The Concept of Model: An Introduction to the Materialist Epistemology of Mathematics
re.press, 2007 - 182 من الصفحات
The Concept of Model is the first of Alain Badiou’s early books to be translated fully into English. With this publication English readers finally have access to a crucial work by one of the world’s greatest living philosophers. Written on the eve of the events of May 1968, The Concept of Model provides a solid mathematical basis for a rationalist materialism. Badiou’s concept of model distinguishes itself from both logical positivism and empiricism by introducing a new form of break into the hitherto implicated realms of science and ideology, and establishing a new way to understand their disjunctive relation. Readers ...
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Alain Badiou Althusser Althusser’s Althusserian apparatus articulation axiom of choice axiomatic Bachelard Carnap category of model closed formula Concept de modèle Concept of Model consistent construction critique deduction theorem definition demonstration dialectic Dialectical Materialism discourse distinction domain effect element ematical epistemological break Event example exists experimental fact formal system free variable given Gödel Hilbert ideology individual constant infinity-point inscription insofar interpretation Jacques-Alain Miller Justin Clemens L-valid Lacan Lévi-Strauss Logiques des mondes marks Marque et manque material math mathematical logic Michel Serres model theory notion object ontology operation Paris particular philosophy Platonism political pose positivist practice precisely predicate presentation production pure multiplicity purely logical quantifier question relation representation rules of deduction schema scientific semantic set theory situation statement structure subset suture syntactic syntax theorem thesis thought tion trans translated truth procedures universe valid void well-formed expressions word model
الصفحة xliv - The chief defect of all hitherto existing materialism — that of Feuerbach included — is that the thing, reality, sensuousness, is conceived only in the form of the object or of contemplation, but not as human sensuous activity, practice, not subjectively.
الصفحة lvii - The object of philosophy is the logical clarification of thoughts. Philosophy is not a theory but an activity. A philosophical work consists essentially of elucidations. The result of philosophy is not a number of 'philosophical propositions,' but to make propositions clear.
الصفحة liv - The unity of all science consists alone in its method, not in its material. The man who classifies facts of any kind whatever, who sees their mutual relation and describes their sequences, is applying the scientific method and is a man of science.
الصفحة xxix - Math. Ann., Vol. 50. THE FIVE GROUPS OF AXIOMS. 1. THE ELEMENTS OF GEOMETRY AND THE FIVE GROUPS OF AXIOMS. EiT us consider three distinct systems of things. The things composing the first system, we will call points and designate them by the letters A, B, C, . . . .; those of the second, we will call straight lines and designate them by the letters a, b, c, . . . . ; and those of the third system, we will call planes and designate them by the Greek letters a...
الصفحة xxviii - If one is looking for other definitions of a 'point', eg through paraphrase in terms of extensionless, etc., then I must indeed oppose such attempts in the most decisive way; one is looking for something one can never find because there is nothing there; and everything gets lost and becomes vague and tangled and degenerates into a game of hide and seek" (p. 39). This is an allusion to definitions like Euclid's "a point is that which has no parts.
الصفحة lvii - Philosophy is not one of the natural sciences. (The word " philosophy " must mean something which stands above or below, but not beside the natural sciences.) 4.112 The object of philosophy is the logical clarification of thoughts.
الصفحة 16 - For, though many models may be used as convenient devices to describe and explain the phenomena, it is obvious that the best model will always be that which is true, that is, the simplest possible model which, while being derived exclusively from the facts under consideration, also makes it possible to account for all of them.
الصفحة xxxviii - Its value will vary according to the amount stamped upon it and according to its use inside or outside a political boundary. This is even more true of the linguistic signifier, which is not phonic but incorporeal — constituted not by its material substance but by the differences that separate its sound-image from all others.
الصفحة 10 - Second, for any given model there should be a possibility of ordering a series of transformations resulting in a group of models of the same type. Third, the above properties make it possible to predict how the model will react if one or more of its elements are submitted to certain modifications.
الصفحة xx - I had entered yesterday, that is, proceed by casting aside all that admits of the slightest doubt, not less than if I had discovered it to be absolutely false; and I will continue always in this track until I shall find something that is certain, or at least, if I can do nothing more, until I shall know with certainty that there is nothing certain.