It seems that we instinctively believe in induction –that patterns which have been repeated will continue to repeat. It seems natural to justify this belief by saying it has worked before, except, as Eric Charles has pointed out, this is circular.
Eric Smith has suggested an alternative justification: If induction were false, our instinctive belief in induction would not have evolved. Is it possible to imagine a world that would favor anti-induction (or the tendency to believe that patterns which have repeated will stop repeating)? This suggests a mathematical question: Suppose a natural phenomenon can either perform action A or action B. Further suppose that organisms which can correctly predict whether A or B will happen have an evolutionary advantage. Suppose that organisms can remember whether an occurrence of A was more often followed by another A or more often by another B (or whether the next action was A exactly as many times as it was B). One type of organism is inductive. If the action A is more often followed by another A, the organism predicts A whenever the previous action was A. If the action A is more often followed by an action B, the organism predicts B and makes no prediction if A and B are equally likely to follow after an A. The organism uses a similar strategy if the previous action was B. Another organism is anti-inductive. It predicts the opposite of what an inductive organism would predict. It is easy to devise a sequence of A's and B's that would favor the inductive organism. For example the sequence (A, A, A, A, A, . . .) which is always A, will greatly favor the inductivist, who always makes correct predictions, over the anti-inductivist who always predicts incorrectly. Even the alternating sequence (A, B, A, B, . . .) will greatly favor the inductivist. But, can we find a sequence which favors the anti-inductivist? Yes. Start the sequence with any action, say A. In the absence of any experience with what happens after an A, both the inductivist and the anti-inductivist will make no prediction. So we can choose another A. Now the inductivist will predict a third A, but the anti-inductivist will predict B. So make the next action B and so forth. But such ani0inductivist sequences must be rare else we would not have evolved as inductivists. (Or did we --some people seem to be anti-inductivists, saying that after two A's it must be the case that we are due for action B.) ________________________________________ From: friam-boun...@redfish.com [friam-boun...@redfish.com] On Behalf Of Nicholas Thompson [nickthomp...@earthlink.net] Sent: Thursday, March 29, 2012 8:17 PM To: 'The Friday Morning Applied Complexity Coffee Group' Subject: Re: [FRIAM] Clarifying Induction Threads Thanks, Eric. I am sure Bayes and and Peirce would have got on famously. Unfortunately, this can only be surmise for me, because despite attempts by many kind people to explain Bayes to me, nothing has ever stuck. I am ever hopeful, but afraid I am demonstrably not worth further investment by others. In connection with your other comments below, there are passages in Pierce that are eerily reminiscent of Schroedinger’s what is life and like things that Kaufmann wrote. From his MAN’S GLASSY ESSENCE, I give you … Protoplasm, when quiescent, is broadly speaking, solid; but when it is disturbed in an appropriate way, or sometimes even spontaneously without external disturbance, it becomes, broadly speaking liquid. A moner in this state is seen under the microscope to have streams within its matter. … Long-continued or frequently repeated liquefaction of the protoplasm results in an obstinate retention of the solid state, which we call fatigue.” He relates this fatigue to the formation of habits. After a few pages, he reveals where he is headed: “But what is to be said of the property of feeling? If consciousness belongs to all protoplasm, by what mechanical constitution is this to be accounted for. The slime is nothing but a chemical compound. There is no inherent impossibility in its being formed synthetically in the laboratory, out of its chemical elements: and if it were so made, it would present all the characters of natural protoplasm. No doubt, then, it would feel. To hesitate to admit this would be puerile and ultra-puerile. “ Have to fix dinner. Nick From: friam-boun...@redfish.com [mailto:friam-boun...@redfish.com] On Behalf Of Eric Smith Sent: Thursday, March 29, 2012 3:36 PM To: The Friday Morning Applied Complexity Coffee Group Subject: Re: [FRIAM] Clarifying Induction Threads Thanks greatly Nick, It is very helpful to me to see these premises laid out in a systematic way, since I am nowhere near having the resources of either time or brain to try to read this material myself. As you say, it fits well as a description of the events that make up a problem-solver's practical day. I think it leaves me with more unsatisfied questions perhaps than I had before, or maybe just a larger urge to try to formalize. I think of Vygotsky (Thought and Language) and "family relations" as precursor to predicates, when I read your description of abduction. I think of Bayesian inference when I read your description of his notions of validity in weak form, as an alternative to Popper. Each of these seems to be an attempt by one or another worker to get at rules that could be used to build a machine -- of which we knew all the internal parts -- that would commit these acts. Then we could study the overlap and differences with our own choices, and perhaps update our categories. Interesting, always interesting, Eric On Mar 29, 2012, at 12:29 PM, Nicholas Thompson wrote: 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> [mailto:friam-boun...@redfish.com]<mailto:[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, lrudo...@meganet.net<mailto: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 ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps athttp://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 ============================================================ 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
