We now know of a number of ways of developing real analysis on a basis of abstraction principles and second-order logic. One, outlined by Shapiro in his contribution to this volume, mimics Dedekind in identifying the reals with cuts in the series of rationals under their natural order. The result is an essentially structuralist conception of the reals. An earlier approach, developed by Hale in his "Reals byion" program differs by placing additional emphasis upon what I here term Frege's (...) class='Hi'>Constraint, that a satisfactory foundation for any branch of mathematics should somehow so explain its basic concepts that their applications are immediate. This paper is concerned with the meaning of and motivation for this constraint. Structuralism has to represent the application of a mathematical theory as always posterior to the understanding of it, turning upon the appreciation of structural affinities between the structure it concerns and a domain to which it is to be applied. There is, therefore, a case that Frege's Constraint has bite whenever there is a standing body of informal mathematical knowledge grounded in direct reflection upon sample, or schematic, applications of the concepts of the theory in question. It is argued that this condition is satisfied by simple arithmetic and geometry, but that in view of the gap between its basic concepts (of continuity and of the nature of the distinctions among the individual reals) and their empirical applications, it is doubtful that Frege's Constraint should be imposed on a neo-Fregean construction of analysis. (shrink)

Two general principles have played a crucial role in the recent debate on concepts. On the one hand, we want to allow different subjects to have the same concepts, thus accounting for concept publicity: concepts are ‘the sort of thing that people can, and do, share’. On the other hand, a subject who finds herself in a so-called ‘Frege case’ appears to have different concepts for the same object: for instance, Lois Lane has two distinct concepts SUPERMAN and CLARK KENT (...) which refer to the same person. Several theories have tried to meet both of these constraints at the same time. But should we really try to satisfy both principles? This paper will argue that the traditional project of fulfilling these two constraints has been a misguided one. Through a variation on classic identity mistake cases, I will show that our two desiderata are inconsistent: it would thus be impossible to incorporate both of them in our best theory of concepts. (shrink)

We present a new logic -based approach to the reasoning about knowledge which is independent of possible worlds semantics.? k is a non- Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom K i??? and some minimal conditions concerning common knowledge in a group. Knowledge is explicit and all forms of the logical omniscience (...) problem are avoided. Various stronger epistemic properties such as positive and/or negative introspection, the K-axiom, closure under logical connectives, etc, can be restored by imposing additional semantic constraints. This yields corresponding sublogics for which we present sound and complete axiomatizations. As a useful tool for general model constructions we study abstract versions of some 3-valued logics in which we interpret truth as knowledge. We establish a connection between? k and the well-known syntactic approach to explicit knowledge proving a result concerning equi-expressiveness. Furthermore, we discuss some self - referential epistemic statements, such as the knower paradox, as relaxations of variants of the liar paradox and show how these epistemic "paradoxes" can be solved in? k. Every specific? k - logic is defined as a certain extension of some underlying classical abstract logic. (shrink)

This note sketches how a theory of procedural semantics may offer a solution to the problem of the unity of the proposition. The current revival of the notion of structured meaning has made the problem of propositional unity pressing. The problem, stated in its simplest form, is how an individual a and a property F combine into the proposition P that a is an F; i.e. how two different kinds of objects combine into a third kind of object capable of (...) having properties that neither of its constituents could have. Constraints imposed on P include that P must be capable of being true/false, being known/believed to be true/false, and occurring as argument of propositional connectives, such as entailment. (shrink)

We present a new logic-based approach to the reasoning about knowledge which is independent of possible worlds semantics. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document} is a non-Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom Kiφ → φ and some minimal conditions concerning common knowledge in a group. Knowledge is (...) explicit and all forms of the logical omniscience problem are avoided. Various stronger epistemic properties such as positive and/or negative introspection, the K-axiom, closure under logical connectives, etc. can be restored by imposing additional semantic constraints. This yields corresponding sublogics for which we present sound and complete axiomatizations. As a useful tool for general model constructions we study abstract versions of some 3-valued logics in which we interpret truth as knowledge. We establish a connection between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document} and the well-known syntactic approach to explicit knowledge proving a result concerning equi-expressiveness. Furthermore, we discuss some self-referential epistemic statements, such as the knower paradox, as relaxations of variants of the liar paradox and show how these epistemic “paradoxes” can be solved in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document}. Every specific \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document}-logic is defined as a certain extension of some underlying classical abstract logic. (shrink)

Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either ‘Application Constraint’ ($AC$) or ‘Frege Constraint’ ($FC$), the requirement that a mathematical theory be so outlined that it immediately allows explaining for its applicability. We distinguish between two constraints, which we, respectively, denote by the latter of these two names, by showing how$AC$generalizes Frege’s views while$FC$comes closer to his original conceptions. Different authors diverge on the interpretation (...) of$FC$and on whether it applies to definitions of both natural and real numbers. Our aim is to trace the origins of$FC$and to explore how different understandings of it can be faithful to Frege’s views about such definitions and to his foundational program. After rehearsing the essential elements of the relevant debate (§1), we appropriately distinguish$AC$from$FC$(§2). We discuss six rationales which may motivate the adoption of different instances of$AC$and$FC$(§3). We turn to the possible interpretations of$FC$(§4), and advance a Semantic$FC$(§4.1), arguing that while it suits Frege’s definition of natural numbers (4.1.1), it cannot reasonably be imposed on definitions of real numbers (§4.1.2), for reasons only partly similar to those offered by Crispin Wright (§4.1.3). We then rehearse a recent exchange between Bob Hale and Vadim Batitzky to shed light on Frege’s conception of real numbers and magnitudes (§4.2). We argue that an Architectonic version of$FC$is indeed faithful to Frege’s definition of real numbers, and compatible with his views on natural ones. Finally, we consider how attributing different instances of$FC$to Frege and appreciating the role of the Architectonic$FC$can provide a more perspicuous understanding of his foundational program, by questioning common pictures of his logicism (§5). (shrink)

How do we inferentially unify separately acquired empirical information into a single comprehensive picture of the lives of persistent particulars? This paper argues that hidden in such inferences is a Fregean puzzle that can only be solved by individuating our demonstratives thoughts in terms of object-dependent Fregean Senses. I begin by characterizing some constraints on a non-skeptical account of our inferential unification of empirical information. I then go on to show that traditional Fregean views of Sense cannot (...) explain the rationality of such inferences; the consequence of which would be widespread skepticism concerning fundamental aspects of our empirical worldview. I show how the theory of object-dependent Senses can account for the rationality of the puzzling inferences. Lastly, I consider the alternative that we abandon a Fregean explanation of the rationality of inferences. While not fully dismissing that option, I briefly raise, what I take to be, a daunting challenge that uniquely faces non-Fregean views of rational inference. (shrink)

This volume presents a collection of refereed papers reflecting the state of the art in the area of over-constrained systems. Besides 11 revised full papers, selected from the 24 submissions to the OCS workshop held in conjunction with the First International Conference on Principles and Practice of Constraint Programming, CP '95, held in Marseilles in September 1995, the book includes three comprehensive background papers of central importance for the workshop papers and the whole field. Also included is an introduction (...) by one of the volume editors together with a bibliography listing 243 entries. All in all this is a very useful reference book relevant for all researchers and practitioners interested in hierarchical, partial, and over-constrained systems. (shrink)

An influential tradition holds that thoughts are public: different thinkers share many of their thoughts, and the same applies to a single subject at different times. This ‘publicity principle’ has recently come under attack. Arguments by Mark Crimmins, Richard Heck and Brian Loar seem to show that publicity is inconsistent with the widely accepted principle that someone who is ignorant or mistaken about certain identity facts will have distinct thoughts about the relevant object—for instance, the astronomer who does not know (...) that Hesperus is Phosphorus will have two distinct thoughts Hesperus is bright and Phosphorus is bright. In this paper, I argue that publicity can be defended if we adopt a relational account on which thoughts are individuated by their mutual relations. I then go on to develop a specific relational theory—the ‘linking account’—and contrast it with other relational views. (shrink)

Some have defended a Fregean view of perceptual content. On this view, the constituents of perceptual contents are Fregean modes of presentation (MOPs). In this paper, I propose that perceptual MOPs are best understood in terms of object files. Object files are episodic representations that store perceptual information about objects. This information is updated when sensory conditions change. On the proposed view, when a subject perceptually represents some object a under two distinct MOPs, then the subject initiates two (...) object files that both refer to a. My defense of this view appeals to its satisfaction of four constraints that I argue theories of perceptual MOPs should satisfy. Furthermore, I show that some existent accounts of perceptual MOPs fail to satisfy them. The defended constraints also indicate what is unique about perceptual, as opposed to linguistic or cognitive, MOPs. (shrink)

The Fregean-inspired Principle of Compositionality of Meaning for formal languages asserts that the meaning of a compound expression is analysable in terms of the meaning of its constituents, taking into account the mode in which these constituents are combined so as to form the compound expression. From a logical point of view, this amounts to prescribing a constraint—that may or may not be respected—on the internal mechanisms that build and give meaning to a given formal system. Within the (...) domain of formal semantics and of the structure of logical derivations, the PoC is often directly reflected by metaproperties such as truth-functionality and analyticity, characteristic of computationally well-behaved logical systems. (shrink)

The Generality Constraint is a condition discussed by Gareth Evans that is meant to distinguish candidate subjects into those who have conscious thought of the type needed for a neo-Fregean conception of an objective world and those who are not subjects of that type. I argue that it implicitly applies to free-ranging creatures in a world of objects that they perceive and on which they act. This is quite unlike the behaviour exhibited by pigeons who attempt to maximise (...) rewards in a limited operant response situation where those rewards are indexed to particular numbers of key pecks as the ability needed to master that task is not the kind of thing Evans is interested in and it can be explained much more parsimoniously. (shrink)

The thesis that agents should calibrate their beliefs in the face of higher-order evidence—i.e., should adjust their first-order beliefs in response to evidence suggesting that the reasoning underlying those beliefs is faulty—is sometimes thought to be in tension with Bayesian approaches to belief update: in order to obey Bayesian norms, it’s claimed, agents must remain steadfast in the face of higher-order evidence. But I argue that this claim is incorrect. In particular, I motivate a minimal constraint on a reasonable (...) treatment of the evolution of self-locating beliefs over time and show that calibrationism is compatible with any generalized Bayesian approach that respects this constraint. I then use this result to argue that remaining steadfast isn’t the response to higher-order evidence that maximizes expected accuracy. (shrink)

According to the so-called strong variant of Composition as Identity (CAI), the Principle of Indiscernibility of Identicals can be extended to composition, by resorting to broadly Fregean relativizations of cardinality ascriptions. In this paper we analyze various ways in which this relativization could be achieved. According to one broad variety of relativization, cardinality ascriptions are about objects, while concepts occupy an additional argument place. It should be possible to paraphrase the cardinality ascriptions in plural logic and, as a consequence, (...) relative counting requires the relativization either of quantifiers, or of identity, or of the is one of relation. However, some of these relativizations do not deliver the expected results, and others rely on problematic assumptions. In another broad variety of relativization, cardinality ascriptions are about concepts or sets. The most promising development of this approach is prima facie connected with a violation of the so-called Coreferentiality Constraint, according to which an identity statement is true only if its terms have the same referent. Moreover - even provided that the problem with coreferentiality can be fixed - the resulting analysis of cardinality ascriptions meets several difficulties. (shrink)

The realist versions of mathematical structuralism are often characterized by what I call ‘the insubstantiality thesis’, according to which mathematical objects, being positions in structures, have no non-structural properties: they are purely structural objects. The thesis has been criticized for being inconsistent or descriptively inadequate. In this paper, by implementing the resources of a real-definitional account of essence in the context of Fregean abstraction principles, I offer a version of structuralism – essentialist structuralism – which validates a weaker version (...) of the insubstantiality thesis: mathematical objects have no non-structural essential properties. Next, I show how this rendition of structuralism alleviates a Fregean worry against insubstantiality, which is directed at the explanation of the applicability of mathematics from the structuralist perspective. (shrink)

ABSTRACT. Fodor characterizes concepts as consisting of two dimensions: one is content, which is purely denotational/broad, the other the Mentalese vehicle bearing that content, which Fodor calls the Mode of Presentation (MOP), understood "syntactically." I argue that, so understood, concepts are not interpersonally sharable; so Fodor's own account violates what he calls the Publicity Constraint in his (1998) book. Furthermore, I argue that Fodor's non-semantic, or "syntactic," solution to Frege cases succumbs to the problem of providing interpersonally applicable functional (...) roles for MOPs. This is a serious problem because Fodor himself has argued extensively that if Fregean senses or meanings are understood as functional/conceptual roles, then they can't be public, since, according to Fodor, there are no interpersonally applicable functional roles in the relevant senses. I elaborate on these relevant senses in the paper. (shrink)

In this short monograph, John Horty explores the difficulties presented for Gottlob Frege's semantic theory, as well as its modern descendents, by the treatment of defined expressions. The book begins by focusing on the psychological constraints governing Frege's notion of sense, or meaning, and argues that, given these constraints, even the treatment of simple stipulative definitions led Frege to important difficulties. Horty is able to suggest ways out of these difficulties that are both philosophically and logically plausible and Fregean (...) in spirit. This discussion is then connected to a number of more familiar topics, such as indexicality and the discussion of concepts in recent theories of mind and language. In the latter part of the book, after introducing a simple semantic model of senses as procedures, Horty considers the problems that definitions present for Frege's idea that the sense of an expression should mirror its grammatical structure. The requirement can be satisfied, he argues, only if defined expressions--and incomplete expressions as well--are assigned senses of their own, rather than treated contextually. He then explores one way in which these senses might be reified within the procedural model, drawing on ideas from work in the semantics of computer programming languages. With its combination of technical semantics and history of philosophy, Horty's book tackles some of the hardest questions in the philosophy of language. It should interest philosophers, logicians, and linguists. (shrink)

The paper is concerned with the bad company problem as an instance of a more general difficulty in the philosophy of mathematics. The paper focuses on the prospects of stability as a necessary condition on acceptability. However, the conclusion of the paper is largely negative. As a solution to the bad company problem, stability would undermine the prospects of a neo-Fregean foundation for set theory, and, as a solution to the more general difficulty, it would impose an unreasonable (...) class='Hi'>constraint on mathematical practice. (shrink)

The debate about concepts has always been shaped by a contrast between subjectivism, which treats them as phenomena in the mind or head of individuals, and objectivism, which insists that they exist independently of individual minds. The most prominent contemporary version of subjectivism is Fodor's RTM. The Fregean charge against subjectivism is that it cannot do justice to the fact that different individuals can share the same concepts. Proponents of RTM have accepted shareability as a 'non-negotiable constraint'. At (...) the same time they insist that by distinguishing between sign-types and -- tokens the Fregean objection cannot just be circumvented but revealed to be fallacious. My paper rehabilitates the Fregean argument against subjectivism. The RTM response rests either on an equivocation of 'concept'--between types which satisfy the non-negotiable constraint and tokens which are mental particulars in line with RTM doctrine--or on the untenable idea that one and the same entity can be both a shareable type and hence abstract and a concrete particular in the head. Furthermore, subjectivism cannot be rescued by adopting unorthodox metaphysical theories about the type/token and universal/particular contrasts. The final section argues that concepts are not representations or signs, but something represented by signs. Even if RTM is right to explain conceptual thinking by reference to the occurrence of mental representations, concepts themselves cannot be identical with such representations. (shrink)

The debate about concepts has always been shaped by a contrast between subjectivism, which treats them as phenomena in the mind or head of individuals, and objectivism, which insists that they exist independently of individual minds. The most prominent contemporary version of subjectivism is Fodor's RTM. The Fregean charge against subjectivism is that it cannot do justice to the fact that different individuals can share the same concepts. Proponents of RTM have accepted shareability as a ‘non-negotiable constraint’. At (...) the same time they insist that by distinguishing between sign-types and – tokens the Fregean objection cannot just be circumvented but revealed to be fallacious. My paper rehabilitates the Fregean argument against subjectivism. The RTM response rests either on an equivocation of ‘concept’—between types which satisfy the non-negotiable constraint and tokens which are mental particulars in line with RTM doctrine—or on the untenable idea that one and the same entity can be both a shareable type and hence abstract and a concrete particular in the head. Furthermore, subjectivism cannot be rescued by adopting unorthodox metaphysical theories about the type/token and universal/particular contrasts. The final section argues that concepts are not representations or signs, but something represented by signs. Even if RTM is right to explain conceptual thinking by reference to the occurrence of mental representations, concepts themselves cannot be identical with such representations. (shrink)

A formal theory of oppositions and opposites is proposed on the basis of a non- Fregean semantics, where opposites are negation-forming operators that shed some new light on the connection between opposition and negation. The paper proceeds as follows. After recalling the historical background, oppositions and opposites are compared from a mathematical perspective: the first occurs as a relation, the second as a function. Then the main point of the paper appears with a calculus of oppositions, by means of (...) a non-Fregean semantics that redefines the logical values of various sorts of sentences. A num- ber of topics are then addressed in the light of this algebraic semantics, namely: how to construct value-functional operators for any logical opposition, beyond the classical case of contradiction; Blanché's "closure problem", i.e., how to find a complete structure connecting the sixteen binary sentences with one another. All of this is meant to devise an abstract theory of opposition: it encompasses the relation of consequence as subalternation, while relying upon the use of a primary "proto- negation" that turns any relatum into an opposite. This results in sentential negations that proceed as intensional operators, while negation is broadly viewed as a difference-forming operator without special constraints on it. (shrink)

The debate about concepts has always been shaped by a contrast between subjectivism, which treats them as phenomena in the mind or head of individuals, and objectivism, which insists that they exist independently of individual minds. The most prominent contemporary version of subjectivism is Fodor's RTM. The Fregean charge against subjectivism is that it cannot do justice to the fact that different individuals cansharethe same concepts. Proponents of RTM have accepted shareability as a ‘non-negotiable constraint’. At the same (...) time they insist that by distinguishing between sign-types and – tokens the Fregean objection cannot just be circumvented but revealed to be fallacious. My paper rehabilitates the Fregean argument against subjectivism. The RTM response rests either on an equivocation of ‘concept’—between types which satisfy the non-negotiable constraint and tokens which are mental particulars in line with RTM doctrine—or on the untenable idea that one and the same entity can bebotha shareable type and hence abstractanda concrete particular in the head. Furthermore, subjectivism cannot be rescued by adopting unorthodox metaphysical theories about the type/token and universal/particular contrasts. The final section argues that concepts arenotrepresentations or signs, butsomething representedby signs. Even if RTM is right to explainconceptual thinkingby reference to the occurrence of mental representations,concepts themselvescannot be identical with such representations. (shrink)

I argue that a certain initially appealing Fregean conception of our shared semantic competence in our shared language cannot be made good. In particular, I show that we must reject two fundamental Fregean principles‐what I call Frege's Adequacy Condition and what I call Frege's Cognitive Constraint on Reference Determination. Frege's adequacy condition says that in an adequate semantic theory, sentence meanings must have the same fineness of grain as attitude contents. The Cognitive Constraint on Reference Determination (...) says that in an adequate semantic theory mechanisms of reference determination will fix routes of epistemic access to referents and will mediate one‐sided recognition judgments about referents. I argue against Frege's adequacy condition that if meanings are sliced as finely as it requires there will be too many meanings to go around. I argue against the cognitive constraint on reference determination that even in an adequate theory of reference, mechanisms of reference determination must be sharply distinguished from routes of epistemic access. If so, we have little reason to expect an adequate theory of reference determination to directly illuminate Frege's cognitive puzzles or be sufficient to explain the basis of our one‐sided recognition judgments. (shrink)

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a (...) methodology is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance. (shrink)

Bob Hale has defended a new conception of properties that is broadly Fregean in two key respects. First, like Frege, Hale insists that every property can be defined by an open formula. Second, like Frege, but unlike later definabilists, Hale seeks to justify full impredicative property comprehension. The most innovative part of his defense, we think, is a “definability constraint” that can serve as an implicit definition of the domain of properties. We make this constraint formally precise (...) and prove that it fails to characterize the domain uniquely. Thus, we conclude, there is no easy road to impredicative definabilism. (shrink)

Content nonconceptualism and State conceptualism are motivated by different readings of what I want to call here Bermúdez’s conditions on content-attribution (2007). In one read- ing, what is required is a neo-Fregean content to solve problems of cognitive significance at the nonconceptual level (Toribio, 2008; Duhau, 2011). In the other reading, what is required is a neo-Russellian or possible-world content to account for how conspecifics join attention and cooperate, contemplating the same things from different perspectives in the same perceptual (...) field. The solution to this apparent contradiction is the rejection of the real content view and the adherence to what I call here Content-pragmatism: there is no such thing as the content of experience. According to content pragmatism, “proposition” is not as real as a mental state, but rather, it is a term of art that semanticists use, as a matter of theoretical convenience, to classify mental states. What follows from Content-pragmatism is Content- pluralism: there are so many contents that are required to meet Bermúdez’s condition on content attribution. Because both criticism and the defense of State conceptualism overlook the real scope of Bermúdez’s condition on content attribution, they are ineffective. In this paper, I will argue that the opposition between State and Content nonconceptualism is a real one, but only a relative one, that is, relative to the opposite constraints to be met. If we want to solve the problems of cognitive significance, the best we can do is to let the content of experience be modeled as neo-Fregean content, namely, a compound of nonconceptual modes of presentation of objects and properties. In this case, Content-nonconceptualism prevails. In contrast, if we want to account for how conspecifics join attention to the same entities in the same perceptual field from different perspectives, the best we can do is let the content of experience be modeled either as a structured Russellian proposition or as a function from possible worlds to truth-values. In this case, State-nonconceptualism prevails. (shrink)

We can think about ourselves in a variety of ways, but only some of the thoughts that we entertain about ourselves will be thoughts which we know concern ourselves. I call these first-person thoughts, and the component of such thoughts that picks out the object about which one is thinking—oneself—the self-concept. In this thesis I am concerned with providing an account of the content of the self-concept. The challenge is to provide an account that meets two conditions on first-person thought. (...) The account must show how we are aware of ourselves when we entertain first-person thoughts, so that we have an account that establishes the cognitive significance of first-person thoughts. But, in addition, this awareness must be as robust as the thinker’s ability to entertain first-person thoughts if our account is to respect the guaranteed referential success of the self-concept. I introduce both the subject matter of the thesis, and the constraints on a satisfactory account of that subject matter in the first chapter. In the second chapter I then set up a further problem: much of our self-knowledge is knowledge of our current mental states and it is often argued that we know about and can ascribe those mental states on the basis of introspection alone. The first constraint on an account of first-person thought described in the preceding paragraph requires that we be aware of ourselves in some way if our thoughts are to have the special cognitive significance of first-person thoughts. Yet, I argue, we neither do nor can introspectively observe a subject of thought and experience when we come to know about our mental states and experiences. The failure of introspection to supply us with perceptual information about a subject of thought presents us with the further potential problem. According to Fregean semantics sense determines reference: we count on the content of the elements of thought to determine the reference of terms that are used to express those elements. If we do not introspectively observe a subject of thought then we seem to be at a loss to account for the concept and we are at risk of having to accept that neither the self-concept nor the first-person pronoun are referential. In the remainder of my thesis I consider various responses that we can offer to this problem. First, I examine whether we can avoid the problem with an alternative account of first-person reference according to which reference is fixed by a reflexive rule, and whether we can also base an account of first-person thought on this account of first-person reference. Secondly, I look at the descriptivist view of first-person thought which could potentially provide both an account of first-person thought and first-person reference. These two suggestions must be rejected on the grounds that they fail to accommodate the special cognitive significance of first-person thought. A third approach to first-person thought argues that we employ an objective self-concept when we think about ourselves, a concept that is informed by bodily experience, rather than by introspective observation of a subject. Yet such an account cannot make sense of first-person thoughts in which we question our own embodiment. Lastly I consider whether it is possible to explain the cognitive significance of first-person thought in terms of non-conceptual first-person contents. (shrink)

How are we to understand the notion of concept, the very concept of concept itself? One natural way, it seems to me, is to take Fregean sense as a model, and imposing similar constraints on a theory of concepts. This approach has the advantage, among others, of allowing for a distinction to be made between publicly shared, objective concepts, on the one hand, and private, subjective mental representations on the other - a distinction which, I believe, is desirable for (...) various reasons. One problem with Frege. (shrink)

Content nonconceptualism and State conceptualism are motivated by constraints of content-attribution that pull in opposite directions, namely, the so-called cognitive significance requirement and what I would like to call here the same representing constraint. The solution to this apparent contradiction is the rejection of the real content view and the adherence to what I call here Content-pragmatism. In CPR, “proposition” is not as real as a mental state, but rather is a term of art that semanticists use, as a (...) matter of theoretical convenience, to classify mental states. What follows from CPR is Content-pluralism : there is no such a thing as the content of experience. Because both criticisms and the defense of SNC overlook CPR and CP, they are ineffective. In this paper, I will argue that the opposition between SNC and CNC is a real one, but only a relative one, that is, relative to the opposite constraints to be met, namely CSR and SRR. If we want to meet CSR, the best we can do is to let the content of experience be modeled as neo-Fregean content, namely a compound of non-conceptual modes of presentation of objects and properties. In this case, CNC prevails. In contrast, if we want to meet SRR, the best we can do is let the content of experience be modeled either as a Russellian compound of objects and properties or as a function from possible worlds to truth-values. In this case, SNC prevails. (shrink)

The Snark is an intentional object. I examine the general philosophical characteristics of thoughts of objects from the perspective of Husserl's, hyle, noesis, and noema and show how this meets constraints of opacity, normativity, and possible existence as generated by a sensitive theory of intentionality. Husserl introduces terms which indicate the normative features of intentional content and attempts to forge a direct relationship between the norms he generates and the actual world object which a thought intends. I then attempt to (...) relate Husserl's account to Fregean insights about the sense and reference of a term. Neither Husserl nor Frege suggest plausible routes to a naturalistic account of intentionality and I turn to Wittgenstein to provide a naturalistic reading of the crucial terms involved in the analysis of intentional content. His account is normative in a way required by both Husserl and Frege and yet manages a kind of Aristotelian naturalism which avoids crude biologism. (shrink)

The Snark is an intentional object. I examine the general philosophical characteristics of thoughts of objects from the perspective of Husserl’s, hyle, noesis, and noema and show how this meets constraints of opacity, normativity, and possible existence as generated by a sensitive theory of intentionality. Husserl introduces terms which indicate the normative features of intentional content and attempts to forge a direct relationship between the norms he generates and the actual world object which a thought intends. I then attempt to (...) relate Husserl’s account to Fregean insights about the sense and reference of a term. Neither Husserl nor Frege suggest plausible routes to a naturalistic account of intentionality and I turn to Wittgenstein to provide a naturalistic reading of the crucial terms involved in the analysis of intentional content. His account is normative in a way required by both Husserl and Frege and yet manages a kind of Aristotelian naturalism which avoids crude biologism. (shrink)

In this paper, I will provide a counterexample to Recanati's account of first-person communication (1995, 2010, 2012). In particular, I will show that Recanati's constraints are not sufficient for the success of first-person communication. My argument against Recanati's account is parallel to Recanati's argument against neo-Russellian accounts, and shows that the same problem resurfaces even in the presence of linguistically encoded mode of presentation in a neo-Fregean framework of mental files.

What does it mean to be a rational language user? What is it to obey linguistic rules? What is the proper account of linguistic competence? A Fregean answer to these questions would make essential appeal to the notion of sense: we are masters of a language to the extent that we are able to recognise the cognitive value of its expressions; we are rational judges regarding truth-value assignments to the extent that we are sensitive to the ways in which (...) the sense of an expression guides us in the semantic evaluation process; and as for obeying rules, it is our ability to respond to how sense directs us, for a particular assertion of a sentence, towards the determination of its truth-value that best exemplifies what it is like to follow a linguistic rule. My thesis explores a cluster of closely interrelated issues arising from these questions. Accordingly, in tracing the routes of sense my dissertation places itself at the intersection of the philosophy of language, linguistics, philosophy of logic, and meta-ethics—and indeed, I end up agreeing with Allan Gibbard that the theory of meaning really belongs to meta-ethical reflection. Chapter 1 introduces some of the main research questions that I try to address in the rest of the thesis. In chapter 2 I state a number of theses which I take to be the defining ones for semanticism. I show that they form a class of jointly incompatible commitments. I choose nonsense as a problem case for compositionality and I argue that it forces the semanticist to abandon either the learnability or the compositionality constraint. The escape route I adopt, going radically minimalist about content, is incompatible with another key semanticist thesis, namely, that grasp of meaning is grasp of truth-conditions. In chapter 3, I consider the account of atomic meanings given by both the semanticist and the pragmaticist and I conclude that on neither account does interpretation come out as a process of rational choice between candidate bearers of content. Again, I suggest the lesson from indeterminacy is that we ought to embrace an ineradicably minimal conception of content. In chapter 4 I turn my attention to the meaning of the logical constants and I argue that indeterminacy worries extend to the very heart of the compositional machinery. Chapter 5 examines the view that logic is the science of reasoning. Unsurprisingly, I conclude that a defence of this claim requires endorsing content-minimalism. In chapter 6 I conclude my dissertation by sketching a radical view of content minimalism and I try to show how it can solve the puzzles I had been considering over the course of the previous chapters. (shrink)

It is argued that Davidson's basic objection to the Building Block Method in semantics is neither that it gives the wrong explanation of how a first language is learned nor that it assigns a meaning to Single words prior to interpreting a whole language. The arguments against Fregean concepts and truth-values as the references of predicates and sentences are found to be equally superficial as the arguments against a primitive notion reference defmed in causal terms.Davidson's basic objection turns out (...) to be that thoughts do not have a deep-structure which can be revealed by a correct analysis. His constraints on a theory of meaning do not allow for a distinction, as suggested by Dummett, between analysis and decomposition of thoughts. This forces us to a very general decision about how to do philosophy. As a non-reductivist I think it makes sense to assume a basic thought-structure. From this perspective the use of buildingblocks in semantics is vindicated. (shrink)

It is argued that Davidson's basic objection to the Building Block Method in semantics is neither that it gives the wrong explanation of how a first language is learned nor that it assigns a meaning to Single words prior to interpreting a whole language. The arguments against Fregean concepts and truth-values as the references of predicates and sentences are found to be equally superficial as the arguments against a primitive notion reference defmed in causal terms.Davidson's basic objection turns out (...) to be that thoughts do not have a deep-structure which can be revealed by a correct analysis. His constraints on a theory of meaning do not allow for a distinction, as suggested by Dummett, between analysis and decomposition of thoughts. This forces us to a very general decision about how to do philosophy. As a non-reductivist I think it makes sense to assume a basic thought-structure. From this perspective the use of buildingblocks in semantics is vindicated. (shrink)

It is argued that Davidson's basic objection to the Building Block Method in semantics is neither that it gives the wrong explanation of how a first language is learned nor that it assigns a meaning to Single words prior to interpreting a whole language. The arguments against Fregean concepts and truth-values as the references of predicates and sentences are found to be equally superficial as the arguments against a primitive notion reference defmed in causal terms.Davidson's basic objection turns out (...) to be that thoughts do not have a deep-structure which can be revealed by a correct analysis. His constraints on a theory of meaning do not allow for a distinction, as suggested by Dummett, between analysis and decomposition of thoughts. This forces us to a very general decision about how to do philosophy. As a non-reductivist I think it makes sense to assume a basic thought-structure. From this perspective the use of buildingblocks in semantics is vindicated. (shrink)

John Perry is known for his work on personal identity, and Jon Barwise, Director of the Center for the Study of Language and Information at Stanford, is a logician who works on model theory. Their cryptically titled collaboration is a first book-length foray into the semantics of natural language. Situations and Attitudes is programmatic even where detailed, and a sequel is promised which will carry through the program extensively and with full-dress technical detail. The program, for which the basic theoretical (...) machinery, the central categories, and the broad rationale are provided in this book, is an "innocent" model-theoretic semantics of natural language, in the spirit of realism and with debts to the likes of Putnam, Kripke, Donnellan, Montague, and psychologist J. J. Gibson. The authors describe their realism as "ecological" because they view meaning as a ubiquitous phenomenon of sentient organisms' natural and necessary attunement to constraints on the flow of information throughout their surrounds. They see an adequate semantic theory accounting for how language fits into the general flow of information. Their view is a realism not only in stressing the external significance of language, the primacy of its function of conveying information about the external world, but in seeing meaning itself as an objective uniformity in that world, a systematic relation of a special sort between different types of situations. The "innocence" of this semantics emerges in its leading concern--a correct treatment of the famously troublesome verbs of attitude which are used to embed sentences and so to report perception and cognition. Barwise and Perry refuse to sacrifice the view that sentences embedded in attitude reports "work just as they do elsewhere," i.e., are about situations, parts of the real world. The broader innocence is that of non-collaboration in the "Fregean tradition" of philosophical semantics which is "seriously flawed" by its inappropriate emphases, due to preoccupation with mathematics and symbolic logic, on univocal expressions, eternal sentences, entailments between sentences, arbitrariness and uniqueness of the name-named mapping, and a general tendency to think that all information available from an utterance must be part of its interpretation. The book counters that tradition on these points and others. (shrink)

According to Frege's principle the denotation of a sentence coincides with its truth-value. The principle is investigated within the context of abstract algebraic logic, and it is shown that taken together with the deduction theorem it characterizes intuitionistic logic in a certain strong sense.A 2nd-order matrix is an algebra together with an algebraic closed set system on its universe. A deductive system is a second-order matrix over the formula algebra of some fixed but arbitrary language. A second-order matrix A is (...) Fregean if, for any subset X of A, the set of all pairs a,b such that X{a} and X{b} have the same closure is a congruence relation on A. Hence a deductive system is Fregean if interderivability is compositional. The logics intermediate between the classical and intuitionistic propositional calculi are the paradigms for Fregean logics. Normal modal logics are non-Fregean while quasi-normal modal logics are generally Fregean.The main results of the paper: Fregean deductive systems that either have the deduction theorem, or are protoalgebraic and have conjunction, are completely characterized. They are essentially the intermediate logics, possibly with additional connectives. All the full matrix models of a protoalgebraic Fregean deductive system are Fregean, and, conversely, the deductive system determined by any class of Fregean second-order matrices is Fregean. The latter result is used to construct an example of a protoalgebraic Fregean deductive system that is not strongly algebraizable. (shrink)

Neo-Fregeanism in the philosophy of mathematics consists of two main parts: the logicist thesis, that mathematics (or at least branches thereof, like arithmetic) all but reduce to logic, and the platonist thesis, that there are abstract, mathematical objects. I will here focus on the ontological thesis, platonism. Neo-Fregeanism has been widely discussed in recent years. Mostly the discussion has focused on issues specific to mathematics. I will here single out for special attention the view on ontology which underlies the neo-Fregeans’ (...) claims about mathematical objects, and discuss this view in a broader setting. (shrink)

A deductive system (in the sense of Tarski) is Fregean if the relation of interderivability, relative to any given theory T, i.e., the binary relation between formulas.

We begin by setting out the posision dubbed 'Fregean descriptivism', that Kripke attributed to Frege. We then set out various descriptivist theses. We proced to argue that Kripke’s interpretation of Frege as a reference-fixing descriptivist stems from his ascription of two other views, each logically weaker than reference-fixing descriptivism itself, to Frege. These are sense descriptivism and the view that sense fixes reference. The meaning descriptivism and the reference-fixing descriptivism of Kripke’s Frege have sense descriptivism as their common, logically (...) weaker, core. Since we do not concur with Kripke’s view that Frege was a sense descriptivist, we do not share his reasons for thinking that Frege was a reference-fixing descriptivist. (shrink)

A deductive system \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{S}$$ \end{document} (in the sense of Tarski) is Fregean if the relation of interderivability, relative to any given theory T, i.e., the binary relation between formulas\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\{ \left\langle {\alpha,\beta } \right\rangle :T,\alpha \vdash s \beta and T,\beta \vdash s \alpha \},$$ \end{document}is a congruence relation on the formula algebra. The multiterm deduction-detachment theorem is a natural generalization of (...) the deduction theorem of the classical and intuitionistic propositional calculi (IPC) in which a finite system of possibly compound formulas collectively plays the role of the implication connective of IPC. We investigate the deductive structure of Fregean deductive systems with the multiterm deduction-detachment theorem within the framework of abstract algebraic logic. It is shown that each deductive system of this kind has a deductive structure very close to that of the implicational fragment of IPC. Moreover, it is algebraizable and the algebraic structure of its equivalent quasivariety is very close to that of the variety of Hilbert algebras. The equivalent quasivariety is however not in general a variety. This gives an example of a relatively point-regular, congruence-orderable, and congruence-distributive quasivariety that fails to be a variety, and provides what apparently is the first evidence of a significant difference between the multiterm deduction-detachment theorem and the more familiar form of the theorem where there is a single implication connective. (shrink)

Many philosophers, including direct reference theorists, appeal to naively to 'modes of presentation' in the analysis of belief reports. I show that a variety of such appeals can be analyzed in terms of a precise theory of modes of presentation. The objects that serve as modes are identified intrinsically, in a noncircular way, and it is shown that they can function in the required way. It is a consequence of the intrinsic characterization that some objects are well-suited to serve as (...) modes that present individuals and while others are well-suited to serve as modes that present properties (though such modes do not `determine' the objects they present---there is no necessary connection between a mode m and the individual x or property F that it presents). Moreover, it is also a consequence that the modes for properties and individuals can be organized into complexes that are structurally identical to Russellian propositions having the represented properties and individuals as constituents. Not only is the relationship between modes and Fregean senses and modes of presentation explored in the paper, but also the idea that the theory of modes of presentation developed in the paper can serve as a theory of concepts. (shrink)

We study the non-Fregean propositional logic with propositional quantifiers, denoted by $\mathsf{SCI}_{\mathsf{Q}}$. We prove that $\mathsf{SCI}_{\mathsf{Q}}$ does not have the finite model property and that it is undecidable. We also present examples of how to interpret in $\mathsf{SCI}_{\mathsf{Q}}$ various mathematical theories, such as the theory of groups, rings, and fields, and we characterize the spectra of $\mathsf{SCI}_{\mathsf{Q}}$-sentences. Finally, we present a translation of $\mathsf{SCI}_{\mathsf{Q}}$ into a classical two-sorted first-order logic, and we use the translation to prove some model-theoretic properties (...) of $\mathsf{SCI}_{\mathsf{Q}}$. (shrink)