Dear Eric Smith (and other patient people),
I have been trying to get the chance to lay this out for three days, and have just not had the time. I am enthralled at the moment by the scientific philosophy of Charles Saunders Peirce because, weird as it is, it seems to capture a lot of what I think about a lot of things. It also, it stands at the root of many of our institutions. You can access this connection through Menand's, The Metaphysical Club. Many of the foundational beliefs we hold about education and science and even jurisprudence are partly due to Peirce. I am not sure Peirce thought he needed (1) below, but I need it to get him started, so I will attribute it to him. (1) Humans are a knowledge-gathering species by nature. Darwinism tells us that humans have survived both as communities and as a species because their cognitive processes have brought their beliefs into concert with the world. (Peirce is a bit of a group Selectionist.) A belief is that on which I act. There are no latent beliefs in Peirce. Doubt is an incapacity to act. (2) True propositions and the best methods for discovering them are those on which the human species, as a community of inquiry, will converge ULTIMATELY. By ultimately, I mean the infinite future. Note that this is a definition of "true." There is no other truth in Peirce, no correspondence theory, except possibly that inferred by me in (1 ) . The current views of contemporary communities of inquiry may be our best shot at the truth, but they are NOT true, by definition, unless they happen to be that on which the human community of inquiry will ultimately converge. Peirce was a chemist, a mathematician and an expert in measurement. There was no doubt in his mind that the best methods for producing enduring convergence of opinion were what we think of as Scientific methods -- experiments and mathematical analysis . (3) The real world consists of all that is true. (4) Our knowledge of the world is through a stream of logical inferences. All human beings are informal scientists by nature. All human belief is arrived at, whether consciously or unconsciously, whether by scientist or by layman, whether by infant or mature adult, by the application of forms of inference and by experiments and observations whether formal or informal. (5) Contrary to what many of us were taught in graduate school, there are three forms of valid inference. Communities of inquiry (principally “Sciences” to Peirce) use all three forms of inference, to produce networks of inference. (6) Deductive inferences such as "A. All Swans are White; B. this bird is a swan; C. This bird is white." are categorically true. However, those who taught us in Graduate School that only deductive inferences are valid, failed to tell us how we come by either the Major (A) or the Minor (B) premise of such inferences. Popper, who influenced many of the scientists in my generation, used to tell us that they were "bold conjectures." Big lot of help THAT is! One of the great strengths of Peirce’s work is that he gives an account of the origin of “bold conjectures”. (7) Peirce honors two additional forms of valid logical inference, which he calls forms of "probable" inference. . A probable inference is one whose strength improves with the multiplication of concordant cases. Probably inference can supply the major (A) and minor (B) premises of deductive inferences from empirical observations. Much of scientists’ daily work consists in improving the strength of our probable inferences. (8) The first of these types is induction. “C. This bird is white; B. This bird is a swan; A. All Swans are White.” It generates the major premise of the deductive inference above (A), but needs other inferences to supply C. and B. With a single case, an inductive inference is valid, but extremely weak. With the discovery of larger and larger numbers of swans that are white, the strength (probability) of the inference approaches 1.00. (9) The second of these types of probable inference is “abduction”. “C. This bird is white; A. All Swans are White; B. This bird is a swan.” Abductions can generate the minor premise of the deductive inference above (B) but need other inferences to supply A and C. An abductive inference based on the discovery of a single concordant property between swans and the bird at hand is valid but extremely weak. As more concordant properties are discovered, our certainty that the bird is a swan approaches 1.00. (10) The beliefs in the self and in an inner private world are all arrived at in this manner. They are the result of inferences (“signs, Peirce would say”) arising from our experience with the world. The self’s view of the self is no more privileged an inference than the other’s view of the self. In fact, on Peirce’s account, the former is probably based upon the latter by abductive inference. (11) On the account of Many Wise Persons, all the above is based upon Peirce’s theory of signs. I confess I don’t really understand that theory, and tried very hard to get to this point without invoking it. Your skepticism should be heightened by this admission. I will send this off to some people who know Peirce better than I in the hope that they will correct me. I will send along any corrections I receive. Nick FN#1. Yes, I know that all swans are not white. I know my ornithology, my childhood literature and my chaotic economics as well as the next guy. FN#2. Some readers may struggle with the idea that calling a bird “white” is itself an inference. But, think about how you would go about deciding the color of something. You would observe it over time, you would observe it in various lights, etc., and then DECIDE that it was white. Whether that process is conscious or unconscious, systematic or unsystematic, is irrelevant to Peirce. It is still an inference. -----Original Message----- From: friam-boun...@redfish.com [mailto:friam-boun...@redfish.com] On Behalf Of Eric Smith Sent: Wednesday, March 28, 2012 5:10 PM To: The Friday Morning Applied Complexity Coffee Group Subject: Re: [FRIAM] Clarifying Induction Threads Thank you Lee and Glen both, Yes, I could not disagree. There is an interesting question, Glen, on which I don't have a dog in the fight either way. Is the worry about induction only (or even mostly) about the origin of conjectures, or is it (equally much, or even mostly) about the source of confidence in conjectures? The issue of what we would like to regard as truth values seems to me to suggest at least large weight on the latter. I think, "truth" descending from a common root of "trust" and so forth. I look forward to Lee's particular refutation, because I was wondering whether I would argue against the same point myself, say for flipping coins where there are only two possibilities, and trying to decide whether it is better to expect that the next one will be the same as previous ones, or not. But even there, I might niggle with something on algorithm complexity and description length, and argue that it is "harder" to expect a violation of a long string of repeats, than it is for a short string. But, I look forward to listening to Lee's refutation. All best, Eric On Mar 28, 2012, at 4:06 PM, <mailto:lrudo...@meganet.net> lrudo...@meganet.net wrote: > Eric Smith: > >> every child knows there can be no discussion of induction that is not >> predicated on the availability of infinities. > > Not so (independent of what every child knows)! I have to rush off > but will try to get back to this later. > > ============================================================ > FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe > at St. John's College lectures, archives, unsubscribe, maps at > <http://www.friam.org> http://www.friam.org ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at <http://www.friam.org> http://www.friam.org
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
