‎BEAULIEU, Michel‎
‎Variables‎

‎Identity, Variables, and Impredicative Definitions + Vicious Circle Principles and the Paradoxes. (In Journal of Symbolic Logic, Volume 21, Number 3, 1956 + Volume 22, Number 3, 1957). - [HINTIKKA'S TRANSFORMATION RULES]‎

‎(No place), The Association for Symbolic Logic, Inc., 1956 + 1957. 8vo. Both entire issues present, both in original printed wrappers. Volume 21, 3 w. a small loss to lower corner of front wrapper, minor loss to lower capital and a tear to lower front hinge, no loss. Upper corner of least few leaves and back wrappers creased (w. tear to wrapper). Volume 22, 3. w. minor loss to capitals. Both issues internally near mint. Vol. 21, 3: pp. 225-248 (entire issue: pp. 225-336)" Vol. 22, 3: pp. 245-249 (entire issue: pp. 225-336).‎

‎First printing of these two important, but for long overlooked, articles, which together constitute Hintikka's attempt to cope with Wittgenstein's elimination of identity as proposed in the ""Tractatus"". With the translation rules that Hintikka here put forward, he is the first to try to carry out Wittgenstein's suggestions systematically. The Finnish born philosopher and logician, Jaakko Hintikka (born 1929), Professor of Philosophy at the University of Boston, is generally accepted as the founder of formal epistemic logic and of game semantics for logic. He has contributed seminally to the fields of philosophical and mathematical logic, philosophy of mathematics and science, language theory and epistemology. Independently of Evert Willem Beth he discovered the semantic tableau, and he is famous for his work on game semantics and logical quantifiers. In 2005 Hintakka was awarded the Schock Prize in logic and philosophy, the philosophical equivalent to the Nobel prize, ""for his pioneering contributions to the logical analysis of modal concepts, in particular the concepts of knowledge and belief "". In the 1950'ies Hintikka took it upon himself to follow Wittgentein's suggestion of elimination of identity suggested in the ""tractatus"", and in the two offered articles, he succeeds in constructing a logic without identity. The main point of the two connected articles is to show that variables can be used in two ways. One way does not exclude coincidences of the values of different variables (inclusive interpretation of variables), the other does (exclusive interpretation of variables) and can be either weakly or strongly exclusive. He now claims that in the ""Tractatus"" Wittgenstein adopts the weakly exclusive interpretation of variable and then proves that the weakly exclusive quantifiers are able to express everything that the inclusive quantifiers plus identity can express, and without a sign for identity, - for the first time systematically supporting Wittgenstein's claim that identity is not an essential constituent of logical notation. ""There are a number of references to the exclusive interpretations of variables in current logical literature. An exclusive reading of variables was, in effect, suggested by Ludwig Wittgenstein in ""Tractatus logico-philosophicus. As far as I know, however, no one has previously tried to carry out his suggestions systematically. Several misconceptions seem to be current concerning the outcome of an attempts of this kind. Carnap expects radical changes in the rules of substitution. If I am not mistaken, however, at least one form of the exclusive interpretation may be formalized by making but slight alterations in the axioms and/or in the transformation rules of the predicate calculus. Also I hope to say that it is not correct to say (as Russell has done) that Wittgenstein tried to dispense with the notion of identity. What a systematic use of an exclusive reading of variables amounts to is a new way of coping with the notion of identity in a formalized system of logic. Under the most natural formalization of the new interpretations, the resulting system is equivalent to the old predicate calculus (with identity): every formula of the latter admits of a translation into the former, and vice versa."" (Vol. 21, Nr. 3, p. 228).""A deviation from standard English. Recent discussion serves to bring out, amply and convincingly, the utility of observing the ordinary correct use of words and phrases for the purpose of clearing up philosophical problems. In this paper, I shall endeavour to show, by means of an example, that the reverse method may have its interest, too. "" (Vol. 21, Nr. 3, p. 225). ""This note is a sequel to the previous paper of mine which was entitled ""Identity, variables, and impredicative definitions"" and published in this JOURNAL, vol. 21 (1956, pp. 225-245. That early paper served to call attention to the dependency of the set-theoretic paradoxes on the interpretation of the variables that may occur in the critical ""abstraction principle"". (Vol. 22, Nr. 3, p. 245).Besides these two articles, the two issues also include other important articles within logic, e.g. Quine, ""Unification of Universes in Set Theory"" and Symonds and Chisholm ""Inference by Complementary Elimination"".‎

‎Identity, Variables, and Impredicative Definitions + Vicious Circle Principles and the Paradoxes. (In Journal of Symbolic Logic. - [HINTIKKA'S TRANSFORMATION RULES]‎

‎(No place), The Association for Symbolic Logic, Inc., 1956 + 1957. 8vo. Bound with the original wrappers in contemporary full cloth with black title label in leather with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 21, Number 3, 1956 + Volume 22, Number 3, 1957. Small tear to lower right corner of back wrapper of volume 21 and front wrapper of volume 22. Small repair on back wrapper of volume 22. Otherwise a very fine and clean set. Pp. 225-248" Pp. 245-249 [entire issue: Pp. 225-336" Pp. 225-336].‎

‎First printing of these two important, but for long overlooked, articles, which together constitute Hintikka's attempt to cope with Wittgenstein's elimination of identity as proposed in the ""Tractatus"". With the translation rules that Hintikka here put forward, he is the first to try to carry out Wittgenstein's suggestions systematically. The Finnish born philosopher and logician, Jaakko Hintikka (born 1929), Professor of Philosophy at the University of Boston, is generally accepted as the founder of formal epistemic logic and of game semantics for logic. He has contributed seminally to the fields of philosophical and mathematical logic, philosophy of mathematics and science, language theory and epistemology. Independently of Evert Willem Beth he discovered the semantic tableau, and he is famous for his work on game semantics and logical quantifiers. In 2005 Hintakka was awarded the Schock Prize in logic and philosophy, the philosophical equivalent to the Nobel prize, ""for his pioneering contributions to the logical analysis of modal concepts, in particular the concepts of knowledge and belief "". In the 1950'ies Hintikka took it upon himself to follow Wittgentein's suggestion of elimination of identity suggested in the ""tractatus"", and in the two offered articles, he succeeds in constructing a logic without identity. The main point of the two connected articles is to show that variables can be used in two ways. One way does not exclude coincidences of the values of different variables (inclusive interpretation of variables), the other does (exclusive interpretation of variables) and can be either weakly or strongly exclusive. He now claims that in the ""Tractatus"" Wittgenstein adopts the weakly exclusive interpretation of variable and then proves that the weakly exclusive quantifiers are able to express everything that the inclusive quantifiers plus identity can express, and without a sign for identity, - for the first time systematically supporting Wittgenstein's claim that identity is not an essential constituent of logical notation. ""There are a number of references to the exclusive interpretations of variables in current logical literature. An exclusive reading of variables was, in effect, suggested by Ludwig Wittgenstein in ""Tractatus logico-philosophicus. As far as I know, however, no one has previously tried to carry out his suggestions systematically. Several misconceptions seem to be current concerning the outcome of an attempts of this kind. Carnap expects radical changes in the rules of substitution. If I am not mistaken, however, at least one form of the exclusive interpretation may be formalized by making but slight alterations in the axioms and/or in the transformation rules of the predicate calculus. Also I hope to say that it is not correct to say (as Russell has done) that Wittgenstein tried to dispense with the notion of identity. What a systematic use of an exclusive reading of variables amounts to is a new way of coping with the notion of identity in a formalized system of logic. Under the most natural formalization of the new interpretations, the resulting system is equivalent to the old predicate calculus (with identity): every formula of the latter admits of a translation into the former, and vice versa."" (Vol. 21, Nr. 3, p. 228).""A deviation from standard English. Recent discussion serves to bring out, amply and convincingly, the utility of observing the ordinary correct use of words and phrases for the purpose of clearing up philosophical problems. In this paper, I shall endeavour to show, by means of an example, that the reverse method may have its interest, too. "" (Vol. 21, Nr. 3, p. 225). ""This note is a sequel to the previous paper of mine which was entitled ""Identity, variables, and impredicative definitions"" and published in this JOURNAL, vol. 21 (1956, pp. 225-245. That early paper served to call attention to the dependency of the set-theoretic paradoxes on the interpretation of the variables that may occur in the critical ""abstraction principle"". (Vol. 22, Nr. 3, p. 245).Besides these two articles, the two issues also include other important articles within logic, e.g. Quine, ""Unification of Universes in Set Theory"" and Symonds and Chisholm ""Inference by Complementary Elimination"".‎

‎Identity, Variables, and Impredicative Definitions - [HINTIKKA'S TRANSFORMATION RULES]‎

‎(No place), The Association for Symbolic Logic, Inc., 1956. Lev8vo. Bound in two uniform red half cloth with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 21. Barcode label pasted on to back boards. Small library stamp to lower part of 5 pages. A very fine copy. Pp. 225-248"" [Entire volume: (4), 426 pp]‎

‎First printing of this important, but for long overlooked, paper, which together constitute Hintikka's attempt to cope with Wittgenstein's elimination of identity as proposed in the ""Tractatus"". With the translation rules that Hintikka here put forward, he is the first to try to carry out Wittgenstein's suggestions systematically.In 1957 Hintikka published ""Vicious Circle Principles and the Paradoxes"", also in Journal of Symbolic Logic, in which he introduced the the ""abstraction principle"".The Finnish born philosopher and logician, Jaakko Hintikka (born 1929), Professor of Philosophy at the University of Boston, is generally accepted as the founder of formal epistemic logic and of game semantics for logic. He has contributed seminally to the fields of philosophical and mathematical logic, philosophy of mathematics and science, language theory and epistemology. Independently of Evert Willem Beth he discovered the semantic tableau, and he is famous for his work on game semantics and logical quantifiers. In 2005 Hintakka was awarded the Schock Prize in logic and philosophy, the philosophical equivalent to the Nobel prize, ""for his pioneering contributions to the logical analysis of modal concepts, in particular the concepts of knowledge and belief "". In the 1950'ies Hintikka took it upon himself to follow Wittgentein's suggestion of elimination of identity suggested in the ""tractatus"", and in the two offered articles, he succeeds in constructing a logic without identity. The main point of paper is to show that variables can be used in two ways. One way does not exclude coincidences of the values of different variables (inclusive interpretation of variables), the other does (exclusive interpretation of variables) and can be either weakly or strongly exclusive. He now claims that in the ""Tractatus"" Wittgenstein adopts the weakly exclusive interpretation of variable and then proves that the weakly exclusive quantifiers are able to express everything that the inclusive quantifiers plus identity can express, and without a sign for identity, - for the first time systematically supporting Wittgenstein's claim that identity is not an essential constituent of logical notation. ""There are a number of references to the exclusive interpretations of variables in current logical literature. An exclusive reading of variables was, in effect, suggested by Ludwig Wittgenstein in ""Tractatus logico-philosophicus. As far as I know, however, no one has previously tried to carry out his suggestions systematically. Several misconceptions seem to be current concerning the outcome of an attempts of this kind. Carnap expects radical changes in the rules of substitution. If I am not mistaken, however, at least one form of the exclusive interpretation may be formalized by making but slight alterations in the axioms and/or in the transformation rules of the predicate calculus. Also I hope to say that it is not correct to say (as Russell has done) that Wittgenstein tried to dispense with the notion of identity. What a systematic use of an exclusive reading of variables amounts to is a new way of coping with the notion of identity in a formalized system of logic. Under the most natural formalization of the new interpretations, the resulting system is equivalent to the old predicate calculus (with identity): every formula of the latter admits of a translation into the former, and vice versa."" (Vol. 21, Nr. 3, p. 228).""A deviation from standard English. Recent discussion serves to bring out, amply and convincingly, the utility of observing the ordinary correct use of words and phrases for the purpose of clearing up philosophical problems. In this paper, I shall endeavour to show, by means of an example, that the reverse method may have its interest, too. "" (Vol. 21, Nr. 3, p. 225). ""This note is a sequel to the previous paper of mine which was entitled ""Identity, variables, and impredicative definitions"" and published in this JOURNAL, vol. 21 (1956, pp. 225-245. That early paper served to call attention to the dependency of the set-theoretic paradoxes on the interpretation of the variables that may occur in the critical ""abstraction principle"".‎

‎Analyse infinitésimale à l'usage des ingénieurs - 2 volumes (complet) - Tome 1. Calcul différentiel : Dérivées et différentielles, Changements de variables, Séries, Formule de Taylor, Courbes planes et gauches, Surfaces congruences, Complexes, Lignes tracées sur les surfaces - Tome 2. Calcul intégral : Intégrales définies et indéfinies, Séries de Fourier, Fonctions elliptiques, Equations différentielles ordinaires et aux dérivées partielles, Calcul des variations‎

‎Gauthier-Villars et Fils, à Paris , Encyclopédie Industrielle Malicorne sur Sarthe, 72, Pays de la Loire, France 1902 Book condition, Etat : Bon relié, demi-basane vert foncé à 4 faux-nerfs, titre et tomaison dorés au dos (2 volumes homogènes) grand In-8 2 vol. - 1424 pages‎

‎95 figures dans le texte au total des deux volumes 1ere édition, 1900-1902 Contents, Chapitres : Tome 1 (1900). Préface, erratum, viii, Texte, 557 pages, 45 figures dans le texte - Tome 2 (1902). Préface, errata, xi, Texte, 848 pages, 50 figures dans le texte - Tome 1. Objet de l'analyse infinitésimale - Les fonctions continues - Propriétés des dérivées - Les règles de dérivation - La différentielle - Dérivées et différentielles d'ordre supérieur au premier - Les fonctions implicites - Changement de variables - Les séries numériques - Formules de Talor et de Laclaurin - Formules de Taylor et de McLaurin pour les fonctions de plusieurs variables - Formes indéterminées - Maxima et minima - Séries de fonctions, séries entières - Courbes planes - Contact et enveloppes, osculation et courbure - Courbes gauches, surfaces, congruences, complexes de droites - Lignes tracées sur les surfaces - Tome 2. Des intégrales indéfinies - Des intégrales définies - Applications géométriques - Intégrales triples, multiples, application aux volumes, centres de gravité, moments d'inertie - Formule de Green, potentiel - Fonctions elliptiques - Equations différentielles de premier order et de second à deux variables - Equations différentielles d'ordre quelconque à deux variables, cas d'abaissement - Equations linéaires d'ordre quelconque - Equations différentielles simultanées - Equations aux dérivées partielles du premier ordre - Equations aux dérivées partielles du second ordre - Calcul des variations - Eugène Rouché est un mathématicien français, né le 18 août 1832 à Sommières (Gard) et mort le 19 août 1910 à Lunel (Hérault). Ancien élève de l'École polytechnique (X1852), il est professeur de mathématiques au lycée Charlemagne, à l'École centrale et examinateur dadmission à l'École polytechnique. Il est l'auteur du théorème de Rouché en analyse complexe, publié dans le Journal de l'École polytechnique (1862). Il a été élu à l'Académie des Sciences en 1896. bon exemplaire, complet en 2 tomes homogènes de la première édition de 1900-1902, les dos sont élégants et propres, à peine frottés au bas sans aucune gravité, légère épidermure discrète sur le bord droit du plat inférieur du tome 1 (bord du dos), discrète, coin supérieur gauche du plat inférieur un peu frotté, intérieur sinon frais et propre, papier légèrement jauni, une signature avec un cachet de particulier sur la page de titres du tome 2, infimes déchirures sans manques sur le bord de 3-4 pages, très léger, un feuillet à peine décalé au centre du tome 2 mais bien solidaire de la reliure, cela reste un bon ensemble complet de cet ouvrage très détaillé sur l'analyse infinitésimale avec ses deux facettes, calcul différentiel et calcul intégral - NB : L'ensemble pèse plus de 3 kilos, il peut y avoir des frais de port additionnels selon les destinations‎

‎Variables. ‎

‎Paris, Émile-Paul Frères, 1929 ; in-8, 216 pp., broché, couverture à rabats. Un des 1500 exemplaires numérotés, sur papier vélin. Ecrivain français, né à Marseille, en 1868., compagnon de Romain Rolland à la rue d'Ulm. Il est l'un des fondateurs de la "Nouvelle Revue Française". Il fut pourchassé par les Allemands pendant la Seconde Guerre mondiale. Il est un des écrivains trop méconnus de la première moitié du 20ème siècle. Il a influencé les écrivains de son époque et a été ami avec beaucoup de peintres et musiciens de son temps. Ses biographies le rapprochent d'un Zweig français. Très bon état.‎