Seminario di Logica e Filosofia della Scienza Anno 2023
Martedì 19 dicembre 2023 ore 11:00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
Sala Altana
Michael Rathjen (University of Leeds)
Searching for the ideal framework
Abstract: Proofs in mathematics often have a narrative quality to them, taking the reader on a long journey. Sometimes the reader has to wait for new mathematical characters (like imaginary numbers) to be created so the journey can be continued. Hilbert called these novel characters ideal elements. His conservation program was the idea that, while being important for the advancement of mathematics, ideal elements should be eliminable from proofs of concrete mathematical theorems. Investigations by a long list of mathematicians/logicians (e.g. Weyl, Hilbert, Bernays, Lorenzen, Takeuti, Feferman, Friedman, Simpson to name a few) have shown that large swathes of ordinary mathematics can be undergirded by theories of fairly modest consistency strength. This confirms what Hilbert surmised in his program, namely that elementary results (e.g. those expressible in the language of number theory) proved in abstract, non-constructive mathematics can often be proved by elementary means. The best known program for calibrating the strength of theorems from ordinary mathematics is reverse mathematics (RM). RM's scale for measuring strength is furnished by certain standard systems couched in the language of second order arithmetic. However, its language is not expressive enough to be able to talk about higher order objects, such as function spaces, directly. Richer formal systems, in which higher order mathematical objects can be directly accounted for, have been suggested. The price for maintaining conservativity over elementary theories, however, is that one has to use different logics for different ontological realms, allowing classical logic to reign at the level of numbers whereas higher type mathematical objects obey only intuitionistic logic. In the talk, I'd like to present some of these semi-intuitionistic systems, give a feel for carrying out mathematics within them, and relate them to systems considered in RM.
Venerdì 24 novembre 2023 ore 11:00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
Sala Altana
Matteo Tesi (Scuola Normale Superiore, Pisa)
Infinito e teoria strutturale della dimostrazione
Abstract: La teoria della dimostrazione per le logiche infinitarie ha trovato ampio impiego nell’analisi di teorie aritmetiche. I calcoli impiegati sono alberi ben fondati, con infiniti rami di lunghezza finita e in cui ogni nodo è occupato da sequenti finiti. Nel presente talk discutiamo la teoria strutturale della dimostrazione per logiche infinitarie con sequenti infiniti. L’analisi si concentrerà su calcoli classici, intuizionistici, sottostrutturali e modali e mostrerà che il passaggio a sequenti infiniti produce esiti diversi in base al sistema di partenza.
Venerdì 17 novembre 2023 ore 11:00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
Sala Altana
Erik Curiel (University of Bonn and Harvard) visiting scholar presso il DILEF dal 1 al 30 novembre 2023
Math Does Not Represent
Abstract: On the standard---almost universally (albeit often only implicitly) accepted---picture of the relation of mathematics in a physical theory to the world, mathematical entities represent physical entities, mathematical structures represent physical structures, and so on. The relation of representation is---again, almost universally, often implicitly---taken to be one of a designative, depictive or verisimilar character. I first present nine problems for this standard picture, which I consider damning. I conclude that math does not represent, at least not in any standard sense from formal semantics, philosophical logic or ontology, nor even in any sense based on more informal ideas such as similarity. The essential relation to study to comprehend the nature of physical theories and to understand the structure and character of our knowledge in physics is that between our concepts and the world. Mathematics provides us with a wealth of different tools to use in order to bring our concepts and the world into contact (and that itself in a number of different ways), nothing more, nothing less. Some of those tools function in ways that superficially resemble standard ideas of representation, even though they are nothing like it in any important sense; others do not. All of them conduce to knowledge and understanding of the world. I conclude with a few consequences of this view for the epistemology of science and for the numbingly endless debates about realism
Venerdì 10 novembre 2023 ore 11:00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
Sala "Altana"
Edoardo Rivello (Università di Torino)
Reasoning about truth: Gupta's puzzle as a case study
Abstract: Examples of reasoning taken from ordinary language are often employed in the philosophical debate to sustain arguments in favour or against theories of truth and paradox. Is the rationale behind these uses of logic puzzles either normative or descriptive? By taking from the field of formal theories of truth a paradigmatic example – Gupta’s puzzle – as our case study, we will argue that the answer to the above question cannot be simply either “purely normative” or “purely descriptive”, rather we will point to a necessary and fruitful interplay between normative and descriptive aspects of such kinds of philosophical investigation.
Venerdì 3 novembre 2023 ore 11:00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
sala "Altana"
Francesca Biagioli (Università di Torino)
Dedekindian Abstraction and Its Philosophical Background
Abstract: Dedekind is known to have made fundamental contributions to the modern axiomatization of number theory using various abstraction procedures in a series of writings from 1872-1888. However, his way of proceeding has been interpreted in different ways. Whereas some saw it as offering a clear example of structural or axiomatic definitions of abstract mathematical objects (regardless – and sometimes despite – his language of “abstraction” and “creation”), others deemed it to show a psychological understanding of abstraction conflating genetic with axiomatic methods. This paper aims to gain insight into the notion of abstraction at work in these writings by placing it in the context of nineteenth-century attempts to conceptualize ideal objects such as Moritz Wilhelm Drobisch’s and Hermann Lotze’s. Dedekind’s connections to nineteenth-century logic open the door to a non-psychologistic rendering of his procedure as first proposed by the neo-Kantian philosopher Ernst Cassirer, and more recently by Erich Reck and Audrey Yap. It will be suggested that this line of interpretation is worth exploring further, not only because it sheds light on the philosophical background of Dedekind’s notion, but also because it brings out the premises for a specific version of mathematical structuralism.
Venerdì 29 settembre 2023 ore 11:00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
sala "Altana"
Matteo Michelini (Ruhr University, Bochum)
Minority of Contrarians, Socially Adaptive Beliefs and Network Epistemology
Abstract: Empirical investigations reveal that even when scientific evidence is unequivocal, such as in the case of the causes of climate change, epistemic communities tend to polarize, and small groups of contrarians emerge. This phenomenon is usually attributed either to the reasoning style of contrarians, to the sub-optimal quality of the evidence they receive, or to their political affiliation. In this talk, I propose a new possible explanation of such phenomenon using network epistemology. I argue that a heterogeneous social network -- i.e.\ any network in which certain agents have more links than others -- is sufficient to foster the emergence of minorities of contrarians even if agents share the same independent access to evidence, same starting beliefs, same cognitive abilities and political affiliation. I do so under the minimal assumptions that agents distribute social rewards to agents with similar beliefs (social exchange theory) and that agents may form beliefs to obtain the highest possible social rewards, that is that beliefs are socially adaptive. To achieve this, I simulate the belief formation process of a community of agents through an agent-based model, which predicts the agents' behaviour from the way they interact.
Venerdì 26 maggio 2023 ore 11:00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
sala "Altana"
Matteo Plebani (University of Turin)
Truthmakers, Incompatibility, and Modality
(joint work with Giuliano Rossella e Vita Saitta)
Abstract: We present a new version of truthmaker semantics, where the relation of incompatibility between states is taken as a primitive. We discuss the advantages of the new framework over traditional truthmaker semantics, its relations with other accounts, and conclude by showing some interesting applications.
Venerdì 19 maggio 2023 ore 11:00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
sala "Altana"
Orly Shenker (Hebrew University of Jerusalem)
The Emperor's New Clothes: Functionalism is Dualism
Abstract: During the second half of the 20th century it appeared as if we no longer need to face the dilemma between materialism and dualism: varieties of so-called Non-Reductive Physicalism (NRP) promised a third option, and became the dominant view in the philosophy of mind, as well as in understanding the role and nature of the special sciences. Most popular among the varieties of NRP are varieties of functionalism, and among those the most popular view is computational functionalism, which is the basis for scientific research programs like computational neuroscience. However, this whole line of thinking is misguided: two major problems lurk at the foundations of NRP, and their analysis shows that the availability of a third option was an illusion, since it is an incoherent view: to remain coherent we need to decide between reductive physicalism (such as the recently developed theory called Flat Physicalism) and (any form of) non-reductive dualism (I don’t discuss idealism and varieties of double-aspect theories). In this talk, I will discuss mainly one of the two major problems with NRP, namely, that of multiple realizability, and if time permits will comment also on the second major problem, that of multiple computations.
Venerdì 12 maggio 2023 ore 11:00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
sala "Altana"
Giorgio Venturi (Università di Pisa)
The modal logic of generic absoluteness
Abstract: In this talk we will investigate two modal logics of forcing: the logic of forceability and truth and the logic of forcing persistency. Following the interpretation that Hamkins and Löwe gave of the normal modality in terms of forcing ( is read as is valid in all set-generic extensions), we will investigate two modal logics that capture the generic invariance of a formula. In order to do so, we will introduce a class of modal logics called Reflexive Insensitive (RI-logics) and we will provide an extension of the validity of the Boxdot-Conjecture.
Lunedì 3 aprile 2023, ore 11:00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
sala "Altana"
Luca San Mauro (TU, Wien)
Learning mathematical structures
Abstract: Algorithmic Learning Theory (ALT), initiated by Gold and Putnam in the 1960s, comprehends several formal frameworks for the inductive inference. Broadly construed, ALT models the ways in which a learner may achieve systematic knowledge about a given environment, by accessing more and more data about it. In classical paradigms, the objects to be inferred are either formal languages or computable functions. In this talk, we present the following framework: An agent receives larger and larger pieces of an arbitrary copy of a countable structure and, at each stage, is required to output a conjecture about the isomorphism type of such a structure. The learning is successful if the conjectures eventually stabilize to a correct guess. We offer a complete model theoretic characterization of which families of structures are learnable. Finally, we describe how to apply our framework to develop an innovative response to a widely debated question in the philosophy of mathematics, i.e., how does one single out the standard model of the natural numbers from nonstandard ones?
Ultimo aggiornamento
12.02.2024