Robert J. Matthews

Many believe that the grammatical sentences of a natural language are a recursive set. In this paper I argue that the commonly adduced grounds for this belief are inconclusive, if not simply unsound. Neither the native speaker's ability to classify sentences nor his ability to comprehend them requires it. Nor is there at present any reason to think that decidability has any bearing on first-language acquisition. I conclude that there are at present no compelling theoretical grounds for requiring that transformational grammars enumerate only recursive sets. Hence, the fact that proposed transformational grammars do not satisfy this requirement does not, as some have claimed, represent a shortcoming in current theory.

Classicists and connectionists alike claim to be able to explain systematicity. The proposed classicist explanation, I argue, is little more than a promissory note, one that classicists have no idea how to redeem. Smolensky's (1995) proposed connectionist explanation fares little better: it is not vulnerable to recent classicist objections, but it nonetheless fails, particularly if one requires, as some classicists do, that explanations of systematicity take the form of a‘functional analysis’. Nonetheless, there are, I argue, reasons for cautious optimism about the prospects of a connectionist explanation.

  Fodor and Pylyshyn (1988), Fodor and McLaughlin (1990) and McLaughlin (1993) challenge connectionists to explain systematicity without simply implementing a classical architecture. In this paper I argue that what makes the challenge difficult for connectionists to meet has less to do with what is to be explained than with what is to count as an explanation. Fodor et al. are prepared to admit as explanatory, accounts of a sort that only classical models can provide. If connectionists are to meet the challenge, they are going to have to insist on the propriety of changing what counts as an explanation of systematicity. Once that is done, there would seem to be as yet no reason to suppose that connectionists are unable to explain systematicity

This paper defends the commonsense conception of linguistic competence according to which linguistic competence involves propositional knowledge of language. More specifically, the paper defends three propositions challenged by Devitt in his Ignorance af Language. First, Chomskian linguists were right to embrace this commonsense conception of linguistic cornpetence. Second, the grammars that these linguists propose make a substantive claim about the computational processes that are presumed to constitute a speaker’s linguistic competence. Third, Chomskian linguistics is indeed a subfield of psychology, in the business of characterizing the linguistic competence of speakers.

Putnam and Searle famously argue against computational theories of mind on the skeptical ground that there is no fact of the matter as to what mathematical function a physical system is computing: both conclude (albeit for somewhat different reasons) that virtually any physical object computes every computable function, implements every program or automaton. There has been considerable discussion of Putnam's and Searle's arguments, though as yet there is little consensus as to what, if anything, is wrong with these arguments. In the present paper we show that an analogous line of reasoning can be raised against the numerical measurement (i.e., numerical representation) of physical magnitudes, and we argue that this result is a reductio ad absurdum of the challenge to computational skepticism. We then use this reductio to get clearer about both (i) what's wrong with Putnam's and Searle's arguments against computationalism, and (ii) what can be learned about both computational implementation and numerical measurement from the shortcomings of both sorts of skeptical argument.