In this paper, the authors discuss Frege''s theory of logical objects (extensions, numbers, truth-values) and the recent attempts to rehabilitate it. We show that the eta relation George Boolos deployed on Frege''s behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstract objects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the eta relation to assert the existence of logical objects under certain highly restricted conditions, the theory of abstract objects uses (...) unrestricted Comprehension for Logical Objects and banishes encoding (eta) formulas from Comprehension for Properties. The relative mathematical and philosophical strengths of the two theories are discussed. Along the way, new results in the theory of abstract objects are described, involving: (a) the theory of extensions, (b) the theory of directions and shapes, and (c) the theory of truth values. (shrink)

Due programmi diversi si intersecano nel lavoro di Frege sui fondamenti dell’aritmetica: • Logicismo: l’aritmetica `e riducibile alla logica; • Estensionalismo: l’aritmetica `e riducibile a una teoria delle estensioni. Sia nei Fondamenti che nei Principi, Frege articola l’idea che l’aritmetica sia riducibile a una teoria logica delle estensioni.

Frege's and Russell's views are obviously different, but because of certain superficial similarities in how they handle certain famous puzzles about proper names, they are often assimilated. Where proper names are concerned, both Frege and Russell are often described together as "descriptivists." But their views are fundamentally different. To see that, let's look at the puzzle of names without bearers, as it arises in the context of Mill's purely referential theory of proper names, aka the 'Fido'-Fido theory.

Examines Frege's theory of judgement, according to which a judgement is, paradigmatically, the assertion that a particular object falls under a given concept. Throughout the book the aim is to both state Frege's views clearly and concisely, and to defend, modify or reject these where appropriate.

Call a family F of subsets of a set E inductive if ∅ ∈ F and F is closed under unions with disjoint singletons, that is, if ∀X∈F ∀x∈E–X(X ∪ {x} ∈ F]. A Frege structure is a pair (E.

Gottlob Frege famously rejects the methodology for consistency and independence proofs offered by David Hilbert in the latter's Foundations of Geometry. The present essay defends against recent criticism the view that this rejection turns on Frege's understanding of logical entailment, on which the entailment relation is sensitive to the contents of non-logical terminology. The goals are (a) to clarify further Frege's understanding of logic and of the role of conceptual analysis in logical investigation, and (b) to point out the extent (...) to which his understanding of logic differs importantly from that of the model-theoretic tradition that grows out of Hilbert's work. Many thanks for helpful comments to Wilfrid Hodges, to Bob Hale, and to an anonymous referee. (shrink)

Tyler Burge presents a collection of his seminal essays on Gottlob Frege (1848-1925), who has a strong claim to be seen as the founder of modern analytic philosophy, and whose work remains at the centre of philosophical debate today. Truth, Thought, Reason gathers some of Burge's most influential work from the last twenty-five years, and also features important new material, including a substantial introduction and postscripts to four of the ten papers. It will be an essential resource for any historian (...) of modern philosophy, and for anyone working on philosophy of language, epistemology, or philosophical logic. (shrink)

The paper scrutinizes Frege's Euclideanism - his view of arithmetic and geometry as resting on a small number of self-evident axioms from which non-self-evident theorems can be proved. Frege's notions of self-evidence and axiom are discussed in some detail. Elements in Frege's position that are in apparent tension with his Euclideanism are considered - his introduction of axioms in The Basic Laws of Arithmetic through argument, his fallibilism about mathematical understanding, and his view that understanding is closely associated with inferential (...) abilities. The resolution of the tensions indicates that Frege maintained a sophisticated and challenging form of rationalism, one relevant to current epistemology and parts of the philosophy of mathematics. (shrink)

Hintikka and Sandu have recently claimed that Frege's notion of function was substantially narrower than that prevailing in real analysis today. In the present note, their textual evidence for this claim is examined in the light of relevant historical and biographical background and judged insufficient.

Several scholars have argued that Wittgenstein held the view that the notion of number is presupposed by the notion of one-one correlation, and that therefore Hume's principle is not a sound basis for a definition of number. I offer a new interpretation of the relevant fragments on philosophy of mathematics from Wittgenstein's Nachlass, showing that if different uses of ‘presupposition’ are understood in terms of de re and de dicto knowledge, Wittgenstein's argument against the Frege-Russell definition of number turns out (...) to be valid on its own terms, even though it depends on two epistemological principles logicist philosophers of mathematics may find too ‘constructivist’. (shrink)

This paper concentrates on some aspects of the history of the analytic-synthetic distinction from Kant to Bolzano and Frege. This history evinces considerable continuity but also some important discontinuities. The analytic-synthetic distinction has to be seen in the first place in relation to a science, i.e. an ordered system of cognition. Looking especially to the place and role of logic it will be argued that Kant, Bolzano and Frege each developed the analytic-synthetic distinction within the same conception of scientific rationality, (...) that is, within the Classical Model of Science: scientific knowledge as cognitio ex principiis . But as we will see, the way the distinction between analytic and synthetic judgments or propositions functions within this model turns out to differ considerably between them. (shrink)

In this paper, I want to contribute to understanding and improving on Keenan'sintriguing equivalence result about reducible type quantifiers (Keenan, 1992).I give an alternative proof of his result which generalizes to type quantifiers, andI show how the reduction of a reducible type quantifier to (the composition of) ntype quantifiers can be effected.

This paper has three goals: (i) to show that the foundational program begun in theBegriffsschrift, and carried forward in theGrundlagen, represented Frege's attempt to establish the autonomy of arithmetic from geometry and kinematics; the cogency and coherence ofintuitive reasoning were not in question. (ii) To place Frege's logicism in the context of the nineteenth century tradition in mathematical analysis, and, in particular, to show how the modern concept of a function made it possible for Frege to pursue the goal of (...) autonomy within the framework of the system of second-order logic of theBegriffsschrift. (iii) To address certain criticisms of Frege by Parsons and Boolos, and thereby to clarify what was and was not achieved by the development, in Part III of theBegriffsschrift, of a fragment of the theory of relations. (shrink)

Scholars of Frege have spent a good deal of energy in discussing his views about truth, logic, and the relation between them.1 To one set of clues, however, scant attention has been paid. Repeatedly throughout his career, Frege attempted to illuminate the relation between logic and truth by comparing it to the relations between ethics and the good and aesthetics and the beautiful. Truth, beauty and goodness, of course, have had a long history in platonic philosophy. By the beginning of (...) Frege's career, they were also coming to play a prominent role in neo−Kantian thought, particularly that of Wilhelm Windelband. It is plausible to conjecture that Frege was inspired to look at ethics and aesthetics to understand the link between logic and truth by their connection in the work of Windelband or other neo−Kantians, though I know of no direct evidence that he was.2 But whatever the sources of Frege's use of the analogy, it is to his own writing that we must look for its meaning. (shrink)