Jouko Väänänen
Biographic Data
| ID | 460519 |
|---|---|
| NAME | Jouko Väänänen |
| GIVEN NAMES | Jouko |
| FAMILY NAME | Väänänen |
| SIGNATURE | VÄÄNÄNEN J |
| AFFILIATIONS | University of Helsinki |
| ORCID | 0000-0003-4356-7974 |
| VERIFIED | Yes |
| TOTAL WORKS | 6 |
| TOTAL CITATIONS | 3 |
| WORKS AS AUTHOR | 6 |
| WORKS AS EDITOR | 0 |
| FIRST PUBLICATION YEAR | 2008 |
| LATEST PUBLICATION YEAR | 2023 |
| H-INDEX | 1 |
Philosophical Uses of Categoricity Arguments
This Element addresses the viability of categoricity arguments in philosophy by focusing with some care on the specific conclusions that a sampling of prominent figures have attempted to draw – the same theorem might successfully support one such conclusion while failing to support another. It begins with Dedekind, Zermelo, and Kreisel, casting doubt on received readings of the latter two and highlighting the success of all three in achieving wha…
Tracing Internal Categoricity
Informally speaking, the categoricity of an axiom system means that its non‐logical symbols have only one possible interpretation that renders the axioms true. Although non‐categoricity has become ubiquitous in the second half of the twentieth century whether one looks at number theory, geometry or analysis, the first axiomatizations of such mathematical theories by Dedekind, Hilbert, Huntington, Peano and Veblen were indeed categorical. A common…
Second-Order Logic and Set Theory
Both second-order logic and set theory can be used as a foundation for mathematics, that is, as a formal language in which propositions of mathematics can be expressed and proved. We take it upon ourselves in this paper to compare the two approaches, second-order logic on one hand and set theory on the other hand, evaluating their merits and weaknesses. We argue that we should think of first-order set theory as a very high-order logic
In Memoriam
From IF to BI
The Craig Interpolation Theorem in abstract model theory
The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will argue in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic. My argument is supported by the observation that logics which satisfy the interpolation property usually also satisfy a Lindst…
The Craig Interpolation Theorem in abstract model theory
The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will argue in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic. My argument is supported by the observation that logics which satisfy the interpolation property usually also satisfy a Lindst…
From IF to BI
In Memoriam
Second-Order Logic and Set Theory
Both second-order logic and set theory can be used as a foundation for mathematics, that is, as a formal language in which propositions of mathematics can be expressed and proved. We take it upon ourselves in this paper to compare the two approaches, second-order logic on one hand and set theory on the other hand, evaluating their merits and weaknesses. We argue that we should think of first-order set theory as a very high-order logic
Tracing Internal Categoricity
Informally speaking, the categoricity of an axiom system means that its non‐logical symbols have only one possible interpretation that renders the axioms true. Although non‐categoricity has become ubiquitous in the second half of the twentieth century whether one looks at number theory, geometry or analysis, the first axiomatizations of such mathematical theories by Dedekind, Hilbert, Huntington, Peano and Veblen were indeed categorical. A common…
Philosophical Uses of Categoricity Arguments
This Element addresses the viability of categoricity arguments in philosophy by focusing with some care on the specific conclusions that a sampling of prominent figures have attempted to draw – the same theorem might successfully support one such conclusion while failing to support another. It begins with Dedekind, Zermelo, and Kreisel, casting doubt on received readings of the latter two and highlighting the success of all three in achieving wha…
Mathematics (6 works) · Computer Science (4 works) · Pure mathematics (4 works) · Computability, Logic, AI Algorithms (3 works) · Discrete mathematics (3 works) · Epistemology (3 works) · Philosophy (3 works) · Philosophy and Theoretical Science (3 works) · Advanced Algebra and Logic (2 works) · Algebra over a field (2 works)