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LECTURE NOTES #17 LISP: LANGUAGE AND LITERATURE June 7, 1984
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Lecture Notes #17 — The Computational Claim on Mind

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Last edited:June 7, 1984 11:43 AM

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A. Introductory Notes

—Four handouts today:

—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.

—Solutions to problem set #2;

—Lecture notes for today.

—Questionnaire; please fill out and return as soon as possible.

—Plus "Knights of the Lambda calculus" pins for those stalwart few who have attended all quarter.

—There were some lectures for which lecture notes were not handed out:

—Specifically, #s 2, 3, 6, 7, 12, 14, and 15.

—I will be preparing notes for all of these over the next month, in preparation for the Coling course.

—Send me a note if you would like copies of these, and I will distribute them at the beginning of July.

—Today:

—Review (and borrow) some of what is in the first few sections of The Computational Metaphor, distributed last time.

—Suggest we need a genuinely semantic notion of computation.

—End up with a critique (and partial reconstruction) of the formality condition.

2. The Computation Claim

—The computational claim:

—Not news that computational vocabulary is used to describe the mind

—in linguistics, philosophy, psychology, AI, etc.

—Rests on a claim, basically, that the mind, or mental processes, or belief revision, or intelligence — something of that sort — is computational.

—Lots of questions to be asked, such as: Is the computational claim true?

—Before one can begin even to explore such a question, however, need to know what claim it is.

—Curiously, if you press people, they defer hard questions (about what computation is) to computational practice or practitioners:

—Typically: "Well, I don’t know exactly, but it is just like what goes on in a computer."

—My standard reaction: if your understanding rests on my understanding, you’re in trouble. We don’t know what we are talking about.

—So need a theory of computation.

—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.

—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.

—I.e., treading a thin line between vacuity on the one hand, and falsity on the other.

3. Semantic Computation

—First some simple intuitions:

—Standard story:

—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.

—take up this practice, and invite you over to see a demonstration of my new world-shaking computer that calculates oriental trajectories.

—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).

—You object that it isn’t a computer.

—You are of course right; question is what underlies your (perfectly reasonable) objection?

—That the device be rule-governed is not sufficient (hope that cars are rule-governed).

—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.

—And anyway (as we will see) Turing equivalence is a weak, behaivoural metric, and we want a strong, constitutional one.

—Rather, assume that somewhere burined in the informal concept of computation is a consensus that language-like structures

—some constituents or patterns of constituents that we can non-trivially call symbols

should act as causal ingredients in producing the overall behaviour.

—It is not required that these ingredients contribute to the overall behaviour qua symbols.

—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.

—a requirement we call the formality condition.

—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.

—I.e., on the standard story, a computer is:

—symbolic (consitutents bear semantic weight), but

—formal (those consitutents not used in ways that depend on this semantic weight).

—So a computer is semantically coherent, in spite of the fact that it is formally defined.

—it not have been so; that we can is one of the great triumphs of the formal tradition.

—exactly when computational design coheres with our semantical attribution that results can be viewed as significant.

—for example, when you type

(= 3 (+ 1 2))

to the computer, and it types back

$TRUE

you are delighted because you know that (= 3 (+ 1 2)) is true, and you take that symbol ‘$TRUE’ to designate truth.

—The computer preserved designation, without, so to speak, knowing it.

—That’s why the car wasn’t a computer.

—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.

—These are not interpreted notions; we don’t posit a semantical interpretation function in order to make sense of the car’s suspension.

—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.

—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.

—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.

—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.

—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.

—In other words, I do not want to rest conclusions about the computational metaphor on arm-chair philosophising about automobiles

—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.

—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).

—The more complex the computer, the more important the interpreted account becomes to our understanding, and the more variegated the kinds of interpretation

—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.

—Have already seen all of these issues in described 3-LISP throughout the course.

—Formality condition itself betrays this universality of semantics

—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.

—but it would be hard to treat an eggplant formally, even though eggplants have perfectly lovely shapes.

—trouble is that we don’t interpret eggplants — don’t typically take them to be signs or symbols at all.

—having shape isn’t enough; if you don’t have any semantics, then you don’t have it around to ignore, either.

—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.

—Two comments:

—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.

—will require a successful theory of semantics and information, not surprisingly.

—i.e., answer will only emerge if CSLI is successful; stay tuned.

—If you worry, in other words, that I have brought undischarged semantical predicates into the very foundations of computer science, you’re absolutely right.

—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 dispositions

—Must not because, if we are to rescue the term ‘computational’ from vacuity, we cannot have it mean simply ‘apprehendable by the human mind’

—don’t know what interpretation and semantics are, but they can’t be everything.

—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.

—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).

—touches on age-old debate about the distinctions between reasons and causes: whether "computational" is a predicate on behaviour or on accounts of behaviour.

—also raises all kinds of issues of theory reduction, supervenience, etc.

—and about the difference between description, explanation, and understanding.

—Need to go into them somewhere, but won’t go into them here.

—terrible mess, but so be it.

—So: want a semantic theory of computation

—Not satisfied by doing proof theory over an axiomatization of semantics

—cf. Oxford talk: pseudo-agreement.

—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.

—want the computation to be genuinely semantic in and of itself; not to be syntactic manipulation of semantic representations.

—This distinction is utterly crucial.

—Rest of the talk:

—Four questions to be asked (and answers suggested):

—What evidence is there for such a view?

—How does it compare with other views?

—What about the formality condition?

—What are its consequences for cognitive science?

—Take on each one in the time remaining.

4. What Evidence?

—First, a methodological remark:

—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.

—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).

—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.

—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.

—It is therefore unclear what data, if any, we are responsible for — unclear before what jury a proposed theory of computation should stand trial.

—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.

—If we are scattered or confused — surely not impossible — there might be no underlying essence at all.

—I.e., I am about to give evidence: to what judge do we repair if you challenge that evidence?

—must judge any candidate account by its ability to rationally reconstruct expert computational practice.

—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.

—will argue that this account does not intrinsically identify the class of artefacts that computer science studies.

—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.

—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.

—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.

—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).

—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.

—Will present three types of evidence.

—First, computational jargon:

—name, semantics, interpreter, value, variable, expression, identifier, representation

—this technical vocabulary would be truly extraordinary if computer science weren’t linguistically based

—Won’t spend much time here on this, because we have talked of it before.

—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.

—Second, claim that F is a coherent notion in describing 3-LISP.

—Point of F, models, a, etc., is that they relate the computation to the world it is about.

—even though, of course, 3-LISP is still a pretty traditional language, formluated by and large on the old view.

—Point of more standard accounts is that all one is told is about Q and Y, even if they are talked about abstractly.

—Hope it has been clear that to do that would have impoverished our understanding.

—Again, don’t want to spend more time today; hope this has been clear all along.

—Third, the necessity of the kind of computation in the large discussion that we had last time (lecture 16).

—Admittedly, have so far made only the most tentative progress.

—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.

—And the analysis of computational concepts and models in general theory construction

—model, of course, is a semantic notion: a theory of what a model is will require a theory of information and semantics.

—Recall our discussion of the differences between interpretable computational processes from the processes that we understand them as signifying.

—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.

—As opposed to a computational model of mind, which is supposed to think, not simply model thinking.

—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 domain

—surely, but uninterestingly, true

but that the mind is itself computational — the mind is assumed actually to be an interpretable computational process.

—Again: if you don’t make this distinction, the notion "computational" is emptied of meaning, and the computational claim on mind is vacuous.

5. How does it Compare with Other Approaches?

—Examine very briefly the most serious competing model, based on an underlying conception of the behaviour of digital and uninterpreted devices.

—Call this alternative a model of digital computation, in contrast to our own, which we will call semantic.

—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.

—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.

—With all of this going for it, it certainly deserves our attention

—it would even deserve our allegiance, if only it were true.

—problem, however, is that it too, like recursive function theory, fails to provide any insight into what computer scientists actually do.

—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 computation

—Our rejection of the first is coupled with our rejection of the second.

—Digital computation:

—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.

—note ‘digital’ has to do with fingers; notion is of discrete parts; not having to do with numerals or arithmetic notation.

—On Haugeland’s view, to define a particular such system or game, you need to specify three things:

a.what the tokens are;

b.what the starting position is; and

c.what moves are legal (in any given position)

—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).

—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.

—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.

—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.

—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.

—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.

—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).

—However as it happens this is not the case; we will argue that the two proposals are extensionally distinct as well.

—Consider a Venn diagram comparing the two notions:

<==<lecture-17-figure-1.press<

—presumably clear (especially given the arguments we have already laid out) that most current computers falls into area DyS; symbolic and digital. What we will argue is that there are also

—devices in D (digital non-computers), and

—devices in S as well (non-digital computers).

—Digital non-computers:

—child’s Tinker Toy set.

—because of the types of connection allowed by the shapes of the pieces, Tinker Toy is essentially a digital construction kit; a finite set of lengths of piece can be connected in a finite and discrete set of angles and so on.

—On the digital view, then, any mechanism that anyone has ever built out of Tinker Toy is (or at least embodies) a computer (since, given any device, it is trivial to abstract a set of rules and starting positions from it).

—But this surely violates intuition, showing that the digital conception is too broad. It seems derivative on our notion of a computer to say that the crane that my niece has built computes where to unload her toy dump truck. Unless, of course, we want to use the word ‘compute’ to cover essentially everything. But then the term becomes vacuous, and the computational hypothesis of mind is emptied of meaning.

—chess (an example Haugeland actually uses):

—won’t doubt that a device that plays chess may be computational (in our sense, since parts of it would probably designate chess positions

—however, would seem odd to say that a chess game is itself computational.

—and yet wouldn’t want to deny either its digital nature, or (on some readings) that it is formal

—chess games don’t compute anything, except their own future — and they don’t mean anything: that’s why chess is a game.

—It is true that, in being digital and abstract (medium independent), chess bears a strong resemblence to most current computational devices, but nonetheless it does not seem to be a device where we are disposed to apply any of the actual terms of computer science.

—Semantic (i.e., interpretable) but non-digital devices:

—fuel injection example is a simple example, although it can be uninterestingly countered by someone who claims that all physical devices falls into the class of digital systems — who argues, in other words, that D outside of DyS is empty.

—recourse would be to show that some aspect of physical reality was not describable by a recursive function

—a question to which I gather we don’t know the answer, but presumably it might be true.

—Suppose physics turns out this way, and consider a device designed to solve arbitrary three-body problems in mechanics (for which it happens that we do not know closed-form algorithmic solutions).

—We imagine that this device contains not only digital circuitry of a familiar sort, but also analog circuitry (say, with program-controllable gates) so arranged that the relevant part of its electronic physiology can be set up to correspond with any three-body problem in mechanics.

—Such a machine might be wonderfully efficient at solving problems, say, for NASA having to do with stability in the space shuttle.

—we would still be disposed to call this crucially analog device a computer, although perhaps an odd computer (but not that odd: analog-digital hybrids are actually built).

—Digital computation, in this instance, is too narrow; our pre-theoretic intuitions about future practice seem to come down on the semantic side.

—These contortions, however, are a little beside the point: device that is not digital at the level of description at which it is called a computer would seem enough of an answer, and that we surely have in present day analog computers.

—More importantly: specualte as to why discreteness and medium-independence might be salient characteristics of devices that we interpret — might be generally good characteristics to have in linguistic substrates — even if we don’t rest on them as criterial properties.

—In general, this is an important part of this analysis, which I want to stress:

—we want to reconstruct the intuitions underlying alternative acounts, as well as dismissing them.

—will do this as well for the formality condition.

—Obvious issues that would arise inlude modularity, freedom from error, and so forth.

—might expect extant medium-independent systems to be interpretable; why else would we have medium-independent devices? Two obvious reasons:

a.to interpret them (i.e., as computers), or

b.for their own structures (as a game, say, or for pure aesthetics)?

and in fact we have instances of both.

—xxx

—Another important point of comparison: how does semantics arise in a computational system:

—i.e., on the standard view, computer science is definable without reference to semantics, and computational processes run without access to semantics; so how does or can semantics arise in such a setting?

—Searle and Dreyfus argue that it cannot;

—Haugeland and Fodor, though different in many ways, argue that sufficient causal embedding in the world may suffice

—On our view, you have it if you have computation at all.

—So the questions are then subsidiary: what kinds are there (attributed, authentic or original); social or individual, etc.

—Story of "We found it" bumper stickers.

—There are lots of things that are hard to have (intelligence), but I suspect reference and semantics are not one of them.

—Looks to be a problem only because the field has been analysed up the wrong way.

—So what would a semantic theory of computation look like:

—Not like 3-LISP; hope that’s clear.

—Tree rings (as opposed to a two-state counter) as base case.

—No way to support hypotheticals; too much causal connection between sign and significant.

—But get started. Imagine then pulling the sign away from what it signifies, and yet doing so in such as a way that the uniformities and natural laws of the universe keep it in sufficient coordination with the significant so that it can genuinely bear information about that significant.

—Can imagine failure, and consequential notion of negation arising.

—And the drive towards medium independence, so that the right regularities can be the dominant ones.

—and gradually build up all the notions of language that we know so well.

—Will need (I am pretty convinced) notions of representation, and intensional information, and so on: all the fine-grained distinctions that sthe syntactic and formal theorists rely on as defenses of their view.

—Again, point is not to say those requirements are bad, only that they arise out of a genuine semantic connection, and therefore don’t need to be posited out of the air as ad-hoc properties of an otherwise unexplainable linguistic system.

6. The Formality Condition?

—xxx

7. Consequnces for Cognitive Science

—xxx

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