As a survey of many technical results in probability theory and probability logic, this monograph by two widely respected scholars offers a valuable compendium of the principal aspects of the formal study of probability. Hugues Leblanc and Peter Roeper explore probability functions appropriate for propositional, quantificational, intuitionistic, and infinitary logic and investigate the connections among probability functions, semantics, and logical consequence. They offer a systematic justification of constraints for various types of probability functions, in particular, an exhaustive account of probability (...) functions adequate for first-order quantificational logic. The relationship between absolute and relative probability functions is fully explored and the book offers a complete account of the representation of relative functions by absolute ones. The volume is designed to review familiar results, to place these results within a broad context, and to extend the discussions in new and interesting ways. Authoritative, articulate, and accessible, it will interest mathematicians and philosophers at both professional and post-graduate levels. (shrink)

On the basis of Anton Marty’s 1867 Preisschrift, this article offers a reconstruction of the semiotic and linguistic investigations the Swiss philosopher develops just before becoming a student of Brentano. The paper then compares this account with the view on signs that will be given in Marty’s later work, as well as within the Austro-German tradition.

Intellectual historians have rarely attended to the genre of fighting manuals, but these provide a new window on long-debated questions such as the relationship between Scholasticism and Humanism. This article offers a close comparison of the first known fencing manual, the 14-th century Liber de Arte Dimicatoria (Leeds, Royal Armouries FECHT 1, previously and better known as MS I.33), and the corpus of fighting manuals which underwent a remarkable expansion during the 15th and 16th centuries. While the former clearly shows (...) its origins in a scholastic background, the latter is mainly viewed as reflecting its humanist context. To this historiographical division corresponds a linguistic one: MS I.33 is a Latin text, while the rest of the corpus is mainly written in German and Italian. However, exceptions arise, amongst which, Heinrich von Gunterrodt’s Sciomachia et Hoplomachia: sive de Veris Principiis Artis Dimicatoriae (1579), the first text which explicitly refers to I.33. This article will compare these two texts, in order to interrogate their common relation to Scholasticism, namely the traditional frame of the knowledge within the medieval and early modern universities. The intent is to show that (at least some) Renaissance fight books include references to Scholasticism and to provide a better qualification of the nature of such references. The general hypothesis is that a large part of the texts―and products of culture―of the Renaissance that have been read, until recently, exclusively in relation to a humanist intellectual background can valuably be interpreted in the context of a Scholasticism that is still vivid during the period in question. (shrink)

Provability, Computability and Reflection.

This edited collection of eight original essays pursues the aim of bringing the spotlight back on Anton Marty. It does so by having leading figures in the contemporary debate confront themselves with Marty’s most significative contributions, which span from philosophy of mind, philosophy of language and ontology to meta-metaphysics and meta-philosophy. -/- The book is divided in three parts. The first part is dedicated to themes in philosophy of language, which were at the centre of Marty’s philosophical thinking throughout his (...) life. The second part focuses on the problem of the objectivity and phenomenology of time and space, upon which Marty was working in the final years of his life. The final part turns to Marty’s meta-metaphysical and meta-philosophical considerations. The intended audience of this book are primarily scholars and students interested in the relevant contemporary debates, as well as scholars working on the Austrian tradition. (shrink)

Introductions to the parts of the book cover the history of the contributions and their importance. The essays have been thoroughly revised since their publication in learned journals.

Kolmogorov's account in his [1933] of an absolute probability space presupposes given a Boolean algebra, and so does Rényi's account in his [1955] and [1964] of a relative probability space. Anxious to prove probability theory ‘autonomous’. Popper supplied in his [1955] and [1957] accounts of probability spaces of which Boolean algebras are not and [1957] accounts of probability spaces of which fields are not prerequisites but byproducts instead.1 I review the accounts in question, showing how Popper's issue from and how (...) they differ from Kolmogorov's and Rényi's, and I examine on closing Popper's notion of ‘autonomous independence’. So as not to interrupt the exposition, I allow myself in the main text but a few proofs, relegating others to the Appendix and indicating as I go along where in the literature the rest can be found. (shrink)

Teddy Seidenfeld recently claimed that Kolmogorov's probability theory transgresses the Substitutivity Law. Underscoring the seriousness of Seidenfeld's charge, the author shows that (Popper's version of) the law, to wit: If (∀ D)(Pr(B,D)=Pr(C,D)), then Pr(A,B)=Pr(A,C), follows from just C1. 0≤ Pr(A,B)≤ 1 C2. Pr(A,A)=1 C3. Pr(A & B,C)=Pr(A,B & C)× Pr(B,C) C4. Pr(A & B,C)=Pr(B & A,C) C5. Pr(A,B & C)=Pr(A,C & B), five constraints on Pr of the most elementary and most basic sort.

tic sequenzen-kalkul of Gentzen, into rules for PCc, the classical sequenzenkalkul. We shall limit ourselves here to sequenzen or turnstile statements of the form A„A„..., A„ I- B, where A„A„..., A„(n ~ 0), and B are wffs consisting of propositional variables, zero or more of the connectives '5', "v', ' ', ')', and '=', and zero or more parentheses. One can pass from PCi to PCc by amending the intelim rules for ' a result of long standing, or by amending (...) the intelim rules for either one of.. (shrink)

La Divine Comédie est le récit poétique d'une vision, d'une expérience surnaturelle qui se fait toujours plus intense, et que le langage peine toujours davantage à traduire. La mission de Dante consiste à rapporter cette vision. La question que nous pose la Divine Comédie réside dans la différence entre l'intraduisible et l'indicible: y a-t-il un intraduisible dicible? Ou en d'autres termes : quelle est, au-delà du topos de l'indicible poétique, et au-delà de la figure rhétorique de la prétérition, la signification (...) conceptuelle de l'expression du "dire" dans la Divine Comédie? (shrink)

L’histoire de la pensée sémiotique se caractérise par une oscillation entre définition large et définition étroite de son objet. Au Moyen Âge, la définition augustinienne du signe est jugée trop étroite, car elle ne concerne que le signe sensible. De nouvelles définitions tentent alors de faire des concepts des signes qui renvoient aux choses. L’Âge moderne, au contraire, affirme une volonté de rétrécissement à l’égard de la notion de signe. Cet article montrera les caractéristiques d’une telle réflexion sémiotique à travers (...) deux auteurs représentatifs d’un premier empirisme moderne : Pierre Gassendi et Thomas Hobbes. Le retour à une sémiotique étroite s’effectue par la référence aux traditions stoïcienne, sceptique et épicurienne, ainsi qu’à un Aristote renouvelé, et par une prédilection affichée pour la valeur indiciaire du signe par rapport à sa valeur sémantique. Ceci veut dire que les empiristes vont insister avant tout sur la fonction remémorative du signe et sur sa valeur de probabilité. L’indice en tant que trace sera ainsi privilégié par rapport au signe communicationnel, et il s’agira d’en défendre la validité en tant qu’il s’inscrit dans une échelle de certitude, au sommet de laquelle se situe la preuve. (shrink)

Consider a language SL having as its primitive signs one or more atomic statements, the two connectives ‘∼’ and ‘&,’ and the two parentheses ‘’; and presume the extra connectives ‘V’ and ‘≡’ defined in the customary manner. With the statements of SL substituting for sets, and the three connectives ‘∼,’ ‘&,’and ‘V’ substituting for the complementation, intersection, and union signs, the constraints that Kolmogorov places in [1] on probability functions come to read:K1. 0 ≤ P,K2. P) = 1,K3. If (...) ⊦ ∼, then P = P + P,K4. If ⊦ A ≡ B, then P = P.2. (shrink)