Článek poukazuje na problém, do jaké míry je smysluplné rozlišovat přírodní vědy, sociální vědy a humanitní vědy, respektive co mají tyto vědy společného potud, pokud je lze skutečně nazývat vědou. Jde o následující otázky: Jaký je rozdíl mezi humanitními a sociálními vědami? Je možné vést ostrou demarkační linii mezi humanitními a přírodními vědami a jejich metodami? Co vlastně opravňuje dotyčný systém výpovědí k tomu nazývat se vědou? Je osudem humanitních věd "kvantitativní smrt" či je naopak možné vedle hi-tech úspěšných exaktních (...) věd považovat humanitní vědy za nepostradatelné know-how pro přežití lidské společnosti? Odpovědi na tyto otázky se budou opírat o definici sociální vědy Maxe Webera, požadavek autonomie metod humanitních věd klasické hermeneutiky, univerzální hermeneutiku Hans-Georga Gadamera, scientistický návrh novopozitivismu a v neposlední řadě o řešení problému hodnotové neutrality vědy Hanse Alberta. (shrink)

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

Conventionalism about logic is the view that logical principles hold in virtue of some linguistic conventions. According to explicit conventionalism, these conventions have to be stipulated explicitly. Explicit conventionalism is subject to a famous criticism by Quine, who accused it of leading to an infinite regress. In response to the criticism, several authors have suggested reconstructing conventionalism as implicit in our linguistic behaviour. In this paper, drawing on a distinction from proof theory between derivable and admissible rules, I argue that (...) implicit conventionalism has not been stated in a sufficiently precise way, as it leaves open what one needs to say about admissible yet underivable rules. Moreover, it turns out that this challenge cannot be easily met, and that any attempt to meet the challenge makes conventionalism much less attractive a thesis. (shrink)

Badania nad podstawami matematyki przyniosły w ostatnich dziesięcioleciach wyniki, które wydają mi się ciekawe nie tylko dla nich samych, lecz także z uwagi na wnioski, jakie płyną z nich w odniesieniu do tradycyjnych problemów filozoficznych dotyczących natury matematyki. Same wyniki są dość szeroko znane, mimo to jednak sądzę, że warto raz jeszcze przedstawić je w zarysie, zwłaszcza w obliczu faktu, że dzięki pracy szeregu matematyków zyskały one znacznie doskonalszą formę, niż miały pierwotnie. Największy postęp, mający decydujące znaczenie dla tych wyników, (...) stał się możliwy dzięki precyzyjnemu zdefiniowaniu pojęcia skończonej procedury. Definicję taką można uzyskać na różne sposoby, które w efekcie dają dokładnie to samo pojęcie. Najbardziej zadowalający sposób polega moim zdaniem na sprowadzeniu pojęcia skończonej procedury do pojęcia maszyny o skończonej liczbie części, co uczynił brytyjski matematyk Turing. Co do filozoficznych konsekwencji wspomnianych wyników, nie sądzę, by kiedykolwiek należycie je przedyskutowano, czy choćby zwrócono na nie uwagę. (shrink)

Nous publions sous ce titre la traduction française de l'essai philosophique de Kurt Gödel intitulé: «Is Mathematics Syntax of Language?» Inédit jusqu'à présent, l'original paraîtra dans le 3e volume des Collected Works de Gödel, dont la publication est imminente. Nous savons par Hao Wang que, le 15 mai 1953, Paul Arthur Schilpp avait invité Gödel à apporter sa contribution au volume consacré à Carnap dans The Library of Living Philosophers. Le manuscrit de Gödel «Carnap and the Ontology of Mathematics», devait (...) être remis au plus tard le 2 avril 1954. Dés le 2 juillet 1953, Gödel donnait son accord à Schilpp pour la rédaction d'un article intitulé «Some Observations on the Nominalistic View of the Nature of Mathematics.» Cependant, le volume consacré à Carnap paraîtra en 1963 sans qu'y figure la contribution de Gödel. En effet — toujours selon Wang — Gödel avait informé Schilpp, le 2 février 1959, qu'il renonçait à l'envoi de l'article, dont il avait composé, surtout en 1954–1955, plusieur s versions sous le titre «Is Mathematics Syntax of Language?» Pour expliquer cet abandon, Wang avance les raisons suivantes: En premier lieu, Gödel était bien convaincu d'avoir réfuté la thése syntaxique, mais il n'était pas satisfait de son argumentation en faveur du platonisme. Deuxiémement, les critiques de Gödel s'adressent aux théses soutenues par Carnap en 1934 plutôt qu'à celles que ce dernier défendra vingt ans aprés, et qui paraissent moins hostiles au platonisme de son interlocuteur. II pouvait paraître douteux, en troisieme lieu, que Carnap ait eu le temps de rédiger, en 1959, la réponse qu'il aurait du faire, conformément aux régies de la collection, à Gödel. Or, en 1943 déjà, Gödel avait voulu retirer sa contribution au volume consacré à Russell dans la même serie, parce que ce dernier n'avait pu répondre à l'article de Gödel dont la rédaction lui avait été communiquée trop tardivement. (shrink)

Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. -/- The book begins by first challenging the (...) assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​. (shrink)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...) or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

This dissertation consists of three parts. Part I is a defense of an artificial language methodology in philosophy and a historical and systematic defense of the logical empiricists' application of an artificial language methodology to scientific theories. These defenses provide a justification for the presumptions of a host of criteria of empirical significance, which I analyze, compare, and develop in part II. On the basis of this analysis, in part III I use a variety of criteria to evaluate the scientific (...) status of intelligent design, and further discuss confirmation, reduction, and concept formation. (shrink)