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articles in english
1. Proceedings of the XXII World Congress of Philosophy: Volume > 41
Joongol Kim Numbers, Quantities and Hume’s Principle
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This paper argues against neo-Fregeans that Frege was right to conclude that we cannot obtain the concept of number from Hume's Principle. Neo-Fregeans have claimed that Hume's Principle is analytic since it can be viewed as an implicit definition of the concept of cardinal number. But it will be shown that if taken as an implicit definition, Hume's Principle is satisfied not just by the concept of number but also by the concept of discrete quantity, and hence it cannot be viewed as an implicit definition of the concept of cardinal number as distinct from the concept of discrete quantity.
2. Proceedings of the XXII World Congress of Philosophy: Volume > 41
Woosuk Park Isn’t the Indispensability Argument Necessarily Analogical?
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Both the defenders and the challengers of the indispensability argument seem to ignore the obvious fact that it is meant to be an analogical inference. In this note, I shall draw attention to this fact so as to avoid unnecessary confusions in any future discussion of the indispensability argument. For this purpose, I shall criticize Maddy’s version of the indispensability argument. After having noted that Quinean holism does not have to be one of the necessary premises, I shall suggest alternative formulations of the indispensability argument as an analogical inference. Also, some further reflections on how to evaluate Maddy’s objections to the indispensability argument will be in due order.
3. Proceedings of the XXII World Congress of Philosophy: Volume > 41
AhtiVeikko Pietarinen Why Pragmaticism is Neither Mathematical Structuralism nor Fictionalism
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Despite some surface similarities, Charles Peirce’s philosophy of mathematics, pragmaticism, is incompatible with both mathematical structuralism and fictionalism. Pragmaticism has to do with experimentation and observation concerning the forms of relations in diagrammatic and iconic representations ofmathematical entities. It does not presuppose mathematical foundations although it has these representations as its objects of study. But these objects do have a reality which structuralism and fictionalism deny.
4. Proceedings of the XXII World Congress of Philosophy: Volume > 41
Donald V. Poochigian Mathematical Identity: The Algebraic Unknown Number and Casuistry
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David Hilbert’s distinction between mathematics and metamathematics assumes mathematics is not metamathematics, cardinality of mathematics is less than cardinality of metamathematics, and metamathematics contains mathematics. Only by abandoning the last renders these characteristics consistent. Every set identifiable only in a metaset, following Kurt Gödel, the metaset is convertible into the set by translation of its constituents into constituents of the set, rendering the set indistinguishable from the metaset. Reversing Kurt Gödel, the set is convertible into the metaset by translation of its constituents into constituents of themetaset, rendering the set indistinguishable from the metaset. Set being indistinguishable from metaset, the set of mathematics is unidentifiable as constituent of the set of metamathematics. Only inductively by exclusive resolution of all constituents of the set of all disjunctives of the sets of mathematics and metamathematics is the set of mathematics identifiable. Generated is endless arbitrary qualification of mathematical identity exhibited in continual proofsof its axioms. Understood as clarification, when everything is unique, no concealed contradiction is contained. Constituted is the endless non-repeating digit to the left of the decimal of an algebraic unknown number. Manifest is casuistry, now neither objective nor specious identity, but instead necessary subjective identity distinguishing sets.
5. Proceedings of the XXII World Congress of Philosophy: Volume > 41
Andrei Rodin Category Theory and Mathematical Structuralism
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Category theory doesn't support Mathematical Structuralism but suggests a new philosophical view on mathematics, which differs both from Structuralism and from traditional Substantialism about mathematical objects. While Structuralism implies thinking of mathematical objects up to isomorphism the new categorical view implies thinking up to general morphism.
6. Proceedings of the XXII World Congress of Philosophy: Volume > 41
Milan Tasic On What Should be Before All in the Philosophy of Mathematics
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In the philosophy of mathematics, as in its a meta-domain, we find that the words as: consequentialism, implicativity, operationalism, creativism, fertility, … grasp at most of mathematical essence and that the questions of truthfulness, of common sense, or of possible models for (otherwise abstract) mathematical creations,i.e. of ontological status of mathematical entities etc. - of second order. Truthfulness of (necessary) succession of consequences from causes in the science of nature is violated yet with Hume, so that some traditional footings of logico-mathematical conclusions should equally be falled under suspicion in the last century. We have in mind, say, strict-material implication which led the emergence of relevance logics, or the law of excluded middle that denied intuitionists i.e. paraconsistent logical systems where the contradiction is allowed, as well as the quantum logic which doesn't know, say, the definition of implication etc. Kant's beliefs miscarried hereafter that number (arithmetic) and form (geometry) would bring a (finite) truth on space and time, when they revealed relative and curvated, just as it is contradictory essentially understanding of basic phenomena in the nature: of light as an unity of wave – particle, or that both "exist" and "don't exist" numbers as powers of sets between 0א and c (the independence of continuum hypothesis) etc. Mathematical truths are ''truths of possible worlds'', in which we have only to believe that they will meet once recognizable models in reality. At last, we argue in favour of thesis that a possible representing "in relief" of mathematical entities and relations in the "noetic matter" (Aristotle) would be of a striking heuristic character for this science.
7. Proceedings of the XXII World Congress of Philosophy: Volume > 41
Alfred A. Vichutinsky Of a Real Philosophy and the Natural Sciences Free of the Paranoia
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The bases of tenets of the World came from the East; Pythagoras learnt all there up the 26 years. At a home, the east ideas where took in no; then he bound the mathematics with the elements of matter. This was the best way to a blood feud of the all Humanity. The 17th age gave the bases of mathematics and the Greek atomism; this had led to the paranoia in all sciences. The LCE was brought in 19th age with bases no; really it was the box of Pandora in the form of wrong sciences of the Nature. The wise revenge of Pythagoras was in the form of riddle for the best thinkers in the World in all times; us solved one in the 50th years. A base of the World is of the material space (MS) with praatoms (PAs) Ao; they are of the affinity to matter. A density of the MS is of ~ 5.10‐6 kg/m3 close to the Ears. PA Ao is of quant of matter and antimatter; they are of rotate in the different sides. All matter takes up Ao and to grow. In the giant stars to go the bursts giving Ao, or caloric. The matter of being in the World on base of the key law of conservation of heat (caloric) and matter by loss of energy; it is main. Leibniz offered to the conservation of mv2 in the World. But Newton knew that any move is damped, and it need in filled up. This the author proved by tests over the 300 years just. D.Bernoulli given to the model of gas. I. Kant proved that mv2 is the quantity of heat by stop of the body; it is no the energy! A key leitmotiv of thought is blocked the grasp of facts if ones not leaded to an accepted concept. P. Mayer had the blunder in base of the LCE; a work of gas expansion in Torricelli tube is equal nil strong! This is the gross blunder of a sick paranoiac! The 21 age gave up a new philosophy and a way to endless engine. The super skills from ideal quartz with moving jaws to respond to the all new philosophy and sciences.
articles in russian
8. Proceedings of the XXII World Congress of Philosophy: Volume > 41
Vitali Tselishchev Intuition and Reality of Signs
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The progress in computer programming leads to the shift in traditional correlation between intuitive and formal components of mathematical knowledge. From epistemological point of view the role of intuition decreases in compare with formal representation of mathematical structures. The relevant explanation is to be found in D. Hilbert’s formalism and corresponding Kantian’s motives in it. The notion of sign belongs to both areas under consideration: on the one hand it is object of intuition in Kantian de re sense, on the other hand, it is part of formal structure. Intuitive mathematical knowledge is expressed by primitive recursive reasoning. The W. Tait’s thesis, namely, that finitism as methodology of mathematics is equivalent to primitive recursive reasoning is discussed in connection with some explications of Kantian notion of intuition. The requirements of finitism are compared with normative role of logic.
9. Proceedings of the XXII World Congress of Philosophy: Volume > 41
А. Ж. Жафяров Формирование Вариативного И Творческого Мышления Учащихся На Основе Решения Математических Задач С Параметрами
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Practically all the countries require the highly skilled staff. It is natural, that it is necessary to prepare them in higher educational institutions. In many high schools students were enlisted and are enlisted on the basis of knowledge and skills. It not an optimum variant because the second integrated parameter of an entrant, his mental potential and fundamentality of knowledge, is not taken into account. The specified very important parameter of an entrant is opened in the best way with sums with parameters, that is sums with parameters serve some kind of a litmus piece of paper in definition of quality of the future student. It is the first reason to increase in number of sums with parameters on entrance examinations. The second, not less important reason, is connected with the following:these sums promote better development of the personality of a pupil, its individual propensities and abilities; they help to learn to work in conditions of small and significant uncertainties which are in abundance in our today's life. They develop variative and creative thinking and by those promote development of intelligence and increase of a level of fundamentality of knowledge. Existing textbooks and educational supplies do not contain adequate volume of a material doing of mathematical sums with parameters: there is no system, there are only separate examples, some of them are rather unsuccessful. The author leads ordering of sums with parameters, the technique of doing such sums is developed and corresponding educational supplies on paper and electronic carriers are published.
articles in chinese
10. Proceedings of the XXII World Congress of Philosophy: Volume > 41
FangWen Yuan Query the Triple Loophole of the Proof of Gödel Incompleteness Theorem
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Kurt Godel’s “Incompleteness Theorem” is generally seen as one of the three main achievements of modern logic in philosophy. However, in this article, three fundamental flaws in the theorem will be exposed about its concept, judgment and reasoning parts by analyzing the setting of the theorem, the process of demonstration and the extension of its conclusions. Thus through the analysis of the essence significance of the theorem, I think the theorem should be classified as "liar paradox" or something like that. Therefore, the theorem is not reliable and then the content of the theorem itself is questionable. At the same time, please note, the root of the problem exposed in Godel's “Incompleteness Theorem” is a typical example o f existing loopholes in traditional logic.