A generalization of the axioms of choice says that all the Skolem functions of a true first‐order sentence exist. This generalization can be implemented on the first‐order level by generalizing the rule of existential instantiation into a rule of functional instantiation. If this generalization is carried out in first‐order axiomatic set theory, it is seen that in any model of FAST, there are sentences S which are true but whose Skolem functions do not exist. Since this existence is what the (...) truth of S means in a combinational sense, in any model of FAST there are sentences which are set‐theoretical “true” but false in the normal sense of the word. This shows that the assumptions on which the axiom of choice rests cannot be fully implemented in FAST. The axiom choice is not a set‐theoretical principle. (shrink)

Jaakko Hintikka’s work in logic and epistemology has won him the Rolf Schock Prize for Logic and Philosophy, widely viewed as the Nobel of its field. He is also one of only four philosophers this century to be the subject of a volume of the Library of Living Philosophers. Hintikka is professor of philosophy at Boston University.

Jaakko Hintikka’s work in logic and epistemology has won him the Rolf Schock Prize for Logic and Philosophy, widely viewed as the Nobel of its field. He is also one of only four philosophers this century to be the subject of a volume of the Library of Living Philosophers. Hintikka is professor of philosophy at Boston University.

A generalization of the axioms of choice says that all the Skolem functions of a true first‐order sentence exist. This generalization can be implemented on the first‐order level by generalizing the rule of existential instantiation into a rule of functional instantiation. If this generalization is carried out in first‐order axiomatic set theory , it is seen that in any model of FAST, there are sentences S which are true but whose Skolem functions do not exist. Since this existence is what (...) the truth of S means in a combinational sense, in any model of FAST there are sentences which are set‐theoretical “true” but false in the normal sense of the word. This shows that the assumptions on which the axiom of choice rests cannot be fully implemented in FAST. The axiom choice is not a set‐theoretical principle. (shrink)

Interviews met wijsgeren en andere wetenschapsmensen over de reden waarom zij zich met de persoon en het werk van de Oostenrijks-Engelse filosoof (1889-1951) bezighouden.

After the works of Jaako Hintikka, David Stern and, more recently, Denis Perrin, the idea that there is a wittgensteinian reflection upon the time and that it is at the origin of the abandonment of the project of a phenomenological language is nothing surprising, but we cannot consider it established yet. It seems to me that an important element in this debate is in chapter VII of the Philosophical Remarks : indeed, we find there the very first sustained discussion (...) on the possibility of a phenomenological language —a discussion obviously centred on the question of time. Without aiming to propose an “alternative” reading of Wittgenstein’ reflections on time and the phenomenological language, I would like to bring to light the importance of this chapter for this problem and also try to show that the interpretation key must be looked for in a reductio ad absurdum whose base is the impossibility to measure time. (shrink)

After the works of Jaako Hintikka, David Stern and, more recently, Denis Perrin, the idea that there is a wittgensteinian reflection upon the time and that it is at the origin of the abandonment of the project of a phenomenological language is nothing surprising, but we cannot consider it established yet. It seems to me that an important element in this debate is in chapter VII of the Philosophical Remarks : indeed, we find there the very first sustained discussion (...) on the possibility of a phenomenological language —a discussion obviously centred on the question of time. Without aiming to propose an “alternative” reading of Wittgenstein’ reflections on time and the phenomenological language, I would like to bring to light the importance of this chapter for this problem and also try to show that the interpretation key must be looked for in a reductio ad absurdum whose base is the impossibility to measure time. (shrink)

Many criticisms of epistemic logic have centered around its use of devices such as idealized knowers with logical omniscience and perfect self-knowledge. One possible response to such criticisms is to say that these idealizations are normative devices, and that epistemic logic tells us how agents ought to behave. This paper will take a different approach, treating epistemic logic as descriptive, and drawing the analogy between its formal models and idealized scientific models on that basis. Treating it as descriptive matches the (...) way in which some philosophers, including one of its founders, Jaako Hintikka, have thought about epistemic logic early in its history. Further, the analogy between the two fields will give us a way to defuse criticisms that see epistemic logic as unrealistic. For example, criticizing models of epistemic logic in which agents know all propositional tautologies as being unrealistic would be like criticizing frictionless planes in physics for being unrealistic. Each one would certainly be an unsuitable model for studying some kinds of phenomena, but is entirely appropriate for others. After outlining the analogy between epistemic and scientific models, we will discuss some ways in which idealizations are used by different research programs in epistemic logic. (shrink)

In Physics, Aristotle starts his positive account of the infinite by raising a problem: “[I]f one supposes it not to exist, many impossible things result, and equally if one supposes it to exist.” His views on time, extended magnitudes, and number imply that there must be some sense in which the infinite exists, for he holds that time has no beginning or end, magnitudes are infinitely divisible, and there is no highest number. In Aristotle's view, a plurality cannot escape having (...) bounds if all of its members exist at once. Two interesting, and contrasting, interpretations of Aristotle's account can be found in the work of Jaako Hintikka and of Jonathan Lear. Hintikka tries to explain the sense in which the infinite is actually, and the sense in which its being is like the being of a day or a contest. Lear focuses on the sense in which the infinite is only potential, and emphasizes that an infinite, unlike a day or a contest, is always incomplete. (shrink)

This book focuses on the game-theoretical semantics and epistemic logic of Jaakko Hintikka. Hintikka was a prodigious and esteemed philosopher and logician, and his death in August 2015 was a huge loss to the philosophical community. This book, whose chapters have been in preparation for several years, is dedicated to the work of Jaako Hintikka, and to his memory. This edited volume consists of 23 contributions from leading logicians and philosophers, who discuss themes that span across the entire range (...) of Hintikka’s career. Semantic Representationalism, Logical Dialogues, Knowledge and Epistemic logic are among some of the topics covered in this book's chapters. The book should appeal to students, scholars and teachers who wish to explore the philosophy of Jaako Hintikka. (shrink)

Ve svém článku ‘Je elementární logika totéž co predikátová logika prvního řádu?’ (Pokroky matematiky, fyziky a astronomie 42, 1997, 127-133) klade Jiří Fiala nesmírně zajímavou otázku, zda je opodstatněné ztotožňovat elementární logiku s predikátovou logikou prvního řádu; s pomocí argumentů propagovaných již delší dobu finským logikem a filosofem Jaako Hintikkou (viz již jeho Logic, Language-Games and Information, Clarendon Press, Oxford, 1973; nejnověji jeho The Principles of Mathematics Revisited, Cambridge University Press, Cambridge, 1996) naznačuje, že by tomu tak být nemuselo. (...) Myslím, že uváděná argumentace stojí za bližší rozbor. Hintikka v podstatě říká: Kvantifikované formule predikátové logiky jsou svou podstatou o vybírání prvků z univerza; například ∀x∃yR(x,y) neříká nic jiného než to, že ke každému x můžeme vybrat y, které je k němu ve vztahu R. Obecněji říká Hintikka to, že každá formule je vlastně zápisem určité hry (ve smyslu matematické teorie her), jejíž některé tahy spočívají ve vybírání individuí. Na základě tohoto se pak ptá: je nějaký rozumný důvod, proč se omezovat jenom na hry toho typu, které jsou vyjádřitelné formulemi standardního predikátového počtu? Proč připouštět jen hry s úplnou informací (tj. ty, při kterých jsou při každém tahu k dispozici všechny tahy předchozí), proč vylučovat hry jiné; tudíž proč připouštět jen lineárně uspořádané kvantifikátory, a nepřipustit i kvantifikátory uspořádané třeba jen částečně? Hintikkova argumentace je příkladem argumentace typu formule logiky prvního řádu jsou ve skutečnosti o tom a o tom, tudíž ... . Uveďme pro ilustraci jiný nedávný příklad stejného argumentačního schématu, který pochází od Johana van Benthema (Exploring Logical Dynamics, CSLI, Stanford, 1997). Ten říká: Kvantifikátory jsou v podstatě modality, kvantifikované formule jsou tedy formule modální a jsou tudíž o existenci nějakých alternativ: formule ∀xP(x) říká, že P(x) je nutné, neboli že P(x) platí v každém „dosažitelném možném stavu věcí“, zatímco formule ∃xP(x) říká, že P(x) je možné, neboli že platí alespoň v jednom takovém stavu věcí.. (shrink)

During his long and continuing scholarly career, Patrick Suppes contributed significantly both to the sciences and to their philosophies. The volume consists of papers by an international group of Suppes colleagues, collaborators, and students in many of the areas of his expertise, building on or adding to his insights. Michael Friedman offers an overview of Suppes accomplishments and of his unique perspective on the relation between science and philosophy. Paul Humphreys, Stephen Hartmann, and Tom Ryckman present essays in the philosophy (...) of physics. Jens-Erik Fenstad, Harvey Friedman, and Jaako Hintikka consider problems in the foundations of mathematics, while the late Duncan Luce, Jean-Claude Falmagne, Brian Skyrms, and Hannes Leitgeb have contributed essays in theory of measurement, decision theory and probability. Foundations of economics and political theory are addressed by Adolfo Garcia de la Sienra, Russell Hardin, and Kenneth Arrow. Psychology, language, and philosophy of language are addressed by Elizabeth Loftus, Anne Fagot-Largeault, Willem Levelt, Dagfinn Follesdal, and Marcos Perreau-Guimares and some of Suppes most recent research in neurobiology is addressed in essays by Colleen Crangle, Acadio de Barros and Claudio Carvalhes. Finally Nancy Cartwright and Alexandre Marcelles consider the alignment (or misalignment) of method and policy. Each of the essays is accompanied by a response from Suppes.". (shrink)

The aim of this paper is to frame briefly Chateaubriand’s conception of logical forms in the distinction between logic and language as calculus and logic as universal language, devised by Jean van Heijenoort and later generalized by Jaakko Hintikka. The most important reasons to connect Chateaubriand’s conception with this distinction are perhaps Chateaubriand’s criticism of the linguistic approach to logical forms and the role Chateaubriand assigns to symbolism in his own account.O propósito deste artigo é localizar brevemente a concepção de (...) forma lógica de Chateaubriand com relação à distinção entre lógica e linguagem como cálculo e lógica como linguagem universal, introduzida por Jean van Heijenoort e depois generalizada por Jaako Hintikka. Talvez a razão mais importante para conectar a concepção de Chateaubriand com esta distinção sejam suas críticas ao tratamento linguístico das formas lógicas, e o papel que Chateaubriand atribui ao simbolismo em seu próprio tratamento. (shrink)

The essays in this volume are based on addresses given during a colloquium on free logic, modal logic, and related areas held at the University of California in 1968. The majority of the contributors are well known for their writings in these fields and their papers are as illuminating as they are technical. In the first paper, Lambert and Bas C. Van Fraassen apply free logic to several controversies in quantified modal logic. One of these is Putman's argument that 'Nothing (...) is both red and green all over' can be had as a theorem of modal logic. Lambert and Van Fraassen provide a counter example to this claim and then show that the argument only holds in systems allowing possible individuals. Jaako Hintikka's essay also deals with 'free' modal logics in much the same way as Hintikka's other papers and discusses some of the criticisms of Quine of the entire enterprise of quantified modal logic. In another paper, H. Leblanc and R. K. Meyer provide truth-value semantics for the theory of types and hence an alternative semantic structure for functional calculi of any order. In addition to these essays, there are papers by R. Thomason and Dana Scott on modal logic, J. Vickers on probability logic, and Peter Woodruff on truth value gaps. To anyone interested in these various areas this collection is sure to be welcome.--R. P. M. (shrink)

This is the second volume in the new monograph series sponsored by the American Philosophical Quarterly and judging by the high quality of most of the essays in this collection the idea for such a series seems to be a good one. A wide variety of topics in contemporary philosophical logic are discussed in seven essays, as suggested by the following brief account of their contents: Montgomery Furth's "Two Types of Denotation" is a careful study of Frege's views of denotation, (...) function, and object which manages to make some original suggestions as well as to clear up some confusing features of Frege's discussion. Jaako Hintikka's "Language Games for Quantifiers" develops interesting connections between the uses of quantifiers and various verbs related to seeking and finding and with these connections in mind offers a game theoretic interpretation of quantifiers. J. W. Cornman's admirably clear essay "Types, Categories and Nonsense" discusses the views of Ryle, Russell, Black, Pap, and Sommers on categories and types, formulating criteria of type difference close to that of Sommers. In "A Theory of Conditionals," R. C. Stalnaker takes some clues from the semantical analysis of modal logics in order to present an analysis of 'if... then...' statements and to deal with some epistemological problems about counterfactuals. In "Goodman's Nominalism," A. Hausman and C. Echelberger discuss certain facts which, in their view, no nominalist ontology, including Goodman's can deal with. Ted Honderlich's "Truth: Austin, Strawson, Warnock" is a discussion of Austin's views on truth and some of the confusions surrounding commentary on and criticism of it. Honderlich suggests his own definition of truth in the article. Finally, Colwyn Williamson in "Propositions andPropositions" discusses the various arguments which have been put forward to show that propositions are entities of a sort distinct from sentences. He rejects all such arguments as well as their conclusion.--R. H. K. (shrink)