From bronze!sol.ctr.columbia.edu!caen!nic.umass.edu!dime!orourke Mon Mar 16 21:21:25 EST 1992 Article: 5367 of comp.ai.philosophy Xref: bronze comp.ai.philosophy:5367 sci.philosophy.tech:7347 Path: bronze!sol.ctr.columbia.edu!caen!nic.umass.edu!dime!orourke From: orourke@sophia.smith.edu (Joseph O'Rourke) Newsgroups: comp.ai.philosophy,sci.philosophy.tech Subject: A rock implements every FSA Keywords: Putnam, implementation Date: 14 Mar 92 03:05:10 GMT Sender: news@dime.cs.umass.edu Followup-To: comp.ai.philosophy Organization: Smith College, Northampton, MA, US Status: RO A while back there was some discussion of Putnam's proof that, roughly, a rock implements every Finite State Automaton (FSA). I was unfamiliar with (and skeptical of) this theorem, so I studied it a bit. As a public service (some might say disservice!), I herewith offer a synopsis of the argument. [Hilary Putnam, "Representation and Reality" (1988), Appendix, 121-5] Let S represent the state of a physical system (the rock). Assumption 1 (Continuity): S is a continuous function S(t) of time t. Assumption 2 (Noncyclical): For t1 != t2, S(t1) != S(t2) [where "!=" means "not equal"]. Thus if S were representable as a single variable, it would be a strictly monotonic function with respect to time, something like this: S ^ | + | + | + | + | + | + | + | + | + | + | + +---------------------------------> t Let the FSA go through states A,B,A,A,B in that order. Lay out those states along the t-axis. By the assumptions, the physical states are partitioned as shown below: S ^ 5 | + 4-| + 3-| + -| + 2 | + | + -| + 1 | + -| + 0 | + | + | | | | | +---------------------------------> t A B A A B Simply define "state A" of the rock to be the union of the physical states s1+s3+s4 corresponding to the times when the FSA is in state A, and define physical "state B" to be s2+s5. Then it is immediate that rock is in "state A" precisely when the FSA is in its state A, and similarly for state B. Moreover, Putnam argues that physical "state B" is *caused by* physical "state A," in the sense that the information that the system is in "state A" at a certain time determines that it must be in "state B" at the next time. That's it. You can see that the mathematical content of his "theorem" is nearly trivial. All the subtlety and complexity resides in the I/O to and from the math: whether his assumptions which form the input to the mathematics are justified, and whether his interpretation of the output of the mathematics is sound. :-j From bronze!sol.ctr.columbia.edu!caen!nic.umass.edu!dime!orourke Mon Mar 16 21:21:58 EST 1992 Article: 5343 of comp.ai.philosophy Xref: bronze comp.ai.philosophy:5343 sci.philosophy.tech:7332 Path: bronze!sol.ctr.columbia.edu!caen!nic.umass.edu!dime!orourke From: orourke@sophia.smith.edu (Joseph O'Rourke) Newsgroups: comp.ai.philosophy,sci.philosophy.tech Subject: Functionalism ==> behavioralism Keywords: functionalism, behaviorism, Putnam Date: 12 Mar 92 04:36:30 GMT Sender: news@dime.cs.umass.edu Followup-To: comp.ai.philosophy Organization: Smith College, Northampton, MA, US Status: RO Many discussants in these newsgroups claim to be functionalists about mind, but few admit to being behavorists (although their arguments often indicate otherwise). The functionalists who reject behaviorism might be interested to know that Hilary Putnam claims to establish in "Representation and Reality" that functionalism implies behaviorism. The last sentence of his book is: If it is true that to possess given mental states is simply to possess a certain "functional organization" [functionalism], then it is also true that to possess given mental states is simply to possess certain behavior dispositions [behaviorism]! His argument is based on his "a rock implements any FSA" proof in the Appendix. From bronze!chalmers Mon Mar 16 21:23:23 EST 1992 Article: 5411 of comp.ai.philosophy Newsgroups: comp.ai.philosophy Path: bronze!chalmers From: chalmers@bronze.ucs.indiana.edu (David Chalmers) Subject: Re: A rock implements every FSA Organization: Indiana University References: <44855@dime.cs.umass.edu> Date: Tue, 17 Mar 92 01:45:00 GMT Status: RO In article <44855@dime.cs.umass.edu> orourke@sophia.smith.edu (Joseph O'Rourke) writes: > That's it. You can see that the mathematical content of >his "theorem" is nearly trivial. All the subtlety and complexity >resides in the I/O to and from the math: whether his assumptions >which form the input to the mathematics are justified, and whether >his interpretation of the output of the mathematics is sound. Well, if we're doomed to endure Nietzsche's eternal recurrence on this newsgroup, at least Putnam's rocks haven't cycled around as many times as the Chinese room. The mathematics is indeed trivial; its main point is to establish that an object will be in different states at different times. But as I said last time the subject comes up, to implement an FSA it is not sufficient that an object go through a particular sequence of states (e.g. "ABABAB...") compatible with that FSA. It must also satisfy all the counterfactual conditionals corresponding to the transitions in the FSA's state table. >From my last posting on this subject, which didn't meet with any serious argument (I'd hate to see it become folk wisdom that a rock implements any FSA, just through the claim being repeated enough times): ---- My problems with Putnam's "proof" are roughly 1. He sets it up so that the rock does indeed go through some actual sequence of states ABABAB... during a given time interval. But an FSA must also satisfy counterfactuals e.g. of the form "if it had been in state C, then it would have transited into state D". Given that the physical states corresponding to most states C (i.e., all those that aren't in the actual desired sequence between 12:00 and 12:07) aren't even defined, this would seem to be a problem. and, perhaps more seriously, 2. An FSA certainly must satisfy counterfactuals of the form "if in state S, input I had come in, then it would have transited to state T", for all counterfactual inputs I. Putnam makes some tentative gestures in the direction of handling a certain pattern of actual inputs, but says nothing at all about handling counterfactual inputs. As far as I can tell, the required counterfactual sensitivity is entirely lacking. ---- Elsewhere (the "functionalism implies behaviorism article) Joseph O'Rourke writes: >Many discussants in these newsgroups claim to be functionalists >about mind, but few admit to being behavorists (although their >arguments often indicate otherwise). The functionalists who reject >behaviorism might be interested to know that Hilary Putnam claims to >establish in "Representation and Reality" that functionalism >implies behaviorism. There's no reason to be impressed by this either, as it's entirely derivative on the rock/FSA "theorem". -- Dave Chalmers (dave@cogsci.indiana.edu) Center for Research on Concepts and Cognition, Indiana University. "It is not the least charm of a theory that it is refutable." From bronze!news.cs.indiana.edu!mips!zaphod.mps.ohio-state.edu!caen!nic.umass.edu!dime!orourke Tue Mar 17 17:42:06 EST 1992 Article: 5431 of comp.ai.philosophy Path: bronze!news.cs.indiana.edu!mips!zaphod.mps.ohio-state.edu!caen!nic.umass.edu!dime!orourke From: orourke@unix1.cs.umass.edu (Joseph O'Rourke) Newsgroups: comp.ai.philosophy Subject: Re: A rock implements every FSA Date: 17 Mar 92 21:40:02 GMT References: <44855@dime.cs.umass.edu> <1992Mar17.014500.8635@bronze.ucs.indiana.edu> Sender: news@dime.cs.umass.edu Organization: Smith College, Northampton, MA, US Status: RO In article <1992Mar17.014500.8635@bronze.ucs.indiana.edu> chalmers@bronze.ucs.indiana.edu (David Chalmers) writes: >[...](I'd hate to see it become folk wisdom that a rock >implements any FSA, just through the claim being repeated enough >times): It is not completely clear to me what Putnam himself thinks of his "theorem." (It is odd, isn't it, that he calls it a "theorem"? I feel this is a weakening of the force of the word "theorem.") In "Representation and Reality," he treats it more like "a rock 'implements' any FSA," with emphasis on the scare quotes around 'implements.' He uses it mainly as a tool in his argument against functionalism. >My problems with Putnam's "proof" are roughly > >1. He sets it up so that the rock does indeed go through some actual >sequence of states ABABAB... during a given time interval. But an >FSA must also satisfy counterfactuals [...] > >2. An FSA certainly must satisfy counterfactuals of the form "if >in state S, input I had come in, then it would have transited to >state T", for all counterfactual inputs I. [...] As far as I can tell, >the required counterfactual sensitivity is entirely lacking. Putnam is well aware of the counterfactuals objection, and devotes pages 96-105 of his book to refuting it. But the refutation is curious. He focuses exclusively on David Lewis's theory, which is perhaps not inappropriate since (a) Lewis wrote a paper in direct response to Putnam (a paper which I have not read), and (b) Lewis is Mr. Counterfactual if anyone is. Putnam characterizes Lewis's theory of causality as having two main points (p. 96): (1) Counterfactuals: if "A caused B," then "if A had not been the case, then B would not have occurred." (2) The states cannot be arbitrary disjunctions (as in Putnam's "proof"), but rather must satisfy some criteria of "naturalness." Putnam then argues that Lewis's theory does not hold up in various (to me) nebulous ways. But I think the upshot is that, if you (David Chalmers) want to reject Putnam's rock-theorem, then you have to be prepared to offer a theory of causality more robust than Lewis's possible worlds theory; or you have to find reason to reject his rebuttal of Lewis. To just say "counterfactual sensitivity is lacking" is not enough: Putnam well knows this. Of course, what I mean by "you have to" is: if you were to try to publish your theory in a reputable journal of philosophy. And this may not be your goal at all. From bronze!chalmers Tue Mar 17 18:03:03 EST 1992 Article: 5433 of comp.ai.philosophy Newsgroups: comp.ai.philosophy Path: bronze!chalmers From: chalmers@bronze.ucs.indiana.edu (David Chalmers) Subject: Re: A rock implements every FSA Organization: Indiana University References: <44855@dime.cs.umass.edu> <1992Mar17.014500.8635@bronze.ucs.indiana.edu> <44993@dime.cs.umass.edu> Date: Tue, 17 Mar 92 22:41:56 GMT Status: RO In article <44993@dime.cs.umass.edu> orourke@sophia.smith.edu (Joseph O'Rourke) writes: >Putnam is well aware of the counterfactuals objection, and devotes pages >96-105 of his book to refuting it. But the refutation is curious. He >focuses exclusively on David Lewis's theory, which is perhaps not >inappropriate since (a) Lewis wrote a paper in direct response to >Putnam (a paper which I have not read), and (b) Lewis is Mr. Counterfactual >if anyone is. All this is irrelevant to my point. On those pages, Putnam is concerned with the question of the satisfaction of counterfactuals like "if A had not happened, B would not have happened", and points out that the truth-conditions for statements like these are problematic. I'm concerned with the much more straightforward matter of making sure that the implementation actually satisfies all the transition relations in the state-table; e.g. such that if it is in state C, it will transit to state D, and so on. There's nothing problematic about *these* counterfactuals, as C and D should have well-defined sets of maximal states corresponding to them (if they were defined at all, which they're not). i.e. I'm not concerned, as Lewis is, with using counterfactuals to make sure that certain conditions are met in backing the "A causes B" statement. I'm happy to accept Putnam's construal of causation here as "B always follows A", but I'm concerned with making sure that *all* the causal statements are satisfied, not just those that actually come up in a given sequence, like "if A then B", but all the others specified by the machine table, like "if C then D". So Lewis' and my objections have little to do with each other, and Putnam's response to Lewis is irrelevant here. Incidentally Lewis's published response to Putnam ("Putnam's Paradox", in Australasian Journal of Philosophy circa 1984), was not on this topic at all, but rather on Putnam's argument about reference and realism. -- Dave Chalmers (dave@cogsci.indiana.edu) Center for Research on Concepts and Cognition, Indiana University. "It is not the least charm of a theory that it is refutable." From bronze!sol.ctr.columbia.edu!caen!nic.umass.edu!dime!orourke Tue Mar 17 20:14:06 EST 1992 Article: 5442 of comp.ai.philosophy Path: bronze!sol.ctr.columbia.edu!caen!nic.umass.edu!dime!orourke From: orourke@unix1.cs.umass.edu (Joseph O'Rourke) Newsgroups: comp.ai.philosophy Subject: Re: A rock implements every FSA Date: 18 Mar 92 00:19:47 GMT References: <44855@dime.cs.umass.edu> <1992Mar17.014500.8635@bronze.ucs.indiana.edu> <44993@dime.cs.umass.edu> <1992Mar17.224156.9177@bronze.ucs.indiana.edu> Sender: news@dime.cs.umass.edu Organization: Smith College, Northampton, MA, US Status: RO In article <1992Mar17.224156.9177@bronze.ucs.indiana.edu> chalmers@bronze.ucs.indiana.edu (David Chalmers) writes: >In article <44993@dime.cs.umass.edu> orourke@sophia.smith.edu (Joseph O'Rourke) writes: > >>Putnam is well aware of the counterfactuals objection, and devotes pages >>96-105 of his book to refuting it. [...] > >All this is irrelevant to my point. On those pages, Putnam is concerned >with the question of the satisfaction of counterfactuals like "if >A had not happened, B would not have happened", and points out >that the truth-conditions for statements like these are problematic. >I'm concerned with the much more straightforward matter of making >sure that the implementation actually satisfies all the transition >relations in the state-table; e.g. such that if it is in state C, >it will transit to state D, and so on. [...] Ah, I see! That is an excellent point! He does seem to show only that a particular *trace* of the running of an FSA can be 'implemented' by a rock, not that the FSA itself, with all its inherent possibilities, can be implemented. Your point seems to me to be devastating. From bronze!news.cs.indiana.edu!att!linac!uwm.edu!caen!nic.umass.edu!dime!orourke Wed Mar 18 12:37:16 EST 1992 Article: 5468 of comp.ai.philosophy Xref: bronze comp.ai.philosophy:5468 sci.philosophy.tech:7386 Path: bronze!news.cs.indiana.edu!att!linac!uwm.edu!caen!nic.umass.edu!dime!orourke From: orourke@unix1.cs.umass.edu (Joseph O'Rourke) Newsgroups: comp.ai.philosophy,sci.philosophy.tech Subject: Re: A rock implements every FSA Keywords: Putnam's rock theorem Date: 18 Mar 92 12:25:08 GMT References: <44855@dime.cs.umass.edu> <1992Mar17.014500.8635@bronze.ucs.indiana.edu> <44993@dime.cs.umass.edu> <1992Mar17.222238.9969@husc3.harvard.edu> Sender: news@dime.cs.umass.edu Followup-To: comp.ai.philosophy Organization: Smith College, Northampton, MA, US Status: RO In article <1992Mar17.222238.9969@husc3.harvard.edu> zeleny@zariski.harvard.edu (Mikhail Zeleny) writes: [in response to David Chalmers' critique of Putnam's rock theorem]: >I've said it once, I've said it a thousand times: whatever the laws that >guarantee the state-transitions of a FSA, the same laws guarantee the >state-transitions of a rock. Since physical necessity is the same, so is >the counterfactual force. I don't see how this blunts the force of David Chalmers' point, a point which I misunderstood the first time around. I think perhaps David should not phrase his objection in terms of "counterfactuals," as that term carries quite another connotation in the context of Putnam's book. His point is that the rock 'implements' a particular trace of the FSA, a sequence of "table calls" as Putnam says. Although Putnam does not make this clear in his proof, he is arranging for the rock to mirror a particluar sequence of state transitions that the FSA might go through during some "run." He can do this because he initially assumes that the FSA has no inputs and no outputs. So it only has only one possible trace when it is run. He modifies this assumption after the proof, by saying that I/O can be handled by imagining an FSA that, roughly, hallucinates its input, and behaves as the original would if it were to receive such and such an input. But now the rock states are fixed to a particular hallucinated input. It is stretching the notion of "implementation" beyond anything reasonable to say that this rock implements the FSA: rather it mirrors the trace of the FSA on a particular input. By now I've put a lot of words in David Chalmer's mouth. If this is not his objection, then consider it my objection. From bronze!news.cs.indiana.edu!mips!zaphod.mps.ohio-state.edu!rpi!news-server.csri.toronto.edu!neat.cs.toronto.edu!cbo Wed Mar 18 19:05:50 EST 1992 Article: 5500 of comp.ai.philosophy Xref: bronze sci.philosophy.tech:7404 comp.ai.philosophy:5500 Path: bronze!news.cs.indiana.edu!mips!zaphod.mps.ohio-state.edu!rpi!news-server.csri.toronto.edu!neat.cs.toronto.edu!cbo Newsgroups: sci.philosophy.tech,comp.ai.philosophy From: cbo@cs.toronto.edu (Calvin Bruce Ostrum) Subject: Re: A rock implements every FSA Organization: Department of Computer Science, University of Toronto References: <1992Mar17.224156.9177@bronze.ucs.indiana.edu> <1992Mar17.231452.9979@husc3.harvard.edu> <1992Mar18.045939.3084@bronze.ucs.indiana.edu> <1992Mar18.095140.9984@husc3.harvard.edu> Date: 18 Mar 92 23:27:58 GMT Status: O Joseph O'Rourke observes: jor| That's it. You can see that the mathematical content of jor| his "theorem" is nearly trivial. All the subtlety and complexity jor| resides in the I/O to and from the math: whether his assumptions jor| which form the input to the mathematics are justified, and whether jor| his interpretation of the output of the mathematics is sound. Indeed. Someone else in this thread has suggested that Putnam may be attempting to bamboozle us with a show of technical special effects. His muched touted "cats and cherries" proof is of the same nature. It reminds me of the proof of the existence of God with with Euler is said to have bamboozled Diderot. According to de Morgan, the proof went as follows, and effectively humiliated Diderot: "Monsieur, (a+b^n)/n = x, donc Dieu existe; re'pondez!". But unlike this proof, when the jargon is scraped off of Putnam's proof, something of interest remains to be considered. To date, I don't believe anyone has either defended Putnam's proof correctly; nor has anyone criticised it with complete effectivness. Dave Chalmers starts off with this consolation: dc| Well, if we're doomed to endure Nietzsche's eternal recurrence on dc| this newsgroup, at least Putnam's rocks haven't cycled around as many dc| times as the Chinese room. A detail, with respect to the Chinese room: to recur, a thing must first disappear... And expresses his wishes that dc|(I'd hate to see it become folk wisdom that a rock dc| implements any FSA, just through the claim being repeated enough dc| times): To that end, he gives us dc| My problems with Putnam's "proof" are roughly dc| dc| 1. He sets it up so that the rock does indeed go through some actual dc| sequence of states ABABAB... during a given time interval. But an dc| FSA must also satisfy counterfactuals e.g. of the form "if it had dc| been in state C, then it would have transited into state D". Given dc| that the physical states corresponding to most states C (i.e., all dc| those that aren't in the actual desired sequence between 12:00 and dc| 12:07) aren't even defined, this would seem to be a problem. One does not even have to go to states C and D, but can stick with states A and B. Consider the counterfactual that if the rock had been started in state B, as defined by Putnam, that it would then continue in the appropriate manner. This is false, since the integrity of the definition of its states may very well rely upon its particular situation (for what is outside the machine at a given time was constitutive of the definition of these states). So this seems to ruin Putnam's argument as it stands. But the essense of it remains. Although substantially weaker, we can still state this result: | Any sufficiently causally isolated rock with an internal clock | implements any FSA without input. This still seems unpleasant. And, mutatis mutandis, it will satisfy the counterfactuals formed using the state names that occur in its actual trace. Thus, we can say that it implements a particular subautomaton of the original automaton. Dave's point remains that this is not enough, and it is here that Mikhail Zeleny jumps in with an attempted rejoinder: mz| Nonsense. As I've demonstrated in the previous posting, Putnam considers mz| every possible state of the automaton, not just a particular trace thereof. Far from "the single trace objection" being nonsense, Mikhail finds it necessary to retreat upon being confronted with Putnam's actual text: mz| I call for charity: to me, Putnam's text is suggesting a sequence mz| exhaustive of all states that characterize the FSA. As can be expected, Mikhail uses a great deal of charity when the result is to his liking. I don't know what Putnam intended here, but if he did intend what Mikhail suggests he did, then his result does not apply to all FSA without inputs, as he claims. For there are numerous such FSA which do not have single execution sequences which actually enter every state. Choosing FSA's at random, in fact, one would have to say that most lack such sequences, I think. Mikhail has used charity toward Putnam in order to have him believing a falsehood! Let's try a different tack. Consider the C and D states mentioned by Dave. The problem is that these states aren't provided with a definition. We can provide them with a definition, however, by picking for each one of them some particular state of the rock which is not entered into during its actual trace. (This is not done by Putnam: here we are attempting to exercise charity in correcting/extending his result. cf. Ayn Rand, below). Now we are starting to see some actual constraints come out upon this multipurpose Rock. Not just any rock will do! First of all, its actual trace must not exhaust all of its states. There must be left an adequate number of physical rock states to represent the possible automaton states which are not realised in the trace. This doesn't seem like much of a restriction, but it does eliminate the example I usually use myself (where the rock's physical state at time N is simply the integer N). Further, the rock states representing C and D must be such that they are consistent with the states already defined. Suppse the FSA started in C leads to D,E,F, etc, but never to A. In such a case, we must be sure that the definitions for D,E,F do not ever actually overlap those for A. (Of course, if a rock started in C is supposed to lead to A, we must disjoin the new physical states it reaches in with the previous definition of A, but this is no real problem). This is an actual constraint upon the rocks which is nowhere mentioned by Putnam. A programming analogy here might result when someone placed some memory on the free list and then reallocated it, although the memory was still in use elsewhere. Yechh! It does seem likely that we should be able to choose physical states corresponding to C,D, etc, such that the argument will still go through, but it is not obvious how to prove this. Moreover, Putnam does not consider it at all. Nevertheless, I am willing to assume that it can be proven easily, for only a slightly less limited class of rocks (Can someone please do this for us?) This result still seems far too liberal (in Ned Block's terminology) for functionalists to remain comfortable with. For one, I am certainly not comfortable with this result. Fortunately, I believe there are other ways to block it. Pace most of the commentators to date, however, I don't think these are directly related to Putnam's treatment of inputs and outputs, which, modulo the above considerations, seems unproblematic. But I'll leave that for now, pleading in the words of Jerry Fodor from Psychosemantics: "Don't ask me about the inputs and outputs right now. I'm very busy". Well, perhaps substitute "lazy" for "busy". --------------------------------------------------------------------------- Calvin Ostrum cbo@cs.toronto.edu --------------------------------------------------------------------------- One further suggestion: if you undertake the task of philosophical detection, drop the dangerous little catch phrase which advise you to keep an "open mind". -- Ayn Rand --------------------------------------------------------------------------- From bronze!chalmers Wed Mar 18 19:08:20 EST 1992 Article: 5503 of comp.ai.philosophy Xref: bronze sci.philosophy.tech:7407 comp.ai.philosophy:5503 Newsgroups: sci.philosophy.tech,comp.ai.philosophy Path: bronze!chalmers From: chalmers@bronze.ucs.indiana.edu (David Chalmers) Subject: Re: A rock implements every FSA Organization: Indiana University References: <1992Mar18.045939.3084@bronze.ucs.indiana.edu> <1992Mar18.095140.9984@husc3.harvard.edu> <92Mar18.182726est.14357@neat.cs.toronto.edu> Date: Thu, 19 Mar 92 00:05:44 GMT Status: RO In article <92Mar18.182726est.14357@neat.cs.toronto.edu> cbo@cs.toronto.edu (Calvin Bruce Ostrum) writes: >It does seem likely that we should be able to choose physical states >corresponding to C,D, etc, such that the argument will still go through, >but it is not obvious how to prove this. Moreover, Putnam does not >consider it at all. Nevertheless, I am willing to assume that it can >be proven easily, for only a slightly less limited class of rocks (Can >someone please do this for us?) This result still seems far too liberal >(in Ned Block's terminology) for functionalists to remain comfortable >with. It's pretty straightforward to do this. We need only assume that the system has (a) an internal clock, and (b) an independent internal "dial", which can be set to one of an arbitrary number of settings, and which remains in that setting over time. So think of states of the system as ordered pairs (k,n), where k (the dial) stays fixed with time and n (the clock) varies with time. Then mapping an arbitrary FSA without input onto this system is easy. We can divide the states of such an FSA into a number of parallel "streams", by following its evolution from a given state. Of course streams may eventually converge, and may eventually go into loops. Each stream will have an initial state, which cannot be reached from any other state. Map each of these states to the physical state (k,1) for various values of k. Map the nth state in each stream to (k,n) for the appropriate k. If a given state appears in different streams (as will happen if streams converge), or numerous times within a stream (as will happen if the stream goes into a loop), then map the state to the appropriate disjunction. That's all we need to do. It's actually a very weak constraint on the system (I'm sure that most rocks satisfy it). The moral, I take it, is that inputless FSAs are an inherently trivial formalism. As an earlier poster said, FSAs have to be sensitive to inputs for the formalism to have any bite. (Of course, there are nontrivial FSAs that may *happen* not to receive any input, but that's a different matter, as long as they're potentially capable of dealing with it. There may seem to be a potential problem with blind-deaf-and-everything paralytics, but I think those can be handled by placing the input boundary correctly.) -- Dave Chalmers (dave@cogsci.indiana.edu) Center for Research on Concepts and Cognition, Indiana University. "It is not the least charm of a theory that it is refutable." From bronze!ux1.cso.uiuc.edu!uwm.edu!caen!nic.umass.edu!dime!orourke Wed Mar 18 19:37:22 EST 1992 Article: 5505 of comp.ai.philosophy Xref: bronze comp.ai.philosophy:5505 sci.philosophy.tech:7409 Path: bronze!ux1.cso.uiuc.edu!uwm.edu!caen!nic.umass.edu!dime!orourke From: orourke@unix1.cs.umass.edu (Joseph O'Rourke) Newsgroups: comp.ai.philosophy,sci.philosophy.tech Subject: Re: A rock implements every FSA Date: 19 Mar 92 00:00:49 GMT References: <1992Mar17.224156.9177@bronze.ucs.indiana.edu> <1992Mar17.231452.9979@husc3.harvard.edu> <1992Mar18.045939.3084@bronze.ucs.indiana.edu> <1992Mar18.095140.9984@husc3.harvard.edu> Sender: news@dime.cs.umass.edu Followup-To: comp.ai.philosophy Organization: Smith College, Northampton, MA, US Status: RO In article <1992Mar18.095140.9984@husc3.harvard.edu> zeleny@zariski.harvard.edu (Mikhail Zeleny) writes: >In article <1992Mar18.045939.3084@bronze.ucs.indiana.edu> > chalmers@bronze.ucs.indiana.edu (David Chalmers) writes: >>At best, it [Putnam's rock] implements a "trace" of a particular run >>of the FSA, as Joseph O'Rourke nicely put it. Thanks :-). >This is easy: first, you interpret the states of Putnam's automaton as >ordered pairs of a FSA (cf. the relevant comments on p.124); >follow this by running through enough input/state combinations to exhaust >the finite combinatorial possibilities afforded by the machine's table. >Finally, you do the mapping. In this way, there will be no counterfactual >possibilities left unaccounted for. There was an objection to your [MZ's] extension of Putnam's rock theorem to handle I/O by Anthony Francis based on the need for inputs of unbounded length. But it is clear from Putnam's description (p.124) that he is imagining that the I/O is not actually present, but rather talks of an automaton that behaves "as if" they were. So I don't see that Francis's point kills your idea. To rephrase Mikhail Zeleny's idea (which goes beyond what is present in Putnam's book): if we list out all possible traces that the FSA could make on any input, string them end-to-end, and map those lists of traces to the rock's physical states, then all possibile state transitions of the FSA are "realized" in the rock. It seems to me that this is right. (It also may not be precisely what MZ had in mind.) But it is only right by a significant weakening of what it means to "realize" or "implement" an FSA. Since Putnam doesn't seem to define the key notion of "realization" (at least I couldn't find it in the Appendix or book proper), it is not easy to claim this is a departure from what he had in mind. But according to this new, implied definition of realization, a rock not only realizes every FSA, it also realizes every sonnet written by Shakespeare. For one could string out the symbols in a sonnet end-to-end and map them onto physical states of the rock. In other words, a rock realizes every FSA only in a very uninteresting sense of realization. Incidentally, I think it is possible to quibble with Putnam on other grounds, in particular, his physical assumptions. But since his theorem is rather weak when all the important terms are explicated, it is not worth attacking his physics. From bronze!chalmers Sat Mar 21 16:48:25 EST 1992 Article: 5565 of comp.ai.philosophy Newsgroups: comp.ai.philosophy Path: bronze!chalmers From: chalmers@bronze.ucs.indiana.edu (David Chalmers) Subject: Re: A rock implements every FSA Organization: Indiana University References: <1992Mar19.011133.10015@husc3.harvard.edu> <1992Mar20.142954.19624@cs.ucf.edu> <45216@dime.cs.umass.edu> Date: Sat, 21 Mar 92 21:47:41 GMT Status: RO In article <45216@dime.cs.umass.edu> orourke@sophia.smith.edu (Joseph O'Rourke) writes: > clarke@acme.ucf.edu (Thomas Clarke) writes: >>Putnam then goes on to talk about "an object S which ...behaves... exactly >>as if it had a certain description D." The same mathematical identification>>technique can be applied to S to establish that it realizes input/output >>automaton D. > >This is a restatement of what Putnam says, yes. But I'm still not sure >I understand it. If you do, I would appreciate a rephrasing that makes >it clearer. If it says something definite, then there should be many >ways to make the same point; and the description could be fleshed out >with detail. I think what he's saying is very straightforward: by "behaves as if it and description D", he means it has exactly the same input/output behaviour as the automaton D. (Though of course he only considers the inputs and outputs in a single actual sequence, not all possible sequences.) He then claims that his argument shows that anything that satisfies this condition will actually be a realization of the automaton D. Of course that argument is flawed, for the same reason as before. (If we wanted to play semantic games, we might equivalently say that the argument succeeds, but only by using a notion of "realization" so weak that the result has no bite at all against functionalism. Certainly the notion of realization that a functionalist should appeal to is the stronger, counterfactual-supporting version. I note that even Putnam in his earlier paper "The Nature of Mental States" (one of the founding tracts of functionalism, written before he changed his mind), invokes the need to support conditionals in his characterization of the notion of description of a system by an FSA.) -- Dave Chalmers (dave@cogsci.indiana.edu) Center for Research on Concepts and Cognition, Indiana University. "It is not the least charm of a theory that it is refutable." From bronze!ux1.cso.uiuc.edu!moe.ksu.ksu.edu!zaphod.mps.ohio-state.edu!rpi!news-server.csri.toronto.edu!neat.cs.toronto.edu!cbo Mon Mar 23 21:53:35 EST 1992 Article: 5577 of comp.ai.philosophy Xref: bronze sci.philosophy.tech:7456 comp.ai.philosophy:5577 Path: bronze!ux1.cso.uiuc.edu!moe.ksu.ksu.edu!zaphod.mps.ohio-state.edu!rpi!news-server.csri.toronto.edu!neat.cs.toronto.edu!cbo Newsgroups: sci.philosophy.tech,comp.ai.philosophy From: cbo@cs.toronto.edu (Calvin Bruce Ostrum) Subject: Re: A rock implements every FSA Organization: Department of Computer Science, University of Toronto References: <1992Mar18.045939.3084@bronze.ucs.indiana.edu> <1992Mar18.095140.9984@husc3.harvard.edu> <92Mar18.182726est.14357@neat.cs.toronto.edu> <1992Mar19.000544.22634@bronze.ucs.indiana.edu> Date: 23 Mar 92 05:33:03 GMT Status: RO According to Stephen Schiffer's remarks on the dust jacket of _Representation_and_Reality_, Hilary Putnam is "one of the greatest philosophers of this century". Not only that, but his book is "clear, powerfully argued, and thoroughly accessible", as well as "fascinating" to boot. Given the first two claims, one might hope and expect that charity would not be necessary, but as we have discovered, charity indeed is required to make sense of his claims in the Appendix. Given the first claim alone, perhaps it is worth our while to endeavour in this task a while longer. The main claim of that appendix has been expressed in our vernacular as "A rock implements every FSA". Many commentators have criticised this using the argument that a rock has a bounded number of states, and hence cannot implement an automaton with a larger number of states, and seem to feel that they are done. In the literal sense, this may indeed by true, but much of the impact of his argument could remain. That impact is that for *many* rocks, each of these rocks implements a *large* class of FSAs. Hence, there is *no* matter of fact that is being expressed when the claim is made that a rock implements one particular automaton from that class. A much weaker claim, but still a very annoying one for functionalists. Dave Chalmers initially argued against the idea that this claim went through by maintaining that the rocks being considered did not support the counterfactual statements implied by the automaton's table, especially statements involving states in the table which do not occur in the actual trace of the rock-implemented automaton. Dave appears to have given in on this, and agreed that Putnam's theorem does go through for automata without input, for a very large class of rocks at least. He blunts the impact of this result with the observation that: dc| The moral, I take it, is that inputless FSAs are an inherently dc| trivial formalism. As an earlier poster said, FSAs have to be dc| sensitive to inputs for the formalism to have any bite. I therefore presume that he still endorses his second criticism, which was originally expressed as follows: dc| 2. An FSA certainly must satisfy counterfactuals of the form "if dc| in state S, input I had come in, then it would have transited to dc| state T", for all counterfactual inputs I. Putnam makes some dc| tentative gestures in the direction of handling a certain pattern dc| of actual inputs, but says nothing at all about handling dc| counterfactual inputs. As far as I can tell, the required dc| counterfactual sensitivity is entirely lacking. I believed originally that this objection was no more serious than the first one. This was mistaken, since the problem that bothered us in the first case is much worse here. First, note that since this does go way beyond straight interpretation of his text, I think we have to agree that Putnam had neglected the fact that the implementation must support the counterfactuals implied by the automaton table. Surely, however, he must believe this, especially given his history as "the inventor of functionalism". To his credit, however, we must admit that it is not clear, in general, what counterfactuals statements must be true in order to make a given (apparently) non-counterfactual statement true. If I believe that P, for example (make P an "occurent" belief), then I must also have dispositions to behave in various ways, depending upon what situations could have obtained but didn't. However, pace Skinner, who considered similar problems a mere piece of "hackwork" that he once idly thought of offering to do in order to avoid his doctoral exam in psychology, it is notoriously difficult to state what these dispositions are: this is an outgrowth of meaning holism, a position endorsed by Putnam, and a position which so far, no one has refuted by giving a positive account of the counterfactuals required. Fodor's best has been to stand with his back to the wall, defensively deflecting the meaning-holistic swipes aimed in his direction. When it comes to automata, there is a very natural class of counterfactual provided by the defining table. But perhaps these are not all so relevant as we think. When it comes to consciousness, a property whose discussion is inordinately favored in this group, Dave Chalmers reminds me of Tim Maudlin's recent paper in the Journal of Philosophy, in which relevance of these counterfactuals, not to the implementation of the automaton, but to the implementation of what the automaton itself allegedly implements, i.e. consciousness, is effectively questioned. The problem at hand, however, is how to state Putnam's Theorem in the case of FSA with input and output. Let's use the simplest possible such automata, Moore machines, with a fixed input/output language L and a fixed set of internal states S. Let us also assume a unique initial state (to do otherwise was necessary in the no-input case to get a reasonable set of counterfactuals, but here it only complicates matters, we can maintain for now. All states will assumed to be those reachable by some input sequence). Without loss of generality, this initial state can be fixed for all automata, so that our definition of an automaton is a NextState function from L x S into L, and an output function Output from S to L which gives the output of each state. Now, the counterfactually possible input/output relation of such an automaton is defined by a map Trace from L* to L*, subject to the constraint that if i1 is an initial sequence of i2, then Trace(i1) is an initial sequence of Trace(i2). This can looked upon as the obvious tree with branches labelled by L for input, and nodes labelled by L for output. Given this, we can express Putnams Theorem in strongest form: PT1| Every rock satisfying a given input/output Trace PT1| implements every automaton satisfying that Trace. We need some definitions to make sense of this. Let R be the arbitrary rock, and P its set of physical states, A the arbitrary automaton, S its set of physical states. Each physical state p is associated ahead of time with an output symbol from L, call this Output(R,p), analogously to the case with the automaton being implemented. Similarly, we can have an analogous NextState(R,p) function to say what the next physical state of the rock is. Given these, I'll also define Result(A,i) to be the automata state resulting from running A on i from L*, and Result(R,i) to be the physical rock state resulting from "running" the rock R on i. Devices "satisfy" a Trace T in the obvious circumstances. It is clear that there are many interesting and meaningful Traces, which are each satisfied by many automata. Now, we need a definition of implements: I| A rock R implements automaton A iff, for each automaton state s I| there exists a set of rock states Imp(s) such that I| 1) Output(p) = Output(s) for each p in Imp(s) I| 2) for each i in L* I| Result(R, i) is in Imp( Result(A, i) ) I| 3) for each distinct s1,s2 in S, Imp(s1) is disjoint from Imp(s2) If any Imp satisfies this definition, the minimal one inductively defined by (2) does so. It only remains to show that this definition is well defined. Here, of course, is where the problem lies. For there may very well be distinct states s1, s2 which are forced to contain the same physical state p. This is the same problem that we had in the case of FSA without input. However, this time we cannot solve the problem by starting out the different input strings in different physical states of the rock, because they are all required to start at the same physical state: the rock is highly constrained by the input output relations. The following possibility could be considered: if any two abstract states are mapped to the same physical state, it follows that once the automata enters one of these states, it produces the same output from then on: the two states serve exactly the same purpose, so there is no reason they cannot be identified without loss. We can take the automata table, before we even start, and throw out the redundant states, redirecting their input edges, and calling the resulting automaton "reduced". Then we can say: pt2| A rock satisfying trace T implements all reduced automata pt2| satisfying that trace. Sounds impressive until you realise that there is only one reduced automata possible for each class of automata satisfying a given trace. But at least Putnam can claim the result that without any internal examination, by his definition, we know immediately at least one automaton that is implemented by the rock. It's really an a priori thing. If we believe that the rock implements some "intended" non-reduced automaton as well (as we well might, if it's an artefact), we will thus have that it implements a number of other automata, which are linearly ordered by the reducibility relation. What is not obvious (to me) is if there are any commonly occuring natural conditions under which there must be multiply implemented automata, such that many of these automata are not only non-isomorphic, but also not comparable under this "reducibility ordering". Despite all this, it still seems that we do not have an adequate refutation of Putnam's position. All we've got so far is that it is "darn unlikely" that there are multiple non-comparable automata implemented. Since even the conceptual possibility of multiple implementations seems somewhat repugnant, this result may not be completely satisfying to all. I think the problem lies elsewhere. --------------------------------------------------------------------------- Calvin Ostrum cbo@cs.toronto.edu --------------------------------------------------------------------------- It [Functionalism] speaks as if there were objective causal facts about physical objects, physical concrete computing machines, that allow them to be confused with abstract computing machines, and then human beings compared in a confused matter to those, right. -- Saul Kripke, unpublished lecture, U of Toronto, early 1980's --------------------------------------------------------------------------- From bronze!chalmers Mon Mar 23 21:54:45 EST 1992 Article: 5597 of comp.ai.philosophy Xref: bronze sci.philosophy.tech:7466 comp.ai.philosophy:5597 Newsgroups: sci.philosophy.tech,comp.ai.philosophy Path: bronze!chalmers From: chalmers@bronze.ucs.indiana.edu (David Chalmers) Subject: Re: A rock implements every FSA Organization: Indiana University References: <92Mar18.182726est.14357@neat.cs.toronto.edu> <1992Mar19.000544.22634@bronze.ucs.indiana.edu> <92Mar23.003224est.14362@neat.cs.toronto.edu> Date: Tue, 24 Mar 92 02:51:28 GMT Status: RO [Warning: This post is long and nontrivial. The most interesting stuff is toward the end.] In article <92Mar23.003224est.14362@neat.cs.toronto.edu> cbo@cs.toronto.edu (Calvin Bruce Ostrum) writes: >That impact is that for *many* rocks, each of these rocks implements a >*large* class of FSAs. Hence, there is *no* matter of fact that is >being expressed when the claim is made that a rock implements one >particular automaton from that class. A much weaker claim, but still >a very annoying one for functionalists. This wouldn't be annoying at all. Any dynamic system of any complexity is describable as an FSA in a large number of different ways; one doesn't need any complex Putnam-style proofs to see that. As has been said a number of times in connection with the Chinese room thread, there's no canonical mapping from objects to systems. A matter of fact is certainly being expressed when we say that object O implements FSA A, and it's a fact that's quite compatible with O implementing another FSA B. >Dave Chalmers initially argued against the idea that this claim went >through by maintaining that the rocks being considered did not support the >counterfactual statements implied by the automaton's table, especially >statements involving states in the table which do not occur in the >actual trace of the rock-implemented automaton. > >Dave appears to have given in on this, and agreed that Putnam's theorem does >go through for automata without input, for a very large class of rocks at >least. Hang on. I didn't give in on anything. Putnam's construction fails, for the reasons I mentioned. I gave another construction that succeeded, for inputless FSAs, although it requires a more constrained class of "rocks". As I said in my initial post, my second point about the need to support input-based counterfactuals is a more serious objection; this is precisely because of the existence of alternative constructions to handle inputless FSAs. >When it comes to automata, >there is a very natural class of counterfactual provided by the defining >table. But perhaps these are not all so relevant as we think. When it >comes to consciousness, a property whose discussion is inordinately favored >in this group, Dave Chalmers reminds me of Tim Maudlin's recent paper >in the Journal of Philosophy, in which relevance of these >counterfactuals, not to the implementation of the automaton, but to the >implementation of what the automaton itself allegedly implements, >i.e. consciousness, is effectively questioned. Right. Take a system that supports all the relevant counterfactuals, required to make it implement an FSA that suffices for consciousness. Now somehow take all the mechanisms that aren't used in a particular computation, but that are needed to support counterfactual computations, and somehow block them (don't give them any grease, or put a stick in the cogs, or something). Now run the system on the original sequence of inputs. It produces the usual behaviour fine, and the blocked mechanisms don't matter, as they were never needed. Presumably, if someone believes that a certain FSA structure is required for consciousness, this system won't be conscious, because it no longer implements the FSA (its overall causal structure is now much simpler). It seems strange that the property of consciousness could be sensitive to those blockages in unused mechanisms, which never even get tested out (if the blockage was only slight, perhaps the mechanism might just have worked; it's weird that consciousness could be sensitive to this without having to try it out). But we already know that consciousness is strange. In any case, this is quite orthogonal to Putnam's question about whether a given object implements a given FSA. >Now, the counterfactually possible input/output relation of such an >automaton is defined by a map Trace from L* to L*, subject to the constraint >that if i1 is an initial sequence of i2, then Trace(i1) is an initial >sequence of Trace(i2). This can looked upon as the obvious tree with >branches labelled by L for input, and nodes labelled by L for output. OK, though I should note for clarity's sake that this is different from the notion of "trace" that has been used previously in the thread. The previous notion (1) was restricted to behaviour upon a particular sequence of inputs, not all possible sequences; (2) was only concerned with behaviour over a finite interval; and (3) explicitly referred to internal states. >Given this, we can express Putnams Theorem in strongest form: > >PT1| Every rock satisfying a given input/output Trace >PT1| implements every automaton satisfying that Trace. This result would be worrying if true. e.g. any rock that outputs zero for all inputs at all steps would implement the complex automaton that, given any integer N (from a bounded range) as input, goes through a long algorithm that checks all map structures with less than N countries for their minimal colourization, and outputs 1 if some map structure requires more than 4 colours, else outputs 0. [Of course most intermediate steps won't have any "outputs" (or relevant inputs) by this description, but we can stipulate that on those steps the output will always be 0, and inputs will be ignored.] This is especially worrying as nothing in your proof even appeals to Putnam's point about being in different states at different times, so if the proof were correct, a single-physical-state automaton would implementing the complex automaton, and that's obviously false. (Of course this falsity is closely tied to the hole in the proof that you point out below.) >We need some definitions to make sense of this. Let R be the arbitrary >rock, and P its set of physical states, A the arbitrary automaton, S its >set of physical states. Each physical state p is associated ahead of time >with an output symbol from L, call this Output(R,p), analogously to >the case with the automaton being implemented. Similarly, we can have >an analogous NextState(R,p) function to say what the next physical state >of the rock is. Given these, I'll also define Result(A,i) to be the >automata state resulting from running A on i from L*, and Result(R,i) to be >the physical rock state resulting from "running" the rock R on i. Devices >"satisfy" a Trace T in the obvious circumstances. It is clear that there >are many interesting and meaningful Traces, which are each satisfied by >many automata. I note that the very fact that NextState(R,p) is well defined means that the rock is an autonomous system, whose state doesn't depend on extraneous influences (except those summarized in the input symbol). This already makes the system quite unlike Putnam's rocks, which relied on extraneous influences to cause them to go through different states. It's definitely nicer to consider autonomous systems (they're reliable for a start, so can support counterfactuals), although they're something of an idealization. >Now, we need a definition of implements: > >I| A rock R implements automaton A iff, for each automaton state s >I| there exists a set of rock states Imp(s) such that >I| 1) Output(p) = Output(s) for each p in Imp(s) >I| 2) for each i in L* >I| Result(R, i) is in Imp( Result(A, i) ) >I| 3) for each distinct s1,s2 in S, Imp(s1) is disjoint from Imp(s2) I would object to (2) if we were dealing with non-autonomous systems like Putnam's, as I want the system to satisfy the conditional that a physical state in Imp(s) combined with an input i should lead to a physical state in Imp(NextState(i,s)) -- and this would require that the conditional not just be supported on those particular instances when s comes up in the trace. But the well-definedness of the NextState relation means that if the conditional is supported once for a given physical state, it will be supported everywhere, so that's OK. At least it will be supported for states that actually appear in the trace. Whether it's necessary or relevant to consider states that never appear in the trace is an interesting question (we might have got to those states by starting in a different initial state, for instance), but leave that aside for now. >If any Imp satisfies this definition, the minimal one inductively defined >by (2) does so. It only remains to show that this definition is well >defined. Here, of course, is where the problem lies. For there may very well >be distinct states s1, s2 which are forced to contain the same physical >state p. This is the same problem that we had in the case of FSA without >input. However, this time we cannot solve the problem by starting out the >different input strings in different physical states of the rock, because >they are all required to start at the same physical state: the rock is >highly constrained by the input output relations. OK, this is the obvious problem, e.g. it's the reason why the single-state machine I mentioned above really doesn't implement the five-colour-map checker (each state of the complex machine would map onto the same state, which is no good). However, one might get around this by adding the constraint that the rock maintains a list of all inputs so far. This ensures that it will always be in a distinct physical state after any sequence in L*. Of course we would now be far from any ordinary "rock", but there is a sense in which what we added is trivial, and we wouldn't expect it to add amazing cognitive powers to a system, so that if the result goes through with this extra constraint, functionalism may may still be in trouble. I'll come back to this. >The following possibility could be considered: if any two abstract states >are mapped to the same physical state, it follows that once the automata >enters one of these states, it produces the same output from then on: the >two states serve exactly the same purpose, so there is no reason they >cannot be identified without loss. We can take the automata table, before >we even start, and throw out the redundant states, redirecting their input >edges, and calling the resulting automaton "reduced". Then we can say: > >pt2| A rock satisfying trace T implements all reduced automata >pt2| satisfying that trace. > >Sounds impressive until you realise that there is only one reduced automata >possible for each class of automata satisfying a given trace. This is interesting, and not initially obvious. Your "reduction" relation is just the implementation relation, as it applies between pairs of automata rather than automata and physical systems. So given any two input/output equivalent automata, either one implements the other, or both implement a single simpler FSA. I suppose that's right, by your argument above. Although this fact seems to defang the Putnam-style argument, it raises new problems. One is tempted to say that if a complex FSA implements a simpler FSA with the same input/output function, then the complex FSA has the behaviour it does *in virtue* of implementing the simpler one, and the extra complexity is just irrelevant implementational detail. (As you say above, the extra detail is "redundant".) Any cognitive properties that the system has, one would think, would exist in virtue of implementing the simpler system -- a higher level description that seems to capture everything relevant to cognitive function. At least this is the standard view we get from the functionalist approach to cognition. But from this it will follow that any two systems that are behaviourally equivalent are cognitively equivalent. Because any two such systems will both be implementations of a single simpler FSA, in virtue of which they behave as they do and have the cognitive properties that they do. But this is just saying that behaviourism (in the sense that has been used in this thread) is true! Or at least that behaviourism is true if FSA-functionalism is true. This would seem to be a problem. We wouldn't have lookup-table intelligence, as lookup tables aren't behaviourally equivalent to infinity as the current criterion requires. But we'd still have cognitive equivalence of me and the hypothetical perfect actor, we'd have problems with Putnam's super-Spartans who suppress their pains, and so on. One can argue about whether such cases are possible, but there is at least a prima facie difficulty here. One way out may be to argue against the "in virtue" clause above, or equivalently to argue that this so-called "implementational detail" is relevant. To make a case for this: consider again the five-colour-map checker and the single-state machine, which were behaviourally equivalent (both always output 0). The result above says that they can be reduced to implementation of a common FSA, and indeed that's true: the map-checker is trivially an implementation of the single-state machine. But is it true that the map-checker produces the behaviour that it does *in virtue* of implementing the single-state machine, and that the rest of its structure is irrelevant implementational detail? It doesn't seem so. On the face of it, the fact that the map-checker implements the single-state machine is as deep as the fact that it always outputs 0. If there's an explanatory relation, it seems the other way around: it implements the single-state machine *because* it always outputs 0. And it outputs 0 because of implementing the complex map-checking algorithm. To say that the details of the map-checking algorithm are implementational detail seems entirely wrong. So what we need now is a way of distinguishing trivial from non-trivial cases of the "implementation" relationship. One way to do it may be through some kind of uniformity requirement on the causal relation involved in a given state-transition. But I'm not entirely sure how to do this right now, and this post is already too long, so I'll leave it. But to summarize the state of play on this issue, it seems to me that the following statements are inconsistent: (1) There is a nontrivial class of cognitive systems that have the cognitive properties they do in virtue of implementing a certain FSA; i.e. any system that implements that FSA will possess those cognitive properties. [FSA-based functionalism.] (2) Within this class there exist systems that are behaviourally equivalent (to infinity) but cognitively distinct. [Anti-behaviourism]. (3) If implementation of an FSA A suffices for the possession of certain cognitive properties, but A is an implementation of a simpler FSA B that is behaviourally equivalent, then implementation of B also suffices for possession of those cognitive properties. [Irrelevance of implementational detail.] (4) Any two behaviourally equivalent FSAs are implementations of a common, behaviourally equivalent FSA. [A theorem of automata theory.] One of thes statements must be rejected, and a case can be made for rejecting any of (1)-(3). A functionalist might reject (1), and move to a formalism more constrained than mere FSAs, e.g. a formalism in which states are complex rather than monadic. This is very tempting, but is problematic for various reasons. One might also move to a formalism that treats inputs and outputs more realistically than FSAs, which require input/output for every computational step. One could reject (2) on the grounds that any two cognitively distinct systems must eventually diverge behaviourally, but if this is true it certainly isn't obvious. Finally, one could reject (3), as I'm tempted to. Or more usefully, as (3) has some content that we might wish to preserve, we could modify it so that it holds for a certain constrained subclass of the "implementation" relation, but doesn't hold for cases like map-checkers implementing single-state machines. >If we believe that the rock implements some "intended" non-reduced >automaton as well (as we well might, if it's an artefact), we will thus >have that it implements a number of other automata, which are linearly >ordered by the reducibility relation. What is not obvious (to me) is if >there are any commonly occuring natural conditions under which there >must be multiply implemented automata, such that many of these automata >are not only non-isomorphic, but also not comparable under this >"reducibility ordering". Almost certainly. It depends on whether you want to individuate inputs and outputs before deciding what the rock implements. If you leave that open, then it will implement any number of distinct systems (not unlike the Chinese room, which implements one system that handles English inputs and another that handles Chinese). But it can happen even if you fix the inputs and outputs. e.g. take a 6-state cyclic FSA (inputs whatever you like, outputs constant 0). This is an implementation of both a 2-state cyclic FSA and a 3-state cyclic FSA, and neither of these is reducible to the other. >Despite all this, it still seems that we do not have an adequate refutation >of Putnam's position. All we've got so far is that it is "darn unlikely" >that there are multiple non-comparable automata implemented. Since even >the conceptual possibility of multiple implementations seems somewhat >repugnant, this result may not be completely satisfying to all. I >think the problem lies elsewhere. This really isn't a problem. Any functionalist with half a brain will allow that a given object will implement any number of distinct systems. There's no canonical map from object to system. There would be a problem if it turned out that for a given FSA, every object implemented it, but that's not what this result says. So to really sum up the state of play (finally), apart from this non-problem, I see two real problems for the FSA-based functionalism. One is the inconsistent triad that I listed above. The other, which I mentioned a while ago and which is closer to the spirit of Putnam's objection, is that given any two behaviourally equivalent FSAs A and B, it seems to be the case that an object consisting of an implementation of A plus a "list" of inputs so far will implement B, and that an implementation of B plus a list will implement A. That seems to be a problem, as the list certainly isn't playing any causal role and would seem to be irrelevant to possession of any cognitive properties; so this is another argument that behaviourally equivalent FSAs are cognitively equivalent. A solution may be again to constrain the implementation relation so the causal properties of states are somehow unified, but this is not entirely obvious. Anyway, enough problems for the functionalist for now, maybe the 3 people who have read this far can take a stab at the solution. -- Dave Chalmers (dave@cogsci.indiana.edu) Center for Research on Concepts and Cognition, Indiana University. "It is not the least charm of a theory that it is refutable." From bronze!sol.ctr.columbia.edu!caen!nic.umass.edu!dime!orourke Tue Mar 24 19:39:20 EST 1992 Article: 5612 of comp.ai.philosophy Xref: bronze sci.philosophy.tech:7475 comp.ai.philosophy:5612 Path: bronze!sol.ctr.columbia.edu!caen!nic.umass.edu!dime!orourke From: orourke@unix1.cs.umass.edu (Joseph O'Rourke) Newsgroups: sci.philosophy.tech,comp.ai.philosophy Subject: Re: A rock implements every FSA Keywords: functionalism, consciousness Date: 24 Mar 92 18:03:25 GMT References: <92Mar18.182726est.14357@neat.cs.toronto.edu> <1992Mar19.000544.22634@bronze.ucs.indiana.edu> <92Mar23.003224est.14362@neat.cs.toronto.edu> <1992Mar24.025128.9379@bronze.ucs.indiana.edu> Sender: news@dime.cs.umass.edu Followup-To: sci.philosophy.tech Organization: Smith College, Northampton, MA, US Status: RO In article <1992Mar24.025128.9379@bronze.ucs.indiana.edu> chalmers@bronze.ucs.indiana.edu (David Chalmers) writes: >Take a system that supports all the relevant counterfactuals, >required to make it implement an FSA that suffices for consciousness. >Now somehow take all the mechanisms that aren't used in a particular >computation, but that are needed to support counterfactual computations, >and somehow block them (...). Now run the system on the original sequence >of inputs. It produces the usual behaviour fine, and the blocked >mechanisms don't matter, as they were never needed. [...] >It seems strange that the property of consciousness could be >sensitive to those blockages in unused mechanisms, which never even >get tested out (...). But we already know that consciousness is strange. This is a fascinating point! It seems possible to me that consciousness could depend on the paths not followed, so to speak: an aspect of consciousness seems to be the sensation or awareness of alternatives, as if the alternative pathways are stimulated even if not taken, and this stimulation is part of consciousness. The flip side of this is that when we go into "numb mode" while e.g. driving a car or washing the dishes, we are not alive to altering the routines, and we cease to be overtly "conscious" of those activities. Perhaps part of consciousness is the constant chatter in our heads over the alternative possibilities at each juncture. I realize this speculation that does not address any of the technical points in Calvin Ostrum's and David Chalmers' posts... From bronze!ux1.cso.uiuc.edu!mp.cs.niu.edu!rickert Tue Mar 24 19:44:30 EST 1992 Article: 5615 of comp.ai.philosophy Xref: bronze sci.philosophy.tech:7476 comp.ai.philosophy:5615 Newsgroups: sci.philosophy.tech,comp.ai.philosophy Path: bronze!ux1.cso.uiuc.edu!mp.cs.niu.edu!rickert From: rickert@mp.cs.niu.edu (Neil Rickert) Subject: Re: A rock implements every FSA Organization: Northern Illinois University References: <1992Mar24.025128.9379@bronze.ucs.indiana.edu> Date: Tue, 24 Mar 1992 19:22:45 GMT Status: RO In article <1992Mar24.025128.9379@bronze.ucs.indiana.edu> chalmers@bronze.ucs.indiana.edu (David Chalmers) writes: [Long article about FSA functionalism and its peculiarities. I include a relatively brief quote to provide part of the flavor.] >So to really sum up the state of play (finally), apart from this >non-problem, I see two real problems for the FSA-based functionalism. >One is the inconsistent triad that I listed above. The other, which >I mentioned a while ago and which is closer to the spirit of Putnam's >objection, is that given any two behaviourally equivalent FSAs A and B, >it seems to be the case that an object consisting of an implementation >of A plus a "list" of inputs so far will implement B, and that an >implementation of B plus a list will implement A. That seems to be >a problem, as the list certainly isn't playing any causal role and >would seem to be irrelevant to possession of any cognitive properties; >so this is another argument that behaviourally equivalent FSAs are >cognitively equivalent. A solution may be again to constrain the >implementation relation so the causal properties of states are somehow >unified, but this is not entirely obvious. Thanks Dave, for some interesting comments. In some possibly obscure way they reminds me of some research papers I saw about 9 years ago on Byzantine Clock Synchronization. Briefly, they dealt with the problem of synchronizing clocks over a distributed network. The articles demonstrated the enormous complexity of the problem, particularly for networks of any size. I remember saying to myself at the time that somebody is bound to ignore all the problems and proceed to implement a clock synchronization methodology anyway. And indeed today many Internet hosts use the 'ntp' protocols to synchronize their clocks. There was nothing wrong with the proofs in the "Byzantine" articles. It is just that the ntp implementers were pragmatists who were willing to ignore requirements that could not be practically implemented. Often in practical problems, near enough is good enough. Back to the FSA. A single 32 bit integer in a computer has 2^32 states. It is not hard to design an FSA with 2^32 states which doesn't use a whole lot more than the single word. But there are other FSAs with 2^32 states which it would be difficult to implement in most available computers today. The point I am making is the formal automata-theory approach is often not a particularly useful way of understanding what is happening. In particular, FSA reduction may not be a useful practical approach. The question "find an FSA to solve this problem with a minimum number of states" may have little or no relation to the question "find an FSA to solve this problem which requires the minimum amount of hardware". An example: Consider the automaton FSA-1. Its function is to process 32 bits of input, and finish up in one of 2^32 states. It so happens that if the input is interpreted as a single precision floating point number 'x', the final state will represent the single precision floating point number computed to be 'sin(x)' with some suitable rounding. Now consider FSA-2. Its function is the same, except its input is restricted to the set of values of 'x' for which I have ever computed 'sin(x)'. However FSA-2 has been simplified by discarding all states not needed for its more limited input. FSA-2 is assumed to be the reduced FSA. It should be pretty obvious that FSA-2 will have far fewer states than are required by FSA-1. One way to implement FSA-1 would be to use a humongous lookup table. Such an approach would be inordinately expensive. But it so happens that FSA-1 can quite easily be implemented with the floating point unit of my computer. There quite possibly may be no easy implementation of FSA-2, so practically speaking we would be better of using FSA-1 and ignoring the superfluous states. We can put this in terms of emulating the mind. One question Dave raises is whether any FSA which produces the correct set of states based on its input will suffice. Will a reduced FSA with a miminal number of states be conscious, for example. It seems to me that this is the wrong approach. The number of states required may well exceed the number of atoms in the universe, and this minimal FSA quite possibly may be unimplementable. The problem is not to find a machine to implement the state transitions, but to find a machine which is also practically implementable in a chemical computer which is subject to the constraints of biology and evolution. It may well be that just the state transitions are not enough for consciousness, and that the consciousness arises from the implementation details required to make a solution practical. I have from time to time supported the Turing Test. The above paragraph might superficially appear to be a change of mind. It is not. My suspicion is that any suitable machine which can be practically implemented in silicon, and which has the correct behavior, will have consciousness. I do not claim that the behavior directly implies consciousness, but rather that the combinatorial complexity is such that there is probably no practical way of implementing the behavior without first implementing consciousness. It is perhaps natural at this point to ask whether it is possible that some types of computing machine might be easily implemented as a chemical computer, yet defy implementation as an electronic computer. This is almost certainly the case. My tendency is to think that it doesn't matter. I think of the brain as a primarily analog device of rather limited accuracy. As such, an exact implementation of behavior is not needed. A sufficiently accurate approximation should be adequate. Near enough is good enough. The floating point units on our computers make pretty effective analog devices, which I believe are up to the job. I have long suspected, and the above comments certainly suggest, that any successful computer implementation of the mind will be quite unlike the expert systems and knowledge systems of today. Roughly speaking, the successful AI program won't be a LISP program after all, it will be a FORTRAN program; and the hardware won't be a symbolic machine, but will be a vector supercomputer. -- =*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Neil W. Rickert, Computer Science Northern Illinois Univ. DeKalb, IL 60115 +1-815-753-6940 From bronze!chalmers Thu Mar 26 00:52:45 EST 1992 Article: 5651 of comp.ai.philosophy Xref: bronze sci.philosophy.tech:7494 comp.ai.philosophy:5651 Newsgroups: sci.philosophy.tech,comp.ai.philosophy Path: bronze!chalmers From: chalmers@bronze.ucs.indiana.edu (David Chalmers) Subject: Re: A rock implements every FSA Organization: Indiana University References: <1992Mar24.025128.9379@bronze.ucs.indiana.edu> <1992Mar24.192245.10324@mp.cs.niu.edu> Date: Thu, 26 Mar 92 05:24:12 GMT Status: O In article <1992Mar24.192245.10324@mp.cs.niu.edu> rickert@mp.cs.niu.edu (Neil Rickert) writes: > A single 32 bit integer in a computer has 2^32 states. It is not hard to >design an FSA with 2^32 states which doesn't use a whole lot more than >the single word. But there are other FSAs with 2^32 states which it would >be difficult to implement in most available computers today. The point I am >making is the formal automata-theory approach is often not a particularly >useful way of understanding what is happening. In particular, FSA reduction >may not be a useful practical approach. The question "find an FSA to >solve this problem with a minimum number of states" may have little or >no relation to the question "find an FSA to solve this problem which >requires the minimum amount of hardware". That's certainly true. Any FSA in practice will have combinatorially structured states, and the state transitions will be constrained to be relatively simple functions of that combinatorial structure. e.g. Turing machines with finite tapes, or connectionist networks. These will be a small subset of the space of all possible FSAs, but they're all we need, and all we'll ever deal with in practice. > One way to implement FSA-1 would be to use a humongous lookup table. Such >an approach would be inordinately expensive. But it so happens that FSA-1 >can quite easily be implemented with the floating point unit of my computer. >There quite possibly may be no easy implementation of FSA-2, so practically >speaking we would be better of using FSA-1 and ignoring the superfluous >states. Right. This is precisely because FSA-1 can be implemented using combinatorially structured states, and FSA-2 can't (at least not in any obvious way). >It seems to me that this is the wrong approach. The number of states required >may well exceed the number of atoms in the universe, and this minimal FSA >possibly may be unimplementable. The problem is not to find a machine to >implement the state transitions, but to find a machine which is also >practically implementable in a chemical computer which is subject to the >constraints of biology and evolution. It may well be that just the state >transitions are not enough for consciousness, and that the consciousness >arises from the implementation details required to make a solution practical. I agree that in practice we'll always use FSAs with combinatorially structured states. The question is whether an FSA with such states will have any cognitive properties that the equivalent FSA with monadic states won't have. I used to think this, and therefore regarded FSAs as an inappropriate formalism -- something more constrained, like finite tape TM's, would be preferable. Formalisms with combinatorial structure certainly seem more appropriate for capturing the idea that cognition arises from the interaction of lots of separate parts at once. There are two reasons why I now think that contrary to this, FSAs with monadic states (MFSAs) may be sufficient in principle. The first is that one can run a "fading qualia" argument from any combinatorially structured FSA (CFSA) to the equivalent MFSA. Just gradually convert pairs of neighbouring "components" of the CFSA into single components. e.g. given a connectionist network with lots of separate 3-state units (n of them, say), one can convert two neighbouring units into a single 9-simple-state units (altering the input and output connections appropriately), and so on until you have a single unit with 3^n simple states, and the right state-transition table to move between those states in response to inputs. Behavioural function is certainly preserved. The question is whether cognitive properties, or qualia, might fade. It's not quite as clear to me that they won't as it is with the neuron-to-silicon case, as it's possible that one might argue that some information is being lost by collapsing combinatorial structure like this, but the plausibility seems to be on the side of no fading, to me. The other reason is that it's difficult to set criteria that rule out MFSAs as implementations of the equivalent CFSAs, without ruling out too much. Presumably one will require that states of each "unit" of a CFSA (e.g. units of a connectionist network, or tape-squares in a TM) have to be separately mapped onto some physical property of the implementation. But we can do this even for a simple implementation of the equivalent MFSA. Given the property "unit X in state A" of the CFSA, there will be a big disjunction of states of the MFSA that correspond. So we can map the unit-state to the disjunction of the corresponding physical properties of the MFSA implementation. Do this for all the unit-states, and we've satisfied the conditions required for the monadic implementation to be an implementation of the CFSA. The obvious objection to this is that the physical properties that determine the state of each unit will be vastly overlapping disjunctive properties, physically tangled up with each other. One might want to require that for each unit in the CFSA, there must correspond a spatially distinct component of the implementation, upon which the unit-state supervenes. This might make things simpler, but at the same time it would rule out a whole lot of apparently acceptable implementations of CFSA, e.g. those using virtual memory (where there may be no determinate physical location corresponding to a single memory location). I don't see any obvious way to rule in things like virtual memories but rule out monadic-state implementations. > I have from time to time supported the Turing Test. The above paragraph >might superficially appear to be a change of mind. It is not. My suspicion >is that any suitable machine which can be practically implemented in >silicon, and which has the correct behavior, will have consciousness. I do >not claim that the behavior directly implies consciousness, but rather that >the combinatorial complexity is such that there is probably no practical way >of implementing the behavior without first implementing consciousness. I think I agree with this. > I have long suspected, and the above comments certainly suggest, that any >successful computer implementation of the mind will be quite unlike the >expert systems and knowledge systems of today. Roughly speaking, the >successful AI program won't be a LISP program after all, it will be a >FORTRAN program; and the hardware won't be a symbolic machine, but will >be a vector supercomputer. Hey, then you should become a connectionist. I've got nothing against symbolic hardware in principle, though. It will just be a bit slower. -- Dave Chalmers (dave@cogsci.indiana.edu) Center for Research on Concepts and Cognition, Indiana University. "It is not the least charm of a theory that it is refutable." From bronze!news.cs.indiana.edu!mips!swrinde!cs.utexas.edu!uunet!psinntp!scylla!daryl Thu Mar 26 01:13:17 EST 1992 Article: 5650 of comp.ai.philosophy Path: bronze!news.cs.indiana.edu!mips!swrinde!cs.utexas.edu!uunet!psinntp!scylla!daryl From: daryl@oracorp.com (Daryl McCullough) Newsgroups: comp.ai.philosophy Subject: Re: A rock implements every FSA Date: 25 Mar 92 16:10:24 GMT Organization: ORA Corporation Status: RO I hate to admit this, but I think I agree with Mikhail Zeleny on this point; Mikhail's arguments have convinced me that Putnam's proof does make a certain amount of sense. As several people have pointed out, the standard notion of implementing a finite state machine involves getting the inputs and outputs right, (which Putnam's rocks manifestly don't). However, that notion of implementation is too strong if you want to say (a) that "being conscious" means to implement a certain kind of state machine, and (b) that sensation-deprived human brains are still conscious. The problem with the latter case (imagine a deaf, blind, paralytic) is that there are no inputs and outputs from the world possible, so whatever it means to implement a conscious being cannot require getting the *actual* inputs and outputs right. If, on the other hand, you drop the input/output requirement, then there is nothing to prevent a rock from implementing every FSM. I don't see how Chalmer's complaints about counterfactuals is even a problem. All that it takes to support counterfactuals is to be able to show, for each possible input sequence, that there is a corresponding trace of the states of the rock showing how the rock would have responded if that input sequence had occurred. Daryl McCullough ORA Corp. Ithaca, NY From bronze!chalmers Thu Mar 26 01:13:31 EST 1992 Article: 5652 of comp.ai.philosophy Newsgroups: comp.ai.philosophy Path: bronze!chalmers From: chalmers@bronze.ucs.indiana.edu (David Chalmers) Subject: Re: A rock implements every FSA Organization: Indiana University References: <1992Mar25.161024.2081@oracorp.com> Date: Thu, 26 Mar 92 06:13:10 GMT Status: RO In article <1992Mar25.161024.2081@oracorp.com> daryl@oracorp.com (Daryl McCullough) writes: [paragraph order inverted] >If, on the other hand, you drop the input/output requirement, then >there is nothing to prevent a rock from implementing every FSM. I >don't see how Chalmer's complaints about counterfactuals is even a >problem. All that it takes to support counterfactuals is to be able to >show, for each possible input sequence, that there is a corresponding >trace of the states of the rock showing how the rock would have >responded if that input sequence had occurred. As I said in another post, inputless FSAs are an inherently trivial formalism. There are still a few counterfactuals that need to be satisfied, namely those concerning the system's behaviour if it were in a different state, but these aren't so hard to satisfy, requiring only that the system incorporate a "dial" of the kind I described. So indeed it is true that most objects implement all inputless FSAs, but that's not a result with any bite. >As several people have pointed out, the standard notion of >implementing a finite state machine involves getting the inputs and >outputs right, (which Putnam's rocks manifestly don't). However, that >notion of implementation is too strong if you want to say (a) that >"being conscious" means to implement a certain kind of state machine, >and (b) that sensation-deprived human brains are still conscious. The >problem with the latter case (imagine a deaf, blind, paralytic) is >that there are no inputs and outputs from the world possible, so >whatever it means to implement a conscious being cannot require >getting the *actual* inputs and outputs right. Sensation-deprived beings don't get any input, but it's still true of them that *if* they got input, *then* they would function in a certain way. i.e. they still satisfy the strong conditionals required of an FSA with I/O. The same goes for deaf/blind paralytics, as I said in an earlier post. These still implement the structure of complex FSAs with I/O, although it happens that they don't get any input. One simply has to place the input boundary at the right place, e.g. at the periphery of the visual cortex rather than the retina, perhaps. If they were stimulated there in various ways, they would function differently in complex ways. And they produce all kinds of outputs, if these are construed as certain firings from the motor cortex, it's just that these outputs aren't causally connected in the right way to body parts. Hence these beings instantiate complex I/O FSAs, and furthermore (at least according to the functionalist) it is in virtue of instantiating these FSAs that they possess their cognitive properties. If their internal structure did not satisfy all those strong conditionals, they would not have the cognitive states that they do. -- Dave Chalmers (dave@cogsci.indiana.edu) Center for Research on Concepts and Cognition, Indiana University. "It is not the least charm of a theory that it is refutable." From bronze!ux1.cso.uiuc.edu!uwm.edu!rpi!news-server.csri.toronto.edu!neat.cs.toronto.edu!cbo Thu Mar 26 02:34:40 EST 1992 Article: 5630 of comp.ai.philosophy Xref: bronze sci.philosophy.tech:7484 comp.ai.philosophy:5630 Path: bronze!ux1.cso.uiuc.edu!uwm.edu!rpi!news-server.csri.toronto.edu!neat.cs.toronto.edu!cbo Newsgroups: sci.philosophy.tech,comp.ai.philosophy From: cbo@cs.toronto.edu (Calvin Bruce Ostrum) Subject: Re: A rock implements every FSA Organization: Department of Computer Science, University of Toronto References: <92Mar18.182726est.14357@neat.cs.toronto.edu> <1992Mar19.000544.22634@bronze.ucs.indiana.edu> <92Mar23.003224est.14362@neat.cs.toronto.edu> <1992Mar24.025128.9379@bronze.ucs.indiana.edu> Date: 25 Mar 92 10:39:18 GMT Status: RO Dave Chalmers describes a recent post of his: dc| [Warning: This post is long and nontrivial... I resolve to attempt a posting that does not rival Dave's in either of these regards. dc| >That impact is that for *many* rocks, each of these rocks implements a dc| >*large* class of FSAs. Hence, there is *no* matter of fact that is dc| >being expressed when the claim is made that a rock implements one dc| >particular automaton from that class. A much weaker claim, but still dc| >a very annoying one for functionalists. dc| dc| This wouldn't be annoying at all. ... A matter of fact is dc| certainly being expressed when we say that object O implements FSA dc| A, and it's a fact that's quite compatible with O implementing another dc| FSA B. True, but not when you add the words "one particular". Maybe this wouldn't bother functionalists, and I admit to being quite hazy as to why it bothers me. It's something like this: if implementing these systems amounts to having a certain psychological characterisation in terms of beliefs and desires, and if they are radically non-isomorphic, it seems like the attributions of belief and desire given to me would be radically different also. That makes me feel uncomfortable. Perhaps its just a bad feeling. Perhaps it cuts no ice, either, and I should be able to live with it. One way in which it might matter in more than an obscure philosophical way, is when someone had partial knowledge of these two implementations, without being aware that the knowledge was drawn from two different ones. It might cause some real troubles trying to make sense of the big picture. But so far we have been ignoring the epistemological for the metaphysical. dc| [Dave discusses the intuition that consciousness does not seem to dc| depend upon the kind of counterfactual that implementing an automata dc| does appear to depend upon, as dealt with in Maudlin's article] dc| In any case, this is quite orthogonal to dc| Putnam's question about whether a given object implements a given FSA. Yes, my point in mentioning it was merely to suggest that when we actually come to apply "implementation of automata" to any problem of interest, it is not absolutely clear what counterfactuals we should be considering. We might want to consider relaxing some of them. We might want to have a better theory of exactly *why* we care about counterfactuals in the first place. I think Dave thinks this is something so obvious that we don't need a theory of it. I'll agree that it's (probably) obvious, but I'm still pretty mystified about counterfactuals (because I'm mystified by their truthmakers. Probably that's just me. Still, I feel a lot of folks, like those who give David Lewis that famous incredulous stare, have their heads in the sand on this point). dc| This is especially worrying as nothing in your proof even appeals to dc| Putnam's point about being in different states at different times, dc| so if the proof were correct, a single-physical-state automaton would dc| implementing the complex automaton, and that's obviously false. dc| (Of course this falsity is closely tied to the hole in the proof that dc| you point out below.) Well, the rock doesn't HAVE to be in different states at different times. It only has to be in different states at the appropriate times (and appropriate possible times in counterfactually relevant possible worlds) to make the definition of implementation well founded. And since that is not guaranteed by his initial assumption about different states at (merely) different times I saw little reason to include this useless antecedent in the statement of the theorem. dc| >If any Imp satisfies this definition, the minimal one inductively defined dc| >by (2) does so. It only remains to show that this definition is well dc| >defined. Here, of course, is where the problem lies. For there may very well dc| >be distinct states s1, s2 which are forced to contain the same physical dc| >state p. This is the same problem that we had in the case of FSA without dc| >input. However, this time we cannot solve the problem by starting out the dc| >different input strings in different physical states of the rock, because dc| >they are all required to start at the same physical state: the rock is dc| >highly constrained by the input output relations. dc| dc| OK, this is the obvious problem, I agree, this *appears* to be the obvious problem, but if it is really the obvious problem, one wonders why so many of the really bright commentators (Mikhail, Jeff, etc.) don't appear to have picked up on it. dc| However, one might get around this by adding the dc| constraint that the rock maintains a list of all inputs so far. This dc| ensures that it will always be in a distinct physical state after any dc| sequence in L*. Of course we would now be far from any ordinary "rock", dc| but there is a sense in which what we added is trivial, and we wouldn't dc| expect it to add amazing cognitive powers to a system, so that if dc| the result goes through with this extra constraint, functionalism may dc| may still be in trouble. I'll come back to this. We are tempted to disallow this by saying that the rock required is too fantastic. I left open whether or not such a rock was too fantastic by saying (although "commonly occuring natural conditions" is too strong, and Dave thinks "multiply implemented" is too weak): cbo| What is not obvious (to me) is if cbo| there are any commonly occuring natural conditions under which there cbo| must be multiply implemented automata, such that many of these automata cbo| are not only non-isomorphic, but also not comparable under this cbo| "reducibility ordering". My feeling is that we still should be able to say something in this case, however. There just seems something wrong with these ad hoc disjunctions, and we want to eliminate them while retaining the natural "multiple realisability" that led away from central-state identity theory in the first place. I have some extremely half-baked (and obvious) ideas about how this might be done. dc| Any cognitive properties dc| that the system has, one would think, would exist in virtue of dc| implementing the simpler system -- a higher level description that dc| seems to capture everything relevant to cognitive function. At least dc| this is the standard view we get from the functionalist approach to dc| cognition. I don't see the argument for this view. However, it is true that it is not obvious how to defeat it either. dc| But from this it will follow that any two systems that are dc| behaviourally equivalent are cognitively equivalent. Because any two dc| such systems will both be implementations of a single simpler FSA, in dc| virtue of which they behave as they do and have the cognitive dc| properties that they do. But this is just saying that behaviourism dc| (in the sense that has been used in this thread) is true! Or at least dc| that behaviourism is true if FSA-functionalism is true. This would dc| seem to be a problem. Compare this to what Putnam thinks to be the upshot of his Appendix: hp| In short, "functionalism", if it were correct, would imply hp| behaviorism. Putnam was trying to get at the idea that somehow, the internal states didn't matter because, in some way, the intended interpretation of those states was in some way arbitrary. He thought it was arbitrary because it could be anything. The suggestion here is that it is arbitrary because it isn't the particular special one, and there is no way to privilege it above that special one. Whichever way you look at it, it seems to come down to: dc| So what we need now is a way of distinguishing trivial from non-trivial dc| cases of the "implementation" relationship... dc| One way out may be to argue against the "in virtue" clause above, or dc| equivalently to argue that this so-called "implementational detail" is dc| relevant. To make a case for this: consider again the five-colour-map dc| checker and the single-state machine, which were behaviourally dc| equivalent (both always output 0). ...To say that the details of the dc| map-checking algorithm are implementational detail seems entirely dc| wrong. Yes, it does seem wrong. But I think the "in virtue of" clause is itself a questionable way to describe things. In fact, one might turn the "in virtue of" relation around in the opposite direction. It is in virtue of the fact that the map-checker implements the map checking that it also implements the constant function. "In virtue of" basically means "because of". And I think its correct to say that a machine implements a simpler function because of the fact that it implements a more complex one. An interpreter for a simple LISP language might be quite a bit more complex than the programs it runs, considered at their own level. I would never have admitted to to the other "in virtue of" in the first place. This relates to the third of the three conditions that Dave suggests can't be simultaneously satisfied: dc| (1) There is a nontrivial class of cognitive systems that have the dc| cognitive properties they do in virtue of implementing a certain FSA; dc| i.e. any system that implements that FSA will possess those dc| cognitive properties. [FSA-based functionalism.] Well, personally, I think this is completely wrong, and I am happy to discard it. This is a generalisation of point (1) in Bill Skaggs' "counterfactualist" position. Obviously many of us don't accept it. Less obviously, some of us not accepted his point (1) still consider it valuable to discuss point (2). dc| (2) Within this class there exist systems that are behaviourally dc| equivalent (to infinity) but cognitively distinct. [Anti-behaviourism]. Many empiricists are happy to discard this. Note that you must discard this if you discard (1), by the way, although there are alternate versions of it that could easily take its place. I think Dave wanted this to be independent of (1). When made independent, it is not "anti-behaviorism". It might very well be anti-Dennett too, for example. dc| (3) If implementation of an FSA A suffices for the possession of dc| certain cognitive properties, but A is an implementation of a dc| simpler FSA B that is behaviourally equivalent, then implementation dc| of B also suffices for possession of those cognitive properties. dc| [Irrelevance of implementational detail.] This one seems more mistaken than the rest. I am not inclined to believe it. It is true that if you take A, it seems like a minor thing to identify two of its states that are behaviorally indistiguishable: if you were designing the automaton, you would consider both of them unneeded, and optimise with zeal. But when this is done repeatedly the resulting automaton looks very different. I would like to rule this condition out even if I don't accept (1), (2), or both, above. Or more accurately, tighten up the definition of implementation to avoid the existence of undesireable B. Given Dave's comment that it's okay for one system to implement non-isomorphic automata, I am not sure why he is concerned about the case where one of the automata is reducible to the other. Nevertheless, let us see if there is a way to tighten the definition of implementation so that we can cut out more implementations, being left with only the more complex "intended implementation". There is one idea which comes to mind: it is something similar to that suggested by Robert Cummins in the Appendix of his book "The Nature of Psychological Explanation" (Q: why are all these things in appendices? A: Because they are hoping no one will read them?). The map-tester implements the constant-function *in virtue of* its doing the map testing. Yes. This means that if it *didnt* do the map testing, it would not (necessarily) implement the constant function. Applying the Ramsey test, it follows that in some worlds which are as similar as possible to the actual world except for the fact that the map-tester *doesn't* do map testing in these worlds, the map-tester *doesn't* implement the constant function. It is easy to see a class of counterfactuals to use in this case: we take the defining table for the map-tester, and we make minimal changes in its entries, by introducing an "error" into the output function or the state transition function. We now insist that the implementation supports counterfactuals such as "if this automaton had been this slightly different one, then it would act in this different manner", in addition to the ones we already require it to support. (I'll spare the formal details of how this would modify the definition of implementation). This may seem like a kludge, but it does have some good points. It naturally suggests the idea of locality: which is that different parts of the automata are really realised by different parts of the implementing system. A change in one of these parts does not affect the other part. We can continue along these lines and point out other kinds of counterfactual whose support would indicate another important kind of locality: the notion that states have internal structure, which as Neil Rickert points out is an important practical consideration, and more importantly may be a very important epistemological consideration when it comes to our attempting to justify our claims about functional organisation: could we ever discover a functional organisation if it were not constrained in such a fashion? --------------------------------------------------------------------------- Calvin Ostrum cbo@cs.toronto.edu --------------------------------------------------------------------------- To call physicalism philosophy is only to pass off an equivocation as a realization of the perplexities concerning our knowledge in which we have found ourselves since Hume. Nature can be thought of as a definite manifold, and we can take this idea as a basis hypothetically. But insofar as the world is a world of knowledge, a world of consciousness, a world with human beings, such an idea is absurd for it to unsurpassable degree. -- Husserl, Crisis of European Sciences --------------------------------------------------------------------------- From bronze!chalmers Thu Mar 26 02:34:55 EST 1992 Article: 5653 of comp.ai.philosophy Xref: bronze sci.philosophy.tech:7495 comp.ai.philosophy:5653 Newsgroups: sci.philosophy.tech,comp.ai.philosophy Path: bronze!chalmers From: chalmers@bronze.ucs.indiana.edu (David Chalmers) Subject: Re: A rock implements every FSA Organization: Indiana University References: <92Mar23.003224est.14362@neat.cs.toronto.edu> <1992Mar24.025128.9379@bronze.ucs.indiana.edu> <92Mar25.053818est.14337@neat.cs.toronto.edu> Date: Thu, 26 Mar 92 07:34:17 GMT Status: RO In article <92Mar25.053818est.14337@neat.cs.toronto.edu> cbo@cs.toronto.edu (Calvin Bruce Ostrum) writes: >True, but not when you add the words "one particular". Maybe this wouldn't >bother functionalists, and I admit to being quite hazy as to why it bothers >me. It's something like this: if implementing these systems amounts to >having a certain psychological characterisation in terms of beliefs and >desires, and if they are radically non-isomorphic, it seems like the >attributions of belief and desire given to me would be radically different >also. That makes me feel uncomfortable. Perhaps its just a bad feeling. >Perhaps it cuts no ice, either, and I should be able to live with it. Well, I think that if you accept that you're a system and not an object, then it's OK. Your body implements a lot of systems, but only one of those systems is you. >Yes, my point in mentioning it was merely to suggest that when we actually >come to apply "implementation of automata" to any problem of interest, it >is not absolutely clear what counterfactuals we should be considering. We >might want to consider relaxing some of them. We might want to have a >better theory of exactly *why* we care about counterfactuals in the >first place. I think Dave thinks this is something so obvious that we >don't need a theory of it. I'll agree that it's (probably) obvious, >but I'm still pretty mystified about counterfactuals (because I'm mystified >by their truthmakers. Probably that's just me. Still, I feel a lot >of folks, like those who give David Lewis that famous incredulous stare, >have their heads in the sand on this point). I agree that the truth-conditions of counterfactuals are a vast and fascinating problem. But as you've said yourself, the truth-conditions of these particular counterfactuals are pretty straightforward. As for why we care about counterfactuals, that's a nontrivial point: but it seems fair enough that it's built into the concept of intelligence, for instance, that an intelligent system be able to cope with a variety of different situations, not just a single situation, for instance; that a correct attribution of a belief gives a certain predictive power across a variety of different conditions; and so on. i.e. I think it's built into our very concepts of cognitive states that certain strong conditionals be satisfied by beings in those states. Qualia and consciousness constitute a more difficult question, as unlike other mental states, these don't seem to conceptually supervene on the physical, but if one accepts that qualia cohere in some strong fashion with cognitive states, then they must also depend on the satisfaction of this kind of conditional. >We are tempted to disallow this by saying that the rock required is too >fantastic. I left open whether or not such a rock was too fantastic by >saying (although "commonly occuring natural conditions" is too strong, and >Dave thinks "multiply implemented" is too weak): Well, I think that it's a strong enough condition that it's going to rule out most naturally occurring systems, like rocks. But the point is that it's still worrying because the addition of a list to such a system seems on the face of things to be fairly trivial, and not the kind of thing that will suddenly endow it with cognitive properties. >dc| Any cognitive properties >dc| that the system has, one would think, would exist in virtue of >dc| implementing the simpler system -- a higher level description that >dc| seems to capture everything relevant to cognitive function. At least >dc| this is the standard view we get from the functionalist approach to >dc| cognition. > >I don't see the argument for this view. However, it is true that it is not >obvious how to defeat it either. I arise at something like this view through the following considerations: any object, e.g. a human body, implements a whole lot of FSAs. How do we decide which FSA is the one in virtue of which the relevant cognitive properties hold? Well, presumably it has to be an FSA that gets the behaviour right, given the inputs (given that we can independently decide what counts as behaviour -- "outputs" such as sweat or even arm-twitches will not, for instance -- and the relevant inputs). There will still be a lot of FSAs that do this, at finer and finer levels of description. The usual thing to do in cognitive science is to take the highest-level description that gets the behaviour right, and to dismiss the finer descriptions as implementational detail. Eventually I think we want to reject this view, but this is roughly the motivation. Without this criterion, it's fairly difficult to see how we are going to pick out the relevant level of description of a being's functional organization. >dc| (1) There is a nontrivial class of cognitive systems that have the >dc| cognitive properties they do in virtue of implementing a certain FSA; >dc| i.e. any system that implements that FSA will possess those >dc| cognitive properties. [FSA-based functionalism.] > >Well, personally, I think this is completely wrong, and I am happy to >discard it. This is a generalisation of point (1) in Bill Skaggs' >"counterfactualist" position. Obviously many of us don't accept it. >Less obviously, some of us not accepted his point (1) still consider it >valuable to discuss point (2). Well, this is the one that I am least willing to discard. At best I would move from FSAs to some other more constrained formalism, such as finite TMs, if that could work out. But something like this seems to be a prerequisite for the truth of functionalism. >dc| (2) Within this class there exist systems that are behaviourally >dc| equivalent (to infinity) but cognitively distinct. [Anti-behaviourism]. > >Many empiricists are happy to discard this. Note that you must discard >this if you discard (1), by the way, although there are alternate versions >of it that could easily take its place. I think Dave wanted this to be >independent of (1). When made independent, it is not "anti-behaviorism". >It might very well be anti-Dennett too, for example. I inserted the "within this class" because without it, the statements are not inconsistent in principle. e.g. it might happen that all behaviourally equivalent FSAs are cognitively equivalent, but there are behaviourally equivalent non-FSAs that are cognitively different. But as long as FSAs are a reasonably good sample of cognitive systems in general, which I think they are, then the reasons for rejecting the broader version should apply to the more constrained version. >dc| (3) If implementation of an FSA A suffices for the possession of >dc| certain cognitive properties, but A is an implementation of a >dc| simpler FSA B that is behaviourally equivalent, then implementation >dc| of B also suffices for possession of those cognitive properties. >dc| [Irrelevance of implementational detail.] > >This one seems more mistaken than the rest. I am not inclined to believe >it. It is true that if you take A, it seems like a minor thing to identify >two of its states that are behaviorally indistiguishable: if you were >designing the automaton, you would consider both of them unneeded, and >optimise with zeal. But when this is done repeatedly the resulting >automaton looks very different. I would like to rule this condition out >even if I don't accept (1), (2), or both, above. Or more accurately, >tighten up the definition of implementation to avoid the existence of >undesireable B. OK, we're agreed on this then. Something like this is motivated by the principle that properties of a being cannot make a difference in behaviour don't make a difference to its cognitive properties. Certainly for almost any common-or-garden cognitive property, it will be possible for it to make a difference to behaviour. The trouble arises for beings like the super-Spartans -- we want to say something like their pains *could* make a difference to behaviour, if they so chose, but it so happens that they never choose to, under any circumstances. There's some kind of equivocation on the modality of the "could". So the simple criterion of cognitive property-hood that one gets by looking at the system's overall capacity to cause behaviour is too simple in principle, though I think it will be fine in practice, and only defeated by outlandish cases like the super-Spartans where capacities to cause behaviour are overridden by some other internal state, like will. >It is easy to see a class of counterfactuals to use in this case: we >take the defining table for the map-tester, and we make minimal changes >in its entries, by introducing an "error" into the output function or the >state transition function. We now insist that the implementation supports >counterfactuals such as "if this automaton had been this slightly >different one, then it would act in this different manner", in addition >to the ones we already require it to support. (I'll spare the formal >details of how this would modify the definition of implementation). Right, something like this seems to make sense, capturing something along the ideas of what I said above. The map-checker has the "capacity" to produce different behaviour from the single-state machine, it's just that this never gets used for complex mathematical reasons. Your new class of counterfactuals might help bring out this "capacity". -- Dave Chalmers (dave@cogsci.indiana.edu) Center for Research on Concepts and Cognition, Indiana University. "It is not the least charm of a theory that it is refutable." From bronze!news.cs.indiana.edu!mips!zaphod.mps.ohio-state.edu!pacific.mps.ohio-state.edu!linac!att!ucbvax!VNET.IBM.COM!kap Thu Mar 26 15:44:51 EST 1992 Article: 5659 of comp.ai.philosophy Path: bronze!news.cs.indiana.edu!mips!zaphod.mps.ohio-state.edu!pacific.mps.ohio-state.edu!linac!att!ucbvax!VNET.IBM.COM!kap From: kap@VNET.IBM.COM (Kenneth A. Presting) Newsgroups: comp.ai.philosophy Subject: Re: A rock implements every FSA Date: 26 Mar 92 16:46:24 GMT References: <92Mar18.182726est.14357@neat.cs.toronto.edu> <1992Mar19.000544.22634@bronze.ucs.indiana.edu> Sender: daemon@ucbvax.BERKELEY.EDU Status: RO <92Mar23.003224est.14362@neat.cs.toronto.edu> <1992Mar24.025128.9379@bronze.ucs.indiana.edu> <92Mar25.053818est.14337@neat.cs.toronto.edu> In <92Mar25.053818est.14337@neat.cs.toronto.edu> Calvin Bruce Ostrum writes: >dc| However, one might get around this by adding the >dc| constraint that the rock maintains a list of all inputs so far. This >dc| ensures that it will always be in a distinct physical state after any >dc| sequence in L*. Of course we would now be far from any ordinary "rock", >dc| but there is a sense in which what we added is trivial, and we wouldn't >dc| expect it to add amazing cognitive powers to a system, so that if >dc| the result goes through with this extra constraint, functionalism may >dc| may still be in trouble. I'll come back to this. > >We are tempted to disallow this by saying that the rock required is too >fantastic. I left open whether or not such a rock was too fantastic by >saying (although "commonly occuring natural conditions" is too strong, and >Dave thinks "multiply implemented" is too weak): This is not a problem. Take a lump of clay as the "rock". "Input" could then be fine scratches on a flattend surface of the clay. To return the lump to the initial state, fold the input surface over on itself and flatten the lump again. (This is supposed to be the way the Babylonians used cuneiform script for taking temporary notes) Now the lump has an internal "record" of everything that was ever written on it. If you're willing to be more abstract in the kinds of things you allow to be a "list of inputs", then you could consider any old rock, and let scratches on it be the inputs. Of course, no rock could implement this trick out to infinity, but then neither could any person or any computer. > >cbo| What is not obvious (to me) is if >cbo| there are any commonly occuring natural conditions under which there >cbo| must be multiply implemented automata, such that many of these automata >cbo| are not only non-isomorphic, but also not comparable under this >cbo| "reducibility ordering". > >My feeling is that we still should be able to say something in this case, >however. There just seems something wrong with these ad hoc disjunctions, >and we want to eliminate them while retaining the natural "multiple >realisability" that led away from central-state identity theory in the >first place. I have some extremely half-baked (and obvious) ideas about >how this might be done. I had a theory on this topic myself. Does anybody out there remember "Implementationism?" >dc| (3) If implementation of an FSA A suffices for the possession of >dc| certain cognitive properties, but A is an implementation of a >dc| simpler FSA B that is behaviourally equivalent, then implementation >dc| of B also suffices for possession of those cognitive properties. >dc| [Irrelevance of implementational detail.] If this principle is accepted, then the consequences could be very adverse for functionalism. Note that when physically implementing an abstract automaton, the physical representation of input and output data formats is entirely arbitrary. Furthermore, the input representation is typically quite different from the output representation (eg keystrokes vs. pixels). With all this arbitrariness in the mappings, any rock with an adequate number of distinct states would be behaviorally equivalent to any automaton. And it it not to difficult to (idealistically) conceive of a rock with countably many states, or a continuum of states. This objection is not meant to be a show-stopper. It is just one more detail that has to be ironed out in the concept of implementation. > ... Nevertheless, let us see if there >is a way to tighten the definition of implementation so that we can cut >out more implementations, being left with only the more complex "intended >implementation". ... >take the defining table for the map-tester, and we make minimal changes >in its entries, by introducing an "error" into the output function or the >state transition function. We now insist that the implementation supports >counterfactuals such as "if this automaton had been this slightly >different one, then it would act in this different manner", in addition >to the ones we already require it to support. (I'll spare the formal >details of how this would modify the definition of implementation). These formal "details" may turn out to be much more challenging than they first appear. The theory of counterfactuals is very controversial; counter-identical statements such as you propose are the among the most problematic topics in the theory. If Functionalism is to be saved only by appealing to unspecified future developments in the theory of counterfactuals, it may be a very long time before the functionalists can answer such basic questions as "which objects instantiate automaton X?" It was bad enough when Functionalism was the only game in town. Now we're supposed to stop playing Functionalism and play Counterfactuals instead? Yuck. There has to be a better way. Ken Presting "Psst - wanna buy a hot concept?" From bronze!chalmers Thu Mar 26 15:45:39 EST 1992 Article: 5663 of comp.ai.philosophy Newsgroups: comp.ai.philosophy Path: bronze!chalmers From: chalmers@bronze.ucs.indiana.edu (David Chalmers) Subject: Re: A rock implements every FSA Organization: Indiana University References: <92Mar18.182726est.14357@neat.cs.toronto.edu> <1992Mar19.000544.22634@bronze.ucs.indiana.edu> <9203261657.AA12526@ucbvax.Berkeley.EDU> Date: Thu, 26 Mar 92 20:44:47 GMT Status: RO In article <9203261657.AA12526@ucbvax.Berkeley.EDU> kap@vnet.ibm.com writes: >Note that when physically implementing an abstract automaton, the >physical representation of input and output data formats is entirely >arbitrary. A number of people seem to be saying things like this, so I should note that Putnam himself is quite explicit on this point (p. 124): The inputs and outputs have certain constrained realizations, or at least their realizations must be of certain constrained kinds depending on our purposes; usually we are not allowed to simply *pick* physical states to serve as their realizations, as we are allowed to do with the so-called "logical states" of the automaton. Of course it's not entirely clear just what these constraints are, but I suggest that at the very least the inputs really have to be *inputs*: i.e. they have to supervene on a spatially distinct region from internal states of the automaton. That's enough to defeat a few of the more bizarre attempts at pan-implementationalism that have been seen around here. >The theory of counterfactuals is very controversial; counter-identical >statements such as you propose are the among the most problematic >topics in the theory. If Functionalism is to be saved only by appealing >to unspecified future developments in the theory of counterfactuals, >it may be a very long time before the functionalists can answer such >basic questions as "which objects instantiate automaton X?" As I've said a number of times, we don't need any sophisticated theory, such as a possible-worlds semantics, to evaluate the simple counterfactuals involved in the definition of implementation. >It was bad enough when Functionalism was the only game in town. Now >we're supposed to stop playing Functionalism and play Counterfactuals >instead? Yuck. There has to be a better way. Some people seem to be running a mile at any mention of the term "counterfactual". There's really no problem. Functionalism has *always* been concerned with these. Or even look at its predecessor, behaviourism. Did Ryle say that mental states were fully determined by actual behaviour? Of course not. He said that mental states were determined by behavioural *dispositions*, i.e. how the system *would* behave, or *would have* behaved, in certain circumstances. There are your counterfactuals. Perhaps I should take Joseph O'Rourke's advice and drop the term "counterfactual", even though it's correct. "Strong conditionals" will do instead. Any vaguely functionalist theory will require a system to satisfy certain conditionals, and it's obvious that these can't just be weak material conditionals, made vacuously true by the falsity of the antecedents in the actual run of things. Rather, they carry some modal force, i.e. if the antecedent *were* true then the consequent *would* come about. The "counterfactuals" in the Putnam case are just these modal conditionals, whose truth is being evaluated after the fact -- i.e. if the antecedent *had* occurred, then the consequent *would have* come about. But obviously after-the-fact evaluation doesn't make any difference to the truth of these conditionals. And if anyone wants to argue that no strong conditional has a determinate truth-value, they have a lot of arguing to do. Most of science will have to be redone, for a start. Most of the Putnam-style refutations come about by implicitly interpreting these conditionals as simple material conditionals, which is just silly. -- Dave Chalmers (dave@cogsci.indiana.edu) Center for Research on Concepts and Cognition, Indiana University. "It is not the least charm of a theory that it is refutable." From bronze!news.cs.indiana.edu!mips!zaphod.mps.ohio-state.edu!rpi!news-server.csri.toronto.edu!psych.toronto.edu!michael Thu Mar 26 17:01:30 EST 1992 Article: 5666 of comp.ai.philosophy Xref: bronze sci.philosophy.tech:7504 comp.ai.philosophy:5666 Newsgroups: sci.philosophy.tech,comp.ai.philosophy Path: bronze!news.cs.indiana.edu!mips!zaphod.mps.ohio-state.edu!rpi!news-server.csri.toronto.edu!psych.toronto.edu!michael From: michael@psych.toronto.edu (Michael Gemar) Subject: Re: A rock implements every FSA Organization: Department of Psychology, University of Toronto References: <1992Mar24.025128.9379@bronze.ucs.indiana.edu> <92Mar25.053818est.14337@neat.cs.toronto.edu> <1992Mar26.073417.14604@bronze.ucs.indiana.edu> Date: Thu, 26 Mar 1992 20:42:39 GMT Status: O In article <1992Mar26.073417.14604@bronze.ucs.indiana.edu> chalmers@bronze.ucs.indiana.edu (David Chalmers) writes: >I arise at something like this view through the following considerations: >any object, e.g. a human body, implements a whole lot of FSAs. How do >we decide which FSA is the one in virtue of which the relevant cognitive >properties hold? Well, presumably it has to be an FSA that gets the >behaviour right, given the inputs (given that we can independently >decide what counts as behaviour -- "outputs" such as sweat or even >arm-twitches will not, for instance -- and the relevant inputs). There >will still be a lot of FSAs that do this, at finer and finer levels >of description. The usual thing to do in cognitive science is to >take the highest-level description that gets the behaviour right, >and to dismiss the finer descriptions as implementational detail. > >Eventually I think we want to reject this view, but this is roughly >the motivation. Without this criterion, it's fairly difficult >to see how we are going to pick out the relevant level of >description of a being's functional organization. > I agree that the view you present above is problematic, and should be rejected, but I have no inkling at what a functionalist does then, i.e., how one would pick out the relevant level of functional analysis. This seems to me to be a rather important problem - do you have any suggested methods of attack? - michael From bronze!sol.ctr.columbia.edu!zaphod.mps.ohio-state.edu!uakari.primate.wisc.edu!usenet.coe.montana.edu!ogicse!das-news.harvard.edu!spdcc!dirtydog.ima.isc.com!ispd-newsserver!psinntp!scylla!daryl Sat Mar 28 19:39:35 EST 1992 Article: 5684 of comp.ai.philosophy Path: bronze!sol.ctr.columbia.edu!zaphod.mps.ohio-state.edu!uakari.primate.wisc.edu!usenet.coe.montana.edu!ogicse!das-news.harvard.edu!spdcc!dirtydog.ima.isc.com!ispd-newsserver!psinntp!scylla!daryl From: daryl@oracorp.com (Daryl McCullough) Newsgroups: comp.ai.philosophy Subject: Re: A rock implements every FSA Date: 27 Mar 92 14:51:07 GMT Organization: ORA Corporation Status: RO One of the original postings in this thread, by Joseph O'Rourke, I think, said that Putnam proved that functionalism reduces to behaviorism, and that Putnam's "A rock implements any FSM" was used in proof. At first, it seemed like nonsense to me; I agreed with the posters who said that Putnam was playing fast and loose with the notion of what it means to implement a finite state machine. However, an argument made by Mikhail Zeleny convinced me otherwise. Now, I am convinced that Putnam is essentially correct---if not in his proof, then in his conclusion that functionalism is essentially equivalent to behaviorism. I would like it if those functionalists, such as David Chalmers and Drew McDermott, who are not behaviorists would tell me what is wrong with the following argument. A deterministic finite state machine can be defined by the following functions: T : State -> State, the internal transition function I : State x Input -> State, the input transition function O : State -> Output, the output function State is the set of states, which we will assume to be called State_0, State_1, State_2, etc. Function T tells how the machine changes state when there are no inputs, and function I tells how the machine is affected by its inputs. The function O tells how outputs are produced from the current state. (This is not the classic definition of finite automata, but I think it has enough features to illustrate the ideas here.) Without getting too bogged down in exactly what it means for one FSM to implement another, let me assume that it is enough to have a mapping from system states to FSM states such that (1) transitions are preserved, and (2) outputs are the same for corresponding states. Now, with this notion of implementation, the Zeleny machine, together with a couple of lookup tables, can implement *any* FSM. The Zeleny machine has states defined by a pair of integers and has the transition relation: --> . Okay, so the mapping: M() = State_n M() = T(M()) We also need input function I', and the output function O': I'(, i) = , where k is given by I(M(),i) = State_k. O'() = O(M() It is clear that the mapping M preserves the transition function, and that the output function gives the same answer on corresponding states, so therefore the state machine with states , input function I', output function O', and transition function --> implements the original state machine. Note, however, that the functions I' and O' are mathematical functions, not state machines. Therefore, it is sufficient to implement them with a table lookup, since for mathematical functions the only thing that matters is the input/output relation. Also, note that the state machine itself is entirely trivial, since it does nothing but count. Since the functional state part of this implementation is so completely trivial, it seems plausible to me that the "intelligence", or "understanding" (if there is any) is all in the input and output functions. If functionalism is correct, then maybe this says something striking about the way brains work. It is common to think of the brain as composed of conscious and unconscious parts. When sensory information (such as visual signals) enter the brain, there is a lot of unconscious processing to get the information in a shape that our conscious mind can use. Then we do our conscious thinking about that information, and decide on a response. Then, once again there is unconscious processing to translate that response into the particular output signals to our muscles to make our bodies do the right thing. However, as this example shows, if you claim that all the pre- and post-processing of information is unconscious, then that might not leave anything at all for the *conscious* mind to do. Maybe the split between conscious and unconscious is less clear than one might at first think. Daryl McCullough ORA Corp. Ithaca, NY From bronze!chalmers Sat Mar 28 19:09:50 EST 1992 Article: 5701 of comp.ai.philosophy Newsgroups: comp.ai.philosophy Path: bronze!chalmers From: chalmers@bronze.ucs.indiana.edu (David Chalmers) Subject: Re: A rock implements every FSA Organization: Indiana University References: <1992Mar27.145107.12415@oracorp.com> Date: Sat, 28 Mar 92 20:47:05 GMT Status: RO In article <1992Mar27.145107.12415@oracorp.com> daryl@oracorp.com (Daryl McCullough) writes: >A deterministic finite state machine can be defined by the following >functions: > > T : State -> State, the internal transition function > I : State x Input -> State, the input transition function > O : State -> Output, the output function This is more or less OK, but there's no need to split the transition function into T and I. T is just a special case of I, for the case where the input is the "null input", or whatever you want to call it. What you have above is harmless, but more complex than necessary (and we'll see below that you exploit this split to do more work than it can). >Okay, so the mapping: M() = State_n > M() = T(M()) > >We also need input function I', and the output function O': > > I'(, i) = , where k is given by I(M(),i) = State_k. > > O'() = O(M() This is bizarre. This seems to me to be a perfectly good implementation of an FSA (the issue is complicated somewhat by the special treatment of the "T" subset of the transition function, leading to disjunctivitis on machine states, but let that slide). But it certainly doesn't prove anything. This machine is far more complex than Putnam's rocks. Its complex structure derives, of course, almost entirely from the trans