Page Numbers: Yes X: 306 Y: 1.0" First Page: 1 Margins: Top: 1.0" Bottom: 1.3" Heading: z18344l3000e2qk40(0,65535) LECTURE NOTES #17 LISP: LANGUAGE AND LITERATURE June 7, 1984 l3000d2469y756e2qk40(0,2999)(1,8079)(2,16839)(13,0)\f7 1f1 69f8 44f1 l3528d2999e2jk40(0,3528)(1,4798)(2,6068)(3,7338)(4,8608)(5,9878)(6,11148)(7,12418)(13,65535) Lecture Notes #17 The Computational Claim on Mindl3528d2999e2ck40\f5b21f8B1f5b Filed as: [phylum]<3-lisp>course>notes>Lecture-17.notes User.cm: [phylum]system>user.classic Last edited: June 7, 1984 11:43 AMe17k40(0,5248)(1,7680)\f1 e10jk40(0,3528)(1,4798)\f8 44f0 A. Introductory Notesl3528d2999e15jk40\b22B Four handouts today:l3528d2999x0e10j\f8 1f0 Problem set #3 (recommend doing it over the next few weeks, if you can; Coling course starts June 25, which will use up all the Dandelions). We will try to grade any solution handed in over the summer.l4798d4269x0e3j Solutions to problem set #2;l4798d4269x0e3j\f8 1f0 Lecture notes for today.l4798d4269x0e3j Questionnaire; please fill out and return as soon as possible.l4798d4269x0e3j Plus "Knights of the Lambda calculus" pins for those stalwart few who have attended all quarter.l3528d2999x0e3j There were some lectures for which lecture notes were not handed out:l3528d2999x0e3j\f8 1f0 Specifically, #s 2, 3, 6, 7, 12, 14, and 15.l4798d4269x0e3j I will be preparing notes for all of these over the next month, in preparation for the Coling course.l4798d4269x0e3j Send me a note if you would like copies of these, and I will distribute them at the beginning of July.l4798d4269x0e3j Today:l3528d2999x0e3j Review (and borrow) some of what is in the first few sections of The Computational Metaphor, distributed last time.l4798d4269x0e3j\67i26I Suggest we need a genuinely semantic notion of computation.l4798d4269x0e3j End up with a critique (and partial reconstruction) of the formality condition.l4798d4269x0e3j\61i19I 2. The Computation Claiml3528d2999e15jk40\b25B The computational claim:l3528d2999x0e10j\f8 1f0 25f8 Not news that computational vocabulary is used to describe the mindl4798d4269x0e3j\f8 1f0 in linguistics, philosophy, psychology, AI, etc.l6068d5539x0e3j\f8 1f0 Rests on a claim, basically, that the mind, or mental processes, or belief revision, or intelligence something of that sort is computational.l4798d4269x0e3j Lots of questions to be asked, such as: Is the computational claim true?l4798d4269x0e3j\f8 1f0 41i32I Before one can begin even to explore such a question, however, need to know what claim it is.l4798d4269x0e3j\f8 1f0 Curiously, if you press people, they defer hard questions (about what computation is) to computational practice or practitioners:l3528d2999x0e3j\f8 1f0 Typically: "Well, I don't know exactly, but it is just like what goes on in a computer."l4798d4269x0e3j\33i7I My standard reaction: if your understanding rests on my understanding, you're in trouble. We don't know what we are talking about.l4798d4269x0e3j\f8 1f0 26i4I24i2I So need a theory of computation.l3528d2999x0e3j\f8 2f0 Extremely important: if the notion of computation is too broad and encompassing in its scope, the cognitive-science/AI enterprise is correspondingly robbed of content.l4798d4269x0e3j So it is terribly important to get a notion with bite. But if it has too much bite, will restrict us from exploring in powerful directions, and may lead the same cognitive-science/AI enterprise to fail.l4798d4269x0e3j\72i3I67f8 1f0 62f8 I.e., treading a thin line between vacuity on the one hand, and falsity on the other.l4798d4269x0e3qj 3. Semantic Computationl3528d2999e15jk40\b24B First some simple intuitions:l3528d2999x0e10j\f8 1f0 Standard story:l4798d4269x0e3j recently moved to that part of the world known as Silicon Valley, where it is a favorite entertainment to tinker in one's garage for a while, start a company, and earn a million dollars. l6068d5539x0e3j\52i14I take up this practice, and invite you over to see a demonstration of my new world-shaking computer that calculates oriental trajectories.l6068d5539x0e3j unveiling a large object made primarily of steel, but resting on what look for all the world to be four wheels. Taking keys out of my pocket, I open the door, climb in, and drive off into the sunset (sunrise, actually).l6068d5539x0e3j You object that it isn't a computer.l4798d4269x0e3j You are of course right; question is what underlies your (perfectly reasonable) objection?l4798d4269x0e3j That the device be rule-governed is not sufficient (hope that cars are rule-governed).l6068d5539x0e3j\25i9I Equivalent to the l-calculus, Turing machines, post production systems, etc., isn't much better: as Putnam has shown, just about everything is equivalent to some Turing machine.l6068d5539x0j\20f2 1f0 110i10I18i4I And anyway (as we will see) Turing equivalence is a weak, behaivoural metric, and we want a strong, constitutional one.l6068d5539x0j Rather, assume that somewhere burined in the informal concept of computation is a consensus that language-like structuresl3528d2999x0e3j\f8 1f0 some constituents or patterns of constituents that we can non-trivially call symbolsl4798d4269x0e3j\79i7I should act as causal ingredients in producing the overall behaviour.l3528d2999x0e3j It is not required that these ingredients contribute to the overall behaviour qua symbols.l3528d2999x0e3j\8i3I69i11I Computer science is widely assumed to be the study of formal symbol manipulation, meaning that the symbolic ingredients play a causal role without regard to their semantic weight.l4798d4269x0e3j\56i6I79i40I a requirement we call the formality condition.l4798d4269x0e3j\28b19B Just as a proof procedure is denied access to the interpretation of the sentences under its jurisdiction, and just as an adding machine has no access to the set-theoretic number that is encoded in the arrangements of its parts, so too it is assumed that the computer cannot behave in virtue of the referents or designations of its ingredients.l4798d4269x0e3j\300i9I4i12I I.e., on the standard story, a computer is:l3528d2999x0e3j symbolic (consitutents bear semantic weight), butl4798d4269x0e3j\2i8I formal (those consitutents not used in ways that depend on this semantic weight).l4798d4269x0e3j\2i6I So a computer is semantically coherent, in spite of the fact that it is formally defined.l3528d2999x0e3j\19i21I34i16I it not have been so; that we can is one of the great triumphs of the formal tradition.l4798d4269x0e3j exactly when computational design coheres with our semantical attribution that results can be viewed as significant. l4798d4269x0e3j for example, when you typel6068d5539x0e3j (= 3 (+ 1 2))l7338d6809x0e3j\f3 13f0 to the computer, and it types backl6068d5539x0e3j $TRUEl7338d6809x0e3j\1f3 5f0 you are delighted because you know that (= 3 (+ 1 2)) is true, and you take that symbol $TRUE' to designate truth.l6068d5539x0e3j\41f3 13f0 5i4I28f3 5f0 The computer preserved designation, without, so to speak, knowing it.l6068d5539x0e3j\15i21I That's why the car wasn't a computer.l3528d2999x0e3j In describing how a car works, the standard explanation will include an account of how the combustion of gases puts pressure on the piston crowns, which is in turn transmitted through the crankshaft and transmission to the wheels. And so on; the story is not computational, because the salient explanations are given in terms of mechanics forces and torques and plasticity and geometry and heat and so forth.l4798d4269x0e3j These are not interpreted notions; we don't posit a semantical interpretation function in order to make sense of the car's suspension.l4798d4269x0e3j\16i11I However suppose that the car contains an electronic fuel injection system; the story begins to change. There is an explanation of that circuit in terms of voltage levels, transistor thresholds, gain, and so forth, but this is not the description we typically use. Rather, we interpret the voltages as representing throttle opening, load pressure, and so forth; the explanation of why the circuit is the way that it is its structural raison d'etre is formulated in terms of this interpretation, not in terms of its electrical or electronic physiology.l4798d4269x0e3j\112i2I165i9I151i15I This interpretation makes this a computational explanation. Admittedly an inchoate and at best emergent one; in fuel injection systems the connection between symbol and symbolised is so close that the case is hard to call.l4798d4269x0e3j Infamous example of a thermostat is analogous; we understand the device by interpreting it, but we also so clearly comprehend the relationship between the un-interpreted account and the interpreted one that we can shift back and forth at will, and therefore are not inclined to cling to the semantical story when pressed, no matter how happy we are to use it informally.l4798d4269x0e3j\280i5I I.e., fuel injection system a borderline case, in other words, and borderline cases are illustrative only to show where the phenomenon, so to speak, takes hold.l4798d4269x0e3j Brunt of the argument will depend far more on our ability to reconstruct computational practice define concepts, explain programming language semantics, and so forth in terms of semantic notions, than it will depend on the fact of whether fuel injection systems are really computers.l3528d2999x0e3j\272i6I In other words, I do not want to rest conclusions about the computational metaphor on arm-chair philosophising about automobilesl4798d4269x0e3j Rather, I merely want to identify what I think is the crucial psychological step as we move from standard physical accounts into the domain of computational accounts.l4798d4269x0e3j recognisable step: what distinguishes an abacus, a calculator, and even a full scale computer, from other rule-governed complex artefacts like steam plants and food processors, is that the best explanation of the behaviour is formulated in the domain of interpretation, not in the domain of the uninterpreted signs (for example, we are liable to identify a calculator component as the mechanism that divides numbers).l3528d2999x0e3j\256i14I132i15I The more complex the computer, the more important the interpreted account becomes to our understanding, and the more variegated the kinds of interpretationl4798d4269x0e3j once you move past simple calculating devices into full programming languages, you find not just simple names, but quotation and internal reference, complex function designators, and even intensional contexts.l4798d4269x0e3j Have already seen all of these issues in described 3-LISP throughout the course.l4798d4269x0e3j\53f7 6f0 Formality condition itself betrays this universality of semanticsl3528d2999x0e3j to treat a symbol formally is to treat it in virtue of its shape syntax, form, whatever but crucially not in virtue of its reference or attributed semantics.l4798d4269x0e3j\108i3I but it would be hard to treat an eggplant formally, even though eggplants have perfectly lovely shapes.l4798d4269x0e3j\104i1I trouble is that we don't interpret eggplants don't typically take them to be signs or symbols at all.l4798d4269x0e3j\27i9I62i6I having shape isn't enough; if you don't have any semantics, then you don't have it around to ignore, either.l4798d4269x0e3j\47i3I In other words, to treat a symbol formally or syntactically is to put its non-semantic properties on center stage, and to keeps its semantic properties just out of sight in the wings, so to speak so that no one can see them, but so that everyone knows they are there.l4798d4269x0e3j\76i4I54i8I Two comments:l3528d2999x0e3j although I insist on being able to interpret computational processes, I haven't said (nor will I say) exactly what it is to do that.l4798d4269x0e3j\37i9I will require a successful theory of semantics and information, not surprisingly.l6068d5539x0e3j i.e., answer will only emerge if CSLI is successful; stay tuned.l6068d5539x0e3j If you worry, in other words, that I have brought undischarged semantical predicates into the very foundations of computer science, you're absolutely right.l6068d5539x0e3j Can say, however, that to interpret a process must not be simply to categorise it with respect to a set of theoretical terms, to assign it a purposive, teleological, or functional role, or to see it in a way consonant with pre-theoretic dispositionsl6068d5539x0e3j Must not because, if we are to rescue the term computational' from vacuity, we cannot have it mean simply apprehendable by the human mind'l7338d6809x0e3j\2i4I don't know what interpretation and semantics are, but they can't be everything.l6068d5539x0e3j people argue that we interpret' steering wheels as mechanisms for getting cars to go around corners but this is a broader notion than I intend. Mean to refer to something like the relationship that holds between pieces of language, and situations in the world that those pieces of language are about.l6068d5539x0e3j Second, involves one in discussions about the difference between an account of how something works versus what it does (latter requires semantics, one might think, former not).l4798d4269x0e3j\81i19I8i12I touches on age-old debate about the distinctions between reasons and causes: whether "computational" is a predicate on behaviour or on accounts of behaviour.l6068d5539x0e3j\121i9I7i8I also raises all kinds of issues of theory reduction, supervenience, etc.l6068d5539x0e3j and about the difference between description, explanation, and understanding.l6068d5539x0e3j Need to go into them somewhere, but won't go into them here.l6068d5539x0e3j terrible mess, but so be it.l6068d5539x0e3j So: want a semantic theory of computationl3528d2999x0e3j Not satisfied by doing proof theory over an axiomatization of semantics l4798d4269x0e3j cf. Oxford talk: pseudo-agreement.l4798d4269x0e3j if you have the syntax of a language spelled out on a paper, and the semantics described on another piece of paper, then in combination all you have are two pieces of paper, both of them with syntax on them.l4798d4269x0e3j\81i35I want the computation to be genuinely semantic in and of itself; not to be syntactic manipulation of semantic representations.l4798d4269x0e3j This distinction is utterly crucial.l4798d4269x0e3j Rest of the talk:l3528d2999x0e3j Four questions to be asked (and answers suggested):l4798d4269x0e3j What evidence is there for such a view?l6068d5539x0e3j How does it compare with other views?l6068d5539x0e3j What about the formality condition?l6068d5539x0e3j What are its consequences for cognitive science?l6068d5539x0e3j Take on each one in the time remaining.l4798d4269x0e3j 4. What Evidence?l3528d2999e15jk40\b18B First, a methodological remark:l3528d2999x0e10j\f8 1f0 Isn't obvious that computers are a pre-existing natural class, the properties of which we are engaged in uncovering, like meticulous biologists studying some rare species of owl.l4798d4269x0e3j\f8 1f0 Nor is there any observable behaviour in the world that it is our appointed duty to understand (as is arguably the case for physicists and linguists).l6068d5539x0e3j Nor is there, at least in any simple sense, any lay intuition, like that of number or set, the consensual understanding of which we are trying to reconstruct, like meta-mathematicians or philosophers.l6068d5539x0e3j In fact, to the extent that there are folk' conceptions of computers, they probably have to do with blinking lights, tape drives, and arcade games intuitions that are derivative on computational practice, rather than the other way around.l6068d5539x0e3j\172i11I It is therefore unclear what data, if any, we are responsible for unclear before what jury a proposed theory of computation should stand trial.l4798d4269x0e3j In fact we shouldn't blithely assume there are any objective facts of the matter: computers are devised, not discovered, and we can clearly dub as a computer' any artefact, physical or abstract, that we feel like.l6068d5539x0e3j\49i3I46i7I If we are scattered or confused surely not impossible there might be no underlying essence at all.l6068d5539x0e3j I.e., I am about to give evidence: to what judge do we repair if you challenge that evidence?l4798d4269x0e3j must judge any candidate account by its ability to rationally reconstruct expert computational practice.l4798d4269x0e3j lots of other proposal that are easy to dismiss, but one serious contender: the theory of effective computability that traffics in recursive functions, Turing machines, Church's thesis, and the rest.l4798d4269x0e3j will argue that this account does not intrinsically identify the class of artefacts that computer science studies.l6068d5539x0e3j For one thing, it is too broad, in that it includes far more devices within its scope (like chairs and Rubik cubes) than present experts would call computers.l6068d5539x0e3j problem stems from the fact that Turing equivalence (i.e., computing the same function) is a weak, behavioural metric, and we are interested in a theory that enables us to define strong, constitutional concepts.l7338d6809x0e3j\95i4I2i11I69i6I2i15I As a consequence, recourse to it will be of no help in predicting the future course of computer science, and of no help in explicating any strong computational claims made on the mind.l7338d6809x0e3j In addition, we argue that it may at the same time be too narow, excluding imaginable machines that computationalists would embrace (we will look at some examples in a minute).l6068d5539x0e3j Finally (and most importantly), fails to reconstruct the right concepts: program, data structure, implementation, interpreter, compiler, representation, and so forth, that are used not only in the day-to-day life of computer science, but also in fledgling computational models of cognition.l6068d5539x0e3j\75i7I2i14I2i14I2i21I2i14I Will present three types of evidence.l4798d4269x0e3j First, computational jargon:l3528d2999x0e3j\f8 1f0 name, semantics, interpreter, value, variable, expression, identifier, representationl4798d4269x0e3j\f8 2f0i4I2i9I2i11I2i5I2i8I2i10I2i10I2i14f8I this technical vocabulary would be truly extraordinary if computer science weren't linguistically basedl4798d4269x0e3j\f8 2f0 Won't spend much time here on this, because we have talked of it before.l4798d4269x0e3j Hope we have seen, over the quarter, that programming languages are permeated with notions that arise in full-fledged langauges like English, French, and Urdu.l4798d4269x0e3j\f8 2f0 Second, claim that F is a coherent notion in describing 3-LISP.l3528d2999x0e3j\f8 1f0 20f2 1f0 36f7 6f0 Point of F, models, a, etc., is that they relate the computation to the world it is about.l4798d4269x0e3j\11f2 1f0 10f2 1f0 even though, of course, 3-LISP is still a pretty traditional language, formluated by and large on the old view.l4798d4269x0e3j\26f7 6f0 Point of more standard accounts is that all one is told is about Q and Y, even if they are talked about abstractly.l4798d4269x0e3j\42i15I10f2 1f0 5f2 1f0 Hope it has been clear that to do that would have impoverished our understanding.l4798d4269x0e3j Again, don't want to spend more time today; hope this has been clear all along.l4798d4269x0e3j Third, the necessity of the kind of computation in the large discussion that we had last time (lecture 16).l3528d2999x0e3j\f8 1f0 37i24I Admittedly, have so far made only the most tentative progress.l4798d4269x0e3j Point is that the issues we were wrestling with: of physical realisation, and modelling, and semantics crossing implementation boundaries, and all of that, are fundamentally semantic/information notions.l4798d4269x0e3j And the analysis of computational concepts and models in general theory constructionl4798d4269x0e3j model, of course, is a semantic notion: a theory of what a model is will require a theory of information and semantics.l6068d5539x0e3j\2i5I Recall our discussion of the differences between interpretable computational processes from the processes that we understand them as signifying. l6068d5539x0e3j Example: a computational process modelling the flow of rush-hour traffic on Boston's SouthEast Expressway, not to be confused with the traffic flow itself.l6068d5539x0e3j As opposed to a computational model of mind, which is supposed to think, not simply model thinking.l6068d5539x0e3j\53i2I claim, to repeat, is not that the mind can be modelled as a computational process in this interpreted sense (i.e. mind corresponds to phenomena in the semantical domainl7338d6809x0e3j\48i9I35i11I surely, but uninterestingly, truel8608d8079x0e3j but that the mind is itself computational the mind is assumed actually to be an interpretable computational process.l7338d6809x0e3j\19i23I35i2I Again: if you don't make this distinction, the notion "computational" is emptied of meaning, and the computational claim on mind is vacuous.l6068d5539x0e3j 5. How does it Compare with Other Approaches?l3528d2999e15jk40\b46B Examine very briefly the most serious competing model, based on an underlying conception of the behaviour of digital and uninterpreted devices.l3528d2999x0e10j\f8 1f0 110i7I5i13I Call this alternative a model of digital computation, in contrast to our own, which we will call semantic.l4798d4269x0e3j\f8 2f0 33b7B57b8Bi1I digital conception best articulated by John Haugeland is one that coheres with the theories of effective computability (a strong mark in its favour), without leaning on them a priori.l4798d4269x0e3j\180i8I In addition, it is not troubled with irreducible semantic notions; as we will see, it can be presented in a relatively simple way, unarguably less problematic than the account we have just given of symbolic computation.l4798d4269x0e3j With all of this going for it, it certainly deserves our attentionl4798d4269x0e3j it would even deserve our allegiance, if only it were true.l6068d5539x0e3j problem, however, is that it too, like recursive function theory, fails to provide any insight into what computer scientists actually do.l6068d5539x0e3j In fact the two go strongly together: if the theory of effective computability were the right mathematical theory of computation, then Haugeland's definition of a formal system would be the right philosophy of computationl6068d5539x0e3j\198i10I Our rejection of the first is coupled with our rejection of the second.l6068d5539x0e3j Digital computation:l3528d2999x0e3j\f8 1f0 basic idea of a digital system is of a collection of discrete tokens or pieces', moved according to a set of rules, so as to obtain a pattern of positions or configurations.l4798d4269x0e3j\f8 1f0 note digital' has to do with fingers; notion is of discrete parts; not having to do with numerals or arithmetic notation.l6068d5539x0e3j\7f8 1f0 7f8 1f0 On Haugeland's view, to define a particular such system or game, you need to specify three things: l4798d4269x0e3j\f8 1f0 a. what the tokens are; l6068d5539x0e3j b. what the starting position is; andl6068d5539x0e3j c. what moves are legal (in any given position)l6068d5539x0e3j In addition, crucial to the system's formality (his use of the term) is a requirement of a certain medium independence, that is true of games like checkers and chess, but false of, say, billiards or football (football fails the discreteness test as well). l4798d4269x0e3j\f8 1f0 38i9I53i19I Medium independence an advertised lack of concern with the details of embodiment like size, shape, or material depends on a self-contained sense of the system (everything that matters is contained in the statement of rules), and on the perfect definiteness of the system.l4798d4269x0e3j\f8 1f0 It is certainly arguable that all modern digital computers, to say nothing of familiar games like chess, formal logics, and so forth, are digital in this sense.l6068d5539x0e3j This is not a claim without its problems, however: computers with sensors and manipulators and so forth aren't strictly self-contained. An appropriate notion of boundary and specificity of interaction would probably have to be developed to maintain the closed' nature of Haugeland's account in the face of these obvious connections with the world. But we will presume that this could be done, not because we believe it would be possible, but because our doubts about the digital approach stem from another direction.l6068d5539x0e3j\113i8I Note at the outset that the two views are intensionally distinct: they are framed in different language, defined in terms of different phenomena, and so forth.l3528d2999x0e3j\f8 1f0 43i13I Thus even if we were able to show that they described the same devices i.e., that they were extensionally equivalent that would be a claim of substance. l4798d4269x0e3j\f8 1f0 95i13I Furthermore, our arguments for a semantic approach would stand in the face of such a claim, since we require a strong theory able to define terms (support counter-factuals, and so forth).l4798d4269x0e3j\f8 1f0 112i6I However as it happens this is not the case; we will argue that the two proposals are extensionally distinct as well.l4798d4269x0e3j\f8 1f0 Consider a Venn diagram comparing the two notions:l4798d4269x0e3j\f8 1f0 <==