Re: [FRIAM] Clarifying Induction Threads
(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, 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
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
Re: [FRIAM] Clarifying Induction Threads
Nick, Would you explain further your notion that belief is that on which we act. Does this imply for you that a lack of action implies a lack of belief? For example, I believe that the earth is round, but I don't act on that belief. Does that mean I do't really have that belief? How does this work in your framework? Also, you say that true propositions are those on which the human species as a community of inquiry will ultimately (in the infinite future) converge. That bothers me in a number of ways. - This is such a remote definition that it hardly seems worth bothering with in the first place. There is no operational test to determine whether something is the truth under this definition. As you say, this is really just a definition, but it's not even a definition of one concept in terms of others. It simply labels the propositions on which ... as the truth. But giving a label to a set of things doesn't add anything new. It just adds a label. So why bother? And especially why other when the term the truth has some meaning to most people. Why say that we should forget about that meaning and use the term as a label for some set of things -- if that set even exists (see below). - One doesn't know that it will ever refer to anything. We won't converge on anything in the infinite future since there is no end to the infinite future and hence no convergence. - If you are using converge as in mathematics as in the convergence of an infinite series (where there is convergence to infinity), then, as in mathematics, one may be able to determine at this moment what the series (or truth) will converge to. But that's probably not what you (or Peirce) have in mind. But if you reject that, then as in the previous point, there is no convergence since one never reaches infinity. So there is no such set. - Some series don't ever converge. How do we know that the truth in your sense is not one of those? The community of inquiry may split with one part of it converging (assuming there is convergence) on one truth and another part of it converging on another truth. Then what? - Most importantly, why bother attempting to define what you mean by the truth at all? If you had such a definition, what would you do with it? What good would it be? *-- Russ Abbott* *_* *** Professor, Computer Science* * California State University, Los Angeles* * Google voice: 747-*999-5105 Google+: https://plus.google.com/114865618166480775623/ * vita: *http://sites.google.com/site/russabbott/ *_* On Thu, Mar 29, 2012 at 5:17 PM, Nicholas Thompson nickthomp...@earthlink.net wrote: 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
Re: [FRIAM] Clarifying Induction Threads
Owen, Eric is basically correct, although I think he may have misread the order of things (which is easy to do given that one HAS to read threads backwards. My caving in and just stating my position came very late in the game and was a response in part to all the confusion created by my laconic (and perhaps devious) attempts to draw Doug out. So far as I have read,all the responses to my statement have been thoughtful and sensible and not confused at all. … Oh OWEN IS there a software that will turn a thread into a manageable text for editing. I need that so bad.If I had such, I would have made you all my collaborators by now and we should have published hundreds of articles. Generated thousands of offspring from what has become, for want of a way of collecting it, spilled seed. We would be rich and famous. Nick From: friam-boun...@redfish.com [mailto:friam-boun...@redfish.com] On Behalf Of ERIC P. CHARLES Sent: Tuesday, March 27, 2012 10:50 PM To: Owen Densmore Cc: The Friday Morning Applied Complexity Coffee Group Subject: [FRIAM] Clarifying Induction Threads Owen, As I understand it: Doug announced his ordination. After a bit of banter, Doug made some generalizations about religious and non-religious people based on his past experience but... the ability to draw conclusions from past experience is a bit philosophically mysterious. The seeming contradiction between Doug's disavowal of faith and his drawing of conclusion based on induction set off Nick. Nick attempted to draw Doug into an open admittance that he accepted the truth of induction as an act of faith. But Nick never quite got what he was looking for, and this lead to several somewhat confused sub-threads. Eventually Nick just laid the problem out himself. However, this also confused people because, 1) the term 'induction' is used in many different contexts (e.g., to induce an electric current through a wire), and 2) there is lots of past evidence supporting the effectiveness of induction. The big, big, big problem of induction, however, is that point 2 has no clear role in the discussion: If the problem of induction is accepted, then no amount of past success provides any evidence that induction will continue to work into the future. That is, just as the fact that I have opened my eyes every day for the past many years is no guarantee that I will open my eyes tomorrow, the fact that scientists have used induction successfully the past many centuries is no guarantee that induction will continue to work in the next century. These threads have now devolved into a few discussions centered around accidentally or intentionally clever statements made in the course conversation, as well as a discussion in which people can't understand why we wouldn't simply accept induction based on its past success. The latter are of the form Doesn't the fact that induction is a common method in such-and-such field of inquiry prove its worth? Hope that helps, Eric On Tue, Mar 27, 2012 10:05 PM, Owen Densmore o...@backspaces.net wrote: Could anyone summarize the recent several thread that originated with this one? I'm sorry to have to ask, but we seem to have exploded upon an interesting stunt, but with the multiple threads (I Am The Thread Fascist) and the various twists and turns, I'd sorta like to know what's up! -- Owen 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 Eric Charles Professional Student and Assistant Professor of Psychology Penn State University Altoona, PA 16601 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
Re: [FRIAM] Clarifying Induction Threads
Wow, Eric, thanks! Lovely gift this beautiful morning. And Nick, AFAIK, there is no such ThreadMagic software. But lets have a coffee over it. And in terms of the body and blood of Christ, that takes a bit and too can be done over coffee. But it basically has to do with The Wisdom of Metaphor and its place in both evolution of theology and religious belief. All: Did no one discuss the mathematics of induction .. the inductive proof? Certainly that is accepted by us all, even tho anyone can make a sequence of a set of N numbers, who's generator can provide any number for its N+1th number. It is in the fact that the induction works by proving the N=1 case, assuming the Nth and proving the N+1th from that. -- Owen On Wed, Mar 28, 2012 at 12:51 AM, Nicholas Thompson nickthomp...@earthlink.net wrote: Ok. So now it’s probably time for me to admit that as Faith goes, belief in induction is pretty weak tea. ** ** Certainly doesn’t compare with the belief that ritual can change wine in to blood. ** ** Now, I think it’s easy to show that even catholics don’t believe it, using the pragmatic maxim that any thought is not a belief unless it can be shown to guide behavior. ** ** Let us say that christ’s body is exhumed and that its perfectly preserved. The priest comes to you with a cup and a plate and says “thisis the blood and body. Etc.” I think your response, catholic or not, would be OH YUCH! ** ** The logic goes ** ** Catholics will consume what they think is the blood and body of Christ This is the blood and body of Christ This catholic did not consume it. ** ** TILT! ** ** My apologies to any catholics on the list . this is one of the examples in Peirce’s work and it is much on my mind at the moment. I hope I have represented the facts of the ritiual more or less correctly and not been …. Um …too flippant or clever. I am pretty tired and it is pretty late. ** ** Nick ** ** *From:* friam-boun...@redfish.com [mailto:friam-boun...@redfish.com] *On Behalf Of *Russ Abbott *Sent:* Tuesday, March 27, 2012 11:03 PM *To:* The Friday Morning Applied Complexity Coffee Group *Cc:* Owen Densmore *Subject:* Re: [FRIAM] Clarifying Induction Threads ** ** The inductive argument for induction [paraphrased from Eric]: The fact that induction has been so successful in the past should convince of its usefulness in the future. *-- Russ Abbott* *_* * Professor, Computer Science* * California State University, Los Angeles* * Google voice: 747-999-5105* Google+: https://plus.google.com/114865618166480775623/ * vita: **http://sites.google.com/site/russabbott/*http://sites.google.com/site/russabbott/ *_* On Tue, Mar 27, 2012 at 9:49 PM, ERIC P. CHARLES e...@psu.edu wrote: Owen, As I understand it: Doug announced his ordination. After a bit of banter, Doug made some generalizations about religious and non-religious people based on his past experience but... the ability to draw conclusions from past experience is a bit philosophically mysterious. The seeming contradiction between Doug's disavowal of faith and his drawing of conclusion based on induction set off Nick. Nick attempted to draw Doug into an open admittance that he accepted the truth of induction as an act of faith. But Nick never quite got what he was looking for, and this lead to several somewhat confused sub-threads. Eventually Nick just laid the problem out himself. However, this also confused people because, 1) the term 'induction' is used in many different contexts (e.g., to induce an electric current through a wire), and 2) there is lots of past evidence supporting the effectiveness of induction. The big, big, big problem of induction, however, is that point 2 has no clear role in the discussion: If the problem of induction is accepted, then no amount of past success provides any evidence that induction will continue to work into the future. That is, just as the fact that I have opened my eyes every day for the past many years is no guarantee that I will open my eyes tomorrow, the fact that scientists have used induction successfully the past many centuries is no guarantee that induction will continue to work in the next century. These threads have now devolved into a few discussions centered around accidentally or intentionally clever statements made in the course conversation, as well as a discussion in which people can't understand why we wouldn't simply accept induction based on its past success. The latter are of the form Doesn't the fact that induction is a common method in such-and-such field of inquiry prove its worth? Hope that helps, Eric On Tue, Mar 27, 2012 10:05 PM, *Owen Densmore o...@backspaces.net*wrote: Could
Re: [FRIAM] Clarifying Induction Threads
Owen Densmore wrote at 03/28/2012 08:20 AM: All: Did no one discuss the mathematics of induction .. the inductive proof? Certainly that is accepted by us all, even tho anyone can make a sequence of a set of N numbers, who's generator can provide any number for its N+1th number. It is in the fact that the induction works by proving the N=1 case, assuming the Nth and proving the N+1th from that. Yep. Doug listed it as one of the types. Personally, I don't regard it as categorically exceptional. It's defining a a predicate and then establishing whether or not new instances belong to the set or not. I suppose I think there are 3 categories: 1) predicative (well-founded), 2) impredicative (non-well-founded), and 3) psychological induction (what most of this conversation is about). -- glen e. p. ropella, 971-222-9095, http://tempusdictum.com 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
Re: [FRIAM] Clarifying Induction Threads
Nicholas Thompson wrote at 03/28/2012 09:38 AM: I don't think we've been talking about psychological induction, here but logical induction. And I think mathematical induction is actually a species of Deduction. I am in a rush now, but I am putting in this marker in the hope that others will help out. I disagree. I think we've ranged over all sorts of meanings for the word induction ... because we're speaking English. ;-) I tried to make my perspective clear when I challenged the law of the excluded middle ... or by extension this false assumption of _crisp_ sets that underlies your example of grass being green. (RussA gives the same criticism from a different angle.) It's just a plainly flawed argument because the set we refer to as grass is not crisp. There are plants that are a little bit like grass and a little bit not like grass. And just because grass is dead doesn't mean it's no longer grass. And I know a few people whose _hair_ looks like grass! Etc. The same is true of the set we refer to as green things. Ideological arguments like that fail miserably when we disambiguate and wander into math and logic. Anyway, compare and contrast that sort of rhetoric with a predicative definition of a set (like that of the Natural Numbers). That set is crisp. We are still talking about sets and set membership. And we're still talking about the ability to define a set based on previous (predecessor) observations and then establish the membership of a newly constructed object. That's why mathematical induction is a form of induction. Reasoning methods are not entirely disjoint. Any non-trivial act of reasoning requires all 3 forms. Hence, it's reasonable and pragmatic to think that induction and deduction aren't crisp sets either. -- glen e. p. ropella, 971-222-9095, http://tempusdictum.com 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
Re: [FRIAM] Clarifying Induction Threads
That's an awesome essay! Thanks. Of course, I never say anything unless I have something to disagree with... So, I have 2 points to argue about: 1) Your finiteness is illusory because you assume crisp sets, and 2) The problem of induction is about the origins of a conjecture, not merely about the evaluation of candidate set members. I've beaten (1) quite to death. So, I'll just try to lay out (2). Alternatives for the origins of conjecture abound. Not all conjecture is based on previous experience. Or, at least, we can conjecture that not all conjecture is based on previous experience, if we believe in illusion, hallucination, and that ideas are more plastic than things. I don't intend to dicker about the meanings of words like based. But there is a difference between, say, a griffin and a unicorn. The griffin is more fantastic than the unicorn. It's pretty easy for me to imagine all horses are unicorns who have lost their horns. But it would be difficult to think that lions are griffins with mutated heads and no wings. Conjecture can come from _anywhere_ ... from dreams, fevers, and sci-fi novels. They need not be based on previous experiences in the (rigorous?) way we tend to think of them being based on previous experiences. In that sense, the finite nature of our past experiences is fuzzified ... not so finite after all. I can read Heinlein or Vern and form a conjecture based on a fuzzy mix of those experiences. From this alphabet of ideas, I can generate an infinite (or at least indefinite) number of words and sentences. This seems to provide plenty of origins for alternative conjecture beyond induction. Eric Smith wrote at 03/28/2012 12:02 PM: I agree, Wow, to Eric Charles's summary. Can I ask, is there any role for finiteness in this discussion? There seem to me to be two places the constraints of being finite enter, and the specific point at which they seem forced by one of the questions that has been asked (Why would you accept the inductive hypothesis, except on faith?) is to offer the alternative answer (Because I am incapable of doing otherwise). The latter answer seems more operational than invoking the word faith, which for all I know may not mean anything more than I am incapable of doing otherwise because I am finite, or the circularity that the inductive hypothesis is the only premise from which to defend its own use. Here is one argument for finiteness, which I have pestered Nick with in conversations long ago. Suppose I am an input-output machine with a finite number of outputs (and for that matter, of internal states). (I intend here to be in the general domain of Ross Ashby's notions of requisite variation, but let me not get off on that.) If a philosopher objects that I have no _right_ to be finite, and that, like Paris Hilton, I must from now on, promise to pay complete attention to everything, then don't consider me, consider a single type of cell-surface receptor on any of my cells. Surely, for practical purposes, we want to model it as having a finite repertoire of behaviors, whether it has a right to or not. It's only a protein. But a finite thing, in an indefinitely variable world, must then produce at least one of its outputs as the response to an indefinite set of distinct circumstances. (Here, I would be happy to say infinite, but I mean indefinite as that which might grow toward infinity if we could keep accumulating cases.) In practice, of course, for most cases I could think of, _each_ of the output states occurs as a response to indefinitely many distinct circumstances. Thus, my input-output box partitions an indefinite environment into equivalence classes, at least one, and probably many of them, of indefinitely large size. It cannot do otherwise, being finite. But my cell-surface receptor has been (naturally-)selected from a finite history of events. Again, a practical man, being honest about noise and the erasure of memory, about costs, etc., would say that it has probably been selected by a rather short recent history from a rather narrow set of cases. Thus, the response it will generate, for an indefinite range of circumstances, has been chosen from a finite set of selection criteria. It appears that survival-under-selection of finite objects, then, is perforce a commitment to one form of induction. The generation, by the device for however long it survives, of a potentially-indefinitely-large set of input-output pairs is being conditioned on a finite set of input-output pairs. Of course, natural selection is just Bayes's theorem for model selection, with the fitness being the log-likelihood, and selection on spaces with a finite number of types is then Bayesian induction on probability distributions over a finite number of tokens. I think (?) we believe in statistics that Bayesian updating is the best general-purpose method we can formalize (Cosma Shalizi, sometimes
Re: [FRIAM] Clarifying Induction Threads
All - Probably too much to respond to, but for no particularly good reason, a few comments . . . 1.) Whenever I teach about logic / scientific-method, one thing I make sure to do is remind students that deduction is not a truth *producing* system, but is at best a truth *preserving* system. In order to claim that your particular deductive system deals with true statements, you have to inject the truth from outside the system . . . One typical approach is to play the axiomatics game -- but one should be careful to remember that in (good :-) formal mathematics, an axiom is a statement accepted without proof (i.e., the proof of an axiom within the system is one line -- the statement of the axiom). In particular, it is important to very clearly distinguish between I will (for the time being) be using this axiom and I believe this axiom to be *true* . . . A related approach is to play the induction game: I have observed these regularities in the world, so I will inject into my deductive system a new axiom which, to whatever extent makes sense and is feasible, encapsulates the regularity I have observed. I can then wander around in a hypothetical-deductive cycle arena, and see, for example, what other regularities I might expect to see, etc. My habit is to leave the concept truth out of the picture. My experience has been that introducing Platonic Ideals like Truth into the process (almost) inevitably leads to any number of frustrating blind alleys . . . more generally, I'm not a fan of Platonic Ideal-ism. My first direct experience with Platonic Ideals was through the Baltimore Catechism (if you're not familiar, go ahead and Google it . . . :-), and specifically the Ideal God . . . And, perhaps hence, the idea that belief consists of the acceptance of (or commitment to?) some particular Platonic Ideal. 2.) Which leads (back) to the question Do you believe in (the validity of) induction? . . . when I read that question, I went to the word believe, rather than induction . . . Asked whether he believed in full immersion baptism, the apocryphal farmer apparently responded, Believe in it? Hell, I've *seen* it!!! So, do I believe that induction is useful? Hell yes, I use it all the time. Do I believe that induction leads to 'truth' (or 'Truth')? -- see above about truth !!! . . . for me, an at best irrelevant question, but, more likely, more or less meaningless . . . 3.) And then a hint at a digression on some things like law of the excluded middle and finiteness . . . a little personal history . . . long ago (1975) I took my first graduate math course in Logic. The professor was David Nelson (at GWU, who was Kleene's first Ph.D. student). Dr. Nelson identified himself as a negationless intuitionist (or sometimes, a negationless constructivist). He only believed in positive constructive proofs. The logical system he worked in didn't have a negation operator. He didn't believe in the law of excluded middle, or proof by contradiction, or anything like that. He didn't believe in (completed) infinities. But, on the other hand, he taught us traditional mathematical logic, because he knew that we were going to be expected to know all the standard stuff. I'll leave it as an exercise to link this up with some of the discussion -- perhaps most specifically with respect to finiteness, and assumptions one might make about where and when the chimera ( :-) ???) of infinity might enter the discussion . . . But I'll also claim that the effects on me of this (early . . .) exposure to significantly alternative logics weren't *all* harmful . . . :-) . . . David used to say -- mathematics is all tautological, or all subjunctive (or both) . . . Possibly related note: it turns out that characterizing finiteness, or countability, is not possible in first-order logic -- one needs to enter the somewhat counter-intuitive realm of second-order logic . . . wherein things can get very sticky . . . 4.) When you believe in things that you don't understand, then you suffer . . . (S. Wonder) Thanks . . . tom On Mar 28, 2012, at 12:02 PM, Eric Smith wrote: I agree, Wow, to Eric Charles's summary. Can I ask, is there any role for finiteness in this discussion? There seem to me to be two places the constraints of being finite enter, and the specific point at which they seem forced by one of the questions that has been asked (Why would you accept the inductive hypothesis, except on faith?) is to offer the alternative answer (Because I am incapable of doing otherwise). The latter answer seems more operational than invoking the word faith, which for all I know may not mean anything more than I am incapable of doing otherwise because I am finite, or the circularity that the inductive hypothesis is the only premise from which to defend its own use. Here is one argument for finiteness, which I have
[FRIAM] Clarifying Induction Threads
Owen, As I understand it: Doug announced his ordination. After a bit of banter, Doug made some generalizations about religious and non-religious people based on his past experience but... the ability to draw conclusions from past experience is a bit philosophically mysterious. The seeming contradiction between Doug's disavowal of faith and his drawing of conclusion based on induction set off Nick. Nick attempted to draw Doug into an open admittance that he accepted the truth of induction as an act of faith. But Nick never quite got what he was looking for, and this lead to several somewhat confused sub-threads. Eventually Nick just laid the problem out himself. However, this also confused people because, 1) the term 'induction' is used in many different contexts (e.g., to induce an electric current through a wire), and 2) there is lots of past evidence supporting the effectiveness of induction. The big, big, big problem of induction, however, is that point 2 has no clear role in the discussion: If the problem of induction is accepted, then no amount of past success provides any evidence that induction will continue to work into the future. That is, just as the fact that I have opened my eyes every day for the past many years is no guarantee that I will open my eyes tomorrow, the fact that scientists have used induction successfully the past many centuries is no guarantee that induction will continue to work in the next century. These threads have now devolved into a few discussions centered around accidentally or intentionally clever statements made in the course conversation, as well as a discussion in which people can't understand why we wouldn't simply accept induction based on its past success. The latter are of the form Doesn't the fact that induction is a common method in such-and-such field of inquiry prove its worth? Hope that helps, Eric On Tue, Mar 27, 2012 10:05 PM, Owen Densmore o...@backspaces.net wrote: Could anyone summarize the recent several thread that originated with this one? I'm sorry to have to ask, but we seem to have exploded upon an interesting stunt, but with the multiple threads (I Am The Thread Fascist) and the various twists and turns, I'd sorta like to know what's up! -- Owen 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 Eric Charles Professional Student and Assistant Professor of Psychology Penn State University Altoona, PA 16601 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
Re: [FRIAM] Clarifying Induction Threads
The inductive argument for induction [paraphrased from Eric]: The fact that induction has been so successful in the past should convince of its usefulness in the future. *-- Russ Abbott* *_* *** Professor, Computer Science* * California State University, Los Angeles* * Google voice: 747-*999-5105 Google+: https://plus.google.com/114865618166480775623/ * vita: *http://sites.google.com/site/russabbott/ *_* On Tue, Mar 27, 2012 at 9:49 PM, ERIC P. CHARLES e...@psu.edu wrote: Owen, As I understand it: Doug announced his ordination. After a bit of banter, Doug made some generalizations about religious and non-religious people based on his past experience but... the ability to draw conclusions from past experience is a bit philosophically mysterious. The seeming contradiction between Doug's disavowal of faith and his drawing of conclusion based on induction set off Nick. Nick attempted to draw Doug into an open admittance that he accepted the truth of induction as an act of faith. But Nick never quite got what he was looking for, and this lead to several somewhat confused sub-threads. Eventually Nick just laid the problem out himself. However, this also confused people because, 1) the term 'induction' is used in many different contexts (e.g., to induce an electric current through a wire), and 2) there is lots of past evidence supporting the effectiveness of induction. The big, big, big problem of induction, however, is that point 2 has no clear role in the discussion: If the problem of induction is accepted, then no amount of past success provides any evidence that induction will continue to work into the future. That is, just as the fact that I have opened my eyes every day for the past many years is no guarantee that I will open my eyes tomorrow, the fact that scientists have used induction successfully the past many centuries is no guarantee that induction will continue to work in the next century. These threads have now devolved into a few discussions centered around accidentally or intentionally clever statements made in the course conversation, as well as a discussion in which people can't understand why we wouldn't simply accept induction based on its past success. The latter are of the form Doesn't the fact that induction is a common method in such-and-such field of inquiry prove its worth? Hope that helps, Eric On Tue, Mar 27, 2012 10:05 PM, *Owen Densmore o...@backspaces.net*wrote: Could anyone summarize the recent several thread that originated with this one? I'm sorry to have to ask, but we seem to have exploded upon an interesting stunt, but with the multiple threads (I Am The Thread Fascist) and the various twists and turns, I'd sorta like to know what's up! -- Owen 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 Eric Charles Professional Student and Assistant Professor of Psychology Penn State University Altoona, PA 16601 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
