Matthias Schirn
Biographic Data
| ID | 5966460 |
|---|---|
| NAME | Matthias Schirn |
| GIVEN NAMES | Matthias |
| FAMILY NAME | Schirn |
| SIGNATURE | SCHIRN M |
| AFFILIATIONS | Munich School of Philosophy |
| ORCID | 0000-0002-6560-8856 |
| VERIFIED | Yes |
| TOTAL WORKS | 8 |
| TOTAL CITATIONS | 6 |
| AUTHOR COUNT | 8 |
| EDITOR COUNT | 0 |
| FIRST PUBLICATION YEAR | 1978 |
| LATEST PUBLICATION YEAR | 2025 |
| H-INDEX | 2 |
Frege on Identity and Identity Statements
In this essay, I first solve solve a conundrum and then deal with criteria of identity, Leibniz's definition of identity and Frege's adoption of it in his (failed) attempt to define the cardinality operator contextually in terms of Hume's Principle in Die Grundlagen der Arithmetik. I argue that Frege could have omitted the intermediate step of tentatively defining the cardinality operator in the context of an equation of the form ‘NxF(x) = NxG(x)…
Frege’s platonism and mathematical creation
In this three-part essay, I investigate Frege’s platonist and anti-creationist position in Grundgesetze der Arithmetik and to some extent also in Die Grundlagen der Arithmetik. In Sect. 1.1, I analyze his arithmetical and logical platonism in Grundgesetze. I argue that the reference-fixing strategy for value-range names—and indirectly also for numerical singular terms—that Frege pursues in Grundgesetze I gives rise to a conflict with the supposed…
Frege on the introduction of real and complex numbers by abstraction and cross-sortal identity claims
In this article, I try to shed new light on Frege’s envisaged definitional introduction of real and complex numbers in Die Grundlagen der Arithmetik (1884) and the status of cross-sortal identity claims with side glances at Grundgesetze der Arithmetik (vol. I 1893, vol. II 1903). As far as I can see, this topic has not yet been discussed in the context of Grundlagen . I show why Frege’s strategy in the case of the projected definitions of real an…
Frege’s philosophy of geometry
Hume’s Principle and Axiom V Reconsidered
What Finitism Could Not Be
In his paper "Finitism" (1981), W.W. Tait maintains that the chief difficulty for everyone who wishes to understand Hilbert's conception of finitist mathematics is this: to specify the sense of the provability of general statements about the natural numbers without presupposing infinite totalities. Tait further argues that all finitist reasoning is essentially primitive recursive. In this paper, we attempt to show that his thesis "The finitist fu…
Frege
Gottlob Frege, Wissenschaftlicher Briefwechsel
Frege’s philosophy of geometry
Hume’s Principle and Axiom V Reconsidered
Frege on the introduction of real and complex numbers by abstraction and cross-sortal identity claims
In this article, I try to shed new light on Frege’s envisaged definitional introduction of real and complex numbers in Die Grundlagen der Arithmetik (1884) and the status of cross-sortal identity claims with side glances at Grundgesetze der Arithmetik (vol. I 1893, vol. II 1903). As far as I can see, this topic has not yet been discussed in the context of Grundlagen . I show why Frege’s strategy in the case of the projected definitions of real an…
Gottlob Frege, Wissenschaftlicher Briefwechsel
Frege
What Finitism Could Not Be
In his paper "Finitism" (1981), W.W. Tait maintains that the chief difficulty for everyone who wishes to understand Hilbert's conception of finitist mathematics is this: to specify the sense of the provability of general statements about the natural numbers without presupposing infinite totalities. Tait further argues that all finitist reasoning is essentially primitive recursive. In this paper, we attempt to show that his thesis "The finitist fu…
Hume’s Principle and Axiom V Reconsidered
Frege’s philosophy of geometry
Frege on the introduction of real and complex numbers by abstraction and cross-sortal identity claims
In this article, I try to shed new light on Frege’s envisaged definitional introduction of real and complex numbers in Die Grundlagen der Arithmetik (1884) and the status of cross-sortal identity claims with side glances at Grundgesetze der Arithmetik (vol. I 1893, vol. II 1903). As far as I can see, this topic has not yet been discussed in the context of Grundlagen . I show why Frege’s strategy in the case of the projected definitions of real an…
Frege’s platonism and mathematical creation
In this three-part essay, I investigate Frege’s platonist and anti-creationist position in Grundgesetze der Arithmetik and to some extent also in Die Grundlagen der Arithmetik. In Sect. 1.1, I analyze his arithmetical and logical platonism in Grundgesetze. I argue that the reference-fixing strategy for value-range names—and indirectly also for numerical singular terms—that Frege pursues in Grundgesetze I gives rise to a conflict with the supposed…
Frege on Identity and Identity Statements
In this essay, I first solve solve a conundrum and then deal with criteria of identity, Leibniz's definition of identity and Frege's adoption of it in his (failed) attempt to define the cardinality operator contextually in terms of Hume's Principle in Die Grundlagen der Arithmetik. I argue that Frege could have omitted the intermediate step of tentatively defining the cardinality operator in the context of an equation of the form ‘NxF(x) = NxG(x)…
Epistemology (8 works) · Philosophy (8 works) · Philosophy and Theoretical Science (6 works) · Philosophy, Science, and History (6 works) · History and Theory of Mathematics (4 works) · Mathematics (4 works) · Metaphysics (4 works) · Analytic philosophy (3 works) · Computer Science (3 works) · Contemporary philosophy (3 works)