It is sometimes argued that if PDP networks can be trained to make correct judgements of grammaticality we have an existence proof that there is enough information in the stimulus to permit learning grammar by inductive means alone. This seems inconsistent superficially with Gold's theorem and at a deeper level with the fact that networks are designed on the basis of assumptions about the domain of the function to be learned. To clarify the issue I consider what we should learn (...) from Gold's theorem, then go on to inquire into what it means to say that knowledge is domain specific. I first try sharpening the intuitive notion of domain specific knowledge by reviewing the alleged difference between processing limitations due to shortage of resources vs shortages of knowledge. After rejecting different formulations of this idea, I suggest that a model is language specific if it transparently refer to entities and facts about language as opposed to entities and facts of more general mathematical domains. This is a useful but not necessary condition. I then suggest that a theory is domain specific if it belongs to a model family which is attuned in a law-like way to domain regularities. This leads to a comparison of PDP and parameter setting models of language learning. I conclude with a novel version of the poverty of stimulus argument. (shrink)

Richard Holton has drawn attention to a new semantic universal, according to which (almost) no natural language has contrafactive attitude verbs. This semantic universal is part of an asymmetry between factive and contrafactive attitude verbs. Whilst factives are abundant, contrafactives are scarce. We propose that this asymmetry is partly due to a difference in learnability. The meaning of contrafactives is significantly harder to learn than that of factives. We tested our hypothesis by conducting a computational experiment using an artificial (...) neural network. The results of this experiment support our hypothesis. (shrink)

The paper demonstrates that falsifiability is fundamental to learning. We prove the following theorem for statistical learning and sequential prediction: If a theory is falsifiable then it is learnable -- i.e. admits a strategy that predicts optimally. An analogous result is shown for universal induction.

This paper gives a perspectival overview of the semantics of potential property-referring terms and presents new and surprising generalizations about explicit property-referring terms like 'the property of being wise', which raise fundamental issues regarding ontology and learnability and a core-periphery distinction in natural language ontology.

Revised and reprinted; originally in Dov Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic, Volume IV. Kluwer 133-251. -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented in the (...) course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)

Revised and reprinted in Handbook of Philosophical Logic, volume 10, Dov Gabbay and Frans Guenthner (eds.), Dordrecht: Kluwer, (2003). -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented in the (...) course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)

Whether it would take one decade or several centuries, many agree that it is possible to create a *superintelligence*---an artificial intelligence with a godlike ability to achieve its goals. And many who have reflected carefully on this fact agree that our best hope for a "friendly" superintelligence is to design it to *learn* values like ours, since our values are too complex to program or hardwire explicitly. But the value learning approach to AI safety faces three particularly philosophical puzzles: first, (...) it is unclear how any intelligent system could learn its final values, since to judge one supposedly "final" value against another seems to require a further background standard for judging. Second, it is unclear how to determine the content of a system's values based on its physical or computational structure. Finally, there is the distinctly ethical question of which values we should best aim for the system to learn. I outline a potential answer to these interrelated puzzles, centering on a "miktotelic" proposal for blending a complex, learnable final value out of many simpler ones. (shrink)

D O N A L D D AV I D S O N’S “ Meaning and Truth,” re vo l u t i o n i zed our conception of how truth and meaning are related (Davidson    ). In that famous art i c l e , Davidson put forw a rd the bold conjecture that meanings are satisfaction conditions, and that a Tarskian theory of truth for a language is a theory of meaning for that language. (...) In “Meaning and Truth,” Davidson proposed only that a Tarskian truth theory is a theory of meaning. But in “Theories of Me a n i n g and Learnable Languages,” he argued that the finite base of a Tarskian theory, together with the now familiar combinatorics, would explain how a language with unbounded expre s s i ve capacity could be learned with finite means ( Davidson    ). This certainly seems to imply that learning a language is, in p a rt at least, learning a Tarskian truth theory for it, or, at least, learning what is specified by such a theory. Davisdon was cagey about committing to the view that meanings actually a re satisfaction conditions, but subsequent followers had no such scru p l e s . We can sum this up in a trio of claims: Davidson’s Conjecture () A theory of meaning for L is a truth-conditional semantics for L. () To know the meaning of an expression in L is to know a satisfaction condition for that expression. () Meanings are satisfaction conditions. For the most part, it will not matter in what follows which of these claims is at stake. I will simply take the three to be different ways of formulating what I will call Davidson’s Conjecture (or sometimes just The Conjecture). Davidson’s Conjecture was a very bold conjecture. I think we are now in a.. (shrink)

This chapter presents a re-understanding of the contents of our analog magnitude representations (e.g., approximate duration, distance, number). The approximate number system (ANS) is considered, which supports numerical representations that are widely described as fuzzy, noisy, and limited in their representational power. The contention is made that these characterizations are largely based on misunderstandings—that what has been called “noise” and “fuzziness” is actually an important epistemic signal of confidence in one’s estimate of the value. Rather than the ANS having noisy (...) or fuzzy numerical content, it is suggested that the ANS has exquisitely precise numerical content that is subject to epistemic limitations. Similar considerations will arise for other analog representations. The chapter discusses how this new understanding of ANS representations recasts the learnability problem for number and the conceptual changes that children must accomplish in the number domain. (shrink)

Davidson’s 1965 paper, “Theories of Meaning and Learnable Languages”, has invariably been interpreted, by others and by myself, as arguing that natural languages must have a compositional semantics, or at least a systematic semantics, that can be finitely specified. However, in his reply to me in the Żegleń volume, Davidson denies that compositionality is in any need of an argument. How does this add up? In this paper I consider Davidson’s first three meaning theoretic papers from this perspective. I conclude (...) that Davidson was right in his reply to me that he never took compositionality, or systematic semantics, to be in need of justification. What Davidson had been concerned with, clearly in the 1965 paper and in “Truth and Meaning” from 1967, and to some extent in his Carnap critique from 1963, is that we need a general theory of natural language meaning, that such a theory should not be in conflict with the learnability of a language, and that such a theory bring out should how knowledge of a finite number of features of a language suffices for the understanding of all the sentences of that language. (shrink)

Quine’s way of dealing with the semantical paradoxes (Ways of Paradox, pp. 9-10) is criticized. The criticism is based on three premises: (1) no learnable language has infinitely many semantical primitives; (2) any language of which Quine’s theory is true has infinitely many semantical primitives; (3) English is a learnable language. The conclusion drawn is that Quine’s theory is not true of English.

People see five kinds of views in epistemology and ontology as hinging on there being words a person can learn only by private ostensive definitions, through direct acquaintance with his own sensations: skepticism about other minds, 2. skepticism about an external world, 3. foundationalism, 4. dualism, and 5. phenomenalism. People think Wittgenstein refuted these views by showing, they believe, no word is learnable only by private ostensive definition. I defend these five views from Wittgenstein’s attack.

This paper highlights a small selection of cases where crosslinguistic insights have been important to big questions in the theory of semantics and the syntax/semantics interface. The selection includes (i) the role and representation of Speaker and Addressee in the grammar; (ii) mismatches between form and interpretation motivating high-placed silent operators for functional elements; and (iii) the explanation of semantic universals, including universals pertaining to inventories, in terms of learnability and the trade-off between informativeness and simplicity.

Beginning with an examination of the deep history of making things and thinking about making things made-up in our minds, I argue that the resultant declarative understanding of the procedural knowledge of abstracting theories and building models—the essence(s) of the practice of science—embodied in Conceptual Mathematics is worth learning beginning with high school, along with grammar and calculus. One of the many profound scientific insights introduced—in a manner accessible to total beginners—in Lawvere and Schanuel's Conceptual Mathematics textbook is: the way (...) we ought to think about things varies with the nature of things. In light of the universal yearning for understanding, it may be pedagogically unethical not to teach the eminently learnable Conceptual Mathematics. Summing it all, we need to champion the cause of taking Conceptual Mathematics to classrooms. (shrink)