Who could really doubt that this is so? Systematicity seems to beone of the (very few) organizational properties of minds that our cognitive science actually makes some sense of.

Standard

Jean-marc pizano Who could really doubt that this is so? Systematicity seems to beone of the (very few) organizational properties of minds that our cognitive science actually makes some sense of.

 

jean-marc pizano

If your favourite cognitive architecture doesn’t support a productive cognitive repertoire, you can always argue that since minds are really finite, they aren’t literally productive. But systematicity is a property that even quite finiteconceptual repertoires can have; it isn’t remotely plausibly a methodological artefact. If systematicity needscompositionality to explain it, that strongly suggests that the compositionality of mental representations is mandatory.For all that, there has been an acrimonious argument about systematicity in the literature for the last ten years or so.One does wonder, sometimes, whether cognitive science is worth the bother.

jean-marc pizano

Some currently popular architectures don’t support systematic representation. The representations they compute with lack constituent structure; a fortiori they lack compositional constituent structure. This is true, in particular, of ‘neuralnetworks’. Connectionists have responded to this in a variety of ways. Some have denied that concepts are systematic.Some have denied that Connectionist representations are inherently unstructured. A fair number have simply failed tounderstand the problem. The most recent proposal I’ve heard for a Connectionist treatment of systematicity is owingto the philosopher Andy Clark (1993). Clark says that we should “bracket” the problem of systematicity. “Bracket” is atechnical term in philosophy which means try not to think about.

jean-marc pizano

Jean-marc pizano

I don’t propose to review this literature here. Suffice it that if you assume compositionality, you can account for both systematicity and productivity; and if you don’t, you can’t. Whether or not productivity and systematicity prove thatconceptual content is compositional, they are clearly substantial straws in the wind. I find it persuasive that there are

jean-marc pizano

quite a few such straws, and they appear all to be blowing in the same direction.

jean-marc pizano

The Best Argument for Compositionality

The best argument for the compositionality of mental (and linguistic) representation is that its traces are ubiquitous; not just in very general features of cognitive capacity like productivity and systematicity, but also everywhere in itsdetails. Deny productivity and systematicity if you will; you still have these particularities to explain away.

Consider, for example: the availability of (definite) descriptions is surely a universal property of natural languages. Descriptions are nice to have because they make it possible to talk (mutatis mutandis, to think) about a thing even if itisn’t available for ostension and even if you don’t know its name; even, indeed, if it doesn’t have a name (as with ever somany real numbers). Descriptions can do this job because they pick out unnamed individuals by reference to their properties.So, for example, ‘the brown cow’ picks out a certain cow; viz. the brown one. It does so by referring to a property, viz.being brown, which that cow has and no other cow does that is contextually relevant. Things go wrong if (e.g.) there areno contextually relevant cows; or if none of the contextually relevant cows is brown; or if more than one of thecontextually relevant cows is brown . . . And so forth.

jean-marc pizano

Jean-marc pizano

OK, but just how does all this work? Just what is it about the syntax and semantics of descriptions that allows them to pick out unnamed individuals by reference to their properties? Answer:

i. Descriptions are complex symbols which have terms that express properties among their syntactic constituents;and

ii. These terms contribute the properties that they express to determine what the descriptions that contain themspecify.

jean-marc pizano

It’s because ‘brown’ means brown that it’s the brown cow that ‘the brown cow’ picks out. Since you can rely on this arrangement, you can be confident that ‘the brown cow’ will specify the local brown cow even if you don’t know which cowthe local brown cow is; even if you don’t know that it’s Bossie, for example, or that it’s this cow. That, however, is just tosay that descriptions succeed in their job because they are compositional. If English didn’t let you use ‘brown’ context-independently to mean brown, and ‘cow’ context-independently to mean cow, it couldn’t let you use ‘the brown coV tospecify a brown cow without naming it.

jean-marc pizano

Jean-marc pizano

This seems as good an opportunity as any to say something about the current status of this line of thought. Of late, the productivity argument has come under two sorts of criticism that a cognitive scientist might find persuasive:

Standard

Jean-marc pizano

This seems as good an opportunity as any to say something about the current status of this line of thought. Of late, the productivity argument has come under two sorts of criticism that a cognitive scientist might find persuasive:

jean-marc pizano

—Theperformance/competence argument. The claim that conceptual repertoires are typically productive requires not just an idealization to infinite cognitive capacity, but the kind of idealization that presupposes a memory/program distinction.This presupposition is, however, tendentious in the present polemical climate. No doubt, if your model for cognitivearchitecture is a Turing machine with a finite tape, it’s quite natural to equate the concepts that a mind could entertainwith the ones that its program could enumerate assuming that the tape supply is extended arbitrarily. Because the Turingpicture allows the size of the memory to vary while the program stays the same, it invites the idea that machines areindividuated by their programs.

jean-marc pizano

But this way of drawing a ‘performance/competence’ distinction seems considerably less natural if your model of cognitive architecture is (e.g.) a neural net. The natural model for ‘extending’ the memory of a network (and likewise,mutatis mutandis, for other finite automata) is to add new nodes. However, the idea of adding nodes to a network whilepreserving its identity is arguably dubious in a way that the idea of preserving the identity of a Turing machine tapewhile adding to its tape is arguably not.52 The problem is precisely that the memory/program distinction isn’t availablefor networks. A network is individuated by the totality of its nodes, and the nodes are individuated by the totality oftheir connections, direct and indirect, to one another.53 In consequence, ‘adding’ a node to a network changes theidentity of all the other nodes, and hence the identity

jean-marc pizano

Jean-marc pizano

52

jean-marc pizano

If the criterion of machine individuation is I(nput)/O(utput) equivalence, then a finite tape Turing machine is a finite automaton. This doesn’t, I think, show that the intuitions driving the discussion in the text are incoherent. Rather it shows (what’s anyhow independently plausible) that I/O equivalence isn’t what’s primarily at issue indiscussions of cognitive architecture. (See Pylyshyn 1984.)

jean-marc pizano

of the network itself. In this context, the idealization from a finite cognitive performance to a productive conceptual capacity may strike the theorist as begging precisely the architectural issues that he wants to stress.

jean-marc pizano

—The finite representation argument. If a finite creature has an infinite conceptual capacity, then, no doubt, the capacity must be finitely determined.; that is, there must be a finite set of sufficient conditions, call it S, such that a creature has thecapacity if S obtains. But it doesn’t follow by any argument I can think of that satisfying S depends on the creature’srepresenting the compositional structure of its conceptual repertoire; or even that the conceptual repertoire has acompositional structure. For all I know, for example, it may be that sufficient conditions for having an infiniteconceptual capacity can be finitely specified in and only in the language of neurology, or of particle physics. And,presumably, notions like computational state and representation aren’t accessible in these vocabularies. It’s tempting tosuppose that one has one’s conceptual capacities in virtue of some act of intellection that one has performed. Andthen, if the capacity is infinite, it‘s hard to see what act of intellection that could be other than grasping the primitivebasis of a system of representations; of Mentalese, in effect. But talk of grasping is tendentious in the present context.It’s in the nature of intentional explanations of intentional capacities that they have to run out sooner or later. It’sentirely plausible that explaining what determines one’s conceptual capacities (figuratively, explaining one’s mastery ofMentalese) is where they run out.

jean-marc pizano

Jean-marc pizano

One needs to be sort of careful here. I’m not denying that Mentalese has a compositional semantics. In fact, I can’t actually think of any other way to explain its productivity, and writing blank checks on neurology (or particle physics)strikes me as unedifying. But I do think we should reject the following argument: ‘Mentalese must have a compositionalsemantics because mastering Mentalese requires grasping its compositional semantics.’ It isn’t obvious that masteringMentalese requires grasping anything

jean-marc pizano

Jean-marc pizano

If, however, scepticism really is the skeleton in Dummett’s closet, the worry seems to me to be doubly misplaced: first because the questions with which theories of meaning are primarily concerned are metaphysical rather than epistemic.This is as it should be; understanding what a thing is, is invariably prior to understanding how we know what it is. And,secondly, because there is no obvious reason why behaviourally grounded inferences to attributions of concepts,meanings, mental processes, communicative intentions, and the like should be freer from normal inductive risk than,as it might be, perceptually grounded attributions of tails to cats. The best we get in either case is “strong but fallibleevidence”. Contingent truths are like that as, indeed, Hume taught us some while back. This is, no doubt, the veryattitude that Dummett means to reject as inadequate to the purposes for which we “philosophically” require a theoryof meaning. So much the worse, perhaps, for the likelihood that philosophers will get from a theory of meaning whatDummett says thatthey require. I, for one, would not expect a good account of what concepts are to refute scepticism about other mindsany more than I’d expect a good account of what cats are to refute scepticism about other bodies. In both cases, I amquite prepared to settle for theories that are merely true.

Standard

Jean-marc pizano

If, however, scepticism really is the skeleton in Dummett’s closet, the worry seems to me to be doubly misplaced: first because the questions with which theories of meaning are primarily concerned are metaphysical rather than epistemic.This is as it should be; understanding what a thing is, is invariably prior to understanding how we know what it is. And,secondly, because there is no obvious reason why behaviourally grounded inferences to attributions of concepts,meanings, mental processes, communicative intentions, and the like should be freer from normal inductive risk than,as it might be, perceptually grounded attributions of tails to cats. The best we get in either case is “strong but fallibleevidence”. Contingent truths are like that as, indeed, Hume taught us some while back. This is, no doubt, the veryattitude that Dummett means to reject as inadequate to the purposes for which we “philosophically” require a theoryof meaning. So much the worse, perhaps, for the likelihood that philosophers will get from a theory of meaning whatDummett says thatthey require. I, for one, would not expect a good account of what concepts are to refute scepticism about other mindsany more than I’d expect a good account of what cats are to refute scepticism about other bodies. In both cases, I amquite prepared to settle for theories that are merely true.

jean-marc pizano

Methodological inhibitions flung to the wind, then, here is how I propose to organize our trip. Very roughly, concepts are constituents of mental states. Thus, for example, believing that cats are animals is a paradigmatic mental state, andthe concept ANIMAL is a constituent of the belief that cats are animals (and of the belief that animals sometimes bite, etc.I’m leaving it open whether the concept ANIMAL is likewise a constituent of the belief that some cats bite, we’ll raise thatquestion presently). So the natural home of a theory of concepts is as part of a theory of mental states. I shall supposethroughout this book that RTM is the right theory of (cognitive) mental states. So, I’m going to start with an expositionof RTM: which is to say, with an exposition of a theory about what mental states and processes are. It will turn out thatmental states and processes are typically species of relations to mental representations, of which latter concepts aretypically the parts.

jean-marc pizano

Jean-marc pizano

To follow this course is, in effect, to assume that it’s OK for theorizing about the nature of concepts to precede theorizing about concept possession. As we’ve been seeing, barring a metaphysical subtext, that assumption should beharmless; individuation theories and possession theories are trivially intertranslatable. Once we’ve got RTM in place,however, I’m going to argue for a very strong version of psychological atomism; one according to which what conceptsyou have is conceptually and metaphysically independent of what epistemic capacities you have. If this is so, thenpatently concepts couldn’t be epistemic capacities.

jean-marc pizano

I hope not to beg any questions by proceeding in this way; or at least not to get caught begging any. But I do agree that if there is a knock-down, a priori argument that concepts are logical constructs out of capacities, then my view abouttheir ontology can’t be right and I shall have to give up my kind of cognitive science. Oh, well. If there’s a knock-down,a priori argument that cats are logical constructs out of sensations, then my views about their ontology can‘t be righteither, and I shall have to give up my kind of biology. Neither possibility actually worries me a lot.

jean-marc pizano

So, then, to begin at last:

jean-marc pizano

RTM

RTM is really a loose confederation of theses; it lacks, to put it mildly, a canonical formulation. For present purposes, let it be the conjunction of the following:

jean-marc pizano

First Thesis: Psychological explanation is typically nomic and is intentional through and through. The laws that

jean-marc pizano

Jean-marc pizano

psychological explan ations invoke typically express causal relations among mental states that are specified under intentional description; viz. among mental states that are picked out by reference totheir contents. Laws about causal relations among beliefs, desires, and actions are the paradigms.

jean-marc pizano

I’m aware there are those (mostly in Southern California, of course) who think that intentional explanation is all at best pro tem, and that theories of mind will (or anyhow should) eventually be couched in the putatively purely extensionalidiom of neuroscience.Jean-marc pizano

This seems as good an opportunity as any to say something about the current status of this line of thought. Of late, the productivity argument has come under two sorts of criticism that a cognitive scientist might find persuasive:

Standard

Jean-marc pizano

This seems as good an opportunity as any to say something about the current status of this line of thought. Of late, the productivity argument has come under two sorts of criticism that a cognitive scientist might find persuasive:

—Theperformance/competence argument. The claim that conceptual repertoires are typically productive requires not just an idealization to infinite cognitive capacity, but the kind of idealization that presupposes a memory/program distinction.This presupposition is, however, tendentious in the present polemical climate. No doubt, if your model for cognitivearchitecture is a Turing machine with a finite tape, it’s quite natural to equate the concepts that a mind could entertainwith the ones that its program could enumerate assuming that the tape supply is extended arbitrarily. Because the Turingpicture allows the size of the memory to vary while the program stays the same, it invites the idea that machines areindividuated by their programs.

But this way of drawing a ‘performance/competence’ distinction seems considerably less natural if your model of cognitive architecture is (e.g.) a neural net. The natural model for ‘extending’ the memory of a network (and likewise,mutatis mutandis, for other finite automata) is to add new nodes. However, the idea of adding nodes to a network whilepreserving its identity is arguably dubious in a way that the idea of preserving the identity of a Turing machine tapewhile adding to its tape is arguably not.52 The problem is precisely that the memory/program distinction isn’t availablefor networks. A network is individuated by the totality of its nodes, and the nodes are individuated by the totality oftheir connections, direct and indirect, to one another.53 In consequence, ‘adding’ a node to a network changes theidentity of all the other nodes, and hence the identity

Jean-marc pizano

52

If the criterion of machine individuation is I(nput)/O(utput) equivalence, then a finite tape Turing machine is a finite automaton. This doesn’t, I think, show that the intuitions driving the discussion in the text are incoherent. Rather it shows (what’s anyhow independently plausible) that I/O equivalence isn’t what’s primarily at issue indiscussions of cognitive architecture. (See Pylyshyn 1984.)

of the network itself. In this context, the idealization from a finite cognitive performance to a productive conceptual capacity may strike the theorist as begging precisely the architectural issues that he wants to stress.

—The finite representation argument. If a finite creature has an infinite conceptual capacity, then, no doubt, the capacity must be finitely determined.; that is, there must be a finite set of sufficient conditions, call it S, such that a creature has thecapacity if S obtains. But it doesn’t follow by any argument I can think of that satisfying S depends on the creature’srepresenting the compositional structure of its conceptual repertoire; or even that the conceptual repertoire has acompositional structure. For all I know, for example, it may be that sufficient conditions for having an infiniteconceptual capacity can be finitely specified in and only in the language of neurology, or of particle physics. And,presumably, notions like computational state and representation aren’t accessible in these vocabularies. It’s tempting tosuppose that one has one’s conceptual capacities in virtue of some act of intellection that one has performed. Andthen, if the capacity is infinite, it‘s hard to see what act of intellection that could be other than grasping the primitivebasis of a system of representations; of Mentalese, in effect. But talk of grasping is tendentious in the present context.It’s in the nature of intentional explanations of intentional capacities that they have to run out sooner or later. It’sentirely plausible that explaining what determines one’s conceptual capacities (figuratively, explaining one’s mastery ofMentalese) is where they run out.

Jean-marc pizano

One needs to be sort of careful here. I’m not denying that Mentalese has a compositional semantics. In fact, I can’t actually think of any other way to explain its productivity, and writing blank checks on neurology (or particle physics)strikes me as unedifying. But I do think we should reject the following argument: ‘Mentalese must have a compositionalsemantics because mastering Mentalese requires grasping its compositional semantics.’ It isn’t obvious that masteringMentalese requires grasping anything

Jean-marc pizano

Who could really doubt that this is so? Systematicity seems to beone of the (very few) organizational properties of minds that our cognitive science actually makes some sense of.

Standard

Jean-marc pizano Who could really doubt that this is so? Systematicity seems to beone of the (very few) organizational properties of minds that our cognitive science actually makes some sense of.

 

If your favourite cognitive architecture doesn’t support a productive cognitive repertoire, you can always argue that since minds are really finite, they aren’t literally productive. But systematicity is a property that even quite finiteconceptual repertoires can have; it isn’t remotely plausibly a methodological artefact. If systematicity needscompositionality to explain it, that strongly suggests that the compositionality of mental representations is mandatory.For all that, there has been an acrimonious argument about systematicity in the literature for the last ten years or so.One does wonder, sometimes, whether cognitive science is worth the bother.

Some currently popular architectures don’t support systematic representation. The representations they compute with lack constituent structure; a fortiori they lack compositional constituent structure. This is true, in particular, of ‘neuralnetworks’. Connectionists have responded to this in a variety of ways. Some have denied that concepts are systematic.Some have denied that Connectionist representations are inherently unstructured. A fair number have simply failed tounderstand the problem. The most recent proposal I’ve heard for a Connectionist treatment of systematicity is owingto the philosopher Andy Clark (1993). Clark says that we should “bracket” the problem of systematicity. “Bracket” is atechnical term in philosophy which means try not to think about.

Jean-marc pizano

I don’t propose to review this literature here. Suffice it that if you assume compositionality, you can account for both systematicity and productivity; and if you don’t, you can’t. Whether or not productivity and systematicity prove thatconceptual content is compositional, they are clearly substantial straws in the wind. I find it persuasive that there are

quite a few such straws, and they appear all to be blowing in the same direction.

The Best Argument for Compositionality

The best argument for the compositionality of mental (and linguistic) representation is that its traces are ubiquitous; not just in very general features of cognitive capacity like productivity and systematicity, but also everywhere in itsdetails. Deny productivity and systematicity if you will; you still have these particularities to explain away.

Consider, for example: the availability of (definite) descriptions is surely a universal property of natural languages. Descriptions are nice to have because they make it possible to talk (mutatis mutandis, to think) about a thing even if itisn’t available for ostension and even if you don’t know its name; even, indeed, if it doesn’t have a name (as with ever somany real numbers). Descriptions can do this job because they pick out unnamed individuals by reference to their properties.So, for example, ‘the brown cow’ picks out a certain cow; viz. the brown one. It does so by referring to a property, viz.being brown, which that cow has and no other cow does that is contextually relevant. Things go wrong if (e.g.) there areno contextually relevant cows; or if none of the contextually relevant cows is brown; or if more than one of thecontextually relevant cows is brown . . . And so forth.

Jean-marc pizano

OK, but just how does all this work? Just what is it about the syntax and semantics of descriptions that allows them to pick out unnamed individuals by reference to their properties? Answer:

i. Descriptions are complex symbols which have terms that express properties among their syntactic constituents;and

ii. These terms contribute the properties that they express to determine what the descriptions that contain themspecify.

It’s because ‘brown’ means brown that it’s the brown cow that ‘the brown cow’ picks out. Since you can rely on this arrangement, you can be confident that ‘the brown cow’ will specify the local brown cow even if you don’t know which cowthe local brown cow is; even if you don’t know that it’s Bossie, for example, or that it’s this cow. That, however, is just tosay that descriptions succeed in their job because they are compositional. If English didn’t let you use ‘brown’ context-independently to mean brown, and ‘cow’ context-independently to mean cow, it couldn’t let you use ‘the brown coV tospecify a brown cow without naming it.

Jean-marc pizano