Both Frege's Grundgesetze, and Lagrange's treatises on analytical functions pursue a foundational purpose. Still, the former's program is not only crucially different from the latter's. It also depends on a different idea of what foundation of mathematics should be like . Despite this contrast, the notion of function plays similar roles in their respective programs. The purpose of my paper is emphasising this similarity. In doing it, I hope to contribute to a better understanding of Frege's logicism, especially in relation (...) to its crucial differences with a set-theoretic foundational perspective. This should also spread some light on a question arisen by J. Hintikka and G. Sandu in a widely discussed paper, namely whether Frege should or should not be credited with the notion of arbitrary function underlying our standard interpretation of second-order logic. In section 1, I account for Lagrange's notion of function. In section 2, I advance some remarks on connected historical matters. This will provide an appropriate framework for discussing the role played by the notion of function in Frege's Grundgesetze. Section 3 is devoted to this. Some concluding remarks will close the paper. (shrink)

Hans Herzberger as a philosopher and logician has shown deep interest both in the philosophy of Gottlob Frege, and in the topic of the inexpressible and the ineffable. In the fall of 1982, he taught at the University of Toronto, together with André Gombay, a course on Frege's metaphysics, philosophy of language, and foundations of arithmetic. Again, in the fall of 1986, he taught a seminar on the philosophy of language that dealt with 'the limits of discursive symbolism in several (...) domains of human experience.' The course description continues by saying: 'Special attention will be given to the paradoxes underlying various doctrines of the inexpressible and the tensions inherent in those paradoxes. Some doctrines of .. (shrink)

In the opening to his late essay, Der Gedanke, Frege asserts without qualification that the word "true" points the way for logic. But in a short piece from his Nachlass entitled "My Basic Logical Insights", Frege writes that the word true makes an unsuccessful attempt to point to the essence of logic, asserting instead that "what really pertains to logic lies not in the word "true" but in the assertoric force with which the sentence is uttered". Properly understanding what Frege (...) takes to be at issue here is crucial for understanding his conception of logic and, in particular, what he takes to be its normative status vis-à-vis judgement, assertion, and inference. In this paper, I focus my attention on clarifying the latter claim and Frege's motivations for making it, exposing what I take to be a fundamental tension in Frege's conception of logic. Finally, I discuss whether Frege's deployment of the horizontal in his mature Begriffsschrift helps to resolve this tension. (shrink)

In this paper, it is examined how, if at all, the logical laws can be normative for human reasoning, wherein the notion of normativity is analyzed primarily with respect to Wittgenstein’s philosophy. During the ancient and the medieval periods, logic was being considered in terms of discourse and dialogical practice, but since Descartes and especially Kant, it has been treated as a system of laws with which the process of individual human reasoning has been compared. Therefore, normativity can be investigated (...) in the private sphere and in the public sphere. Wittgenstein discussed both aspects of normativity: in his early philosophy, the focus is on the laws of logic that are primarily normative for the state of affairs in the world, while in his later works the emphasis is on a social aspect of normativity, which is derived from the adopted rules that have been applied in a certain community. Taken that way, logic is certainly normative in the public sphere, but the more difficult issue is whether logic is normative for thinking, regarding the difference between the logical laws and those of thought. (shrink)

George Boolos has argued that the iterative conception of set justifies most, but not all, the ZFC axioms, and that a second conception of set, the Frege-von Neumann conception (FN), justifies the remaining axioms. This article challenges Boolos's claim that FN does better than the iterative conception at justifying the axioms in question.

Hume's Principle, dear to neo-Logicists, maintains that equinumerosity is both necessary and sufficient for sameness of cardinal number. All the same, Whitehead demonstrated in Principia Mathematica's logic of relations that Cantor's power-class theorem entails that Hume's Principle admits of exceptions. Of course, Hume's Principle concerns cardinals and in Principia's ‘no-classes’ theory cardinals are not objects in Frege's sense. But this paper shows that the result applies as well to the theory of cardinal numbers as objects set out in Frege's Grundgesetze. (...) Though Frege did not realize it, Cantor's power-theorem entails that Frege's cardinals as objects do not always obey Hume's Principle. (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.

This paper considers the question of whether Mill's account of the nature and justificatory foundations of deductive logic is psychologistic. Logical psychologism asserts the dependency of logic on psychology. Frequently, this dependency arises as a result of a metaphysical thesis asserting the psychological nature of the subject matter of logic. A study of Mill's System of Logic and his Examination reveals that Mill held an equivocal view of the subject matter of logic, sometimes treating it as a set of psychological (...) processes and at other times as the objects of those processes. The consequences of each of these views upon the justificatory foundations of logic are explored. The paper concludes that, despite his providing logic with a prescriptive function, and despite his avoidance of conceptualism, Mill's theory fails to provide deductive logic with a justificatory foundation that is independent of psychology. (shrink)

The paper discusses the emergence of Frege's puzzle and the introduction of the celebrated distinction between sense and reference in the context of Frege's logicist project. The main aim of the paper is to show that not logicism per se is mainly responsible for this introduction, but Frege's constant struggle against formalism. Thus, the paper enlarges the historical context, and provides a reconstruction of Frege's philosophical development from this broader perspective.

Conceptual primitivism is the view that truth is among our most basic and fundamental concepts. It cannot be defined, analyzed, or reduced into concepts that are more fundamental. Primitivism is opposed to both traditional attempts at defining truth (in terms of correspondence, coherence, or utility) and deflationary theories that argue that the notion of truth is exhausted by means of the truth schema. Though primitivism might be thought of as a view of last resort, I believe that the view is (...) independently attractive, and can be argued for directly. In this paper I offer what I take to be the strongest argument in favor of conceptual primitivism, which relies upon the Fregean doctrine of the omnipresence of truth. (shrink)

There is a strong consensus among analytic philosophers that Husserl is an internalist and that his internalism must be understood in conjunction with his methodological solipsism. This paper focuses on Husserl's early work the, Logical Investigations , and explores whether such a reading is justified. It shows that Husserl is not a methodological solipsist: He neither believes that meaning can be reduced to the individual, nor does he assign an explanatory role for meaning to the subject. Explanatory priority is assigned (...) to objects which have an intrinsic property independently of any access or attitude we may have to them. Although not a methodological solipsist, there are nonetheless internalist elements to Husserl's thought: He believes that we can think of non-existent objects and his account of indexicals and demonstratives shows that there are two kinds of meaning: one is context independent and internally individuated, the other is partly determined by context and so externally individuated. The paper leaves it open whether this is sufficient to mark Husserl out as an internalist. However, even if he were considered as such, we can be sure of one thing, namely, that his internalism would not be a species of methodological solipsism. (shrink)

“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)

Frege held that referring expressions in general, and demonstratives and indexicals in particular, contribute more than just their reference to what is expressed by utterances of sentences containing them. Heck first attempts to get clear about what the essence of the Fregean view is, arguing that it rests upon a certain conception of linguistic communication that is ultimately indefensible. On the other hand, however, he argues that understanding a demonstrative (or indexical) utterance requires one to think of the object denoted (...) in an appropriate way. This fact makes it difficult to reconcile the view that referring expressions are "directly referential" with any view that seeks (as Grice's does) to ground meaning in facts about communication. (shrink)