Drew McDermott, Mind and Mechanism, MIT Press, 2001. Chapter 5. [Comments in square brackets are my own thoughts.] CHAPTER 5: SYMBOLS AND SEMANTICS (p.167-214) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The main goal here is to make plausible that it is possible to objectively define "computation", "symbols in the head", and the relation of some of these symbols to reality; and hence to show the question of whether or not an agent possesses a self- model (and under suitable further assumptions, is conscious) is also something to be ultimately determined objectively. Themes: Computers (for a particular function f), p.170: ~~~~~~~~~ i.e., we assume a fixed way C_I of decoding certain states of the entity in question (the putative computer) as inputs in the domain of f, and a fixed way C_O of decoding certain later states (when the computer signals "output available") as outputs in the range of f. 'A' is the output availability signal, which is some (observable?) condition of the entity. The claim is that the entity computes f iff the following holds: whenever a state S is decodable as some x in domain(f) (i.e., C_I(S) = x), then the entity is caused subsequently to enter a state S' where the availability signal is on, and the state decodes as f(x) (i.e., C_I(S') = f(x)). [Fallacy: can hide computation in decodings, as we'll show.] 1. First, one might object that we normally would call an object a computer for f(x) only if it allows us to choose and set the input value x. McDermott makes no such assumption. This is probably because he ultimately wants to consider entities that compute functions for their own "private" purposes (or no purpose at all), perhaps in a way not controllable from the outside. But even if one considers an internal module that performs some information-processing task, wouldn't one want to say that the processes *using* that module chose the values of x? 2. The definition as stated doesn't require the "computer" for function f to "work" for all elements of the domain of f; in fact, it doesn't require that it work for *any* elements of the domain -- just that it obtains the right f(x) *whenever* there's an input that decodes as an element in the domain of x. 3. Worst of all, the decodings are simply assumed to be "mappings". Thus we can hide f in these mappings. E.g., suppose to solve flaw (1) we require that the computer for f must "work" for all values x in the domain of f. Then here's a device that satisfies the stated requirements for a computer for f for any f with domain = closed interval [0,1], by a suitable choice of C_O: The device has a protuding stud whose voltage serves as input or output, and there is also an on/off light. When the light comes on, this means the output is available. The voltage on the I/O stud consists of waves of random height, like this: ____ | | ____ ---- ____ | | | | ____ | | ____| **|____| **|____| **|____| **|____| **|__ The waves vary in height from 0 volts to 1 volt, perhaps as a result of amplified thermal noise, or whatever. Let's say each wave lasts for 2 seconds, and after 1 second, the output availability light comes on, staying on for 1 second. This is indicated by the asterisks above. An input x may be decoded whenever there is a new voltage pulse, and C_I (the input decoding) is just the voltage on the stud at that point in time, measured in volts. (Thus this can be any value in the interval[0,1].) The output is again the voltage when the light comes on (which is by definition unchanged from the "input" value!!) but as an output decoding C_O we use f(x), where f is the function we are claiming the device computes (e.g., f(x) = x^2, or f(x) = inverse sin(x), etc.)! But it is clearly nonsensical to say the device computes an arbitrary function f, on the basis of the above set-up; after all, the "input" voltage is the same as the "output" voltage. One constraint this example may suggest is that we should insist that C_I = C_O. Alas, this doesn't really help, because here's such a C-I/C_O for any f: C_I/C_O: when a pulse is "on", and the light is "off", then C_I/C_O is the voltage of the pulse; when a pulse is "on", and the light is "on", then C_I/C_O is the value of f, applied to the voltage. In fact, since McDermott didn't require C_I, C_O to be in any sense *computable* mappings, this device can even compute functions f that are not Turing-computable! So at the very least a number of "repairs" are needed to McDermott's definition. For example, as noted above, it should be possible to control the inputs to the "computer" for f, setting it to any value in the domain of f. Or at least, for a very large number of x-values in the domain of f, there should be possible initial states and/or operating conditions of the computer such that it *will* go into a state decodable as x sooner or later. But even with such extra constraints, I'm not sure if McDermott's definition can be repaired; I don't see any escape from the trick of hiding f in C_O (or equivalently in C_I, as the inverse of f, if it has an inverse). We would want at least to make the decodings physically implementable, with some measuring/decoding device whose outputs have a fixed format, and are obtained "quickly", in some sense. For example, we might require that it be possible at least in principle to equip the "computer" with a sensing and decoding device for input decoding whose output is a pointer position on a scale from 0 to 1 (if the domain of f is confined to that interval). Similarly we should be able to "instrument" the computer so that we can read off outputs. But even so, if we only require the computer to compute one function f, it seems that for many simple functions f that are "quickly" computable, we could "hide" the computation of f in the input decoding device or outpur decoding device, I suspect that as in the case for Turing machines, one needs to consider some infinite class of physical devices, and fix some way of interpreting inputs and outputs as "easily" (linear-time?) computable values of some "observable" of the devices. Even though the way of interpreting these observables might allow "cheating", by hiding the computation in the interpretation, for a finite number of devices, the "cheating" won't work for all members of the class of devices. But this is probably too weak a claim to allow McDermott to draw his conclusion about the objective decidability of whether an object computes a function f.] Causal influence of a computational system on another system ~~~~~~~~~~~~~~~~ (p.175-180). Notion of "largely computational". McDermott takes causality for granted, i.e., it's an objective fact whether some state S of a system causes some state S' of the same (or another) system. [Hmm...] Symbols: ~~~~~~~~ Symbol sites and symbols: symbol sites are sets of mutually exclusive states of some system at some particular time. (Since the states are mutually exclusive, the system can be in only *one* of the states at the specified time, so the remaining states are just hypothetical alternatives -- the system *could* be in one of those other states, but it isn't.) Any of the states comprising a symbol site can be regarded as encoding a symbol. "Symbol tokens" correspond to a causal chain of states, each state being decodable as a symbol (the *same* symbol??!!), each being caused by its predecessor, and each being a member of a symbol site (thus, by definition, at a particular time). He tries to formalize this causal-chain relation as a "precursor relation" among symbol sites, but since symbol sites have hypothetical states as members, it's not at all clear what this means. I think what he really is trying to get at is that besides the actual causal chain that connects temporal instances of a symbol, there are also other hypothetical chains that could have occurred over the same time span, instantiating a *different* symbol. Analog symbol sites ~~~~~~~~~~~~~~~~~~~ He makes the reasonable point that analog symbolism can be approximated by discrete symbolism. If some continuous quantity in some analog device required arbitrarily high precision in order for the correct computational result to come out, then the tiniest disturbances would throw off the computations of the device, and such a "computer" would be biologically and practically useless. Natural causation in neural nets "vs" rule-governed behavior ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (criticism of Churchland). Algorithms, like neural nets, may not be interpretable in any clear way (Love-match program: you can't formally specify the criterion according to which some person y is a love-match for some person x). Neural nets are just as "symbolic" as digital computers. Syntax & semantics ~~~~~~~~~~~~~~~~~~ Structure, compositional semantics; e.g., OJ, JO might each denote one person, or might each denote 2 persons (Jack & Oprah), one positioned to the left of the other (or in love with the other, etc.) The latter requires a *compositional* semantics. (Each piece means something, and the arrangement of pieces adds further meaning, yielding an overall meaning for the entire symbolic expression.) How symbols get meanings ~~~~~~~~~~~~~~~~~~~~~~~~ He goes for a theory acc. to which the symbols that do the representing are "appropriately linked", under a compositional semantics, to objects and relationships in the world via the agent's perceptual system. [I disagree with the last part: it's a matter of there existing a denotational semantics under which the representations *provide information* about the world -- they are a "good fit"] How we could find out what symbolic representations mean, empirically. "Harmonious" semantics. Qualia -- primitives in the above symbol-world linkage ~~~~~~ Falsehoods -- e.g., Santa Claus ("almost" mappable to reality). ~~~~~~~~~~ He again denies the relevance of what symbols *could* mean (6-day war vs weather report); [unfortunate!] Appearance and reality ~~~~~~~~~~~~~~~~~~~~~~ Even introspections can be mistaken -- they too are physical processes, and our conclusions about what they yield may not be fully "harmonious" with what actually transpired. He speculates about rejecting solipsism with future empirical accounts of how subjective experience works.