Hello Christina, List, Take a look at the first volume of Peirce's Chronological Writings. In the two series of lectures (Harvard and Lowell, 1865-6), we see Peirce digging into Kant's way of thinking about the syllogism. It seems clear to me that he has copies of Kant's lectures on logic and "On a False Subtlety in the Fourth Figure of the Syllogism" in front of him, and that he is carefully sorting through Kant's explanations of the leading principles of deductive inference and the grounds of the validity of this kind of argument one page at a time. He tells us later in the essays collected in Reasoning and the Logic of Things (around 1898), that he first thought Kant's account of the forms of judgment necessary for valid deductive inference were correct on the main points, but that there were only some small irregularities that needed be ironed out. So, he went to work on the problem of trying to figure out where the irregularities might lie. My hunch is that there are probably many insights that are recorded in the Logic Notebook--and that we are hampered by the fact that the notebook is only available in manuscript form. Otherwise, would could just search through it and save many hours and weeks of our time. The same is probably true of his working notes on the theory of the syllogism that are not collected in the notebook. As he labored over the problems, he came to see that the wrinkles he was expecting to find involved much larger issues that had no easy solutions. In the "New List of the Categories," we find a published record of some of the ways that he thought Kant was heading down the wrong track. Instead of organizing two functions of judgment under four headings, we now have a system of only three basic forms necessary for deductive reasoning. Instead of Kant's list of the four most general categories of quality, quantity, modality and relation, we now have only three: quality, brute relation, and representation (or thought). Like Kant, Peirce is trying to argue that all forms of reasoning, both deductive and ampliative, depend upon the same basic formal conceptions and conditions.
Notice that Kant's table is built around the idea that deduction itself only requires two modes under each of the general categories. So, under the mode of quantity, we only need the conceptions of the universal and particular. And, under the mode of quality, we only need affirmative and negative. When we apply deductive forms of inference to our inquiries about the real relations that hold between existing things, we need the conception of an individual (the singular) and the conception of limitation (infinity, totality, and the like). More and more, as he is working his way through Boole's Laws of Thought and through De Morgan's works on the logic of relatives, he sees the importance of different kinds of relations both for demonstrative reasoning in the special sciences, but also for reasoning in mathematics--especially for reasoning about probabilities. So, there are two related problems. Kant seems to offer us a way of thinking about propositions concerning individuals, but his account of the relations between possibilities and actualities leaves something to be desired. My sense is that Peirce saw he needed a dramatically different kind of logical theory if we were to have any hope of building an adequate explanation of why some simple inferences about probabilities go so wrong and why others, as counterintuitive as they might seem, are valid. This drives Peirce to see where Boole's and De Morgan's approaches to using algebraic tools in the development of formal systems of deductive logic might be leaving us short. Over the course of the next 15 or so years, he makes a remarkable discoveries about how we might develop more richly relational systems of formal logic--and how we might use those formal systems to enrich our philosophical theories of the leading principles of deductive logic. So, the "discovery" that all forms of deductive inference cannot be reduced to Barabara was an idea that grew over the course of some decades. Having said that, let me add the following proviso. I think Peirce holds onto the idea to the very end that Aristotle is correct--and Kant is too. The simplest system of deductive logic (propositional logic, which is equivalent to the alpha graphs) rests on a particular principle that is most clearly exemplified in the first figure of the syllogism. When we bring in the ideas of picking out individuals that quantifiers can range over, and that the individuals are connected to wide ranges of possibilities and necessities in remarkably rich ways, we find that more robust systems of logic are needed. So, he builds more formal systems of deductive logics, and then he uses them to improve on his philosophical explanations of logic. Hope that helps. --Jeff Jeff Downard Associate Professor Department of Philosophy NAU (o) 523-8354 ________________________________________ From: Benjamin Udell [[email protected]] Sent: Wednesday, October 28, 2015 10:14 AM To: [email protected] Subject: Re: [PEIRCE-L] Question about Barbara "On the Natural Classification of Arguments" 1867 W 2:42, CP 2:506 The first figure is the fundamental or typical one, and Barbara is the typical mood. On 10/28/2015 12:45 PM, Benjamin Udell wrote: Here's one place where Peirce says that Barbara is not enough: "Relatives (logic of)" in Baldwin's _Dictionary of Philosophy and Psychology_, New York: Macmillan, 1902, DPP 2:447-450; CP 3.636-643 http://www.gnusystems.ca/BaldwinPeirce.htm#Relatives [....] Since Kant, especially, it has been customary to say that deduction only elicits what was implicitly thought in the premisses; and the famous distinction of analytical and synthetical judgments is based upon that notion. But the logic of relatives shows that this is not the case in any other sense than one which reduces it to an empty form of words. Matter entirely foreign to the premisses may appear in the conclusion. Moreover, so far is it from being true, as Kant would have it, that all reasoning is reasoning in _Barbara_, that that inference itself is discovered by the microscope of relatives to be resolvable into more than half a dozen distinct steps. In minor points the doctrines of ordinary logic are so constantly modified or reversed that it is no exaggeration to say that deductive logic is completely metamorphosed by the study of relatives. [End quote] Best, Ben On 10/28/2015 12:17 PM, Christina Da Silva wrote: I am finishing up a masters that focuses on Medieval Islamic philosophy, and this list has been an inestimably useful resource for me, so thank you to all who post here. I am now trying to find the source for some information I have in my notes, and my hope is that someone on the list can help me. Here is my question: where does Peirce suggest that all syllogisms may be reduced to Barbara, and where does he later renounce this idea? Thank you, Christina da Silva
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