-
5Deduction and Ampliativity: A Critical AppraisalIn Antonio Piccolomini D'Aragona (ed.), Perspectives on Deduction: Contemporary Studies in the Philosophy, History and Formal Theories of Deduction, Springer Verlag. pp. 233-250. 2024.The ampliativity of deduction has been defended in several ways—such as the semi-decidability of the theories, the surprise of unexpected consequences, the need of new individuals in deduction, or ampliative inference as deduction with suppressed premises (Dummett, Frege. Philosophy of mathematics. Duckworth, London, 1991; Hintikka, Logic, language-games and information. Oxford University Press, Oxford, 1973; Musgrave, Imre Lakatos and theories of scientific change. Kluwer, Boston, 1989; Rota, I…Read more
-
4What is a financial crash?Rivista di Estetica 84 7-24. 2023.What is a financial crash, and why does it happen? The answers to these fundamental questions require an investigation of the ontological and epistemic state of the financial markets which will identify the causes of a financial crash, the entities involved, and the relations between them.To this end, I examine several theories on financial systems which have conceptualized financial crashes. I analyze how these theories: a) identify different causes of a crash; b) deal with the basic entities a…Read more
-
7From a Heuristic Point of View: Essays in Honour of Carlo Cellucci (edited book)Cambridge Scholars Press. 2014.How do we get new knowledge? Following the maverick tradition in the philosophy of science, Carlo Cellucci gradually came to the conclusion that logic can only fulfill its role in mathematics, science and philosophy if it helps us to answer this question. He argues that mathematical logic is inadequate and that we need a new logic, framed in a naturalistic conception of knowledge and philosophy - the heuristic conception. This path from logic to a naturalistic conception of knowledge and philoso…Read more
-
21On the heuristic power of mathematical representationsSynthese 200 (5): 1-28. 2022.I argue that mathematical representations can have heuristic power since their construction can be ampliative. To this end, I examine how a representation introduces elements and properties into the represented object that it does not contain at the beginning of its construction, and how it guides the manipulations of the represented object in ways that restructure its components by gradually adding new pieces of information to produce a hypothesis in order to solve a problem.In addition, I defe…Read more
-
30Why Finance Needs Philosophy (and Vice Versa): Some Epistemic and Methodological IssuesFoundations of Science 27 (3): 957-974. 2021.As the world economy has for better or worse become more and more dependent on the financial markets, a rethinking of the role of finance in both theory and practice is necessary. I argue that such a rethinking requires a new look at the theories of finance that is philosophical in kind. In effect, as Martha Nussbaum claims, if the absence of philosophy in economics is arguably one of the main reasons for the flaws in certain economic theories, the absence of philosophy in finance is one the mai…Read more
-
22Undecidability of the Spectral Gap: An Epistemological LookJournal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 52 (1): 157-170. 2021.The results of Cubitt et al. on the spectral gap problem add a new chapter to the issue of undecidability in physics, as they show that it is impossible to decide whether the Hamiltonian of a quantum many-body system is gapped or gapless. This implies, amongst other things, that a reductionist viewpoint would be untenable. In this paper, we examine their proof and a few philosophical implications, in particular ones regarding models and limitative results. In more detail, we examine the way thes…Read more
-
10Mathematical Models of Time as a Heuristic ToolIn Lorenzo Magnani & Claudia Casadio (eds.), Model Based Reasoning in Science and Technology. Logical, Epistemological, and Cognitive Issues, Springer International Publishing. 2006.This paper sets out to show how mathematical modelling can serve as a way of ampliating knowledge. To this end, I discuss the mathematical modelling of time in theoretical physics. In particular I examine the construction of the formal treatment of time in classical physics, based on Barrow’s analogy between time and the real number line, and the modelling of time resulting from the Wheeler-DeWitt equation. I will show how mathematics shapes physical concepts, like time, acting as a heuristic me…Read more
-
38Mathematics and Finance: Some Philosophical RemarksTopoi 40 (4): 771-781. 2021.I examine the role that mathematics plays in understanding and modelling finance, especially stock markets, and how philosophy affects it. To this end, I explore how mathematics penetrates finance via physics, constructing a ‘financial physics’, and I outline the philosophical backgrounds of this process, in particular the ‘philosophy of equilibrium’ and that of critical points or ‘out-of-equilibrium’. I discuss the main characteristics and a few weaknesses of these mathematizations of financial…Read more
-
Models and Data in Finance: les Liaisons DangereusesIn Matthieu Fontaine, Cristina Barés-Gómez, Francisco Salguero-Lamillar, Lorenzo Magnani & Ángel Nepomuceno-Fernández (eds.), Model-Based Reasoning in Science and Technology: Inferential Models for Logic, Language, Cognition and Computation, Springer Verlag. 2019.
-
La scoperta scientifica: la ricerca di un metodo e il suo smarrimentoIn Stefano Velotti & Alessandro Conti (eds.), Strumenti del Pensiero. Vol. 2, Laterza. pp. 935-964. 2019.(ENG) The paper examines the first attempts put forward in ancient Greek to build a method for scientific discovery and how they have been progressively neglected. (ITA) L'articolo esamina i primi tentativi effettuati nell'antica grecia di costruire un metodo della scoperta scientifica, e analizza le ragioni che hanno portato al suo progessivo abbandono.
-
La Scoperta Scientifica: Rinascita e Raffinamento dei Metodi.In Stefano Velotti & Alessandro D. Conti (eds.), Gli strumenti del Pensiero, Laterza. pp. 935-964. 2019.(ENG) The paper examines the main approaches developed in the XIX and XX century to account for the way scientific discover unfolds. (ITA) L'articolo esamina le principali teorie filosofico-scientifiche elaborate nell'800 e nle '900 per render conto dei processi di scoperta scientifica.
-
20Logic and Knowledge (edited book)Cambridge Scholars Publications. 2011.The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VIVII of Platos Republic and Aristotles Prior and Posterior Analytics, to Kants Critique of Pure Reason and Mills A System of Logic, Ratiocinative and Inductive. It provides the title of an important collection of papers by Bertrand Russell. However, it has remained an underdeveloped theme in the last century, because logic has been treated as separate …Read more
-
1Dark Data. Some Methodological Issues in FinanceIn Ping Chen & Emiliano Ippoliti (eds.), Methods and Finance: A Unifying View on Finance, Mathematics and Philosophy, Springer Verlag. 2017.
-
14Methods and Finance. A View From InsideIn Ping Chen & Emiliano Ippoliti (eds.), Methods and Finance: A Unifying View on Finance, Mathematics and Philosophy, Springer Verlag. 2017.The view from inside maintains that not only to study and understand, but also to profit from financial markets, it is necessary to get as much knowledge as possible about their internal ‘structure’ and machinery. This view maintains that in order to solve the problems posed by finance, or at least a large part of them, we need first of all a qualitative analysis. Rules, laws, institutions, regulators, the behavior and the psychology of traders and investors are the key elements to the understan…Read more
-
Ways of Advancing Knowledge. A Lesson from Knot Theory and TopologyIn Emiliano Ippoliti, Fabio Sterpetti & Thomas Nickles (eds.), Models and Inferences in Science, Springer. pp. 147--172. 2016.
-
43Methods and Finance: A Unifying View on Finance, Mathematics and Philosophy (edited book)Springer Verlag. 2017.The book offers an interdisciplinary perspective on finance, with a special focus on stock markets. It presents new methodologies for analyzing stock markets’ behavior and discusses theories and methods of finance from different angles, such as the mathematical, physical and philosophical ones. The book, which aims at philosophers and economists alike, represents a rare yet important attempt to unify the externalist with the internalist conceptions of finance.
-
Heuristic Logic. A KernelIn David Danks & Emiliano Ippoliti (eds.), Building Theories: Heuristics and Hypotheses in Sciences, Springer International Publishing. 2018.
-
Building Theories: The Heuristic WayIn David Danks & Emiliano Ippoliti (eds.), Building Theories: Heuristics and Hypotheses in Sciences, Springer International Publishing. 2018.
-
18Heuristics and Inferential Microstructures: The Path to QuaternionsFoundations of Science 24 (3): 411-425. 2019.I investigate the construction of the mathematical concept of quaternion from a methodological and heuristic viewpoint to examine what we can learn from it for the study of the advancement of mathematical knowledge. I will look, in particular, at the inferential microstructures that shape this construction, that is, the study of both the very first, ampliative inferential steps, and their tentative outcomes—i.e. small ‘structures’ such as provisional entities and relations. I discuss how this pa…Read more
-
42Building Theories: Heuristics and Hypotheses in Sciences (edited book)Springer International Publishing. 2018.This book explores new findings on the long-neglected topic of theory construction and discovery, and challenges the orthodox, current division of scientific development into discrete stages: the stage of generation of new hypotheses; the stage of collection of relevant data; the stage of justification of possible theories; and the final stage of selection from among equally confirmed theories. The chapters, written by leading researchers, offer an interdisciplinary perspective on various aspect…Read more
-
58A Role for Representation Theorems†Philosophia Mathematica 26 (3): 396-412. 2018.I argue that the construction of representation theorems is a powerful tool for creating novel objects and theories in mathematics, as the construction of a new representation introduces new pieces of information in a very specific way that enables a solution for a problem and a proof of a new theorem. In more detail I show how the work behind the proof of a representation theorem transforms a mathematical problem in a way that makes it tractable and introduces information into it that it did no…Read more
-
26Manufacturing a Mathematical Group: A Study in HeuristicsTopoi 39 (4): 963-971. 2020.I examine the way a relevant conceptual novelty in mathematics, that is, the notion of group, has been constructed in order to show the kinds of heuristic reasoning that enabled its manufacturing. To this end, I examine salient aspects of the works of Lagrange, Cauchy, Galois and Cayley. In more detail, I examine the seminal idea resulting from Lagrange’s heuristics and how Cauchy, Galois and Cayley develop it. This analysis shows us how new mathematical entities are generated, and also how what…Read more
-
61Scientific Discovery ReloadedTopoi 39 (4): 847-856. 2020.The way scientific discovery has been conceptualized has changed drastically in the last few decades: its relation to logic, inference, methods, and evolution has been deeply reloaded. The ‘philosophical matrix’ moulded by logical empiricism and analytical tradition has been challenged by the ‘friends of discovery’, who opened up the way to a rational investigation of discovery. This has produced not only new theories of discovery, but also new ways of practicing it in a rational and more system…Read more
-
5Methods and Finance: A Unifying View on Finance, Mathematics and Philosophy (edited book)Springer. 2016.The book offers an interdisciplinary perspective on finance, with a special focus on stock markets. It presents new methodologies for analyzing stock markets' behavior and discusses theories and methods of finance from different angles, such as the mathematical, physical and philosophical ones. The book, which aims at philosophers and economists alike, represents a rare yet important attempt to unify the externalist with the internalist conceptions of finance.
-
755Modeling and Inferring in ScienceIn Emiliano Ippoliti, Fabio Sterpetti & Thomas Nickles (eds.), Models and Inferences in Science, Springer. pp. 1-9. 2016.Science continually contributes new models and rethinks old ones. The way inferences are made is constantly being re-evaluated. The practice and achievements of science are both shaped by this process, so it is important to understand how models and inferences are made. But, despite the relevance of models and inference in scientific practice, these concepts still remain contro-versial in many respects. The attempt to understand the ways models and infer-ences are made basically opens two roads.…Read more
-
67Logic and Knowledge (edited book)Cambridge Scholar Publishing. 2011.Logic and Knowledge Editor: Carlo Cellucci, Emily Grosholz and Emiliano Ippoliti Date Of Publication: Aug 2011 Isbn13: 978-1-4438-3008-9 Isbn: 1-4438-3008-9 The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VI–VII of Plato’s Republic and Aristotle’s Prior and Posterior Analytics, to Kant’s Critique of Pure Reason and Mill’s A System of Logic, Ratiocinative and Inductive. It provides the title of an imp…Read more