Psychology Dictionary of ArgumentsHome
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| Continuum: The continuum in mathematics is a compact, connected, metric space. It is a mathematical concept that captures the idea of a continuous, unbroken whole. The real numbers, for example, are a continuum. See also Real numbers, Continuum hypothesis, Compactness._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||
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W.V.O. Quine on Continuum - Dictionary of Arguments
XIII 45 Def Discrete/Discreteness/Quine: an order of numbers or other objects is discrete if each object has an immediate predecessor or successor or both. For example, the integers are discrete. One the other hand: Def dense: fractions are dense and not discrete. Real numbers: are more than dense: they are continuous. Discrete/continuous: here we compare them as opposites. Discreteness: we need it to learn to count by distinguishing the objects. Irrational Numbers/Cantor: Theorem: most will always escape us. Number Theory: deals with integers. Real numbers: are used by the sciences. The contrast of both is illuminated by a pair of theorems: Goedel's Theorem: no proof procedure can encompass all truths of elementary number theory. Tarski's theorem: truth in the parallel theory of real numbers can be checked routinely, e.g. by a computer. N.B.: both systems are identical in their notation! The difference lies in the different interpretation of the variables (or their domains, one time the positive integers with the 0, the other time the positive real numbers with the 0). XIII 47 This leads to a difference in the truth of the formulas! a) real numbers: here the true formulas are a set that can be handled b) elementary number theory: not here. Continuity/Discreteness/Language/Quine: the interaction of the two terms is not limited to mathematics, it also exists in language: phonemes impose discreteness on the phonetic continuum. Discreteness/Quine: also allows yellowed or damaged manuscripts to be returned to a fresh state. The discreteness of the alphabet helps that the small deviations (e.g. yellowing) add up to larger ones. Continuum/Continuity: images, on the other hand, are a continuous medium: i.e. there are no standards for repairing a damaged copy or correcting a poor copy. Technology: here discreteness is often combined with continuity. Example clock: it should give the impression of moving continuously. XIII 48 Film/Quine: Continuity here is due to the weakness of our perception. Similar to the clock or our thinking about atoms over the millennia. Planck time/Quine: here we have the next approach of nature to continuity._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, , Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, , Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, , Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, , Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, , Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, , Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, , Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, , Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, , Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
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