<ul><li><p>Russell's Paradox and Others by W. V. QuineReview by: C. A. BaylisThe Journal of Symbolic Logic, Vol. 7, No. 1 (Mar., 1942), p. 44Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2267567 .Accessed: 17/06/2014 18:27</p><p>Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp</p><p> .JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].</p><p> .</p><p>Association for Symbolic Logic is collaborating with JSTOR to digitize, preserve and extend access to TheJournal of Symbolic Logic.</p><p>http://www.jstor.org </p><p>This content downloaded from 185.2.32.141 on Tue, 17 Jun 2014 18:27:06 PMAll use subject to JSTOR Terms and Conditions</p><p>http://www.jstor.org/action/showPublisher?publisherCode=aslhttp://www.jstor.org/stable/2267567?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp</p></li><li><p>44 REVIEWS </p><p>of 'empirical' descriptive terms. Interpreted in this way, the definitions of analyticity and apriority obviously do not entail the equivalence of these concepts. There might exist true sentences which are a priori on the ground that they do not contain any 'empirical' descriptive terms and which yet are not analytic. </p><p>The author's distinction between 'analytic' and 'axiomatic' interpretation of mathe- matical axioms is not clear. If a set of axioms contains n extra-logical constants, e.g., 'zero,' 'number,' ... , we may form an explicit definition of the class C of all ordered n-tuples which satisfy the same condition that the axioms impose upon the given n-tuple, zero, number, </p><p>(This explicit definition defines a class to which the original n-tuple belongs, not that n-tuple itself.) To each mathematical theorem there then corresponds a theorem of logic to the effect that if any n-tuple belongs to C, then it also satisfies the condition which the theorem imposes upon the n-tuple, zero, number, - - - . If a set of axioms is at all a defini- tion, it is an 'implicit definition' in the author's sense. </p><p>The logical and mathematical relativism expressed by the author seems to rest on a fallacy. Obviously, no formal system can be characterized as logical truth except under a certain interpretation. Now it is true that the axioms determine the possible meanings of the symbols occurring in them, in the sense that a certain isomorphism must obtain between the formal structure of the axioms and any possible true interpretation. But this also conversely implies that only certain systems of axioms can be interpreted as expressing a given segment of logical truth. Variety of expression seems to be the only relativity of which logical truth is capable-but such relativity belongs to all truth. </p><p>The third and last chapter, 'The Empirical Truth of a Theory,' treats the nature and verification of statements about reality. An interesting point is the explicit definition that is suggested for 'disposition predicates.' Let 'Q(x),' 'P(x),' and 'R(x)' abbreviate respectively 'x is an electric conductor,' 'x is connected with a closed electric current,' and 'x makes a magnetic needle swing.' Carnap, in Testability and meaning (II 49), has pointed out the following problem. Using the 'if ... then - *- ' of ordinary discourse, we would unhesitatingly say that 'Q(x)' means the same as 'if P(x) then R(x),' and yet it is obviously impossible to define 'Q(x)' by 'P(x) -* R(x).' Kaila now suggests the fol- lowing explicit definition: </p><p>Q(x) = (3S)IS(x) & (3y)[S(y) & P(y)] & (y) [S(y) & P(y) -, R(y)]}. </p><p>However, if P(x) -+ R(x) is allowed as a possible value for S(x), then Q(x), according to this definition, would still be equivalent to P(x) -+ R(x) provided (3y) [P(y) & R(y)]. It would seem, therefore, that Kaila must have had in mind some restriction upon the range of S. He must have thought that those x's for which P(x) and R(x), have some 'intrinsic' property that distinguishes them from the x's for which P(x) and ,-R(x). The range of S </p><p>consists of 'intrinsic' properties, while P(x) -* R(x) is not 'intrinsic.' Provided that we ould define in a precise manner what properties are 'intrinsic,' Kaila's definition would </p><p>Cllow us to dispense with Carnap's 'reduction sentences.' ANDERS WEDBERG a </p><p>W. V. QUINE. Russell's paradox and others. Technology review, vol. 44 (1941-2), pp. 16-17. </p><p>Quine points out that Russell's paradox about the class of all non-self -membered classes, and allied cases such as the barber that shaves all and only those who do not shave themselves, and the adjective that denotes all and only those adjectives that do not denote themselves, all violate the law: 'No member of (a class) C bears (the relation) R to exactly the members of C that do not bear R to themselves.' He remarks that sundry makeshift remedies pro- vide 'one or another modified relation to supplant the naive relation of class to member.' </p><p>C. A. BAYLIS </p><p>BEPPO LEVI. La noci6n de dominoo deductive' como element de orientaci6n en las cuestiones de fundamentos de las teorias matemdticas. Publicaciones del Instituto de Ma- tematica (Rosario, Argentina), vol. 2 (1940), no. 9, pp. 177-208. </p><p>The author asserts that the notion of natural number, of real number, and of function are, despite past attempts at definition, really 'primitive ideas' and 'simple intuitions.' The </p><p>This content downloaded from 185.2.32.141 on Tue, 17 Jun 2014 18:27:06 PMAll use subject to JSTOR Terms and Conditions</p><p>http://www.jstor.org/page/info/about/policies/terms.jsp</p><p>Article Contentsp. 44</p><p>Issue Table of ContentsThe Journal of Symbolic Logic, Vol. 7, No. 1 (Mar., 1942), pp. i-iv+1-48Volume Information [pp. i-iii]Front MatterErrata [p. iv-iv]The Burali-Forti Paradox [pp. 1-17]New Sets of Postulates for Combinatory Logics [pp. 18-27]A Formal Theorem in Church's Theory of Types [pp. 28-33]A Correction to the Sentential Calculus of Tarski's Introduction to Logic [p. 34]ReviewsReview: untitled [pp. 35-37]Review: untitled [p. 38]Review: untitled [pp. 38-39]Review: untitled [p. 39]Review: untitled [p. 39]Review: untitled [pp. 39-40]Review: untitled [pp. 40-41]Review: untitled [p. 41]Review: untitled [p. 42]Review: untitled [p. 42]Review: untitled [p. 42]Review: untitled [p. 43]Review: untitled [pp. 43-44]Review: untitled [p. 44]Review: untitled [pp. 44-45]Review: untitled [p. 45]Review: untitled [p. 45]Review: untitled [p. 46]Further Citations [p. 46]</p><p>Seventh Meeting of the Association for Symbolic Logic [pp. 47-48]</p></li></ul>
“[Quine] is at once the most elegant expounder of systematic logic in the older, pre-Gödelian style of Frege and Russell, the most distinguished American recruit to logical empiricism, probably the contemporary American philosopher most admired in the profession, and an original philosophical thinker of the first rank… The title essay of Quine’s The Ways of Paradox is a beautifully concise survey of the nature and significance of paradoxes… In general Quine’s style combines a certain rotundity of utterance with a verbal wit that exploits the submerged associations and resonances of technical terms.”—Anthony Quinton, The New York Review of Books
Extensively on ontology perhaps more than on any other specific philosophical subject. The second main theme is ontological reduction: How can an ontol. Logical program and set up its main bases. Quine has concerning this ontology, deriving from the paradoxes of set. The Ways of Paradox and Other Essays. Quine ways of paradox and other essays. Essay the politics of housework essay ecomm umk evaluation essay writing essays in english language and linguistics pdf essay why obama should be president lionel duroy vertiges critique essay nats 1775 essay writer isagoge in artem analytical essay the impossible dream man of la mancha analysis.
“The remarkable feature of this collection of essays is the achievement of profundity without the sacrifice of clarity. More than a clear, concise, nonmathematical presentation of logical perplexities and problems, this work is one written so that any intelligent layman can grasp the ideas wrestled with by Quine and other leading logicians. The manner in which the author interprets the pioneers of logical thought possesses the fascination of an exciting game rather than a dry intellectual exercise.”—William S. Sahakian, The Boston Globe
“Willard Van Orman Quine is the distinguished Harvard logician and philosopher who for more than a generation, and in prose as fresh and provocative as it is precise, has contributed fundamentally to the substance, the pedagogy, and the philosophy of mathematical logic.”--Science