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The author or concept searched is found in the following 7 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Grue | Schurz | I 219 Grue/gred/reen/Goodman/Schurz: logical form: (B: observed. G*: gred). G*: <> ((Bxt0 > Gx) u (~Bxt0 > Rx)). Sa: emerald. Sample: {a:1 ≤ i ≤ n} Then the assertions Sai u Bat0 u Gai and Sai u Bat0 u G*ai are definitionally equivalent. If we apply the inductive generalization inference for both "green" and "gred," our sample yields the two all-hypotheses H:= "All emeralds are green" and H*: = "All emeralds are gred". Problem: However, H and H* imply contradictory predictions (green versus red) for all emeralds not observed before t0. Schurz: There is the following connection to subjective inductive permutability assumptions: for regular probability functions the permutability assumption cannot be valid for a predicate (Gx) and its pathological counterpart (G*) at the same time. Question: What criteria should we use to decide which predicates we consider to be exchangeable or inductively projectable? Many criteria have been proposed and proved to be unsuitable. Carnap: (1947(1),146, 1976(2), 211): Thesis: only qualitative predicates are inducible (projectable) "grue" is a Def "positional" predicate/Carnap, i.e. a predicate that in its definition refers to time t0. Ex grue. Def qualitative predicate/Carnap: has no definitional reference to individual constants. GoodmanVsCarnap: (Goodman 1955/75(3), 105): Problem of language dependence (sic: dependence): By mutual redefinition one can pass from our language (with "green" and "red") to a language equivalent in expressive power, in which "gred" and "reen" (G*x, R*x) function as basic terms (basic predicates): Language L (Gx,Rx primitive) Definitions in L G*x: <> ((Bxt0 > Gx) u (~Bxt0 > Rx)) R*x: <> ((Bxt0 > Rx) u (~Bxt0 > Gx)) Language L* (G*x, R*x primitive) Definitions in L* Gx: <> ((Bxt0 > G*x) u (~Bxt0 > R*x)) Rx: <> ((Bxt0 > R*x) u (~Bxt0 > G*x)). Solution/Schurz: One can distinguish between qualitative and positional predicates language-independently with respect to ostensive learnability! (s) Properties dependent on a future time cannot be shown). I 220 GoodmanVsInduction/Schurz: but this still does not answer why induction should be based on qualitative and not on positional predicates. Induction consists in extending patterns previously observed as constant into the future. In order to formulate induction rules in a meaningful way, we need to know what remained constant! And that depends on qualitative features. Positional features are pseudo-features. Pointe: That individuals are "constant" "grot" means that they change their color from green to red at t0. In this case we have done "anti-induction" and not induction. This is the reason why we have (with Carnap) for induction rules basic predicates for qualitative and not positional features. 1. Carnap, R. "On the Application of Inductive Logic", Philosophy and Phenomenological Research 8, 133-147. 2. Carnap, R. (1976). Einführung in die Philosophie der Naturwissenschaft, 3. Aufl. München: Nymphenburger. (Engl. Orig. 1966). 3. Goodman, N. (1955/75) Tatsache, Fiktion, Voraussage, Frankfurt/M.: Suhrkamp. Engl, Orig. Fact, Fiction and Forecast (1955). |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Humanities | Gadamer | I 9 Humanities/"Geisteswissenschaften"/Tradition/Gadamer: The word "Geisteswissenschaften" has become established primarily through the translator of John Stuart Mill's logic. In his work, Mill seeks to begin by sketching the possibilities of applying induction logic to the moral sciences. The translator says humanities(1). >Humanities/Mill. I 10 GadamerVsTradition/GadamerVsMill/GadamerVsHume/GadamerVsInduction: But now the real problem that the humanities pose to thinking is that one has not correctly grasped the essence of the humanities when one measures them by the yardstick of progressive knowledge of regularity. The experience of the social-historical world cannot be elevated to a science by the inductive method of the natural sciences. Cf. >Hermeneutics, >Understanding, >Interpretation, >Cultural Transmission. 1. J. St. Mill, System der deduktiven und induktiven Logik, übertragen von Schiel, 1863, 6. Buch »Von der Logik der Geisteswissenschaften Oder moralischen Wissenschaften«. |
Gadamer I Hans-Georg Gadamer Wahrheit und Methode. Grundzüge einer philosophischen Hermeneutik 7. durchgesehene Auflage Tübingen 1960/2010 Gadamer II H. G. Gadamer The Relevance of the Beautiful, London 1986 German Edition: Die Aktualität des Schönen: Kunst als Spiel, Symbol und Fest Stuttgart 1977 |
| Induction | Einstein | Genz II 320 EinsteinVsInduction: there is no inductive method that could lead to the basic concepts of physics. |
Gz I H. Genz Gedankenexperimente Weinheim 1999 Gz II Henning Genz Wie die Naturgesetze Wirklichkeit schaffen. Über Physik und Realität München 2002 |
| Induction | Medawar | Anne-Kathrin Reulecke (Hg) Fälschungen Frankfurt 2006 245 Induction/MedawarVsInduction: (following Popper): 1. There is no objective starting point. 2. The process of discovery is confused with that of the proof. 3. It is not possible to certainly arrive at a generalization that contains more information than the sum of the particular sentences on which it is based. >Discoveries, >Proof, Science, >Generalization. Medawar pro Popper: (logic of research(1)): hypothetical-deductive method. Trial and Error. This is to give an account of the process of discovery. Solution/Medawar: style of the traditional literary narrative: premonitions, false starting points, rejected hypotheses, emotional aspects, coincidences. It is possible to use literary language in the sense of a "true narrative". 246 VsMedawar: that is naive! 247 The social use of word and writing invariably introduces fiction as a communicative artifice. >Fiction. 1. Karl Popper: Logik der Forschung. 11. Auflage. Tübingen 2005. |
Meda I P. B. Medawar The Uniqueness of the Individual |
| Induction | Popper | I 110 Induction principle: trying to delete it from the science, would not be different from taking out the decision about truth and falsehood of the theories of science. The induction principle can only be a general proposition. If you try to regard it as an "empirically valid" proposition, so the same questions immediately occur again, which leaded to its introduction. We would have to use inductive reasoning to justify it: regress. --- I 115 Induction: We reject them because there is no suitable criterion of demarcation. No indicator of empirical, non-metaphysical character of a theoretical system. Demarcation criterion: it will be a proposal for a fixing. Solely responsibility of the decision. To be justified only by analyzing its logical consequences: fertility, >explanatory power, etc. --- Schurz I 15f Induction/PopperVsInduction/Schurz: Popper thesis: science can get along entirely without induction - many VsPopper - theoretical term (Popper: Problem: because observation statements are theory-laden, the border between >observation terms and >theoretical terms is not sharp). |
Po I Karl Popper The Logic of Scientific Discovery, engl. trnsl. 1959 German Edition: Grundprobleme der Erkenntnislogik. Zum Problem der Methodenlehre In Wahrheitstheorien, Gunnar Skirbekk Frankfurt/M. 1977 Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Induction | Schurz | I 50 Induction/Schurz: 1. methodological induction: from observations. PopperVsInduction: induction is not the central method of obtaining hypotheses and theories. Confusion between discovery and reasoning. How hypotheses are obtained, perhaps even by guessing, is quite irrelevant to the justification context. Therefore methodological induction is dispensable. >Discoveries, >Justification. 2. logical induction/carnap: not of discovery, but of justification: Method of finding degree of confirmation. >Confirmation, >Degree of confirmation. I 51 PopperVs: one theory may turn out to be closer to the truth than another, but that does not show that there is not a third, even closer to the truth. I.e. there is no absolute claim for theories. Closeness to truth = probability. There is no limited linguistic possibility space which contains all possible alternative theories. But this is only true for logical hypotheses! Empirical hypotheses: here it is possible to make a finite list of all possible alternative hypotheses. Popper: Competing theories can only be evaluated comparatively. >Comparisons, >Comparability. I 52 3 Epistemic induction/Musgrave/Schurz: If a theory has been more successful so far, it is likely that it will be more successful in the future. Here we are not dealing with object hypotheses but with an epistemic meta-hypothesis about degrees of probation. Epistemic induction is indispensable. Without it, Popper's method of proving would be meaningless. Previous success would be irrelevant for future action. >Success, >Epistemology. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Theories | Waltz | Brocker I 625 Theory/Politics/Waltz: A theory should explain the emergence of regularities (1). For Waltz, a theory is not a "series of laws concerning a certain behavior or phenomena". Nor do theories have the function of explaining laws. (2) Laws/Waltz: are obtained by observation. Theories: are obtained through speculative processes designed to explain laws. Theories are speculations. Therefore, they are only loosely connected to the real world. N.B.: from this definitional separation of laws and theories it follows that theories cannot be judged by whether they are true. Solution/Waltz: a good theory is characterized by the fact that it is coherent in its structure and other scientists take it seriously. (3) Laws/Waltz: Laws, on the other hand, can be judged according to the criteria "true" and "false". WaltzVsEmpirism: Waltz propagates a sharp separation between theory and reality. But it also applies: WaltzVsRationalism. Brocker I 626 Pragmatism/Waltz/Masala: Waltz has a pragmatic position close to Sellars and Quine. Reality/Waltz: For Waltz, theories construct a reality without anyone ever being able to say that this is reality (4). ((s) However, this position cannot be easily attributed to Quine). See Theories/Quine, Reality/Quine, Laws/Quine, Empiricism/Quine. Criteria/Waltz: for the formation of theories: 1. Criterion: Theories must discriminate. Reality/Realism/Waltz: Thesis: there is a reality independent of language and theories. ((s) contradiction to the thesis above, according to which there should be several "realities"). ((s) This is a position of extreme realism). The proximity to Quine and Sellars mentioned by Masala cannot be fully understood: See Realism/Quine, Reality/Sellars, Theory/Sellars. Method/WaltzVsPopper: Waltz advocates a pluralistic process of falsification and verification. (5) 2. Criterion for theory building: (WaltzVsBehavioralism): WaltzVsInduction: the inductive method of political theories of the 1960s and 1970s is wrong, since it wants to formulate laws from existing correlations. With the method of correlation, each variable can be related to another one in a statistically significant way. Complexity/WaltzVsInduction: the complexity of the real world cannot be explained by theories. For these theories are not descriptions, but instruments to explain parts of the real world. Brocker I 627 Theories/Waltz: should be simpler than reality; they should be "elegant". (6) To achieve this, a theory must ignore certain factors. Terms/Meaning/WaltzVsSocial Sciences: Problem: not only do meanings vary with viewers, this makes every social science theory inherently black. But even the attempt to specify the meaning of a term by operationalizing definitions is no way out, because any term can be operationalized in any discourse context. (7) See also Concepts/Quine. Solution/Waltz: we have to specify causalities. Brocker I 628 Social Sciences/Waltz: if causal connections and the interaction of variables can be explained, hard social science theories are possible. Theories/Waltz: cannot be tested - only the hypotheses derived from them. Therefore, a theory should not be rejected if one of its hypotheses is not confirmed. (8) 1. Kenneth N. Waltz, „Theory of International Relations“, in: Fred Greenstein/Nelson W. Polsby (Hg.) International Politics: Handbook of Political Science, Reading, Mas. 1975, p. 4 2. Ibid. p. 3. 3. Kenneth N. Waltz, “Assaying Theories: Reflections on Imre Lakatos”, in: Colin Elman/Miriam Fendius Elman (Ed.) Progress in International Relations Theory: Appraising the Field, Cambridge, Mass.2003, S. xii. 4. Kenneth N. Waltz Theory of International Politics, Reading, Mas. 1979, p. 9. 5. Kernneth N. Waltz “Response to my Critics” in: Robert O. Keohane (Ed.) Neorealism and its Critics, New York 1986, p. 336. 6. Waltz 1975, p. 9. 7. Ibid. p. 11 8. Ibid. p. 13. Carlo Masala, „Kenneth N. Waltz, Theory of International Politics” in: Manfred Brocker (Hg.) Geschichte des politischen Denkens. Das 20. Jahrhundert. Frankfurt/M. 2018 |
PolWaltz I Kenneth N. Waltz Man,the State and War New York 1959 Brocker I Manfred Brocker Geschichte des politischen Denkens. Das 20. Jahrhundert Frankfurt/M. 2018 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Best Explanation | Armstrong Vs Best Explanation | Arm III 105 VsInduction/Vs best explanation/BE: inductive skepticism could doubt that it really would be the best explanation; more fundamental: why should the uniformities of the world have an explanation at all (regularities, reg.)? Regularity/Berkeley: through God. He could also abolish the "laws of nature" tomorrow. Berkeley/Armstrong: answering this already means to concede the possibilities. We have no guarantee that the BE is the best scheme. But it is informative. |
Armstrong I David M. Armstrong Meaning and Communication, The Philosophical Review 80, 1971, pp. 427-447 In Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979 Armstrong II (a) David M. Armstrong Dispositions as Categorical States In Dispositions, Tim Crane London New York 1996 Armstrong II (b) David M. Armstrong Place’ s and Armstrong’ s Views Compared and Contrasted In Dispositions, Tim Crane London New York 1996 Armstrong II (c) David M. Armstrong Reply to Martin In Dispositions, Tim Crane London New York 1996 Armstrong II (d) David M. Armstrong Second Reply to Martin London New York 1996 Armstrong III D. Armstrong What is a Law of Nature? Cambridge 1983 |
| Carnap, R. | Goodman Vs Carnap, R. | II 67 GoodmanVsCarnap/Reduction Sentences: the whole thing is pretty absurd. In my opinion, philosophy has the task to explicate, not to describe science (and the everyday language). The explication shall refer to pre-systematic use of the expressions of consideration, but does not need to comply with the order. It s all about economy and standardization. Schurz I 219 Grue/Bleen/Goodman/Schurz: logical form: (B: observes G*: grue) G*: ((Bxt0 > Gx) u (~Bxt0 > Rx)). Sa: Emerald. Sample: {a:1 ‹ i ‹ n} Then the assertions Sai u Bat0 u Gai and Sai u Bat0 u G*ai are equivalent b< definition. If we apply the inductive generalization conclusion both for "green" and for "grue", our sample results in the two universal hypotheses H: = "All emeralds are green" and H*: = "All emeralds are grue". Problem: H and H* imply for all emeralds not observed before t0 conflicting forecasts (green vs red). Schurz: the following relationship exists to subjective inductive exchangeability assumptions: for regular probability functions the exchangeability assumption cannot be valid at the same time for the predicate (Gx) and its pathological counterpart (G*). Question: according to which criteria should we decide which predicates we consider as exchangeable or inductively projectable? Many criteria were proposed and proved to be unsuitable. Carnap: (1947.146 1976, 211): Thesis: only qualitative predicates are inducible (projectable) "grue" is a Def "Positional" Predicate/Carnap, that is a predicate that refers to the time t0 in its definition. E.g. grue. Def Qualitative Predicate/Carnap: has no definitional reference to individual constants. GoodmanVsCarnap: (Goodman 1955/75, 105): Problem of language dependence (sic: dependence): through reciprocal re-definition it is possible to move from our own language (with "green" and "red") to a language which is equivalent in its expressiveness and in which "grue" and "bleen"(G * x * x R,) act as basic concepts (basic predicates): Re-Definition/Language Dependence/Logical Form: Language L (Gx, Rx primitive) language L* (G*x, R*x primitive) Definitions in L Definitions in L* G*x: ‹› ((Bxt0 > Gx) u (~Bxt0 › Rx)) Gx: ‹› ((Bxt0 › G*x) u (~Bxt0 › R*x)) R*x: ‹› ((Bxt0 › Rx) u (~Bxt0 › Gx)) Rx: ‹› ((Bxt0 > R*x) u (~Bxt0 › G*x)). Solution/Schurz: it is possible to distinguish between qualitative and positional predicates in terms of ostensive learnability independent of the language! I 220 GoodmanVsInduction/Schurz: this does not answer why induction should be based on qualitative and not on positional predicates. Induction consists in extending pattern that were so far observed as consistent into the future. To be able to formulate useful induction rules we need to know what remained constant! And that depends on the qualitative features. Positional features are pseudo-features. Important argument: the fact that individuals are "constantly" "grue" means that they change their color from green to red at t0 . In this case, we have carried out "anti-induction" and not induction. That is the reason why we (with Carnap) have basic predicates for qualitative and not positional features for induction rules. |
G IV N. Goodman Catherine Z. Elgin Reconceptions in Philosophy and Other Arts and Sciences, Indianapolis 1988 German Edition: Revisionen Frankfurt 1989 Goodman I N. Goodman Ways of Worldmaking, Indianapolis/Cambridge 1978 German Edition: Weisen der Welterzeugung Frankfurt 1984 Goodman II N. Goodman Fact, Fiction and Forecast, New York 1982 German Edition: Tatsache Fiktion Voraussage Frankfurt 1988 Goodman III N. Goodman Languages of Art. An Approach to a Theory of Symbols, Indianapolis 1976 German Edition: Sprachen der Kunst Frankfurt 1997 Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Induction | Armstrong Vs Induction | Arm III 105 VsInduction/Vs Best explanation/BE: inductive skepticism could doubt that it really would be the best explanation; more fundamental: why should the uniformities (unif.) of the world have an explanation at all? Unif./Berkeley: through God. He could also abolish the "laws of nature" tomorrow. Berkeley/Armstrong: answering this already means to concede the possibilities. We have no guarantee that the BE is the best scheme. But it is informative. Arm III 53 Induction/ArmstrongVsRegularity theory: 1) Induction is rational. We use it to cope with lives. The conclusion is formally invalid and it is extremely difficult to formalize it. HumeVsInduction: with his skepticism of induction he has questioned a cornerstone of our life. (Much worse than skepticism when it comes to God). Moore: defended induction because of the common sense. Armstrong pro. III 54 The best thing the skepticsVsInduction can hope is playing off some of our best justified (inductively gained) everyday certainties. VsVs: it is a coherent system that our everyday certainties (beliefs) form a coherent system. Application to itself. Hume: the doubt of this involves a quantum of mauvaise foi. (Armstrong ditto). He is only a skeptic during his studies and rejects the skepticism in everyday life. VsReg th: it is therefore a serious accusation against a philosophical theory, if it is obliged to skepticism VsInduction. |
Armstrong III D. Armstrong What is a Law of Nature? Cambridge 1983 |
| Induction | Hume Vs Induction | Hume II 244 Empiricism/knowledge/Hume: empirical knowledge is not limited to the determination of facts in the past! E.g. not only that water boils at 100 degrees, but also the prediction that it will behave likewise next time is justified. Past/future: problem: 'I have found' and 'I foresee' do not have the same status. It is not possible to derive the second sentence from the first one a priori. Because there is no contradiction in the fact that nature could change (HumeVsInduction). Nevertheless, 'only a fool or a madman' would deny the regularities in nature. This universal trust that is not rationally justifiable, must lie in extra-rational factors of human nature. |
D. Hume I Gilles Delueze David Hume, Frankfurt 1997 (Frankreich 1953,1988) II Norbert Hoerster Hume: Existenz und Eigenschaften Gottes aus Speck(Hg) Grundprobleme der großen Philosophen der Neuzeit I Göttingen, 1997 |
| Induction | Leibniz Vs Induction | Frege III 45 LeibnizVsInduction: It is not about the history of our discoveries, which is different in every person, but the shortcut and natural order of truths, which is always the same. |
Lei II G. W. Leibniz Philosophical Texts (Oxford Philosophical Texts) Oxford 1998 F I G. Frege Die Grundlagen der Arithmetik Stuttgart 1987 F II G. Frege Funktion, Begriff, Bedeutung Göttingen 1994 F IV G. Frege Logische Untersuchungen Göttingen 1993 |
| Induction | Nozick Vs Induction | II 223 Knowledge/Induction/Connection/Nozick: knowledge is based on facts that would otherwise have been different. (Nozick: In the past!). Therefore, the relevant non-p world is not a possible world which is identical with the actual world until now and differs from now on. (VsInduction). It is logically possible that until now everything proceeded regularly and will be different from the next moment. All possibilities of the skeptic are logically possible. Induction: but it is wrong to deny that we have the connection to facts in the past. And if they had been different, we would have reflected and predicted them differently. Inductive inferences are to be assessed by whether they match with subjunctivic relations (conditionals). Why should our knowledge then be limited to the past? h: is a statement believed on the basis of the evidence e. II 224 Do I know that it is not the case that e and not h or that not tank (tank entailing e and not h)? Probably not. But it does not follow that I do not know that h! If e is true, do I know that h? E.g. e = pain behavior. In that, "e" is held fixed. That's what would vary if h were wrong. Thus, the response is blocked: I know h, because if h were wrong, e would not be true. " If (3) is satisfied? What would you believe if h were wrong? We must examine the possible world that is an e world and not h world. Anyway, the question is if we know that not (e and not h), and that is a different question that may have to be answered in the negative. From the negative response it is easy II 225 to come to the conclusion that we therefore do not know that h. We should avoid that. Nozick: suppose e is true, then I do not know that h. But how can I know h if e is the only evidence? Solution/Nozick: I do not live in a world where e is given and must be kept constant! Therefore, I can know h on the basis of e which is variable! And because it does not vary, it shows me that h is true! Thus (3) is satisfied, and I am in connection with h. |
No I R. Nozick Philosophical Explanations Oxford 1981 No II R., Nozick The Nature of Rationality 1994 |
| Induction | Popper Vs Induction | Schurz I 50 Induction/Schurz: 1) methodological induction: from observations. PopperVsInduction: induction is the central method of extraction of hypotheses and theories. Confusion of discovery and context of justification. How hypotheses are derived, perhaps even through guessing, is quite irrelevant for the context of justification. Therefore, methodical induction is dispensable. 2) Logical Induction/Carnap: not of the discovery but of the justification: method of determination of the degree of confirmation. II 51 PopperVs: one theory may prove to be closer to the truth than another, but that does not show that there is no third theory that is even closer to the truth. I.e. there is no claim to absoluteness for theories. Verisimilitude = probability. There is no limited space of linguistic possibility containing all possible alternative theories. This only applies for logical hypotheses! Empirical hypotheses: here it is possible to establish a finite list of all possible alternative hypotheses. Popper: competing theories can only be evaluated comparatively. I 52 3) Epistemic Induction/Musgrave/Schurz: if a theory was more successful so far, it is likely that it will be more successful in the future. This is not about object hypotheses, but about an epistemic meta-hypothesis on the degree of corroboration. The epistemic induction is indispensable. Without it, the Popperian method of practical tests would be meaningless. Past success would be irrelevant for future action. I 14/15 Criterion of Demarcation/Schurz: for metaphysics. Problem: principles which considered separately have no empirical consequences, can have new empirical consequences together with other theoretical propositions. I 15 Falsification/Asymmetry/Popper: applies with strict (unexceptional all-sentences): they cannot be verified by any finite set of observations, but falsified by a single counter-example. LakatosVsPopper: Theories are never discarded because of a single counter-example, but adapted. PopperVsInduction/Anti-Inductivism/Popper: Thesis: science can dispense with induction altogether. >Induction/Popper. |
Po I Karl Popper The Logic of Scientific Discovery, engl. trnsl. 1959 German Edition: Grundprobleme der Erkenntnislogik. Zum Problem der Methodenlehre In Wahrheitstheorien, Gunnar Skirbekk Frankfurt/M. 1977 Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Induction | Medawar Vs Induction | Anne-Kathrin Reulecke (Hg) Fälschungen Frankfurt 2006 I 245 Induction/MedawarVsInduction: (similar to Popper): 1. There is no objective starting point. 2. The process of discovering is confused with that of proving. 3. It is not possible with certainty to arrive at a generalisation containing more information than the sum of the specific sentences on which it is based. Medawar pro Popper: (Logic of Research): hypothetical-deductive method. Trial and Error. This should account for the process of discovery. Solution/Medawar: Style of the traditional literary narrative: notions, false starting points, rejected hypotheses, emotional aspects, coincidences. It is possible to use literary language in the sense of a "true narrative". I 246 DotzlerVsMedawar: that is naive! I 247 The social use of words and writing inevitably brings fiction into play as a communicative trick. |
Meda I P. B. Medawar The Uniqueness of the Individual |
| McGee, V. | Field Vs McGee, V. | II 351 Second Order Number Theory/2nd Order Logic/HOL/2nd Order Theory/Field: Thesis (i) full 2nd stage N.TH. is - unlike 1st stage N.TH. - categorical. I.e. it has only one interpretation up to isomorphism. II 352 in which the N.TH. comes out as true. Def Categorical Theory/Field: has only one interpretation up to isomorphism in which it comes out as true. E.g. second order number theory. (ii) Thesis: This shows that there can be no indeterminacy for it. Set Theory/S.th.: This is a bit more complicated: full 2nd order set theory is not quite categorical (if there are unreachable cardinal numbers) but only quasi-categorical. That means, for all interpretations in which it is true, they are either isomorphic or isomorphic to a fragment of the other, which was obtained by restriction to a less unreachable cardinal number. Important argument: even the quasi-categorical 2nd order theory is still sufficient to give most questions on the cardinality of the continuum counterfactual conditional the same truth value in all interpretations, so that the assumptions of indeterminacy in ML are almost eliminated. McGee: (1997) shows that we can get a full second order set theory by adding an axiom. This axiom limits it to interpretations in which 1st order quantifiers go above absolutely everything. Then we get full categoricity. Problem: This does not work if the 2nd order quantifiers go above all subsets of the range of the 1st order quantifiers. (Paradoxes) But in McGee (as Boolos 1984) the 2nd order quantifiers do not literally go above classes as special entities, but as "plural quantifiers". (>plural quantification). Indeterminacy/2nd Order Logic/FieldVsMcGee: (see above chapter I): Vs the attempt to escape indeterminacy with 2nd order logic: it is questionable whether the indeterminacy argument is at all applicable to the determination of the 2nd order logic as it is applicable to the concept of quantity. If you say that sentences about the counterfactual conditional have no specific truth value, this leads to an argument that the concept "all subsets" is indeterminate, and therefore that it is indeterminate which counts as "full" interpretation. Plural Quantification: it can also be indeterminate: Question: over which multiplicities should plural quantifiers go?. "Full" Interpretation: is still (despite it being relative to a concept of "fullness") quasi-unambiguous. But that does not diminish the indeterminacy. McGeeVsField: (1997): he asserts that this criticism is based on the fact that 2nd order logic is not considered part of the real logic, but rather a set theory in disguise. FieldVsMcGee: this is wrong: whether 2nd order logic is part of the logic, is a question of terminology. Even if it is a part of logic, the 2nd order quantifiers could be indeterminate, and that undermines that 2nd order categoricity implies determinacy. "Absolutely Everything"/Quantification/FieldVsMcGee: that one is only interested in those models where the 1st. order quantifiers go over absolutely everything, only manages then to eliminate the indeterminacy of the 1st order quantification if the use of "absolutely everything" is determined!. Important argument: this demand will only work when it is superfluous: that is, only when quantification over absolutely everything is possible without this requirement!. All-Quantification/(s): "on everything": undetermined, because no predicate specified, (as usual E.g. (x)Fx). "Everything" is not a predicate. Inflationism/Field: representatives of inflationist semantics must explain how it happened that properties of our practice (usage) determine that our quantifiers go above absolutely everything. II 353 McGee: (2000) tries to do just that: (*) We have to exclude the hypothesis that the apparently unrestricted quantifiers of a person go only above entities of type F, if the person has an idea of F. ((s) i.e. you should be able to quantify over something indeterminate or unknown). Field: McGee says that this precludes the normal attempts to demonstrate the vagueness of all-quantification. FieldVsMcGee: does not succeed. E.g. Suppose we assume that our own quantifiers determinedly run above everything. Then it seems natural to assume that the quantifiers of another person are governed by the same rules and therefore also determinedly run above everything. Then they could only have a more limited area if the person has a more restricted concept. FieldVs: the real question is whether the quantifiers have a determinate range at all, even our own! And if so, how is it that our use (practices) define this area ? In this context it is not even clear what it means to have the concept of a restricted area! Because if all-quantification is indeterminate, then surely also the concepts that are needed for a restriction of the range. Range/Quantification/Field: for every candidate X for the range of unrestricted quantifiers, we automatically have a concept of at least one candidate for the picking out of objects in X: namely, the concept of self-identity! ((s) I.e. all-quantification. Everything is identical with itself). FieldVsMcGee: Even thoguh (*) is acceptable in the case where our own quantifiers can be indeterminate, it has no teeth here. FieldVsSemantic Change or VsInduction!!!. II 355 Schematic 1st Stage Arithmetic/McGee: (1997, p.57): seems to argue that it is much stronger than normal 1st stage arithmetic. G. is a Godel sentence PA: "Primitive Arithmetic". Based on the normal basic concepts. McGee: seems to assert that G is provable in schematic PA ((s) so it is not true). We just have to add the T predicate and apply inductions about it. FieldVsMcGee: that’s wrong. We get stronger results if we also add a certain compositional T Theory (McGee also says that at the end). Problem: This goes beyond schematic arithmetics. McGee: his approach is, however, more model theoretical: i.e. schematic 1st stage N.TH. fixes the extensions of number theory concepts clearly. Def Indeterminacy: "having non-standard models". McGee: Suppose our arithmetic language is indeterminate, i.e. It allows for unintended models. But there is a possible extension of the language with a new predicate "standard natural number". Solution: induction on this new predicate will exclude non-standard models. FieldVsMcGee: I believe that this is cheating (although some recognized logicians represent it). Suppose we only have Peano arithmetic here, with Scheme/Field: here understood as having instances only in the current language. Suppose that we have not managed to pick out a uniform structure up to isomorphism. (Field: this assumption is wrong). FieldVsMcGee: if that’s the case, then the mere addition of new vocabulary will not help, and additional new axioms for the new vocabulary would help no better than if we introduce new axioms simply without the new vocabulary! Especially for E.g. "standard natural number". Scheme/FieldVsMcGee: how can his rich perspective of schemes help to secure determinacy? It only allows to add a new instance of induction if I introduce new vocabulary. For McGee, the required relevant concept does not seem to be "standard natural number", and we have already seen that this does not help. Predicate/Determinacy/Indeterminacy/Field: sure if I had a new predicate with a certain "magical" ability to determine its extension. II 356 Then we would have singled out genuine natural numbers. But this is a tautology and has nothing to do with whether I extend the induction scheme on this magical predicate. FieldVsMysticism/VsMysticism/Magic: Problem: If you think that you might have magical aids available in the future, then you might also think that you already have it now and this in turn would not depend on the schematic induction. Then the only possible relevance of the induction according to the scheme is to allow the transfer of the postulated future magical abilities to the present. And future magic is no less mysterious than contemporary magic. FieldVsMcGee: it is cheating to describe the expansion of the language in terms of its extensions. The cheating consists in assuming that the new predicates in the expansion have certain extensions. And they do not have them if the indeterminist is right regarding the N.Th. (Field: I do not believe that indeterminism is right in terms of N.Th.; but we assume it here). Expansion/Extenstion/Language/Theory/FieldVsMcGee: 2)Vs: he thinks that the necessary new predicates could be such for which it is psychological impossible to add them at all, because of their complexity. Nevertheless, our language rules would not forbid her addition. FieldVsMcGee: In this case, can it really be determined that the language rules allow us something that is psychologically impossible? That seems to be rather a good example of indeterminacy. FieldVsMcGee: the most important thing is, however, that we do not simply add new predicates with certain extensions. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Regularity Theory | Armstrong Vs Regularity Theory | Arm III 13 ArmstrongVsRegularity theory: 1) extensional problems: A) Humean Regularity: there seem to be some that are not laws of nature. (H.R. = Humean regularity). That means being an H.R. is not sufficient for being a law of nature (LoN). B) LoN: there might be some that do not universally apply in time and space. There are also laws of probability. Neither of these two would be Humean regularities (H.R.). That means being an H.R. is not necessary for being an LoN. 2) "intensional" problems: Assuming there is a H.R. to which an LoN, corresponds, and the content of this regularity is the same as that of the law. Even then, there are reasons to assume that the law and the regularity are not identical. Arm III 25 TooleyVsArmstrong: (see below): laws of nature which essentially involve individual things must be admitted as logically possible. Then it must be allowed that laws change from one cosmic epoch to the next. TooleyVsRegularity theory: for them it is a problem that only a narrow conceptual gap separates the cosmic epochs (i.e. H.R.) from just very widely extended regularities which are not cosmic anymore. Assuming there were no cosmic regularities (reg.), but extended ones would indeed exist, then it is logically compatible with all our observations. VsRegularity theory: how can it describe the situation in a way that there are a) no laws but extensive regularities? or b) that there are laws, but they do not have cosmic reach? The latter is more in line with the spirit of reg.th. III 27 VsReg. th.: it cannot assert that every local reg. is a law. III 52 ArmstrongVsRegularity theory: makes induction irrational. Arm III 159 ArmstrongVsIdealism: being forced to assume an unspecified absolute because of the requirement of the necessity of existence. There are no principles of deduction from the absolute downwards. There has never been a serious deduction of this kind. Explanation/Armstrong: if the explanation has to stop shortly before coming to the absolute, then idealism must accept contingency. At what point should we accept contingency? ArmstrongVsRegularity theory: it gives up too soon. Universals theory: can the atomic bonds of universals be explained that we have assumed to be molecular uniformities? Necessity/Armstrong: can only ever be asserted, it cannot be demonstrated or even be made plausible. Arm III 53 Induction/ArmstrongVsRegularity theory: 1) Induction is rational. We use it to cope with lives. The conclusion is formally invalid and it is extremely difficult to formalize it. HumeVsInduction: with his skepticism of induction he has questioned a cornerstone of our life. (Much worse than skepticism when it comes to God). Moore: defended induction because of the common sense. Armstrong pro. III 54 The best thing the skepticsVsInduction can hope is playing off some of our best justified (inductively gained) everyday certainties. VsVs: it is a coherent system that our everyday certainties (beliefs) form a coherent system. Application to itself. Hume: the doubt of this involves a quantum of mauvaise foi. (Armstrong ditto). He is only a skeptic during his studies and rejects the skepticism in everyday life. VsReg th: it is therefore a serious accusation against a philosophical theory, if it is obliged to skepticism VsInduction. |
Armstrong III D. Armstrong What is a Law of Nature? Cambridge 1983 |
| Tooley, M. | Armstrong Vs Tooley, M. | III 104 Tooley: if relations between universals are truthmakers, then these are "atomic facts". Then the standard principles could ascribe a probability of >0 to the confirmation theory. III 105 ArmstrongVsTooley: this is an initial possibility or logical possibility of a tautology. Empiricist should have doubts there. ForrestVsTooley: There could be infinitely many possible universals. Would the attributable initial probabilities not be infinitesimally small then? That would be no justification for the induction. VsInduction/VsBest Explanation: inductive skepticism could doubt that it really would be the best explanation, more fundamentally: why should the regularities in the world ever have an explanation (reg.)?. Regularity/Berkeley: through God. He could abolish the "laws of nature" tomorrow. Berkeley/Armstrong: Answering to this already means to concede the possibility. We have no guarantee that the best explanation is the best scheme. But it is informative. Arm III 120 Then all universals would only be substances in Hume’s sense: i.e. something that logically might have an independent existence. III 121 ArmstrongVsHume/ArmstronVsTooley: it is wrong to think of universals like that. Then there are problems regarding how universals are related with their particulars (part.). E.g. If a rel. between particulars a and b is something that is able to have an independent existence without a and b and any other particulars, would there not have to be at least one other relation to relate it to a and b?. And if this rel. can be uninstantiated itself (e.g. in a universe with monads!), then this rel. is just as questionable, etc. ad infinitum. (Bradley’s regress). One can avoid this only if universals are merely abstract factors of states of affairs (but real). |
Armstrong III D. Armstrong What is a Law of Nature? Cambridge 1983 |
| Various Authors | Deutsch Vs Various Authors | DeutschVsinduction. I 36 Deutsch: induction needs no understanding, you could just explore all the character strings sequentially and randomly find a proper proof. ((s) but not randomly recognize it as correct! In addition, the evidence would not just happen to be right.) Deutsch: Hilbert’s rules could tell us almost nothing about reality. They would all be predicted, but not explained. Just like the "theory of everything". (DeutschVsTOE) I 220 Hilbert: "On the Infinite": scoffed at the idea that the demand for a "finite number of steps" was essential. DeutschVsHilbert: he was wrong. I 236 What is a "step" and what is "finite"? |
Deutsch I D. Deutsch Fabric of Reality, Harmondsworth 1997 German Edition: Die Physik der Welterkenntnis München 2000 |
| Various Authors | Duhem Vs Various Authors | I XXIII DuhemVsLord Kelvin: (in which mechanical models play a fundamental role). Kelvin: If I have a model, I understand, if I have none, I do not understand. - Today more set-theoretic models that Duhem certainly would not have challenged. I 254 DuhemVsMaxwell: Helmholtz established an electrodynamic theory which arises completely logically from the best-supported principles of the theory of electricity, in which no fallacies occur in the formulation of the equations, which are so common in the works of Maxwell. I 115 Newton Thesis: in healthy physics, every theorem is deduced from the phenomena and generalized by induction (DuhemVs). I 255 DuhemVsNewton: on closer inspection, the method is not as strict and simple as Newton claimed. I 257 Question: is this principle of universal gravitation then rather a simple generalization of two expressions provided by Kepler and extrapolated by Newton on the satellites? Can induction derive it from these principles? DuhemVsNewton: not at all! In fact, it is not only more general than the two expressions, it is not only different, it contradicts them. If the theory of Newton is correct, Kepler’s laws are necessarily false. I 261 DuhemVsAmpère: The mathematical theory of electrodynamics is not derived solely from experience: the raw facts of the experiment as they are by nature would not be accessible to the mathematical treatment. They must be reformed and brought into symbolic form. (Ampere did this in reality) I 263 DuhemVsInduction: The need for the physicist to express the experimental data symbolically before introducing them into his thoughts, makes the purely inductive path unusable! I 357 DuhemVsEuler: Euler follows a circular argument: Definition: A force is the force which brings a body from rest to movement. (everyday language use). I 355 We would say instead: A body which is not subjected to any force remains motionless. A body that is subjected to a constant force moves at constant speed. If the force with which a body is moved is increased, the speed of that body is increased as well. |
Duh I P. Duhem La théorie physique, son objet et sa structure, Paris 1906 German Edition: Ziel und Struktur der physikalischen Theorien Hamburg 1998 |
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The author or concept searched is found in the following 2 theses of the more related field of specialization.
| Disputed term/author/ism | Author |
Entry |
Reference |
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| Vs Induction | Deutsch, D. | I 63 Thesis: DeutschVsInduction. |
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| Vs Induction | Popper, K. | Schurz I 15 PopperVsInduction / Anti-inductivism / Popper: Science can live entirely without induction. (Many authors VsPopper). |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
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