An investigation of Frege’s various contributions to the study of language, focusing on three of his most famous doctrines: that concepts are unsaturated, that sentences refer to truth-values, and that sense must be distinguished from reference.

Frege begins his exposition of the symbol system employed in his Begriffsschrift by introducing the sign ⟝, whereby, he says, “[a] judgment is always to be expressed”.[The judgment sign] stands to the left of the sign or complex of signs in which the content of the judgment is given. If we omit the little stroke at the left of the horizontal stroke, then the judgment is to be transformed into a mere complex of ideas; the author is not expressing his (...) recognition or nonrecognition of the truth of this. (shrink)

The paper argues, as against Thau and Caplan, that the traditional interpretation that Frege abandoned his earlier views about identity and identity--statements is correct.

The deviation of mathematical proof—proof in mathematical practice—from the ideal of formal proof—proof in formal logic—has led many philosophers of mathematics to reconsider the commonly accepted view according to which the notion of formal proof provides an accurate descriptive account of mathematical proof. This, in turn, has motivated a search for alternative accounts of mathematical proof purporting to be more faithful to the reality of mathematical practice. Yet, in order to develop and evaluate such alternative accounts, it appears as a (...) necessary prerequisite to first possess a clear picture of what the deviation of mathematical proof from formal proof consists in. The present work aims to contribute building such a picture by investigating the relation between the elementary steps of deduction constituting the two types of proofs—mathematical inference and logical inference. Many claims have been made in the literature regarding the relation between mathematical inference and logical inference, most of them stating that the former is lacking properties that are constitutive of the latter. Such differentiating claims are, however, usually put forward without a clear conception of the properties occurring in them, and are generally considered to be immediately justified by our direct acquaintance, or phenomenological experience, with the two types of inferences. The present study purports to advance our understanding of the relation between mathematical inference and logical inference by developing a detailed philosophical analysis of the differentiating claims, that is, an analysis of the meaning of the differentiating claims—through the properties that occur in them—as well as the reasons that support them. To this end, we provide at the outset a representative list of the different properties of logical inference that have occurred in the differentiating claims, and we notice that they all boil down to the three properties of formality, generality, and mechanicality. For each one of these properties, our analysis proceeds in two steps: we first provide precise conceptual characterizations of the different ways logical inference has been said to be formal, general, and mechanical, in the philosophical and logical literature on formal proof; we then examine why mathematical inference does not appear to be formal, general, and mechanical, for the different variations of these notions identified. Our study results in a precise conceptual apparatus for expressing and discussing the properties differentiating mathematical inference from logical inference, and provides a first inventory of the various reasons supporting the observations of those differences. The differentiating claims constitute thus a set of data that any philosophical account of mathematical inference and proof purporting to be more faithful to mathematical practice ought to be able to accommodate and explain. (shrink)

The translation of both ‘bedeuten’ and ‘Bedeutung’ in Frege's works remains sufficiently problematic that some contemporary authors prefer to leave these words untranslated. Here a case is made for returning to Russell's initial choice of ‘to indicate’ and ‘indication’ as better alternatives than the more usual ‘meaning’, ‘reference’, or ‘denotation’. It is argued that this choice has the philosophical payoff that Frege's controversial doctrines concerning the semantic values of sentences and predicative expressions are rendered far more comprehensible by it, and (...) that this translational strategy fulfills the desiderata of offering a translation which is acceptable both before and after Frege introduced the distinction between sense and reference or, as this paper would have it, between the sense of an expression and what it indicates. (shrink)

Simon Blackburn has shown that there is an analogy between the problem of moral motivation in ethics (how can moral reasons move us?) and the problem of what we might call the power of logical reasons (how can logical reasons move us, what is the force of the 'logical must?'). In this paper, I explore further the parallel between the internalism problem in ethics and the problem of the power of logical reasons, and defend a version of psychologism about reasons, (...) although not one of the Humean form. I discuss two forms of cognitivism: (i) a pure cognitivism and 'hard' realism modelled after Dancy's parallel conception in ethics: when we grasp logical reasons we grasp facts, which are directly known to us; (ii) a Kantian form of cognitivism, based on the idea that compulsion by reason goes with the capacity of reflection. I argue that (i) is implausible, and that (ii) fails to meet the internalist requirement. One would then seem to be left with what Dancy calls, about practical reasoning, psychologism about reasons. I sketch what might be such a psychologism. But it fails to account for the objectivity of logical reasons. I argue that the relevant state here is a form of dispositional knowledge of logical reasons. (shrink)

The paper challenges a widely held interpretation of Frege's conception of logic on which the constituent clauses of basic law V have the same sense. I argue against this interpretation by first carefully looking at the development of Frege's thoughts in Grundlagen with respect to the status of abstraction principles. In doing so, I put forth a new interpretation of Grundlagen §64 and Frege's idea of ‘recarving of content’. I then argue that there is strong evidence in Grundgesetze that Frege (...) did not hold the relevant sense-identity claim regarding basic law V. (shrink)

Standard first-order logic plus quantifiers of all finite orders ("SFOLω") faces four well-known difficulties when used to characterize the behavior of certain English quantifier phrases. All four difficulties seem to stem from the typed structure of SFOLω models. The typed structure of SFOLω models is in turn a product of an asymmetry between the meaning of names and the meaning of predicates, the element-set asymmetry. In this paper we examine a class of models in which this asymmetry of meaning is (...) removed. The models of this class permit definitions of the quantifiers which allow a desirable flexibility in fixing the domain of quantification. Certain SFOLω type restrictions are thereby avoided. The resulting models of English validate all of the standard first-order logical truths and are free of the four deficiencies of SFOLω models. (shrink)

Ontology played a very large role in Quine’s philosophy and was one of his major preoccupations from the early 30’s to the end of his life. His work on ontology provided a basic framework for most of the discussions of ontology in analytic philosophy in the second half of the Twentieth Century. There are three main themes (and several sub-themes) that Quine developed in his work. The first is ontological commitment: What are the existential commitments of a theory? The second (...) is ontological reduction: How can an ontology be reduced to (or substituted by) another? And what is the most economical ontology that can be obtained for certain given purposes? The third is criteria of identity: When are entities of some kind (sets, properties, material objects, propositions, meanings, etc.) the same or different? In this paper I discuss Quine’s development of these three themes and some of the problems that were aised in connection with his work. (shrink)

This paper concerns the three great modal dichotomies: (i) the necessary/contingent dichotomy; (ii) the a priori/empirical dichotomy; and (iii) the analytic/synthetic dichotomy. These can be combined to produce a tri-dichotomy of eight modal categories. The question as to which of the eight categories house statements and which do not is a pivotal battleground in the history of analytic philosophy, with key protagonists including Descartes, Hume, Kant, Kripke, Putnam and Kaplan. All parties to the debate have accepted that some categories are (...) void. This paper defends the contrary view that all eight categories house statements—a position I dub ‘octopropositionalism’. Examples of statements belonging to all eight categories are given. (shrink)

The aim of this paper is to provide a dynamic interpretation of Kant’s logical hylomorphism. Firstly, various types of the logical hylomorphism will be illustrated. Secondly, I propose to reevaluate Kant’s constitutivity thesis about logic. Finally, I focus on the design of logical norms as specific kinds of artefacts.

“Feminicity” is the term for a predicate register that enables feminist work be accounted for as relational “active-points” that collectively can be seen through what they have achieved. But going further, it marks where those active-points contribute to the dynamic field of feminist epistemologies and where change occurs. This article contributes to my larger project’s discussion of this concept. Broadly, feminicity argues that the active-points of feminist practices need to be understood within their situated fields as materialist informatics. In the (...) digital era, examples of the affects of digital feminicity are as identified in works such as those by Wajcman ; Haraway, Hayles, VNSMatrix, Adam, Plant. Collectively, such authors and artists opened a creative, and sometimes radical discourse of the digital field as multidirectional, multidimensional, multitemporal platform of “gender actions”. Taken as a predicated field sense of the term “predicate”), this work contributes to the feminist materialist reappraisal of feminist epistemology, and larger radical feminist deconstructive projects. Thus conceived, the genealogy of digital feminicity problematizes the monopolitical terms of feminism in its collation of actions, enabling a re-situation of feminist practices as positive material interventions and expressions of the ontological constitution of the political sphere. Feminicity does not propose a chronological account of the active-points, but processually and systemically addresses the terms of generational epistemological political change. This article describes the ways in which a materialist constructed register – “feminicity”– can be used to think about encounters between the domains of gender, politics and technology, as manifested by materialist informatics. For reasons of brevity, this article focuses on just two aspects of feminicity: the terms of predication of the female as gendered, and the issue of the image, as digital informatics, comprised of activitypoints of feminist practice. Consequently, these are measurable and offer practical resources for the general problem of gendering politics that operate in governance, resource distribution and a non-equal opportunity social/cultural power structure, under which minorities are disadvantaged. Feminist practice here refers to forms produced through feminist activities, ie, forms generated through relations with the matter of life through specific modalities of needs-based practices. (shrink)

Wittgenstein responds in his Notes on Logic to a discussion of Russell's Principles of Mathematics concerning assertion. Russell writes: "It is plain that, if I may be allowed to use the word assertion in a non-psychological sense, the proposition "p implies q" asserts an implication, though it does not assert p or q. The p and the q which enter into this proposition are not strictly the same as the p or the q which are separate propositions." (PoM p35) Wittgenstein (...) replies: "Assertion is merely psychological. In not-p, p is exactly the same as if it stands alone; this point is absolutely fundamental." (NB p95) Wittgenstein's response is intriguing, not least because of the centrality to his Tractatus of the idea that a proposition says something. This paper will examine that idea, distinguishing it from 'merely psychological' assertion, and explore in this context how we should understand the occurrence of a Tractarian proposition within another. (shrink)

This paper argues that Frege is not the metaphysical platonist about mathematics that he is standardly taken to be. It is shown that Frege’s project has two distinct stages: the identification of what is true of our ordinary notions, and then the provision of a systematic account that shares the identified features. Neither of these stages involves much metaphysics. The paper criticizes in detail Dummett’s interpretation of §§55-61 of Grundlagen. These sections fall under the heading ‘Every number is a self-subsistent (...) object’ and are described by Dummett as containing the worst arguments put forward by Frege. It is argued that essentially all of Dummett’s interpretive points are mistaken. Finally, I show that Frege’s claims about the independence of mathematics from humans and their activities does not commit him to any particularly metaphysical position either. (shrink)

I argue here that Frege’s eventual view on the relation between sentences and the thoughts they express is that, ideally, a sentence expresses exactly one thought, and a thought is expressed by exactly one (canonical) sentence. This may clash with some mainstream views of Frege, for it has the consequence of de-emphasizing the philosophical significance of the question of how it is possible for someone to regard one sentence as true yet regard another sentence that expresses the same thought as (...) false. This account of Frege was developed by taking a long-range look at his writings over the course of his life. (shrink)