Logic and Knowledge - Conference - 16-19 June 2010 - Villa Mirafiori



  • Description


  • Program


  • Wednesday 16 June, Room V

9:30 – 9:45 Opening

9:45 – 10:30 D. Gillies (University College London), The empiricist view of logic

10:30 – 10:45 Discussant: P. Pecere (University of Cassino)

10:45 – 11:00 Coffee Break

11:00 – 11:45 M. De Caro (University Roma Tre of Rome), What can the neurosciences tell us about freedom and morality?

11:45 – 12:00 Discussant: A. Paese (University La Sapienza of Rome)

12:00 – 12:30 General discussion


15:00 – 15:45 M. Detlefsen (University of Notre Dame), Rigor, logic and intuition

15:45 – 16:00 Discussant: M. Antonutti (University of Bristol)

16:00 – 16:45 G. Sundholm (University of Leiden), A garden of grounding trees

16:45 – 17:00 Discussant: L. Incurvati (University of Cambridge)

17:00 – 17:15 Coffee Break

17:15 – 18:00 C. Posy (The Hebrew University of Jerusalem), On the finite: Part I, Lessons learned from Kant about knowledge and indeterminacy

18:00 – 18:15 Discussant: S. Di Paolo (University La Sapienza of Rome)

18:15 – 19:00 General discussion


  • Thursday 17 June, Room V

9:00 – 9:45 R. Chiaradonna (University Roma Tre of Rome), Galen’s medical epistemology

9:45 – 10:00 Discussant: D. Quarantotto (University La Sapienza of Rome)

10:00 – 10:45 M. Capozzi (University La Sapienza of Rome), The importance of sight and hearing in XVII and XVIII Century logic 10:45 – 11:00 Discussant: C. Fabbrizi (University La Sapienza of Rome)

11:00 – 11:15 Coffee Break

11:15 – 12:00 J. von Plato (University of Helsinki), On the dimensionality of deductive arguments12:00 – 12:15 Discussant: A. Iacona (University of L'Aquila)

12:15 – 12:45 General discussion


15:00 – 15:45 T. Williamson (University of Oxford), Logics and metalogics

15:45 – 16:00 Discussant: C. Cozzo (University La Sapienza of Rome)

16:00 – 16:45 C. Cozzo (University La Sapienza of Rome), Is knowledge the most general factive stative attitude?

16:45 – 17:00 Discussant: T. Williamson (University of Oxford)

17:00 – 17:15 Coffee Break

17:15 – 18:00 E. Ippoliti (University La Sapienza of Rome), Between data and hypotheses: the quest for knowledge

18:00 – 18:15 Discussant: F. Sterpetti (University La Sapienza of Rome)

18:15 – 19:00 General discussion


  • Friday 18 June, Room V

9:45 – 10:30 D. Prawitz (University of Stockholm), Perfect syllogisms, proofs, and knowledge10:30 – 10:45 Discussant: J. Murzi (University of Sheffield)

10:45 – 11:00 Coffee Break

11:00 – 11:45 R. Hersh (University of New Mexico), Mathematical intuition (Poincare, Polya, Dewey)

11:45 – 12:00 Discussant: C. Bernardi (University La Sapienza of Rome)

12:00 – 12:45 General discussion


15:00 – 15:45 C. Cellucci (University La Sapienza of Rome), Classifying and justifying inferences

15:45 – 16:00 Discussant: N. B. Goethe (Fellow Lichtenberg-Kolleg/Göttingen)

16:00 – 16:45 E. Grosholz (Penn State University), Referring and analyzing: Logic, Mathematics, Mechanics

16:45 – 17:00 Discussant: V. Giardino (Institut Jean Nicod Paris)

17:00 – 17:15 Coffee Break

17:15 – 18:00 R. Thomas (University of Manitoba), Assimilation: Not only indiscernibles are identified

18:00 – 18:15 Discussant: D. De Simone (University La Sapienza of Rome )

18:15 – 19:00 General discussion


  • Sidetalk

Friday 18 June, Room V

14:00 - 15:00 Jean-Baptiste Joinet (University Paris 1 Panthéon-Sorbonne), Negation and protological foundations for logic

Sidetalk organized by  “Gruppo di ricerca in Logica e Geometria della Cognizione” - Roma Tre University (http://logica.uniroma3.it)


  • Saturday 19 June, Room V

9:30 – 10:15 R. Cordeschi (University La Sapienza of Rome), Artificial Intelligence, cognitive science and evolutionary theory: a unifying framework by Herbert Simon

10:15 – 10:30 Discussant: F. Ervas (Institut Jean Nicod Paris)

10:30 – 11:15 J. Azzouni (Tuft University), The nonexistence of nominalistic content and its impact on metaphysics

11:15 – 11:30 Discussant: S. De Bianchi (University La Sapienza of Rome)

11:30 – 11:45 Coffee Break

11:45 – 13:00 Round Table


  • Abstracts of the papers 


Jody AZZOUNI (Tuft University), The nonexistence of nominalistic content and its impact on metaphysics


A widely held metaphysical myth is that there is the way the world is, and  that the way that it is can be characterized or represented in purely nominalistic terms.  The indispensability of mathematics to the languages of the sciences shows definitively that this is false.  There are important implications of these facts for the practice of metaphysics.  I try to deflect the possibility that the indispensable use of mathematics in the sciences screens us off from what the world itself is like; I try to deflect the Kantian possibility that scientific descriptions of the world can only provide appearances (descriptions of  the world that are false to things in the world themselves because they must be characterized in the language of applied abstracta).  That is, I mean to deflect the possibility that the way the world really is is a thing-in-itself that’s out of reach of our abstract-saturated scientific descriptions of things in the world.  I try to show that instead we can characterize aspects of the world that are really out there, and that we can do this despite our scientific languages enabling these characterizations only in terms of applied mathematical formalisms.


Mirella CAPOZZI (University of Roma La Sapienza), The importance of sight and hearing in XVII and XVIII Century logic


Abstract n.a.


Carlo CELLUCCI (University of Roma La Sapienza), Classifying and justifying inferences


It is a widespread view that inferences can be either deductive, that is, necessarily truth preserving, or ampliative, that is, not necessarily truth preserving.  This view, however, is inadequate because there are inferences, such as abductive inferences, which are neither ampliative nor truth preserving.  In this paper an alternative classification of inferences is proposed, as well as a justification of both deductive, non-deductive and abductive inferences which takes into account their role in knowledge, distinguishing their justification from their usefulness.  It is argued that the justification of deductive, non-deductive and abductive inferences raises similar problems and is to be approached much in the same way.


Riccardo CHIARADONNA (University of Roma Tre), Galen’s medical epistemology


This paper focuses on Galen’s (2nd century CE) distinctive views about the epistemic status of medicine. I will argue that, while taking the Aristotelian views as his starting point (see An.Pst. I; Metaph., I.1-2), Galen develops a more extended and flexible conception of scientific knowledge, adapted to the distinctive features of medicine. He regards medicine as a demonstrative science that also involves empirical and conjectural features when its general theorems come to be applied to individual patients. The use of logical methods, however, makes the good doctor able to minimise the possibility of erring in his practice. Interestingly, then, Galen seeks to integrate the treatment of empirical and contingent matters within the domain of demonstrative knowledge. Hence, e.g., Galen's interest in a (still rudimentary and non mathematical) idea of probability, according to which the stochastic and accidental character of medicine can be seen as approximating to truth and certain knowledge. This is closely connected with the further anti-aristotelian idea that science should extend to sensible particulars (in fact, Galen’s comes close to the view that each man is determined by a quasi-leibnizean individual form corresponding to the distinctive ratio of its elementary components). Finally, Galen argues that logical demonstrative methods have an intrinsic heuristic value and he seeks to transpose the ‘analytical’ geometrical method of resolution of problems into the domain of medicine.


Roberto CORDESCHI (University of Roma La Sapienza), Artificial Intelligence, cognitive science and evolutionary theory: a unifying framework by Herbert Simon


Herbert Simon’s approach to the study of rational choice was originally based on a criticism of classical game theory as it was usually applied to economics and organization science. The model of rational choice he pointed out was that of “bounded rationality”, which profoundly influenced both Artificial Intelligence and cognitive science. Once it was applied to Darwinian evolution, game theory raised much controversies, and Simon’s claims on bounded rationality and related concepts (e.g., docility) seem to converge with some criticisms to the application of classical game-theoretical models to evolutionary theory. Simon’s claims might thus be considered as more than a starting point for evaluating an integrated approach to the study of behavior.


Cesare COZZO (University of Roma La Sapienza), Is knowledge the most general factive stative attitude?


In Knowledge and its Limits Timothy Williamson maintains that «knowing is the most general factive stative attitude, that which one has to a proposition if one has any factive stative attitude to it at all». In a language the characteristic expression of a factive stative attitude is a factive mental state operator (FMSO). Williamson’s proposal is that «if F is any FMSO, then ‘S Fs that A’ entails ‘S knows that A’». However, Williamson does not prove that every FMSO conforms to his principle that factive-stative attitudes entail knowledge. I shall consider a possible counterexample. If it is a genuine counterexample, knowledge is not the most general factive stative attitude.


Mario DE CARO (University of Roma Tre), What can the neurosciences tell us about freedom and morality?


According to many philosophers and scientists, we are on the verge of solving some of the most venerable philosophical issues, thanks to the astonishing progress of the neurosciences. I will in particular discuss some proposals that concern free will and the nature of morality. My general conclusion will be that, if we have many reasons for believing that neurobiology can enrich our understanding of the features of the human mind, there is no sound reason for thinking it will ever explain them all.


Michael DETLEFSEN (University of Notre Dame), Rigor, logic and intuition


In this paper I consider various conceptions of rigor, what the benefits of rigor so conceived are, and have been supposed to be, what role(s) logical reasoning has been taken to play in the attainment of rigor and whether and/or under what conditions it may indeed serve in such a role(s). Special attention will be given to the relationship between rigor and the formalization of logical reasoning.


Donald GILLIES (University College London), The empiricist view of logic


The empiricist view of logic is the view that logic is not justified a priori, but by its empirical success in applications.  It is claimed that this view was first introduced by Quine in his famous 1951 paper:  'Two Dogmas of Empiricism'.  Quine used the example of a new logic for quantum mechanics which had earlier been suggested by Birkhoff and von Neumann.  This example was later taken up and developed by Putnam.  In this paper, however, it is suggested that quantum logic does not give a decisive argument in favour of the empiricist view of logic, but that such an argument is provided by the successful application of non-classical logics in artificial intelligence (AI).


Emily GROSHOLZ (The Pennsylvania State University), Referring and analyzing: Logic, Mathematics, Mechanics


Logic must treat its terms (S,P,M) or propositions (p, q, r) as if they were homogeneous, to exhibit forms of valid deductive inference. But the kinds of representations that make successful reference possible and those that make successful analysis possible in mathematics and the sciences are often not the same, so that significant scientific and mathematical claims (or demonstrations) often juxtapose heterogeneous terms (or propositions).This disparity calls for a philosophical critique of logic.


Reuben HERSH (University of New Mexico), Mathematical intuition (Poincare, Polya, Dewey)

The "philosophy of mathematical practice" is a segment or aspect of the philosophy of human inquiry.  Many great mathematicians, from Cayley to Atiyah,  reported what they did and experienced, even though few philosophers seemed to listen.  On the other hand, while John Dewey and his followers carefully describe the process of inquiry in general, they hardly mention how that theory includes mathematical inquiry. The validity of heuristic and computational reasoning in mathematics – both pure and applied – is a glaring problem and paradox, crying out for explication.


Emiliano IPPOLITI (University of Roma La Sapienza), Between data and hypotheses: the quest for knowledge


The relationship between data and hypotheses is the core of the process ofampliation of knowledge. I argue that understanding such a relationship and such a process requires revising the related notions of inference, logic and knowledge from an informationalpoint of view, examining how information is generated, extracted, processed and transferred. In order to do that, a concept of information different from the classic one is needed. I will analyze the relationship between data and hypotheses from an informational point of view using some examples from sciences.


Carl POSY (The Hebrew University of Jerusalem), On the finite: Part I, Lessons learned from Kant about knowledge and indeterminacy


85 years ago David Hilbert delivered his famous lecture  “On the Infinite”.  He invoked Kant’s philosophy of mathematics to endorse the need for intuitive finitary reasoning in mathematics.  And he invoked Kant’s notion of an “unconditioned” idea of reason as a model for his treatment of completed mathematical infinity. His point:  The set theoretic paradoxes arise from treating the ideal as real, and that is what Kant taught us not to do.  I am going to follow Hilbert in both of those moves: I will discuss Kant's analysis of the notion of a finite grasp,  and I will look at his view about the problems that arise when we mix certain ideal ("unconditioned") ideas of reason into the realm of the empirically real. But rather than apply these moves to the mathematical infinite, I will apply them to problems that arise in finite discourse.  I expect to discuss Moore's Paradox ("The cat is on the mat, but I don't know it") and the hangman paradox.  I may also look at issues surrounding the "Master Argument" of Diodorus Chronos. 


Dag PRAWITZ (University of Stockholm), Perfect syllogisms, proofs, and knowledge


There is no place for Aristotle's distinction between perfect and imperfect syllogisms in the main stream of modern logic. Yet, a distinction of that kind is needed, if we are to say what a proof is, or if we are to explain how the use inferences can generate knowledge. While it is generally agreed that the question whether a certain logical relation obtains between some given sentences depends on the meaning of the sentences, an account of the concept of perfect syllogism seems to depend on the more controversial idea that the meaning of a sentence is somehow based on what is required to justify an assertion of the sentence. Some possibilities of giving such a systematic account will be discussed.


Göran SUNDHOLM (University of Leiden), A garden of grounding trees


A comparison is made between the tree-like representations for the grounding of knowledge and of truths that are offered by Frege (Grundlagen §§ 3,4 and 17) and Bolzano (Wissenschaftslehre §220), while drawing upon historical precedents in Aristotle and Leibniz.  The constructive truth-maker analysis via proof-objects is used to explicate two versions of grounding: one decidable and one infinite, but containing canonical grounds only. An analogy of the latter to Brouwer’s Bewiesführungen in his demonstartion of the Bar Theorem is noted.


Robert THOMAS (University of Manitoba), Assimilation: Not only indiscernibles are identified


In the 2008 paper 'Extreme Science: Mathematics as the Science of  relations as such', I assimilated mathematics to science. In this  paper I discuss the operation of assimilation as a ubiquitous phenomenon of ordinary language that is almost missing from current informal mathematical language. I point to assimilations in history that would not happen today, abandoned assimilations that were failures to make important distinctions, and current assimilations  that are controversial. These examples lead me to suggest that the lack of assimilations in mathematical practice is an important reason for the dependability of arbitrarily long chains of reasoning uniquely in mathematics, a feature that is striking and sometimes considered mysterious.


Jan VON PLATO (University of Helsinki), On the dimensionality of deductive arguments


A text is written as a linear succession of words that make  up sentences, but modern theories of sentence structure represent  sentences in a tree form. The way sentences compose into a deductive  argument in logic and mathematics has likewise been written linearly,  but modern theories of proof represent such arguments in tree form. It is shown mainly through historical examples, from Aristotle, Frege, Hilbert and Bernays, Hertz, Gentzen, and Jaskowski, that the tree form  has decisive advantages over a linear arrangement.


Timothy WILLIAMSON: Logics and metalogics


The lecture will consider Michael Dummett’s contention, in The Logical Basis of Metaphysics, that semantic theories should be formulated in such a way that the logic of the object-language is maximally insensitive to the logic of the meta-language. The controversy over the status of the Barcan formula and its converse in quantified modal logic will be taken as a case study. It will be argued that the insensitivity in question is a less desirable feature of a semantic theory than Dummett suggests. 

  • Pictures

Part 1 - Part 2 - Part 3 - Part 4 - Social dinner