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Seminario di Logica e Filosofia della Scienza

Organizzazione Unità di ricerca LOG-LAB

 

 

Mercoledì 20 marzo 2024 ore 11.00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
Sala Altana

 

Gerhard Jaeger (University of Bern)

Gentzen in the 3- and 4-Valued Jungle

 

Abstract: Starting point is the well known sequent calculus LK for classical propositional logic à la Gentzen. From that we move on to weak and strong 3-valued Schütte valuations and relate them to structural properties of LK. It is then a natural step to look at Kleene’s approach to 3-valued logic. Two central parts of my talk deal with syntactic properties of Kleene’s 3-valued logic and Belnap’s 4-valued logic and sound and complete sequent calculi for both. Belnap’s 4-valued logic is then used as a basis for a formal approach to the Catuskoti, an important principle of reasoning in Indian logic and theology. We end our talk with presenting a corresponding formal framework that also incorporated some ideas due to Graham Priest.

 

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Venerdì 15 marzo 2024 ore 11.00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
Sala Altana

 

Volker Halbach (University of Oxford)

Classical Determinate Truth

 

Abstract: I present an axiomatic theory of truth formulated in classical logic. It is type-free in the sense that its truth predicate can meaningfully applied to sentences containing that very truth predicate. The truth theory serves the purposes of truth predicate in philosophy well. Philosophers have too much focused on the T-sentences or disquotation sentences. My starting point are the compositional clauses, principles like 'a conjunction is true iff both conjuncts are or 'the negation of a sentence is true iff the sentence itself is not'. These general claims are for many purposes more important than disquotational axioms. Unlike the disquotation sentences, they are also consistent, when stated without any restrictions. On top of the compositional clauses I add disquotational principles and arrive at a theory CD, which is introduced and analyzed by Kentaro Fujimoto and me in the paper.

 

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Venerdì 1 marzo 2024 ore 11:00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
Sala Altana
RETTIFICA - a causa di un problema logistico il seminario sarà tenuto a distanza.

 

Paul Gorbow (University of Stockholm and University of Oslo)

Dynamic Structures -- a Modal Explanation of Certain Refinement Processes in Mathematics

 

Abstract: The iterative conception of the natural numbers has been given a modal potentialist explanation by Linnebo and Shapiro. The universe of natural numbers is given as a potentialist structure, i.e. a possible worlds model, P, where each world is an initial segment of the standard model, N, of the natural numbers, and the accessibility relation is given by the substructure relation. The so-called Mirroring theorem establishes a correspondence to the effect that a formula holds in N iff its full modalization holds in P. Any fully modalized formula A is stable in P, meaning that A→□A. However, the richer modal language of P has many unstable formulas, e.g. "x is the largest number". The modal potentialist is committed to that at any stage of the process there is a maximal actualized number. I introduce the notion of dynamic numbers to track such entities. E.g. letting max by the dynamic maximal number, we obtain:
• □"max is maximal"
• □(◊"max is even" ∧ ◊"max is odd")
• For each standard n: ◊□(n < max).

 

Although not in the range of the Mirroring theorem, these truths in P bring forth characteristics of modal potentialism. Generalizing the above, I introduce the notion of dynamic structures. These include:
• Potentialist structures corresponding to standard models.
• Structures corresponding to models constructed as ultrapowers. 

 

Dynamic structures have the following theoretical virtues:
• They explain the properties of the corresponding mathematical structures.
• They are ontologically advantageous compared to the corresponding mathematical structures.
• They are free from the arbitrary choices of the corresponding mathematical structures.
• They are often recursive, even when the corresponding mathematical structure is not.

 

As for applications, philosophical explanations emerge for the following entities:
• "Benign" non-standard numbers.
• The class of truths in the revision semantics of the truth predicate.

 

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Martedì 27 febbraio 2024 ore 11:00
Plesso didattico Capponi, via Capponi 9 - Firenze
Aula 6

 

Josè Ferreiros (Universidad de Sevilla)

Conceptual Structuralism

 

Abstract: In this talk, I defend a conceptualistic version of structuralism as the most convincing way of elaborating a philosophical understanding of structuralism in line with the classical tradition. The argument begins with a revision of the tradition of “conceptual mathematics”, incarnated in key figures of the period 1850 to 1940 like Riemann, Dedekind, Hilbert or Noether, showing how it led to a structuralist methodology. Then the tension between the ‘presuppositionless’ approach of those authors, and the platonism of some recent versions of philosophical structuralism, is presented. In order to resolve this tension, we argue for the idea of ‘logical objects’ as a form of minimalist realism, again in the tradition of classical authors including Peirce and Cassirer, and we introduce the basic tenets of conceptual structuralism. The remainder of the talk is devoted to an open discussion of the assumptions behind conceptual structuralism, and—most importantly—an argument to show how the objectivity of mathematics  can be explained from the adopted standpoint. This includes the idea that advanced mathematics builds on hypothetical assumptions (Riemann, Peirce, and others), which is presented and discussed in some detail. Finally, the ensuing notion of objectivity is interpreted as a form of particularly robust intersubjectivity, and it is distinguished from fictional or social ontology.

 

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Venerdì 23 febbraio 2024 ore 11:00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
Sala Altana

 

Casey McCoy (Yonsei University)

Pursuitworthiness and Epistemic Justification of Scientific Theories

 

Abstract: Much of modern philosophy of science with an epistemological orientation has focused on questions of justification, following on from the classic distinction between the context of discovery and the context of justification. Lately, Laudan's idea of a context of pursuit has been revived as a means of deflating certain justificatory accounts centered on justification, such as inference to the best explanation and meta-empirical confirmation. In this paper, we criticize such efforts to decouple assessments of pursuitworthiness from epistemic assessments, and argue for two main points: that assessing the viability of a theory is essential to assessing its pursuitworthiness, and that pursuitworthiness assessments are worthwhile only to the extent that pursuitworthy theories tend to be epistemically successful.

 

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Ultimo aggiornamento

14.03.2024

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