tag:blogger.com,1999:blog-5801278565856116215.post4904474777682389244..comments2016-11-10T13:57:43.522+00:00Comments on Disagreeable Me: Putnam, Searle and Bishop: The Failure of Physicalist ComputationalismDisagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comBlogger142125tag:blogger.com,1999:blog-5801278565856116215.post-28953055110442231172016-11-10T12:47:50.165+00:002016-11-10T12:47:50.165+00:00>My claim is that the content of our minds come...>My claim is that the content of our minds comes from the patterns in the processing of signals which in isolation have no inherent meaning.<br /><br />But how's that supposed to work? I mean, we could (on standard notions of computation) implement the computation performed by a mind using a network of AND-gates and negations. But, on value agnosticism, these AND-gates don't operate on truth values, but just shuffle voltages around. The output of a mind, however, isn't voltages; it's meaningful symbols. So, where does the transition take place? Say I have a simulation, using AND-gates and negation, of a mind solving the task of finding the AND of 0 and 1. <br /><br />Now, of course, on value agnosticism, 0 and 1 aren't input into the system anywhere---rather, there is some pattern of voltages (meaningless symbols) at the input; these propagate through the network, producing, as output, again a pattern of meaningless symbols. Where does the meaning of 0 and 1 come from?<br /><br />Furthermore, as you quite rightly point out, 0 and 1 aren't physical objects. But all your value-agnosticism really boils down to is physical description. So, again, where do 0 and 1 come from all of a sudden? If all the system does is the value-agnostic shuffling around of meaningless symbols, there's no 0 or 1 to be found anywhere in the system. Yet, we can meaningfully compute the AND of binary digits.<br /><br />>Not only can you interpret an AND gate as computing AND or OR, you can interpret it as computing Microsoft Excel.<br /><br />Well, that's not really true---there aren't enough states, for one---but I get your point. However, I was wondering why, if you hold to the value-agnostic approach, Putnam-style arguments ought to worry you: all Putnam really does is to point out that the interpretation of the physical states of a system is arbitrary; but you do away with such interpretation completely. So, if you have a Putnam-style open system, then there is always a definite value-agnostic interpretation: it's just the sequence of states it actually traverses, viewed as 'meaningless symbols'. Putnam's trick precisely is that one can imbue those with arbitrary interpretations---the exact move you're rejecting here, in favor of value-agnosticism.<br /><br />So, if value-agnosticism were appropriate, it wouldn't just work against my argument, but equally well against those by Putnam, Searle, or Bishop. Yet, you seem to think these arguments work, at least against physicalist computationalism.Jochenhttp://www.blogger.com/profile/07418841955052661428noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-63428355844677381532016-11-10T12:47:31.310+00:002016-11-10T12:47:31.310+00:00>But if I have an isolated mathematical system ...>But if I have an isolated mathematical system f1, and you come along and define another isolated mathematical system f2, we're no longer talking the same language.<br /><br />But f2 is defined using the same language---it's even defined in terms of f1! The function f1 includes all that I need in order to define f2. Anybody familiar with the definition of f1 will immediately understand when I define f2(x,y) as (f1(x',y'))'. I don't need to introduce anything new, that wasn't part of the language needed to define f1 in the first place.<br /><br />>you're assuming that the two x's mean the same thing even though they are used in distinct and isolated contexts.<br /><br />No---I define one x by means of the other, and the machinery needed to make that other one interpretable.<br /><br />>What I mean is that A has no inherent meaning, other than the role it plays in the system.<br /><br />And the role it plays in that system (and the role played by B, and the truth table relating the two) is sufficient to define its role in the system given by f2. <br /><br />>No, you can't. That interpretation is inconsistent with the definition of the function.<br /><br />Yes, you're right, I didn't really think that through. But actually, this was what prompted my worry about your 'computation' really just being a description of the physical behavior of the system---which, again, isn't what one would typically mean by 'computation'. Take, for instance, <a href="http://jeapostrophe.github.io/2013-10-29-tmadd-post.html" rel="nofollow">this</a> very lovely and detailed description of a Turing machine that does binary addition (part 5). Now, most people would agree that this TM indeed performs exactly that function: addition of binary numbers. However, on your conception of computation this (and, in fact, all claims regarding TMs implementing abstract functions) would be false: it just changes some states of the tape to some 'value-agnostic' different states. In essence, this is just a description of the TMs operation, but not of the computation implemented thereby---no TM ever really computes anything, it merely evolves in time.<br /><br />In particular, this plays havoc with the notions of computational equivalence and universality. Typically, for instance, one holds that certain TMs---universal ones---can simulate all other TMs. But there is no requirement that to do so, a UTM must physically mirror the evolution of the TM it emulates---for instance, a TM over the decimal numbers could simulate the addition, without thereby possessing anything like a mapping between its states and those of the binary addition-TM. So this notion wouldn't really make sense on your conception of computation.<br /><br />Moreover, completely differently implemented systems can perform the same computation. An adder made of logical gates will, on the typical conception of computation, perform the same function as the binary addition-TM; but that doesn't mean that it mirrors the 'value-agnostic' process of that TM. Neither, of course, will have much in common with a neural network implementing that computation, or a random-access machine, and so on. Jochenhttp://www.blogger.com/profile/07418841955052661428noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-89802980391177409462016-11-10T12:46:43.854+00:002016-11-10T12:46:43.854+00:00Hi DM,
>But a brain or an AI doesn't have ...Hi DM,<br /><br />>But a brain or an AI doesn't have preconceptions about what it computes.<br /><br />Which actually brings up a larger worry: when an AI, say in the course of a Turing test, claims that 4+3=7, we'd typically not take it to do so in a 'value-agnostic' way; it really means that if you take four, and add three, you get seven. Or at least, barring eliminativisim, that's what it needs to do in order to replicate human performance on this task.<br /><br />So it seems, to me, that computations implementing a mind can't be value agnostic---for the Turing test to have any applicability, it must be the case that the inputs presented to an AI, and the outputs produced by it, must be value-definite. So it doesn't seem plausible that the computation implementing a mind could be value-agnostic.<br /><br />I know that the usual answer to such worries is just to define a structure that's complex enough in order to not make it obvious anymore that if it's value-agnostic at the base, so to speak, it also is at the higher level---but I've yet to see any such attempt where it's not simply the impossibility to completely think through the system that makes it sufficiently opaque to hide the persistence of value-agnositicism.<br /><br />>As soon as you introduce one, you've effectively "implied" a whole lot more<br /><br />Yes; again, this is just Newman's problem. But the point I'm making is simply that I can effectively use the system you say implements f1 to implement f2---you keep claiming they're independent, but they're not: defining one unavoidably defines the other. It's like a painting, where the negative space defines the (outlines of the) figure, and vice versa: you can't have one without the other. <br /><br />>But the structure that models the AND gate has only f1, say.<br /><br />But f1 implies f2. There's no additional information needed: if you give me one, then you've implicitly given me the other.<br /><br />>You don't need f1 to define f2.<br /><br />That's not what I'm saying. I don't need f1---but f1 *suffices*. <br /><br />>But they are only distinct if you create a structure which has both f1 and f2 at the same time<br /><br />Which every structure does: as soon as it has f1, it has f2.<br /><br />>From that perspective, we only have a manipulation of valueless bit-analogues<br /><br />But isn't that just a description of the physical evolution of the system? The set of states it traverses? <br /><br />I don't think this is sufficient as a definition of computation. I mean, basically, all you do is to just write down names for the states that the system could be in. There's nothing there except for, e.g., the phase-space trajectory. It doesn't seem plausible to me that 'computation performed by the system' could reduce to 'the phase-space trajectory traced out by the system': this trivializes the notion of computation. <br /><br />I mean, take a look at what the central thesis of computationalism becomes under this view of computation: 'the brain gives rise to a mind by implementing the appropriate computation' becomes 'the brain gives rise to a mind by tracing out the appropriate phase-space trajectory', which really just means 'the brain gives rise to a mind by being the appropriate kind of physical object'. So really, this just leaves us back to square one: some physical objects give rise to minds. This, we knew already (at least, if we're not admitting some weird nonphysical elements).<br /><br />>I thought we were discussing the bit-flipping argument where we adopt a bit-level perspective.<br /><br />To me, the binary system is just a particularly simple alphabet for a computation to have; but the argument is really quite independent from the particular alphabet, as long as computation is a function over some alphabet. This is, effectively, what you aim to deny: that computations are functions over a given universe, with some definite inputs and outputs. Jochenhttp://www.blogger.com/profile/07418841955052661428noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-64166026425988351152016-11-10T11:25:41.476+00:002016-11-10T11:25:41.476+00:00> And as such, I can again change it: interpret...> And as such, I can again change it: interpret A as meaning 'that symbol which is output when it occurs at least once'.<br /><br />No, you can't. That interpretation is inconsistent with the definition of the function.<br /><br />> As I said, since our minds very much appear to have content, to have definite values<br /><br />My claim is that the content of our minds comes from the patterns in the processing of signals which in isolation have no inherent meaning. Just as we can infer a meaning for A based on the role it plays in the system, so can the meaning in human minds come from the causal/functional roles the signals play. That meaning cannot be imported from outside the system.<br /><br />> So really, parsimony here is just a statement of prejudice---you like the 'simpler' interpretation better. <br /><br />As I've said, I agree with you that parsimony is not a good approach on this particular question -- that is more or less why I think physicalist computationalism does not work. I think parsimony is a good epistemic heuristic to choose between mutually-exclusive hypotheses (whether physical or metaphysical), but not a good way to settle what computation is objectively being computed, because there is no reason to believe that there has to be only one answer to that question.<br /><br />But the appeal of the bit-flipping argument is that it seems to do away even with parsimony as a basis for a preferred interpretation. For the bit-flipping argument to be held up as more important or persuasive than the pixies argument, you need to assume that parsimony matters. If you dispense with parsimony, then you can use any interpretation you like, no matter how arcane, ad hoc and retrospective. Not only can you interpret an AND gate as computing AND or OR, you can interpret it as computing Microsoft Excel.Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-16065288913718746082016-11-10T11:25:29.351+00:002016-11-10T11:25:29.351+00:00> Yes, well, and if we no longer assume that &#...> Yes, well, and if we no longer assume that 'horse' means horse, it could mean buttercup. <br /><br />I don't think that's what I'm doing. When you and I talk about horses, we are conversing in the context of a massively complex shared system of communication called "English", where 'horse' means horse and not buttercup. But if I have an isolated mathematical system f1, and you come along and define another isolated mathematical system f2, we're no longer talking the same language. Newton and Leibniz both invented calculus even though they used different notation -- the differences in notation don't mean that these are really different mathematical systems. So A in one has nothing to do with A in the other. What you're doing is akin to claiming to solve a complex polynomial equation for x in problem 3 on page 231 of a textbook by instead solving a simple equation for x you found in problem 1 on page 23 -- you're assuming that the two x's mean the same thing even though they are used in distinct and isolated contexts.<br /><br />As with the textbook problems, it's a coincidence of no significance that we're using the same symbol in each. I'm saying that A has no meaning other than its role in f1, which means we have no basis other than its role in f1 by which to to compare it to the A in your f2. If we want to see if vertex A in my polygon ABCDE is the same vertex as your vertex A in your polygon ABCDE, we might do so by comparing the Cartesian coordinates of my A with the Cartesian coordinates of your A. If we want to see if my value A in my function f1 is the same as your value A in your function f2, we have to see whether it plays the same role -- i.e. whether a mapping of f1's A to f2's A will form part of an isomorphic mapping. Since it doesn't, it is not the same A. Instead, my A instead corresponds to your B.<br /><br />> You can't really tell me both that 'A is meaningless' and that A means 'that symbol which is only output when it occurs twice'.<br /><br />What I mean is that A has no inherent meaning, other than the role it plays in the system. It is not the first letter of the alphabet. It is not a maximum or a minimum value. It does not correspond to truth or falsity. It is nothing other than what you can infer from the definition of the system, and all you can infer from the definition is that it is "that symbol which is only output when it occurs twice".<br />Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-78085248842381673262016-11-10T11:25:12.415+00:002016-11-10T11:25:12.415+00:00> You should keep in mind that your A and B are...> You should keep in mind that your A and B are not anymore physically real than 1 and 0 are<br /><br />I know. The difference between (A and B) and (1 and 0) is that A and B are intended to be without inherent meaning. I do away with ambiguity not by taking A and B to be physical but by taking A and B to be anything at all -- whatever they need to be to map the function.<br /><br />> On your value-agnostic view, such a computation is impossible, of course.<br /><br />It's possible in a practical, everyday sense, by importing meaning. But that is not the core essence of what is really going on from my hypothetical physicalist computationalist's perspective as he considers the bit-flipping argument. From that perspective, we only have a manipulation of valueless bit-analogues in such a pattern that it can be trivially interpreted as addition.<br /><br />So I accept your view that what I am calling computation in this discussion is not quite how computation is thought of 99.99% of the time, where it is legitimate to import meaning from the mind of an interpreter. But all the same, I think that my approach is more or less how any reasonable physicalist computationalist would answer the bit-flipping argument. If you don't think my answer is representative of physicalist computationalism and is therefore uninteresting and irrelevant, we can drop this discussion and concentrate on the other discussion.<br /><br />> For computations on natural numbers<br /><br />I thought we were discussing the bit-flipping argument where we adopt a bit-level perspective. I'm not sure where you're going with this. Can we stick to a bit perspective?<br /><br />> but an isomorphism just between two truth tables doesn't make sense to me.<br /><br />Well, I would say a truth table is just a set of relations from pairs of symbols to symbols -- these relations are the rows of the truth table. Viewed as a bijenction between sets, an isomorphism would map rows of one truth table to rows of the other and vice versa. But we're not just talking about sets that have no additional structure. The elements of the set (the relations) have structure too. For me at least, an isomorphism is a mapping of all the elements and terms and relations in one structure to those of another. You don't just map the rows arbitrarily, you have to consistently map the values in the rows too. The truth tables of f1 and f2 are isomorphic under the mapping A->B, B->A. This value-level mapping implies a row-level mapping between rows of f1 to rows of f2, e.g. f1(A,B)=A maps to f2(B,A)=B.<br /><br />> And if A, B, C, and D are different points, they aren't.<br /><br />Agreed. But if B in the first figure is the same point as C in the other figure, and vice versa, they are the same figure. Different mathematicians might choose to label these points differently, but these differences in notation don't mean we have different figures. f2 is just f1 with different notational conventions if they are taken in isolation.Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-28789460845654732432016-11-10T11:24:47.590+00:002016-11-10T11:24:47.590+00:00Hi Jochen,
> We always do, whenever we compute...Hi Jochen,<br /><br />> We always do, whenever we compute---that's usually *why* we compute,<br /><br />But a brain or an AI doesn't have preconceptions about what it computes. Whatever the core essence of the computation is or means or experiences, it has to come from within the system, it can't be predicated on your preconceptions. So I think you're just taking the wrong perspective on the problem.<br /><br />> Well, you can't really introduce a structure and then demand to use only half of it.<br /><br />It's far less than half of the structure you're talking about. There's a lot more than two possible truth tables formed from A and B. As soon as you introduce one, you've effectively "implied" a whole lot more -- an infinite family in fact if we allow more than two inputs.<br /><br />But your AND gate is not implementing two or more distinct patterns, and certainly not infinitely many. It's only implementing one pattern of inputs to outputs, so we only need one truth table to describe its behaviour. It may be that there are other possible truth tables but they are irrelevant to describing what the AND gate is doing.<br /><br />> But since f1 is different from f2<br /><br />So f1 is different from f2 if and only if they are taken to be parts of the same structure. But the structure that models the AND gate has only f1, say. You can see that there are other logically possible patterns, but since they are not required to describe the AND gate they can be discarded from your model. The structure we use to describe a computation is not simply the set of all possible structures.<br /><br />> If I have f1, then I can define f2 in terms of it---f1 already implies the structure of f2.<br /><br />It doesn't matter if f1 implies f2. These are mathematical objects. On platonism, they both exist necessarily. You don't need f1 to define f2. There's nothing stopping you defining f2 or any other function you like. On platonism, f2 always exists. f1 always exists. But they are only distinct if you create a structure which has both f1 and f2 at the same time, so that you can say that the A in one is the same value as the A in the other. It is of course possible to have a structure that only has one of them. That doesn't mean the other one doesn't exist, so the fact that you could add the other function to your structure doesn't matter -- you don't have to.<br /><br />> So in some way, it must be possible to combine value-agnostic computations to yield a computation that's non-value-agnostic.<br /><br />Yes. I mean, my view is that meaning can come from the interactions of patterns of bits which are each individually meaningless. So I guess what I said is not strictly true. To realise your AND (not OR) unambiguously, you would have to create an AI which is thinking about your AND function the way you do -- and then its mental representation of AND is unambiguous to it -- but not necessarily to an external observer. The best an external observer could divine would be an association between this representation and what that AI reports as "true" and "false" or "1" and "0".Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-57549951128006482732016-11-08T15:03:09.080+00:002016-11-08T15:03:09.080+00:00>my point is that whatever you do get is the sa...>my point is that whatever you do get is the same core value-agnostic computation in my view<br /><br />But how do we ever get the non-value-agnostic answer 7 for the addition of 3 and 4, if all that goes on are value-agnostic computations?<br /><br />>I'll assume you mean f2(B,A)=B because that is the corresponding row in the truth table for f2.<br /><br />I don't see the relevance: the function f2 yields, if evaluated on the pair (A,B), the outcome B, while the function f1 yields the outcome A. That's what makes them different functions.<br /><br />>f1 and f2 are clearly isomorphic truth tables. <br /><br />I don't know what you mean by an isomorphism between truth tables. Usually, an isomorphism (on sets that don't have any additional structure) is a bijection taking each element of a set to another, possibly different, one. So I could see an isomorphism on the set of truth tables (equivalently, on the set of functions from [0,1]^2-->[0,1]), but an isomorphism just between two truth tables doesn't make sense to me.<br /><br />>you are no longer considering the system of f1 in isolation or the system of f2 in isolation<br /><br />There's simply no such thing as 'the system of f1 in isolation', not in any way I know how to formulate, at least. If I have f1, then I can define f2 in terms of it---f1 already implies the structure of f2.<br /><br />>By your logic, ABCD is not the same figure as ACBD.<br /><br />And if A, B, C, and D are different points, they aren't.<br /><br />>But if we no longer assume that the A in one corresponds to the A in the other,<br /><br />Yes, well, and if we no longer assume that 'horse' means horse, it could mean buttercup. You set a convention with a formalization of the structure you propose; if you then use that formalization differently, you're simply doing something inconsistent.<br /><br />>A is just a placeholder for "that symbol which is only output when it occurs twice in the inputs"<br /><br />You can't really tell me both that 'A is meaningless' and that A means 'that symbol which is only output when it occurs twice'. The latter is as much an interpretation as saying 'the top element of B2'. And as such, I can again change it: interpret A as meaning 'that symbol which is output when it occurs at least once'. After all, there's nothing about high voltage that entails it meaning 'symbol which is only output...' anymore than there is entailing its meaning to be 'top element of B2'. As much as 0 and 1 aren't part of the physical world, so too aren't 'symbol which...'-type of interpretations.<br /><br />>Because I take C_M to be a value-agnostic structure akin to f.<br /><br />As I said, since our minds very much appear to have content, to have definite values, I think that's a significantly harder to justify proposition than standard computationalism.<br /><br />> I'm assuming for the sake of argument that the objectively right computational interpretation of a system is the most parsimonious one<br /><br />Appeal to parsimony is really only justified for physical theories: you need to choose one theory out of infinitely many possible ones explaining the observed data; then, the requirement of having this choice make unique predictions forces you to take the simplest one, as otherwise, from the observation that a stone drops when it's let go in a gravitational field, the prediction that it drops the next time under the same circumstances is as justified as the prediction that it grows wings and flies away.<br /><br />So really, parsimony here is just a statement of prejudice---you like the 'simpler' interpretation better. Clearly, this doesn't do anything to foster any sort of 'objective' answer to the question of what a system computes. Indeed, I would be on equal grounds to assert that the objectively right computation is one acting on binary values, because I like those better: without parsimony, that the same symbol should have the same meaning in all instantiations is just as much of an arbitrary choice.Jochenhttp://www.blogger.com/profile/07418841955052661428noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-41988137208263422972016-11-08T15:01:55.952+00:002016-11-08T15:01:55.952+00:00Hi DM,
>If you have preconceptions about what ...Hi DM,<br /><br />>If you have preconceptions about what you're interested in<br /><br />We always do, whenever we compute---that's usually *why* we compute, in fact. I'm merely pointing out here that your notion of 'computation' is very different both from what's usually meant by the term, and from how specialists typically use it.<br /><br />>It is an error to try to relate the symbols across different truth tables.<br /><br />Well, you can't really introduce a structure and then demand to use only half of it. If there's a function f1(x,y), with x,y taken from {A,B}, there's a set {A,B}, and a set-theoretic complement ' such that A'=B. And then, there's a function f2(x,y)=(f1(x',y'))'. (In fact, this is just Newman's problem again, or a consequence of it.)<br /><br />But since f1 is different from f2, and your 'value-agnostic pattern' doesn't fix which one is implemented, I can again point out that an ambiguity exists as to whether the 'AND-gate' implements one or the other.<br /><br />>The computation AND (and not OR), i.e. your AND, is a purely abstract structure. It cannot be physically realised unambiguously.<br /><br />This is interesting---after all, all computations we take us to perform aren't value-agnostic in your sense, so really, none of what we typically believe we compute corresponds to an instantiable computation in your sense. <br /><br />Nevertheless, we can clearly instantiate these computations, depending on the associations of the user. But on your computationalism, the user itself is just a value-agnostic computation. So in some way, it must be possible to combine value-agnostic computations to yield a computation that's non-value-agnostic. So there should be some way to 'enlarge' the AND-gate by some other value-agnostic computation (say, the one corresponding to a mind) to yield something which computes the AND, in my sense. No?<br /><br />>For it to be unambiguous it would need to exist in a world where 1 and 0 are physical things.<br /><br />You should keep in mind that your A and B are not anymore physically real than 1 and 0 are. I think you're tempted to take high and low voltages as, in some sense, 'just being' those 'meaningless symbols'. But they're not: they're high and low voltage. Combining voltages is not computation; abstract formal manipulation is.<br /><br />>The meaning of those symbols is imported by you and not intrinsic to whatever computation is happening.<br /><br />The computation that's happening---as usually understood---is *addition*: over the Peano axioms, to get 3+4, you apply the successor function to 3 four times. On your value-agnostic view, such a computation is impossible, of course. That's why I think it's not a good formalization of computation.<br /><br />>In your view, it would be performing a different computation, but in my view it would be performing the same computation.<br /><br />Actually, that's not right: if you adjust the I/O devices appropriately, then also on my view, the same computation would be implemented (it's the same as adjusting the interpretive mapping in order to yield the same logical values as before the bit-flip). It's when you use a different interpretational mapping, without then again compensating for it, that a different computation is implemented---a device which gives me the answer to the question 'what is the AND of a and b?' then gives me the answer to the question 'what is the OR of a and b?'. Under an I/O adjustment, I'd get back to the original 'what is the AND of a and b?'.<br /><br />>Multiplication isn't schmaddition, and a bit-flipped 3 is not 3.<br /><br />Certainly, but I only limit myself to bit-flipping for computations that operate on (whose universe is) bit-values. For computations on natural numbers, I can use some function permuting numbers in order to change the interpretation, giving me considerably more freedom.Jochenhttp://www.blogger.com/profile/07418841955052661428noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-35987455541357872902016-11-07T17:10:57.307+00:002016-11-07T17:10:57.307+00:00You're distracted by the symbols. The symbols ...<br />You're distracted by the symbols. The symbols are meaningless. Ignore them. They are there for our convenience only and play no part in the structure we're trying to communicate than do the labels we give to vertices in a triangle. All that matters is the pattern of similarities of differences. A is just a placeholder for "that symbol which is only output when it occurs twice in the inputs" and B is just a placeholder for "that symbol which is only output when it appears at least once in the inputs". This is like how A in a square might be a placeholder for "that vertex which is located at point (0,1)", such that ABCD might indeed be the same figure as ACBD as long as we try to match vertices by structural correspondences rather than by labelling correspondences.<br /><br />> So, are you saying that there is no system such that it computes AND?<br /><br />Not unambiguously, as you define AND.<br /><br />> Then, what grounds do you have to believe that there is a system such that it computes C_M?<br /><br />Because I take C_M to be a value-agnostic structure akin to f.<br /><br />> Only if you admit some meaning into your 'meaningless' symbols, such as, for instance, that the same symbol has the same meaning in all instantiations<br /><br />Yes. I've already acknowledged this. I'm assuming for the sake of argument that the objectively right computational interpretation of a system is the most parsimonious one, which more or less implies it is consistent. I agree with you that it is not plausible that parsimony is sufficient to justify an objective fact of the matter on which computation a physical system is implementing, but that's the pixies argument.<br /><br />Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-34629631026167663592016-11-07T17:10:45.837+00:002016-11-07T17:10:45.837+00:00> then I enter symbols 3 and 4, press '+...<br />> then I enter symbols 3 and 4, press '+', and get out 7<br /><br />That's not quite right. You push buttons with pictures of symbols on them, and an output device draws a picture of symbols on a display. The meaning of those symbols is imported by you and not intrinsic to whatever computation is happening. The value-agnostic pattern I am talking about is just that the values of individual bits in the registers of the device have no intrinsic meaning. As long as the I/O devices were modified accordingly, all the bits could be flipped and the system would still behave in the same way. In your view, it would be performing a different computation, but in my view it would be performing the same computation.<br /><br />If you bit flip the computation for 3+4=7, you don't get the computation for 3*4=12, as far as I can see. Multiplication isn't schmaddition, and a bit-flipped 3 is not 3. What computation you get depends on how many bits we use and whether we're using unsigned values or signed, whether we are using two's complement or one's complement.<br /><br />Whatever -- my point is that whatever you do get is the same core value-agnostic computation in my view. There is nothing in the system which intrinsically identifies what you are doing as adding 3 to 4 to get 7. That's something we bring to it.<br /><br />> we *can* distinguish between different interpretations of the symbols<br /><br />Because the I/O level translates the meaningless symbols into symbols onto which we project meaning.<br /><br />> the only way I can see how to do that would yield a function such that f1(A,B)=A, while there's another function such that f2(A,B)=B.<br /><br />I'll assume you mean f2(B,A)=B because that is the corresponding row in the truth table for f2.<br /><br />f1 and f2 are clearly isomorphic truth tables. You can only justify that they are different structures by assuming that the symbol A in one corresponds to the symbol A in the other. As soon as you do that, you are no longer considering the system of f1 in isolation or the system of f2 in isolation but the system f1+f2.<br /><br />Perhaps my triangle example isn't great because triangle ABC is the same as triangle BCA or ACB or whatever. But take a figure made by tracing 4 points. By your logic, ABCD is not the same figure as ACBD. In the former, A is connected to B and D (assuming the figure is closed). In the latter, A is connected to C and D. But if we no longer assume that the A in one corresponds to the A in the other, then ABCD could indeed be the same figure as ACBD, if for instance B in the former picked out the point identified by C in the latter and C in the former picked out B in the latter.Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-42958308524274793502016-11-07T17:10:15.273+00:002016-11-07T17:10:15.273+00:00Hi Jochen,
> I might learn the value of the AN...Hi Jochen,<br /><br />> I might learn the value of the AND or OR, but that's not what I'm interested in<br /><br />If you have preconceptions about what you're interested in, then you're importing meaning. That's fine. But that meaning isn't inherent in the system.<br /><br />> So I don't see how one could use computers to generate new knowledge on your view<br /><br />I'll just point out that we build computers with interpretations of inputs and outputs in mind. We bring our own meaning which allows us to relate those inputs and outputs to things outside the system. That imported meaning isn't inherent in the system, which is not the same as saying there is no meaning at all in the system.<br /><br />That said, I think we could use computers to generate new knowledge even if they were designed by some sort of automated process, e.g. by evolution by selection, as long as there were some interpretation we could impose on the system that made the system useful to us.<br /><br />> you both want for the symbols A and B (or whichever) to be distinguishable<br /><br />Yes. Within the context of the system. These symbols are only meaningful within a particular truth table. It is an error to try to relate the symbols across different truth tables. f1(A,B)=A) is the same pattern as f2(B,A)=B. There is only a difference if you incorrectly draw analogies between the B in one context and the B in the other context. These contexts need to be viewed in isolation. The B in one is not the B of the other, unless such a correspondence yields isomorphic structures, and it doesn't. If what you care about is isomorphism rather than whatever symbol is used, then B in f1 corresponds to A in f2. to say that f1 is not the same function as f2 is like saying that triangle A=(1,1), B=(1,0), C=(0,0) is not the same as triangle B=(1,1), C=(1,0), A=(0,0). All that has changed is some labels, which have no meaning other than how they are used within the system.<br /><br />Note that the example you gave is not quite right. f1(A,B)=B is not quite the same pattern as f2(A,B)=A, if the order of the inputs is deemed to matter.<br /><br />> So, what would a system computing AND (and not OR) look like?<br /><br />The computation AND (and not OR), i.e. your AND, is a purely abstract structure. It cannot be physically realised unambiguously. For it to be unambiguous it would need to exist in a world where 1 and 0 are physical things. Of course, once you adopt a convention, you can deem an AND gate to implement AND, and for all practical purposes it does. But as you have noted, that's not the same as there being an objective fact of the matter on whether it computes AND.<br />Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-83710293998695200352016-11-07T16:02:58.354+00:002016-11-07T16:02:58.354+00:00>As soon as you interpret an AND gate as interp...>As soon as you interpret an AND gate as interpreting AND specifically, you are importing meaning that wasn't there to begin with.<br /><br />So, are you saying that there is no system such that it computes AND? Then, what grounds do you have to believe that there is a system such that it computes C_M?<br /><br />>AND/OR is not the same pattern as XOR/XNOR.<br /><br />Only if you admit some meaning into your 'meaningless' symbols, such as, for instance, that the same symbol has the same meaning in all instantiations. Generally, that's not true: even in language, the same symbol may mean different things. So why should 'high voltage' over here carry the same meaning as 'high voltage' over there? <br /><br />That's ultimately as arbitrary a choice as having 'high voltage' denote 1, instead of 0. After all, it would be perfectly intelligible to say that 'high voltage at I1' means A, while 'high voltage at I2' means B, and with that convention, we could carry out a computation not in the set {AND,OR}. <br /><br />Why should that be forbidden?Jochenhttp://www.blogger.com/profile/07418841955052661428noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-27106838743983808222016-11-07T16:02:45.617+00:002016-11-07T16:02:45.617+00:00Hi DM,
> It specifies that what is important i...Hi DM,<br /><br />> It specifies that what is important is the computational process carried out, not other aspects such as mass or volume or material it's made of or whatever.<br /><br />OK, I'll accept the point.<br /><br />>No, it means from the perspective I am putting forth, the distinction between excel and schmexel is no distinction at all.<br /><br />Well, but in the way we use computers, it certainly makes a difference: we execute excel, as opposed to schmexcel; we compute the AND, and not the OR, of two inputs. If I have an AND-gate, I can input two binary values, and get the value of their conjunction out in response---in particular, if I didn't already know that value, I would then learn it. I don't see how such a thing could be possible if the computation were just your 'value-agnostic pattern', because then, I wouldn't learn the value of the AND of the two inputs. I might learn the value of the AND or OR, but that's not what I'm interested in; and picking out the value of AND would then necessitate me already knowing that value. So I don't see how one could use computers to generate new knowledge on your view, while that's something we do quite routinely.<br /><br />>If all you have is symbols with no intrinsic meaning, then there is no difference between the truth table for AND and the truth table for OR.<br /><br />I think here you're trying to have your cake, and eat it---you both want for the symbols A and B (or whichever) to be distinguishable, but for the functions f1 and f2, where e.g. f1(A,B)=B while f2(A,B)=A, to be the same. <br /><br />>So my conception of AND/OR is less specific than your conception of AND. It is a different computation.<br /><br />So, what would a system computing AND (and not OR) look like?<br /><br />>It's not a significant departure when you realise that the distinction between my AND and your AND is a subtle one that never makes any practical difference.<br /><br />See, I don't think that's right: if I have, say, a calculator, then I enter symbols 3 and 4, press '+', and get out 7. This is a different operation from entering 3 and 4, pressing '*', and getting out 12---yet on your conception, the 'value-agnostic pattern' is the same. So using computers the ordinary way is precisely not using them as value-agnostic: we *can* distinguish between different interpretations of the symbols, and get out the result of any concrete computation only if we do.<br /><br />>You could define it formally perhaps by giving the truth table in terms of A and B.<br /><br />Well, the only way I can see how to do that would yield a function such that f1(A,B)=A, while there's another function such that f2(A,B)=B. Which of these you then name AND and OR is immaterial---indeed, merely involves switching around whether A or B is the top element---but it's clear that they are different. And even more, I can, if you say that a system implements f1, point to my re-labeling trick to make it into f2.<br /><br />So I don't really think a formal definition of your intuition exists---it's the same kind of 'same, but different' problem we had earlier on with the sets of indistinguishable elements: some elementary mathematical reasoning shows that such a thing simply doesn't exist.<br /><br />>But I don't think that bits intrinsically represent true or false.<br /><br />And neither do I. But the inputs of the AND-function, by virtue of that functions definition, do.Jochenhttp://www.blogger.com/profile/07418841955052661428noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-26712298464141268942016-11-07T15:03:06.142+00:002016-11-07T15:03:06.142+00:00ND/OR as I conceive of it means something. It mean...ND/OR as I conceive of it means something. It means you can discriminate between patterns of inputs, returning one value if the two inputs equal that value and another value in all other cases. That's more abstract than AND or OR but it's not entirely meaningless. Whatever meaning there is has to come from the system and cannot be imported from the minds of people trying to interpret that system. As soon as you interpret an AND gate as interpreting AND specifically, you are importing meaning that wasn't there to begin with.<br /><br />> after all, the pattern of meaningless symbols is the same in every Putnam-style mapping of computational states to physical states.<br /><br />But it isn't. AND/OR is not the same pattern as XOR/XNOR. I already gave the "meaning" of the former pattern. The latter pattern is that one output symbol indicates that the two inputs are equal, another symbol indicates that the two outputs are distinct. So XOR/XNOR is unambiguously a computation to detect if two values are the same. AND/OR is not -- it is instead unambiguously a computation to detect if both input symbols are a specific symbol.<br /><br />Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-24736710872093458132016-11-07T15:02:54.183+00:002016-11-07T15:02:54.183+00:00> I provide a computer with the parameters of s...> I provide a computer with the parameters of star formation, say, and get out the distributions of stars in the galaxy.<br /><br />But that cannot be how brains work, because there is no programmer who is interpreting the input and output. The meaning has to be generated from within the system somehow. It cannot be imported from outside as in your example. If you want to argue that this computation-generated meaning is impossible (you can't get semantics from syntax, as Searle would say), that's a separate argument. But for purposes of the bit-flipping argument, the computationalist contention would be that the manipulation of intrinsically meaningless symbols somehow generates meaning. The meaning arises out of the patterns and how they causally relate to the outside world and not from any meaning intrinsic to the base symbols forming them.<br /><br />> In that, you're basically saying that AND and OR are not computations<br /><br />I'm saying that your way to conceive of AND and OR is not how a computationalist conceives of AND and OR. I would say AND is a computation, but what I mean when I say AND is not quite what you mean when you say AND.<br /><br />> I think this is a significant departure from how just about everybody else understands computation<br /><br />It's not a significant departure when you realise that the distinction between my AND and your AND is a subtle one that never makes any practical difference. It only matters in this debate. I think you'd get a similar or equivalent answer from any computationalist if you pressed them with the bit-flipping argument. They may put it differently -- they may say agree that two bit-flipped computations are distinct computations but insist that they give rise to the same conscious experience. This may seem different to what I'm saying but I think it's just the same intuition phrased differently -- it means that from their perspective the difference between two bit-flipped computations is irrelevant.<br /><br />> How would you define the computation C_? formally? <br /><br />I'm not necessarily so hot on formal definitions. You'd probably make a better job of it than I. Definitions don't usually need to clarify that their symbols are completely unbound and interchangeable. But, in natural language, C_? is a structure that operates on a set of two distinct symbols and that returns one symbol if the two inputs are that symbol and the other symbol in all other cases. You could define it formally perhaps by giving the truth table in terms of A and B. The only problem is that this could be misunderstood as being different from the A/B swapped version, even though the two are isomorphic and the swapping represents a change in notation only. I'm not sure how to express this in a formal definition if it isn't already clear.<br /><br />> Certainly, this is the intention of some computational theories<br /><br />I'm not saying that representationalism is false. I'm a representationalist. But I don't think that bits intrinsically represent true or false. I think that mental representations are patterns of inherently meaningless symbols that come to mean things because of how they interact with each other and the outside world. Meaning only emerges at higher levels.Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-35935094163322300012016-11-07T15:01:56.823+00:002016-11-07T15:01:56.823+00:00Hi Jochen,
> if the set of computations and th...Hi Jochen,<br /><br />> if the set of computations and the set of physical processes are coextensive, specifying 'computation' does not specify anything that isn't already specified by 'physical'.<br /><br />Yes it does. It specifies that what is important is the computational process carried out, not other aspects such as mass or volume or material it's made of or whatever. It means that if you implemented the same computational process on some other substrate, you'd get the same conscious experience.<br /><br />> so that's indeed saying that our computers never compute what we think they compute<br /><br />No, it means from the perspective I am putting forth, the distinction between excel and schmexel is no distinction at all. I'm suggesting that your interpretation of "excel", which cares about the truth-values of bits, is an incorrect interpretation of what "excel" really is.<br /><br />> This is simply not how most people (including most computationalists) conceive of computation.<br /><br />Perhaps. But for most purposes, the distinction between your interpretation and mine is immaterial. It is only important in this specific debate. If pressed with your arguments, my suspicion is that the computationalists would agree with me. Otherwise, they would probably not think about these issues at all.<br /><br />> The truth table of AND (and the complementation relation) imply the 'meaning' of the symbols used, in as much as that meaning exhausts itself in 'top element of B2' and 'bottom element of B2'.<br /><br />If all you have is symbols with no intrinsic meaning, then there is no difference between the truth table for AND and the truth table for OR. They are identical. They only differ in notation -- the symbols used to represent the value that you need two of in order to get that same result -- 1 in the case of AND and 0 in the case of or, and the value that you get out otherwise -- 0 in the case of AND, 1 in the case of OR. Seeing as the two truth tables are identical if interpreted without prior conceptions of meaning, I don't get how you can say that the truth table tells us which is the maximum and which is the minimum value. You could interpret it either way. The truth table is all there is -- there is no need to interpret one value as greater than the other.<br /><br />> 2. The only way to do something that's, as you say, 'value agnostic' would be to forget something about the structure of AND---change it to a different computation. <br /><br />Agreed. So my conception of AND/OR is less specific than your conception of AND. It is a different computation. Sure.Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-6804898954739298092016-11-07T13:22:24.482+00:002016-11-07T13:22:24.482+00:00Or perhaps, to put it another way: it may be a pla...Or perhaps, to put it another way: it may be a plausible thesis that computation, used the way I understand it, underlies mind---after all, in some sense, our minds operate on representations of the world, producing new representations from old ones, generating actions from these representations, and so on. So if there's such a representational aspect to computation, then I could see a computational theory of mind working. Certainly, this is the intention of some computational theories, such as Putnam's functionalism, and even more so for Fodor's semantic account. <br /><br />But on your conception, I have zero reason to believe that a 'value-agnostic pattern' corresponds to a mind, which is, or at least appears, clearly non-value agnostic. In a sense, you are, to me, claiming that all the content of a novel could be reduced to 'subject predicate object', or more complex versions thereof. I'm not saying that's intrinsically impossible, but it strikes me as being a thesis that's much harder to argue for than standard computationalism (and one I don't think is sufficiently well-posed to need rebuttal, as of yet).<br /><br />Additionally, if you view computation entirely as 'value-agnostic patterns', then I don't see why Putnamesque arguments should worry you: after all, the pattern of meaningless symbols is the same in every Putnam-style mapping of computational states to physical states.Jochenhttp://www.blogger.com/profile/07418841955052661428noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-25717623204307245082016-11-07T13:13:44.272+00:002016-11-07T13:13:44.272+00:00>No we can't, because on computationalism o...>No we can't, because on computationalism only some computations are minds.<br /><br />And if all physical processes are computations, then this is the same as saying 'some physical processes are minds'. The idea of computationalism is that some physical processes are minds because they instantiate computations; if the set of computations and the set of physical processes are coextensive, specifying 'computation' does not specify anything that isn't already specified by 'physical'. To the extent that computationalism and physicalism are distinct theses, computation and physics are distinct notions.<br /><br />>These are just two different ways of looking at it, and they are essentially the same function.<br /><br />This is like saying a computer which computes Excel also computes schmexcel, and so on---so that's indeed saying that our computers never compute what we think they compute. When we use an adder to compute the sum of two digits, then we take that adder to compute the function of addition; but under your interpretation, that would be strictly false: it would compute a function corresponding to the equivalence class (x+y, x+y+1), just as you take an AND-gate to compute a function equal to the equivalence class (x*y, x*y+x+y). This is simply not how most people (including most computationalists) conceive of computation.<br /><br />So let's take your enumeration of statements, and let me try and give you my perspective on each.<br /><br />1. The truth table of AND (and the complementation relation) imply the 'meaning' of the symbols used, in as much as that meaning exhausts itself in 'top element of B2' and 'bottom element of B2'. You need nothing else.<br /><br />2. The only way to do something that's, as you say, 'value agnostic' would be to forget something about the structure of AND---change it to a different computation. <br /><br />3. Yes, I agree---you can always forget which computation you were specifically carrying out, to end up with a set of computations such that you need to again specify the deleted information to pick out the original computation, or indeed, pick out different computations upon entering different information.<br /><br />4. The claim of computationalism is that there is a computation, C_M, an element of the set of all computations S, such that a brain gives rise to a mind by implementing C_M (and not, say, some equivalence class of computations produced by deleting structure from C_M).<br /><br />5. As I said before, I'm no longer really certain that a 'value-agnostic pattern' corresponds to any well-defined information processing on its own. It's related to a computation in the same way that 'subject predicate object' is related to 'Harry likes art': knowing only the former, you lack the actual informational content of the sentence; it could just as well be 'Mary hates brussels sprouts'. A computation, as I would understand it, rather relates a certain meaningful input to a meaningful output---at least, that's how we use computations: I provide a computer with the parameters of star formation, say, and get out the distributions of stars in the galaxy. I don't use a computer to transform meaningless strings into other meaningless strings. <br /><br />6. I think that this is really arguing for something very different than usual computationalism. But perhaps, I'm just not intuitive enough to grasp your notion of 'computation'. How would you define the computation C_? formally? <br /><br />>Value-laden AND and OR are not the best interpretations<br /><br />In that, you're basically saying that AND and OR are not computations, if indeed computations are only your 'value-agnostic patterns' and AND and OR are not such patterns. I think this is a significant departure from how just about everybody else understands computation, and basically means that nothing we actually use our computers to do really is computation.Jochenhttp://www.blogger.com/profile/07418841955052661428noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-22386996679050592092016-11-07T13:12:44.431+00:002016-11-07T13:12:44.431+00:00Hi DM,
>I was unaware that implication maps so...Hi DM,<br /><br />>I was unaware that implication maps so neatly onto <=. That is interesting.<br /><br />You can get the intuitive meaning by just considering a set of objects with different properties, which will then be subsets of that set. Say, you have a set of balls, which can either be red or blue, and wooden or stone. Then, <= is just subset inclusion: so if, for instance, the set of wooden balls W is a subset of the set of red balls R, i.e. W<=R, then the property 'wooden' implies the property 'red'. That's why the ordering relation is so important for logic.<br /><br />>But you can choose a different translation to map it to 0,1, right?<br /><br />Any such translation would amount to a renaming only---i.e. 0 gets all the structural properties of 1, and vice versa. So then, it would be true that 1<=0, etc. That's why I chose to rather refer to the top and bottom elements of B2, whether you call them 1 and 0 or the other way around.<br /><br />>Those are concepts from the world of numbers, not concepts from the world of true and false.<br /><br />Well, as I said, if you complete the translation, then you need a concept playing the same role---such as implication in the world of true and false. <br /><br />For instance, if you have an operation '*' on the set of {A,B}, and you define, say, A*B=A and B*B=B, then you've defined B as multiplicative identity, and it'll inherit (suitably translated versions of) all the properties that 1 has. And it's those properties that carry the structure.<br /><br />>For instance, I could map TRUE to McCartney and FALSE to Lennon and I could map implication to the function wasNotBornAfter.<br /><br />In which case you'd have a Boolean algebra whose top element is named 'McCartney' and whose bottom element is 'Lennon', and where <= just means 'NotBornAfter'. You don't change anything about the structure with such renamings, but you do once you neglect the <= (or its equivalent).<br /><br />>It doesn't really matter for my mapping of TRUE and FALSE to Beatles members who was born first. The tables are all I need.<br /><br />Right, but those tables imply that there is a relation playing the role of <=/implication. If you have AND, and negation, then you have implication; and otherwise, you're simply talking about something else.<br /><br />>It doesn't matter if a single bit of a signal is TRUE or FALSE.<br /><br />Yes, because you're not doing a computation on those values. But if you compute the AND, then you are doing such a computation. The truth table of AND, say in terms of A and B:<br /><br />I1 I2 | O<br /> A A | A<br /> A B | A<br /> B A | A<br /> B B | B,<br /><br />together with the relation that A=~B (which is automatically fulfilled on the set {A,B}, if negation is just the complement), implies that B has all the properties of the top element of B2, and A has all the properties of the bottom element. In particular, it implies a lattice ordering relation <= such that x<=y if and only if (x,y)=(A,A),(A,B), or (B,B), i.e. if ~(x&~y)=B. You can't have one without the other.<br /><br />>It does not mean, for instance TRUE or FALSE.<br /><br />No, of course not; I've nowhere claimed that all computations operate on these values. AND, OR, etc., however, do; likewise, addition of binary digits operates on binary digits, and so on.Jochenhttp://www.blogger.com/profile/07418841955052661428noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-51039762662574605762016-11-07T10:49:22.962+00:002016-11-07T10:49:22.962+00:00> I would say that this is the exact opposite o...> I would say that this is the exact opposite of meaningless---after all, what's the meaning of a signal other than what it causes the recipient to do?<br /><br />You miss my point. My point is that the signal has no intrinsic meaning taken in isolation. It doesn't matter if a single bit of a signal is TRUE or FALSE. I agree with you that the meaning of the aggregated inputs and outputs to a system is best understood in terms of its causal associations.<br /><br />> then that voltage level, to that motor, is an instruction for doing precisely that. <br /><br />Exactly. That is what the signal means. It does not mean, for instance TRUE or FALSE. And an 8 bit message sent to a computer means whatever it causes the computer to do. It does not mean, for instance (TRUE,FALSE,FALSE,TRUE,TRUE,TRUE,TRUE,FALSE).<br /><br />> so if every physical system performs some computation, we can just leave the notion of computation out altogether<br /><br />No we can't, because on computationalism only some computations are minds. So it matters what computation the system is performing, and so systems need to be analysed as computations to determine if they are realising minds or not. Or at least, this is how we would go about it if we knew what C_M looked like.<br /><br />> In that case, you're really saying that none of our computers ever compute what we think they compute<br /><br />I'm adopting your hard distinction between AND and OR for the sake of argument. I don't think most computationalists would, on being presented with these subtle arguments at least. In my way of thinking, AND and OR are equivalent and are effectively the same. So, in my language, and in the language of computationalists, an AND gate really is computing AND. It is also computing OR. These are just two different ways of looking at it, and they are essentially the same function.<br /><br />It's only when I adopt the hard distinction you do and accept for sake of argument that it matters for AND and OR what the numerical value of the digits are that I say that an AND gate doesn't compute AND. So my apparent deviation from what computationalists would normally say is explained by my adopting your language for the sake of conversation and is not in fact a deviation at all, I suspect.<br /><br />> I really don't see your issue here.<br /><br />This is equally frustrating for me.<br /><br />OK, which of these statements do you accept?<br /><br />1. It is possible to elide any consideration of intrinsic meaning or value from the symbols in a truth table and have a mathematical structure that represents the common patterns in input and output shared by AND and OR but that nevertheless preserves the difference between distinct values within that structure.<br />2. If we try to interpret what an AND gate is doing in terms of such a value-agnostic pattern, there is a unique way to interpret it as such without any ambiguity<br />3. The same kind of value-agnosticisation trick can be performed with any computation over binary digits.<br />4. The claim of computationalism is that the realisation of a complex information processing flow creates a mind<br />5. A value-agnostic pattern is an information processing flow<br />6. (I say that) the claim of computationalism is that the information processing flow that realises a mind is a value-agnostic pattern.<br /><br />> This claim carries a commitment to the thesis that there's an objective fact of the matter regarding what a system computes.<br /><br />Right, but the computation being realised by a system is not any old computation you want to map it to. It must be the best interpretation. Value-laden AND and OR are not the best interpretations, any more than functions over the Beatles would be the best interpretation. The best interpretation is a value-agnostic interpretation, because it captures what the system is doing but without ambiguity or arbitrary value-laden interpretation. There is an objective fact of the matter regarding what the system is computating and it is not AND or OR as you conceive of them but AND or OR conceived of value-agnostically.Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-84555312231216556982016-11-07T10:26:09.659+00:002016-11-07T10:26:09.659+00:00Hi Jochen,
I was unaware that implication maps so...Hi Jochen,<br /><br />I was unaware that implication maps so neatly onto <=. That is interesting.<br /><br />I agree with you that as long as you translate all the terms appropriately, then TRUE,FALSE maps to 1,0. But you can choose a different translation to map it to 0,1, right? Instead of using implication (~AvB) you could use the inverse function (A&~B) and get the same kind of relationship. There's no reason to think that implication is any more natural a mapping of <= than A&~B, or to map <= to implication rather than some other relationship such as >. So, if what you care about is TRUE and FALSE, then it really doesn't matter that 1 is the maximal number of B2. Whatever number you used to represent TRUE, you could find a mapping that would work.<br /><br />> Heck, wikipedia comes right out with "Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false", for what it's worth. <br /><br />That seems right. I don't get why you would think this disagrees with anything I have said.<br /><br />> No; not until, at least, you've made up your mind whether A<=B or B<=A,<br /><br />But I don't need >= or <=. Those are concepts from the world of numbers, not concepts from the world of true and false. You can map true or false to <= and >= if you want to, but you could map true or false to anything. For instance, I could map TRUE to McCartney and FALSE to Lennon and I could map implication to the function wasNotBornAfter. Or I could map FALSE to McCartney and TRUE to Lennon and map implication to the function wasNotBornBefore. You can always construct such mappings if you want to, but you don't need to. The mappings in terms of functions that are meaningful only outside the system are entirely extraneous (although they might be useful for certain pragmatic purposes, e.g. using a mapping of boolean functions to arithmetic functions in order to use existing well-known theorems in arithmetic to show something about Boolean logic). It doesn't really matter for my mapping of TRUE and FALSE to Beatles members who was born first. The tables are all I need.Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-67317197656356780522016-11-07T09:05:59.738+00:002016-11-07T09:05:59.738+00:00Hi DM,
perhaps let me get in a couple of notes so...Hi DM,<br /><br />perhaps let me get in a couple of notes so as to try and get us somewhat more onto the same page (or at least, let us better triangulate our differences).<br /><br />>These different patterns can have different causal consequences, e.g. driving an I/O device or a robot.<br /><br />I would say that this is the exact opposite of meaningless---after all, what's the meaning of a signal other than what it causes the recipient to do? If you give somebody a slip of paper with some scribbles on it, and they consistently engage in the same actions upon receiving it, and vary those actions based on variations in those scribbles, then I'd say that's a good criterion of them having understood the meaning of the message (in fact, I've defended this view in print). <br /><br />So, for instance, if the voltage level received by a servo motor causes it to spin a particular direction with a particular speed, then that voltage level, to that motor, is an instruction for doing precisely that. <br /><br />Otherwise, you're really running a danger of diluting the meaning of computation so far as to have it be useless---because otherwise, how is not simply any physical state change a computation? Any state of a physical system is a 'meaningless symbol', thus any process transforming states is one taking in meaningless symbols and producing them as output. <br /><br />But this trivializes the notion of computation, and makes computationalism collapse to physicalism---computationalism is the thesis that a physical system implements a mind by performing a computation, so if every physical system performs some computation, we can just leave the notion of computation out altogether---it doesn't add any information. We just have physical systems evolving their respective ways, some of which, we now claim, produce minds.<br /><br />>But it is unreasonable to think that such an interpretation could be considered objectively true,<br /><br />In that case, you're really saying that none of our computers ever compute what we think they compute (if even something as basic as an AND-gate doesn't compute the AND-function). I don't think your typical computationalist would want to go along with that.<br /><br />>You should ask what is the system doing, not whether it implements AND.<br /><br />I really don't see your issue here. Computationalism claims that brains carry out a specific computation, C_M, that gives rise to a mind. This claim carries a commitment to the thesis that there's an objective fact of the matter regarding what a system computes. So I take the analogous claim that an AND-gate computes the AND-function, or that a half-adder adds binary digits, and show that this thesis can't be upheld. <br /><br />I'll respond to the rest once you've found time to reply to my other points.Jochenhttp://www.blogger.com/profile/07418841955052661428noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-18278099537633874702016-11-06T16:42:24.064+00:002016-11-06T16:42:24.064+00:00Will get back to you on the rest probably tomorrow...Will get back to you on the rest probably tomorrow.Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-5801278565856116215.post-28129542932110300652016-11-06T15:50:58.258+00:002016-11-06T15:50:58.258+00:00Hi Jochen,
> You'd be just as well off wit...Hi Jochen,<br /><br />> You'd be just as well off with the original meaningless symbols.<br /><br />Typically, you get a different pattern as output than you put in as input. These different patterns can have different causal consequences, e.g. driving an I/O device or a robot. It's the patterns that are important, not the values of individual bits considered in isolation.<br /><br />> So while all manipulation occurs according to syntactic rules, the symbols will typically have a well-defined meaning; <br /><br />That meaning comes from outside the system, from the mathematician or the programmer or someone interpreting the operation of a computer. It's not plausible (I'm sure you would agree -- Searle certainly thinks so) that the meaning of primitive signals could be inherent to a physical system. So any sensible computationalist will not claim that this meaning plays any role in cognition.<br /><br />> Unreasonable in what sense? <br /><br />Unreasonable because there is nothing inherent in the system that gives any basis for interpreting a signal as TRUE rather than FALSE. There is no reason to think that such an interpretation could be the best description of what the system is computing.<br /><br />> I mean, both the adder and the AND-gate are built with performing a specific computation in mind<br /><br />Intentions in the mind of the designer cannot plausibly be considered to be part of what determines what computation a physical system is actually computing.<br /><br />> To claim it's then unreasonable to interpret them as adding or taking the AND seems a bit strange to me.<br /><br />Well, OK, it's not unreasonable to describe them in such terms for pragmatic reasons, as this is intuitive and useful. But it is unreasonable to think that such an interpretation could be considered objectively true, because there's nothing in the system to recommend such an interpretation over the bit-flipped one.<br /><br />> I'm not saying that: I'm saying that if we want to decide whether a system implements the AND,<br /><br />But this is the wrong question to ask. You should ask what is the system doing, not whether it implements AND.<br /><br />> Again, we don't start by considering a physical system, and then try and find some computation it performs; rather, we want to decide, given a computation, whether the system implements it.<br /><br />Precisely wrong. Other way around.<br /><br />> Because that's the task we'll eventually be faced with regarding computationalism: C_M is the computation producing a mind;<br /><br />No. A brain is performing some computation that realises a mind. Let's call it C_M. Now, from reverse-engineering how a brain processes information, what is C_M? C_M will be more like C_? than C_&. It will not care about the truth-interpretation of signals.<br /><br />> Showing that, in general, no such question of this form can be answered shows that this one in particular can't be answered<br /><br />You haven't shown that. You have shown that there is no basis on which you could pick between C_v and C_&. But you haven't made that point in general. C_? doesn't have the same problem. There is at least one interpretation which describes what the system is doing in detail but which doesn't care about bit-flipping. That is the correct interpretation.<br /><br />> Consequently, there's no objective fact of the matter regarding P implementing C_M.<br /><br />There is no objective fact of the matter regarding whether a system implements C_v or C_&. Your argument shows nothing about whether it implements C_?. C_M is like C_? and not like C_v or C_&.<br /><br />> since AND and OR clearly are different computations; after all, they're different mathematical objects. <br /><br />They are different when taken together. They are the same when taken in isolation and the signals not taken to have inherent meaning. As soon as you use arithmetic operations such as addition and multiplication, you are interpreting the signals as numbers, and so you are taking them to have inherent meaning. Of course they are different functions when you do that. I never said they weren't.<br />Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.com