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The author or concept searched is found in the following 6 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Infinity | Zeno | Thiel I 169 Infinity/Zeno/Thiel: Problem of infinitely small quantities. Could a series of infinitely many points linked to each other be produced? Zeno of Elea (5th century BC). It is precisely because of the possibility of an infinite number of divisions that we cannot build the entire route "from the bottom". There are no first building blocks. Zeno's paradox: the arrow never arrives, it appears to never be able to leave the bow. Thiel I 170 In today's usual computational "resolution" it is preceeded as following: Achilles 5m/s, turtle 5cm/s. Lead over 15 m. The lead of the turtle is increased by 5 cm per sec but simultaneously reduced by 20 m. From 1500 + 5t 500t = 0 is obtained as the time t of the overtaking: t = 1500/495 s, slightly more than 3 seconds. Modern representations use decimal fraction notation: 3.030303 .... Vs: the essential is hidden, namely The sequence 3 + (3 divided by 102, 104, 106, etc.). This sequence can only represent a finite value. But the riddle is only repeated once again for the layman by the decimal fraction. >Paradoxes. |
T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
| Limits | Logic Texts | Sainsbury V 15ff Movement/Zenon/Paradox/Sainsbury: should prove that nothing can begin to move, to get to a point after one meter, one has to come up to the half first, etc. V 33/34 Problem: the correspondence of physical space and mathematical series. - For example, a point divides a distance, the two distance parts have no common point. Does the division point belong to one or the other? (It cannot belong to both, since they have no point in common, otherwise they would not be divided.) It is necessary to regulate this by determination. - But physically nothing can depend on a determination. Logically: we need the concept of a limit which itself does not take up space. V 36 Solution: passing the distance is sufficient, since the boundary point Z* does not belong to the series of Z-points, but Z* belongs to the area of the space corresponding to the Z-series (the preceding points). Problem: we have to assume that we have coherent concepts of space, but we get these only through these mathematical structures. Conclusion: Zenon demands a more careful elaboration of our spatial concepts. V 38 This corresponds essentially to the example of >Achilles and the turtle, cf. >Paradoxes, >Infinity. |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 Sai I R.M. Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 German Edition: Paradoxien Stuttgart 1993 |
| Motion | Logic Texts | Sainsbury V 16ff Motion/movement/Zenon/paradox/Sainsbury: should prove that nothing can begin to move, to get to a point after one meter, one has to come up to the half first, etc. V 33/34 Problem: the correspondence of physical space and mathematical series. For example, a point divides a distance, the two distance parts have no common point. Does the division point belong to one or the other? (It cannot belong to either, because they have no point in common, otherwise they would not be divided.) Must be determined by determination. But physically nothing can depend on a determination. Logically: we need the concept of a boundary which does not occupy any space itself. V 37 Solution: passing the distance is sufficient because the boundary point Z* does not belong to the Series of Z-points, but Z* belongs to the area of the space corresponding to the Z-series (of the preceding points). Problem: we have to assume that we have coherent concepts of space, but we get these only through these mathematical structures. Conclusion: Zenon requires a more careful development of our spatial concepts. V 38 This essentially corresponds to the example of >Achilles and the turtle, cf. >Paradoxes, >Infinity. |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 Sai I R.M. Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 German Edition: Paradoxien Stuttgart 1993 |
| Paradoxes | Nozick | II 276f Achilles/turtle/Carroll/Nozick: logical form: (1) If p then q (2) p. Problem: q is not yet accepted, but it is required that the following will also be accepted explicitly: (3) If (if p then q) and p, then q Regress: the additional assumption (3) (s) in addition to the modus ponens) therefore is: if (1) and (2), q. This then in turn needs an additional premise. >Regress, >Premises. II 277 Solution/tradition: Problem: confusion of premises with inference principles. Then the regress not even begins. >Inference, >Consequence. Solution / Nozick: we need to introduce a premise that has the same shape and all inferences supplies as the other assumptions that are apparently still needed - WittgensteinVs: problems of rule-following, etc. >Zeno, >About Zeno, >Rule following. |
No I R. Nozick Philosophical Explanations Oxford 1981 No II R., Nozick The Nature of Rationality 1994 |
| Terminology | Russell | ad Putnam II 133 ~ Russell: Terminology: a statement corresponds to true facts. Basic constituents of each statement are logically proper names - singular term: all expressions are singular terms. Later self-criticism: not all statements can be reduced to sense data. I XXXII(Annotation) Def Extensionality principle: no two different properties can belong to exactly the same thing ((s) but only intensional). E.g., "tall man"/"fat man" may be the same, they are just different intensions (therefore no properties)). I XVI Def Intensionality principle: to different definitions belong different terms. Def vicious circle principle/Russell: no totality can contain members that can be defined only in terms of this totality, or members which comprise this totality or presuppose it. Hintikka I 180 Def apparent variable/Russell/Hintikka: = bound variable. >Bound variable. II 46 Def "space-like"/Russell: two events are space-like if it is impossible for a body to move fast enough to be present at both events - but it can be "halfway" and perceive both as happening at the same time. Def "time-like"/Russell: two events are time-like if it is possible for a physical body to be present at both events. Borderline case: E.g. two events as part of a light beam or - E.g. an event. perception of the other event: then distance 0. Def Distance/Russell: is a physical fact which is part of the events and does not depend on the circumstances of observer. II 20 Paradox of Tristram Shandy/Russell: The retention of the axiom (that there are infinitely many time points beween two time points) leads to other paradoxes of which I call one: the paradox of Tristram Shandy. It is the reversal of the Zenonian paradox and says that the turtle can get everywhere if you give it only enough time. Tristram Shandy needed two years to list the course of the first two days of his life and complained that the material accumulated faster than he could capture it. Russell: I assert now that if he had lived his life that way further on, he would not have missed any part of his biography. For the hundredth part is written in the thousandth year, and so on. |
Russell I B. Russell/A.N. Whitehead Principia Mathematica Frankfurt 1986 Russell II B. Russell The ABC of Relativity, London 1958, 1969 German Edition: Das ABC der Relativitätstheorie Frankfurt 1989 Russell IV B. Russell The Problems of Philosophy, Oxford 1912 German Edition: Probleme der Philosophie Frankfurt 1967 Russell VI B. Russell "The Philosophy of Logical Atomism", in: B. Russell, Logic and KNowledge, ed. R. Ch. Marsh, London 1956, pp. 200-202 German Edition: Die Philosophie des logischen Atomismus In Eigennamen, U. Wolf (Hg) Frankfurt 1993 Russell VII B. Russell On the Nature of Truth and Falsehood, in: B. Russell, The Problems of Philosophy, Oxford 1912 - Dt. "Wahrheit und Falschheit" In Wahrheitstheorien, G. Skirbekk (Hg) Frankfurt 1996 Putnam I Hilary Putnam Von einem Realistischen Standpunkt In Von einem realistischen Standpunkt, Vincent C. Müller Frankfurt 1993 Putnam I (a) Hilary Putnam Explanation and Reference, In: Glenn Pearce & Patrick Maynard (eds.), Conceptual Change. D. Reidel. pp. 196--214 (1973) In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (b) Hilary Putnam Language and Reality, in: Mind, Language and Reality: Philosophical Papers, Volume 2. Cambridge University Press. pp. 272-90 (1995 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (c) Hilary Putnam What is Realism? in: Proceedings of the Aristotelian Society 76 (1975):pp. 177 - 194. In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (d) Hilary Putnam Models and Reality, Journal of Symbolic Logic 45 (3), 1980:pp. 464-482. In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (e) Hilary Putnam Reference and Truth In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (f) Hilary Putnam How to Be an Internal Realist and a Transcendental Idealist (at the Same Time) in: R. Haller/W. Grassl (eds): Sprache, Logik und Philosophie, Akten des 4. Internationalen Wittgenstein-Symposiums, 1979 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (g) Hilary Putnam Why there isn’t a ready-made world, Synthese 51 (2):205--228 (1982) In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (h) Hilary Putnam Pourqui les Philosophes? in: A: Jacob (ed.) L’Encyclopédie PHilosophieque Universelle, Paris 1986 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (i) Hilary Putnam Realism with a Human Face, Cambridge/MA 1990 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (k) Hilary Putnam "Irrealism and Deconstruction", 6. Giford Lecture, St. Andrews 1990, in: H. Putnam, Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992, pp. 108-133 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam II Hilary Putnam Representation and Reality, Cambridge/MA 1988 German Edition: Repräsentation und Realität Frankfurt 1999 Putnam III Hilary Putnam Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992 German Edition: Für eine Erneuerung der Philosophie Stuttgart 1997 Putnam IV Hilary Putnam "Minds and Machines", in: Sidney Hook (ed.) Dimensions of Mind, New York 1960, pp. 138-164 In Künstliche Intelligenz, Walther Ch. Zimmerli/Stefan Wolf Stuttgart 1994 Putnam V Hilary Putnam Reason, Truth and History, Cambridge/MA 1981 German Edition: Vernunft, Wahrheit und Geschichte Frankfurt 1990 Putnam VI Hilary Putnam "Realism and Reason", Proceedings of the American Philosophical Association (1976) pp. 483-98 In Truth and Meaning, Paul Horwich Aldershot 1994 Putnam VII Hilary Putnam "A Defense of Internal Realism" in: James Conant (ed.)Realism with a Human Face, Cambridge/MA 1990 pp. 30-43 In Theories of Truth, Paul Horwich Aldershot 1994 SocPut I Robert D. Putnam Bowling Alone: The Collapse and Revival of American Community New York 2000 Hintikka I Jaakko Hintikka Merrill B. Hintikka Investigating Wittgenstein German Edition: Untersuchungen zu Wittgenstein Frankfurt 1996 Hintikka II Jaakko Hintikka Merrill B. Hintikka The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989 |
| Zeno | Russell | Bertrand Russell Die Mathematik und die Metaphysiker 1901 in: Kursbuch 8 Mathematik 1967 13 RussellVsZenon: Zenon only made the mistake of drawing the conclusion (if he drew any conclusions at all) that because there is no state of change, the world would be in the same state at any given time. But this conclusion cannot be drawn according to Weierstrass. 15 Time: The banishment of the infinitely small quantities has peculiar consequences: e.g. there is no longer anything like a next moment. (> Time/Russell). If there are to be no infinitely small quantities, no two moments follow one another directly, but there are always other moments inbetween. Consequently there must be an infinite number of additional moments between two arbitrary moments. If the number were finite, then one would be closer to the first of the two moments and so would be the next! This is precisely where the philosophy of the infinite begins. 19 Zenon/Russell: Everyone who attacked Zenon was not right about it, because they allowed his premisses. Zenon probably invoked the assumption that the whole has more elements than a part. 20 Then Achilles must have been in more places than the turtle. And it followed that he could never catch up with them. If we allow the axiom that the whole thing has more elements than a part, Zeno's conclusion fits perfectly. The retention of the axiom leads to other paradoxes of which I call one: the paradox of Tristram Shandy. It is the reversal of the Zenonian paradox and says that the turtle can get everywhere if you give it only enough time. Tristram Shandy needed two years to list the course of the first two days of his life and complained that the material accumulated faster than he could capture it. Russell: I assert now that if he had lived his life that way further on, he would not have missed any part of his biography. For the hundredth part is written in the thousandth year, and so on. >Zeno, >Commentaries on Zeno. |
Russell I B. Russell/A.N. Whitehead Principia Mathematica Frankfurt 1986 Russell II B. Russell The ABC of Relativity, London 1958, 1969 German Edition: Das ABC der Relativitätstheorie Frankfurt 1989 Russell IV B. Russell The Problems of Philosophy, Oxford 1912 German Edition: Probleme der Philosophie Frankfurt 1967 Russell VI B. Russell "The Philosophy of Logical Atomism", in: B. Russell, Logic and KNowledge, ed. R. Ch. Marsh, London 1956, pp. 200-202 German Edition: Die Philosophie des logischen Atomismus In Eigennamen, U. Wolf (Hg) Frankfurt 1993 Russell VII B. Russell On the Nature of Truth and Falsehood, in: B. Russell, The Problems of Philosophy, Oxford 1912 - Dt. "Wahrheit und Falschheit" In Wahrheitstheorien, G. Skirbekk (Hg) Frankfurt 1996 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Best Explanation | Schiffer Vs Best Explanation | I 198 Natural language/E.g. Harvey/Analogy to us/Best explanation/Schiffer: I have an analogy to the sensory perception in mind: E.g. a quick look at a typical collie will have us believe that this being is a dog. Nevertheless, I do not believe at the same that a dog-like appearance is sufficient that something is a dog. I would not think that this animal is a dog, if it turns out to be mutant turtles. Problem: now one might assume that there is something like a conclusion to the best explanation here. Vs: does not work anyway with children. (SchifferVsPeirce, SchifferVsAbduction. Solution/Schiffer: you should trust your perceptions, as long as you do not already have contrary beliefs. |
Schi I St. Schiffer Remnants of Meaning Cambridge 1987 |
| Putnam, H. | Poundstone Vs Putnam, H. | I 95 Quark/Poundstone: are quarks counterfactual? It is impossible to observe an isolated quark. They are what would make a proton split if it could be split, but it cannot be split. I 96 Reason: the color intensity grows with increasing distance instead of diminishing. Endless energy demand. Even if it was possible to provide this energy, new particles would be produced instead of a quark. PoundstoneVsPutnam: the answer to whether these assumptions are merely complications lies not in the skies, but in our minds. I 319 Universe/Turtle/Poundstone: E.g. "The universe rests on the back of a turtle": is to say that the known universe rests on the back of an unknown turtle. We automatically determine the semantic content of "universe" such that it fits into the context of the sentence. Brains in the Vat/PoundstoneVsPutnam: we would do the same with a statement, "We are brains in a vat"! They could say: "I am that which "retort brain" means in the laboratory language". Within the retort language "laboratory language" would be a metaphysical expression without physical equivalent. I 323 Thought Experiment/PoundstoneVsPutnam: possible or impossible physical realization is of importance in thought experiments! E.g. Twin Earth: a long chemical formula would correspond to a thick, sticky mass! Therefore no confusability with our water, other mental state! The only other combination of hydrogen and oxygen (H2O2 hydrogen peroxide) is extremely unstable. Planets with ammonia atmosphere would have to be much colder. When ammonia is liquid, mercury is solid. That would be a very different world. ((s) PoundstoneVsPutnam/(s): brings a holistic argument then). I 324 PoundstoneVsPutnam: our brain is largely composed of water, i.e. we also have the meaning of water in our heads. The inhabitants of the Twin Earth would then have XYZ in their heads! I 326 Twin Earth/Putnam: every experience is ambiguous. The counterparts have made identical experiences, their neuron currents or brain states may be identical, but there is more than one reality to match. I 336 Model Theory/PoundstoneVsPutnam: a key which provides some kind of meaningful text at all will be the right one! Reason: the infinite number of theoretically possible keys. I 339 Meaning/Translation/Coding/Cryptography/Poundstone: where is it? In the message, in the key? In the consciousness of those who understand the message? PoundstoneVsPutnam: only few would argue that the meaning is in the consciousness, after all, i.e. in the mind. Extreme case: if the system puts out "iiii...", then the entire meaning lies in the key. Mostly, the meaning is divided between the text and the key. |
Poundstone I William Poundstone Labyrinths of Reason, NY, 1988 German Edition: Im Labyrinth des Denkens Hamburg 1995 |
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