. While it is a relatively insignificant step in the inquiry, however, Deduction becomes of surpassing importance in logic; and the reason of this is that Logic or rather Critic, which is that branch of logic that evaluates arguments, is itself Deductive. In order to put this remark into a clear light it is requisite to view the three Classes of Argument from another standpoint. I am curious about the shift in standpoint that he is announcing here. What does the change of perspective involve? Here is how he describes it at length. A Deduction is a process of thought by which it is rendered evident that a certain conclusion must be true; and this is so whether this relates to individual single cases or whether it is a statistical proposition concerning a ratio of frequency in indefinitely many single instances. The manner in which the conclusion becomes evident is this. The premisses are stated in general terms. Now the mode of being of a general is that of governing individual cases. Its full expression requires therefore the presentation of something corresponding to those cases,— a quasi-diagram of them. The deduction makes that diagram and when it is made it recognizes that this diagram is and always will be a representation of a state of things describable in a different general statement,— and this latter general statement constitutes the conclusion. To show that this really is a correct description of Deduction, it will suffice to consider the general structure of Euclid's demonstrations,— Euclid's being more formally correct in statement than modern mathematicians think is needful. He invariably begins with a general statement of what he intends to prove. This is called the proposition; in Greek πρότασις, that is the pretension, or preliminary statement. In Aristotle it means a premiss. He then restates the condition of his proposition in such a form as to assign a selective or proper name to every geometrical point, that is every individual of the set concerning which the predication is made. This at the same time and ipso facto describes any diagram of any state of things to which the proposition is applicable. This part ends by stating in terms of those selectives exactly what his assertion makes him responsible for. This part is called the ἔκθεσις, or exposition. Next comes his κατασκευή, or contrivance; which is an ingenious experiment that he performs upon the diagram, by adding lines to it drawn according to an exact precept, or his supposing one part to be moved and superposed in a particular way upon another part. He now shows that it is implied in what is already known that this experiment must give a certain result in every case. This operation is his demonstration ἀπόδειξις, or from-showing. This proof ends by repeating the very statement with which the ἔκθεσις closed, to which he affixes the words, “which is what had to be shown,” ὅπερ ἔδει δεῖξαι. It is, you perceive, simply a showing that the thing is so by actual experience in the imagination. As has often been remarked, by Locke, for example, by Kant, by Stuart Mill, and as is admitted by all logicians the conclusion simply redescribes the state of things which alone is represented in the premisses. Let me draw attention to the point he makes after considering the examples of deductive reasoning drawn from Euclid's Elements. Notice the role of the selectives in the process of reasoning about a geometrical figure: He then restates the condition of his proposition in such a form as to assign a selective or proper name to every geometrical point, that is every individual of the set concerning which the predication is made. This at the same time and ipso facto describes any diagram of any state of things to which the proposition is applicable. This part ends by stating in terms of those selectives exactly what his assertion makes him responsible for. What light, if any, does this point about role of selectives in geometrical reasoning shed on the character of inductive reasoning? In the paragraphs immediately following, he says that inductive reasoning involves a "quasi-experiment" of sorts, and that this experiment is crucial for drawing conclusions about an uncountably large multitude of possible future observations on the basis of a limited number of past observations. He says: Induction concludes more than would conceivably be true in every case in which what is observed would be true. It cannot, therefore, absolutely guarantee the truth of its conclusion. What can it do? Shall it show that the conclusion would be true in a large proportion of the embodiments of its general condition in the course of experience? This would be nothing but a necessary deduction of a statistical kind. It has to conclude that a hypothesis is true because certain predictions based upon it have been verified. Under what modification is it warranted in asserting that? Without exhausting the inexhaustible future it certainly cannot be justified in asserting that absolutely. It can, however, assert this, subject to such modification as further quasi-experimentation may make. (my emphasis in bold) This, I think, is a rather refined restatement of the traditional "problem of induction" that was inherited from the likes of Hume, Kant and Mill. What is more, I think it embodies a rather refined response to this re-statement of the problem. A central feature in his response to this problem is the role of selectives in reasoning about the proportion of a given collection of observations--so that we can reasonably draw valid conclusions about there being a similar proportion in an uncountably large numbers of possible future observations. Or to put the matter more directly, the results of statistics can only take us so far because they are mathematical reasonings of a deductive sort. In order to justify the application of such mathematical conceptions in the context of inductive reasoning, we need to show that it is reasonable to apply one or another statistical model to a real world problem based on the collection of data we have on hand at a given time in the process of inquiry. Yours, Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 _____ From: g...@gnusystems.ca <mailto:g...@gnusystems.ca> <g...@gnusystems.ca <mailto:g...@gnusystems.ca> > Sent: Tuesday, July 17, 2018 9:52:05 AM To: 'Peirce List' Subject: [PEIRCE-L] Lowell Lecture 7 Peirceans, My transcription of Lowell Lecture 7 of 1903 is now available at the SPIN site, https://www.fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-473-474-1903-lowell-lecture-vii , and has been added to the series on my website, at http://gnusystems.ca/Lowell7.htm. This one is all about inductive reasoning. Again I don’t plan to serialize it on the list, as I did with the first three lectures, but any discussion of it is welcome. Here’s a sample paragraph: <https://www.fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-473-474-1903-lowell-lecture-vii> MS 473-474 (1903) - Lowell Lecture VII (C. S. Peirce Manuscripts) | FromThePage www.fromthepage.com <http://www.fromthepage.com> MS 473-474 (1903) - Lowell Lecture VII (C. S. Peirce Manuscripts) - read work. [[ The second order of induction only infers that a theory is very much like the truth, because we are so far from ever being authorized to conclude that a theory is the very truth itself, that we can never so much as understand what that means. Light is electro-magnetic vibrations; that is to say, it [is] something very like that. In order to say that it is precisely that, we should have to know precisely what we mean by electro-magnetic vibrations. Now we never can know precisely what we mean by any description whatever. ] MS 473 CSP 60-2 ] Gary f. } The child finds its mother when it leaves her womb. [Tagore] { http://gnusystems.ca/wp/ }{ Turning Signs gateway
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