In the first section of this paper I review Measurement Theoretic Semantics – an approach to formal semantics modeled after the application of numbers in measurement, e.g., of length. In the second section it is argued that the measurement theoretic approach to semantics yields a novel, useful conception of propositions. In the third section the measurement theoretic view of propositions is compared with major other accounts of propositional content.

In the first section of this paper I present a well known objection to meaning holism, according to which holism is inconsistent with natural language being learnable. Then I show that the objection fails if language acquisition includes stages of partial grasp of the meaning of at least some expressions, and I argue that standard model theoretic semantics cannot fully capture such stages. In the second section the above claims are supported through a review of current research into language acquisition. (...) Finally, in the third section it is argued that contemporary algebraic logical systems consist in a superior formal vehicle through which to capture stages of partial grasp of meaning; this claim is supported by concrete examples. (shrink)

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 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 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 what's wrong with Putnam's and Searle's arguments against computationalism, and what can be learned about both computational implementation and numerical measurement from the shortcomings of both sorts of skeptical argument. (shrink)

In his recent book The Measure of Mind Robert Matthews presents the most elaborate and convincing attempt to date to account for the propositional attitudes in measurement theoretic terms. In the first section of this paper I review earlier applications of measurement-theoretic conceptualization to the discussion of the mind, I outline Matthews' own account, and I raise two questions concerning it. Then, in the second section of the paper, I present a unified measurement-theoretic account of both linguistic meaning and the (...) propositional attitudes, in which a variant of Matthews' position is embedded. Such a unified account, I argue, yields satisfactory answers to the questions raised with respect to Matthews' original view, and demonstrates other advantages. (shrink)

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 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 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 what's wrong with Putnam's and Searle's arguments against computationalism, and what can be learned about both computational implementation and numerical measurement from the shortcomings of both sorts of skeptical argument. (shrink)

In the first section of this paper I present the measurement-theoretic fallacy of 'over-assignment of structure': the unwarranted assumption that every numeric relation holding among two (or more) numbers represents some empirical, physical relation among the objects to which these numbers are assigned as measures (e.g., of temperature). In the second section I argue that a generalized form of this fallacy arises in various philosophical contexts, in the form of a misguided, over-extended application of one conceptual domain to another. Three (...) examples are given: (i) the reduction of arithmetic into set theory, (ii) the ascription of full-blown intentional states to (at least some) non-overtly intentional creatures, such as Wittgenstein's builders, and (iii) the analysis of some modal notions as involving quantification over possible worlds (or their substitutes). The discussion of the third example gives rise to a novel account of possible-worlds talk. (shrink)

In the first two sections I present and motivate a formal semantics program that is modeled after the application of numbers in measurement (e.g., of length). Then, in the main part of the paper, I use the suggested framework to give an account of the semantics of necessity and possibility: (i) I show thatthe measurement theoretic framework is consistent with a robust (non-Quinean) view of modal logic, (ii) I give an account of the semantics of the modal notions within this (...) framework, and (iii) I defend the suggested account against various objections. (shrink)

In the first section of this paper I present a view of linguistic meaning that I label 'Sentence Priority’: the position that semantically primitive language‐world contact is made at the level of complete sentences . Then, in the main part of the paper, I consider and reject an objection against Sentence Priority raised by John Perry, an objection that appeals to Wittgenstein's builders parable. Perry argues that the builder's utterances are utterances of self‐standing nouns, and that therefore they constitute a (...) counter‐example to SP. A sound assessment of Perry's argument, however, depends on a clear distinction between two cases: one in which the four expressions mentioned in Wittgenstein's example exhaust the builders’expressive powers, and one in which they do not. Once these cases are distinguished it can be seen that in neither does Perry's argument go through. (shrink)

What makes our utterances mean what they do? In this work I formulate and justify a structural constraint on possible answers to this key question in the philosophy of language, and I show that accepting this constraint leads naturally to the adoption of an algebraic formalization of truth-theoretic semantics. I develop such a formalization, and show that applying algebraic methodology to the theory of meaning yields important insights into the nature of language. ;The constraint I propose is, roughly, this: the (...) meaning of an utterance of a natural language sentence is derived from the place of that sentence within a system that includes other sentences, and is structured in virtue of primitive semantic facts about complete sentences. This constraint calls for a formal semantics program where the meaning of natural language sentences is represented by an appropriate assignment of the elements of an algebraic structure to sentences, an assignment that represents facts concerning complete sentences. I call the above constraint 'The Algebraic Thesis', and the corresponding formal semantics program 'Algebraic Semantics.' ;I introduce AT by carving it out of the holistic views of language of Quine and Davidson, and I show that it is independent of other important features of these philosophers' views. I then argue for AT, taking into account recent work by Brandom, Dummett, Fodor and Lepore, Gaifman and Perry. In developing Algebraic Semantics I present structures of two basic types: Boolean algebras and cylindric algebras; these structures are construed in the context of AT in a novel way: they are treated as applying to classes of sentences as numbers apply to physical objects in measurement. Applying algebraic methodology to formal semantics and to the theory of meaning, I develop these results: ; An account of the semantics of necessity and possibility that avoids both Quine's dismissal of these notions and their reduction by David Lewis to quantification over possible worlds; ; The application of the model-theoretic notion of expansion to capture the process of our learning progressively more of the meaning of expressions in our first languages. (shrink)

In the first section of this paper I define meaning holism (MH) and compare it to related theses. In the second section I review several theories of meaning that incorporate MH as a feature, and in the third section I discuss the question whether and how MH is consistent with the assignment of semantic values to linguistic expressions. Finally, in the fourth section I present the main objections raised against MH in the literature and the answers given to them.

What is the philosophical significance of the soundness and completeness theorems for first-order logic? In the first section of this paper I raise this question, which is closely tied to current debate over the nature of logical consequence. Following many contemporary authors' dissatisfaction with the view that these theorems ground deductive validity in model-theoretic validity, I turn to measurement theory as a source for an alternative view. For this purpose I present in the second section several of the key ideas (...) of measurement theory, and in the third and central section of the paper I use these ideas in an account of the relation between model theory, formal deduction, and our logical intuitions. (shrink)

In the first section of this paper I follow an important trajectory in the development of Davidson's notion of radical interpretation: From being interpretationally concerned only with language, like Quine's radical translation that precedes it, through involving the ascription of belief in increasingly complex ways, to finally incorporating desire and preference. In the second section of the paper I show that Davidson falls short of incorporating non-linguistic action in radical interpretation, I assess his motivations for doing so, and I criticize (...) these motivations. In the third and final section I propose a unified interpretation scheme for language, action and mind. (shrink)

In their recent paper “Do Accelerating Turing Machines Compute the Uncomputable?” Copeland and Shagrir draw a distinction between a purist conception of Turing machines, according to which these machines are purely abstract, and Turing machine realism according to which Turing machines are spatio-temporal and causal “notional" machines. In the present response to that paper we concede the realistic aspects of Turing’s own presentation of his machines, pointed out by Copeland and Shagrir, but argue that Turing's treatment of symbols in the (...) course of that presentation opens the door for later purist conceptions. Also, we argue that a purist conception of Turing machines plays an important role not only in the analysis of the computational properties of Turing machines, but also in the philosophical debates over the nature of their realization. (shrink)

The content of our propositional attitudes is often characterized by assigning them abstract entities, namely propositions. In decision theory the attitudes are also assigned numerical measures. It may thus be asked how assignments of these two types are related to each other — both metaphysically and structurally. In the first section of this paper I argue for the importance of this question and I review Davidson’s unified account of decision theory and radical interpretation as a failed attempt to answer it. (...) Then, in the main part of the paper, I present a unified measurement-theoretic account of linguistic meaning, propositional mental content, and action, an account that avoids the difficulties of Davidson’s picture. Thus in the second section I outline two theoretical preliminaries (the representational theory of measurement and Savage’s decision theory), in the third section I present the proposed novel account, and in the fourth section I defend it against various objections. (shrink)

Abstract In the first section of the paper I present Alan Turing?s notion of effective memory, as it appears in his 1936 paper ?On Computable Numbers, With an Application to The Entscheidungsproblem?. This notion stands in surprising contrast with the way memory is usually thought of in the context of contemporary computer science. Turing?s view (in 1936) is that for a computing machine to remember a previously scanned string of symbols is not to store an internal symbolic image of this (...) string. Rather, memory consists in the fact that the past scanning of the string affects the behavior of the computer in the face of potential future inputs. In the second, central section of the paper I begin exploring how this view of Turing?s bears upon contemporary discussions in the philosophy of mind. In particular, I argue that Turing?s approach can be used to lend support to dispositional conceptions of the propositional attitudes, like the one recently presented by Matthews (2007), and that his effective memory manifests some of the characteristics of Millikan?s (1996) pushmepullyou mental states. (shrink)

In the first two sections I present and motivate a formal semantics program that is modeled after the application of numbers in measurement. Then, in the main part of the paper, I use the suggested framework to give an account of the semantics of necessity and possibility: I show that the measurement theoretic framework is consistent with a robust view of modal logic, I give an account of the semantics of the modal notions within this framework, and I defend the (...) suggested account against various objections. (shrink)

The Polish logicians' propositional calculi, which consist in a distinct synthesis of the Fregean and Boolean approaches to logic, influenced W. V. Quine's early work in formal logic. This early formal work of Quine's, in turn, can be shown to serve as one of the sources of his holistic conception of natural language.

In the first section of this paper I define a set of measures for proof complexity, which combine measures in terms of length and space. In the second section these measures are generalized to the broader category of formal texts. In the third section of the paper I outline several applications of the proposed theory.