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Arbitrariness | Field | I 24 Identity/Identification/Field: in many areas, there is the problem of the continuous arbitrariness of identifications. - In mathematics, however, it is stronger than with physical objects. I 181 Solution: Intensity relations between pairs or triples, etc. of points. Advantage: that avoids attributing intensities to points and thus an arbitrary choice of a numerical scale for intensities. III 32 Addition/Multiplication: not possible in Hilbert's geometry. - (Only with arbitrary zero and arbitrary 1) Solution: intervals instead of points. II 310 Non-Classical Degrees of Belief/Uncertainty/Field: E.g. that every "decision" about the power of the continuum is arbitrary is a good reason to not assume classical degrees of belief. - (Moderate non-classical logic: That some instances of the sentence cannot be asserted by the excluded third party). III 31 Figure/Points/Field: no Platonist will identify real numbers with points on a physical line. - That would be too arbitrary ("what line?"). - What should be zero - what is supposed to be 1? III 32 f Hilbert/Geometry/Axioms/Field: multiplication of intervals: not possible, because for that we would need an arbitrary "standard interval". Solution: Comparing products of intervals. Generalization/Field: is then possible on products of spacetime intervals with scalar intervals. ((s) E.g. temperature difference, pressure difference). Field: therefore, spacetime points must not be regarded as real numbers. III 48 FieldVsTensor: is arbitrarily chosen. Solution/Field: simultaneity. III 65 Def Equally Divided Region/Equally Split/Evenly Divided Evenly/Equidistance/Field: (all distances within the region equal: R: is a spacetime region all of whose points lie on a single line, and that for each point x of R the strict st-between (between in relation to spacetime) two points of R lies, there are points y and z of R, such that a) is exactly one point of R strictly st-between y and z, and that is x, and -b) xy P-Cong xz (Cong = congruent). ((s) This avoids any arbitrary (length) units - E.g. "fewer" points in the corresponding interval or "the same number", but not between temperature and space units. Field: But definitely in mixed products are possible.Then: "the mixed product... is smaller than the mixed product..." Equidistance in each separate region: scalar/spatio-temporal. III 79 Arbitrariness/Arbitrary/Scales Types/Scalar/Mass Density/Field: mass density is a very special scalar field which, due to its logarithmic structure, is "less arbitrary" than the scale for the gravitational potential. >Objectivity, >Logarithm. Logarithmic structures are less arbitrary. Mass density: needs more fundamental concepts than other scalar fields. Scalar field: E.g. height. >Field theory. |
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 |
Belief Degrees | Field | II 257 Belief Degree/BD/Conditional/Field: the classic laws of probability for belief degrees do not apply with conditionals. - Disquotational Truth/Conditional: refers to the complete: "If Clinton dies, Gore becomes President" is true iff Clinton dies and Gore becomes President. Non-disquotational: behaves like disquotational truth in simple sentences. With conditionals: simplest solution: without truth value. >Disquotationalism, >Truth values, >Conditionals. II 295 Belief Degree/Probability/Field: the classic law of the probability of disjunctions with mutually exclusive disjuncts does not apply for degrees of belief when vagueness is allowed. >Probability, >Probablilty law. II 296 Probability Function/Belief Degree: difference: for probability functions the conditional probability is never higher than the probability of the material conditional. >Probability function. II 300 Indeterminacy/Belief Degree/Field: the indeterminacy of a sentence A is determined by the amount for which its probability and its negation add up to less than 1. ((s) i.e. that there is a possibility that neither A nor ~A applies.) II 302 Indeterminacy/Belief/Field: some: E.g. "belief" in opportunities is inappropriate, because they are never actual. Solution: Acceptance of sentences about opportunities. - Also in indeterminacy. Solution: belief degrees in things other than explanation. II 310 Non-classical Belief Degrees/Indeterminacy/Field: E.g. that every "decision" about the power of the continuum is arbitrary, is a good reason to assume non-classical belief degrees. Moderate non-classical logic: that some instances of the sentence cannot be asserted by the excluded middle. >Excluded middle, >Non-classical logic. |
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 |
Conditional | Field | II 253 Conditional/Deflationism/Field: the nonfactualist view is not the only one possible, both classical and non-classical logic can be used. - >Nonfactualism. Disquotational truth: it seems to require truth conditions. - E.g. "If Clinton dies in office, Danny de Vito will become President" is true iff Clinton dies in office and de Vito becomes President. >Disquotationalism. II 254 Conditional/Facts/Stalnaker/Field: (Stalnaker 1984)(1): Thesis: the conditional facts are not expressible in 1st order logic, but in indicative "If .. then .." clauses. >Logic, >Second order logic. II 255 Conditional/Factualism/Field: 1st Variant: assumes that "if A, then B" has the same truth conditions as "~A v B". Factualism: factualism does not accept counterintuitive conclusions - Non-factualism: seems committed to them. II 255 Material Conditional/Paradoxes of Material Implication/Jackson/Field: Best Solution: (Jackson 1979)(2): Thesis: counterintuitive conclusions are unacceptable here: Thesis: the conclusions are not assertible, but nevertheless they are true. There is a conventional implicature for that when we assert "if A, then B", that not only the probability P (A> B) is high, but also the conditional probability P (A > B I A). Field: the requirement that P(A > B I A) should be high is equivalent to the demand of the nonfactualist that P(B I A) is high - "Surface logic" has to do with assertibility. "Deep logic": says what is truth preserving. II 256 Factualism: must then distinguish between levels of total unacceptability (i.e. on the surface) and the acceptability on a deep level. >Acceptability. Deflationism: in the same way the deflationism can then distinguish between non-factualism and factualism without using the concepts "true" or "fact". Factualism: factualism does not accept counterintuitive conclusions - non-factualism: seems committed to them. >Facts. II 257 Non-Factualism/Field: must assume that the acceptance of conditionals is not regulated by the normal probability laws governing the acceptance of "fact sentences". >Probability laws. 1. Robeert C. Stalnaker. Inquiry. Cambridge, Mass: MIT PRess. 2.Frank Jackson, On Assertion and Indicative Conditionals. The Philosophical Review Vol. 88, No. 4 (Oct., 1979), pp. 565-589 |
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 |
Negation | Field | II 308 Vagueness/indeterminacy/logic/"reject"/Field: Def Rejecting: is not accepting the negation. Moderate non-classical logic/Field: should be defined without "reject": it does not accept any instances of the Law of the Excluded Middle, but also does not accept the negation of any instance. >Excluded middle, >Negation. Reject: the sense of rejecting should be less than the meaning of "accepting the negation". - But it must in turn be stronger than "not accept". >Stronger/Weaker. Def "reject p": "accept that it is not the case that determined p". "Low" acceptance should be more than "not high". If the threshold is >acceptance, then rejecting is stronger than non-accepting. Assumed, belief degrees in a sentence and its negation add up to less than 1, then: rejecting is weaker than accepting the negation. >Belief degrees. |
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 |
Vagueness | Field | II 227 Vagueness/revision of the logic/Field: some authors: to allow double negation, to prohibit explicit contradictions, thus also not to allow negations of the law of the excluded middle (l.e.m.). >Negation, >Double negation, >Contradictions, >Stronger/Weaker, >Excluded middle. Then old version: if Jones is a limiting case for "Jones is bald", we cannot claim either "bald" or "not-bald", so we can now. New: neither claim: E.g. "Jones is bald or not bald" nor "It is not the case that Jones is either bald or not bald." On the other hand: Field: with definite-operator (definite): "It is not the case that Jones is either definitely bald or definitely not bald". - Without law of the excluded middle: "neither bald nor not bald". II 228 Limiting case/vagueness/definite-Operator/Field: we need the definite-operator to avoid a limiting case of the a limiting case. >dft-operator, >Terminology/Field. II 228 Def Weakly true/vagueness/truth/truth-predicate/Field: to be able to say general things about borderline cases. Not only that somebody represents a certain limiting case. >Generalization. Def paradigmatic borderline case: definitely a borderline case. Not weakly true/deflationism: e.g. "Either bald or not-bald is true". Then the Truth-predicate itself inherits the vagueness. It is not definitely true whether or not. Def Strongly true/Field: assuming, Jones is a limiting case: then neither "bald" nor its negation (strongly) plus classical logic: then the disjunction "bald or not bald" should be true even in strong interpretation. Law of the excluded middle: if we give it up: a) weakly true: then the disjunction is not true b) strongly true: then the disjunction is without truth value. Strongly true: is less vague, does not inherit the vagueness. Correctness: which interpretation is the correct one is only dependent on utility. >Correctness. Per weak truth: allows infinite conjunction and disjunction. This corresponds more to the theory of validity. - Only the weak Truth-concept is supplied by the disquotation scheme. Deflationism: deflationism additionally requires the definite-operator to declare the predicate strongly true. >Deflationism. II 230 Inflationism/Vagueness/FieldVsInflationism: Problem: the I. needs a thing that is "neither bald nor not bald". Inflationism: explains e.g. "weakly true" compositional. >Inflationism. Supervaluation/Sorites/Inflationism: "candidate of an extension". >Supervaluation. Def strongly true: is a sentence with a vague predicate then iff it is true relative to each of the candidates of an extension. - Then the limiting case without definite-operator: "Jones is bald in some extensions but not in all". II 233 Vagueness/Ontology/Field: Thesis: vgueness is a deficiency of language, not of the world. >Language dependence. II 234 Vagueness/radical non-classical logic/Field: here we do not need a definite-operator or distinction between strong/weak truth: e.g. Jones is a limiting case iff it is not the case that he is either bald or not bald. Deflationism/Field: seems to save a lot of trouble, because there is no definite-operator, one would have to understand. Vs: that deceives: the trouble is only postponed: here the logical rules for "not", etc. are much more complicated. ... + ... II 228 Weakly true:...++... |
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 |
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Davidson, D. | Dummett Vs Davidson, D. | Dummett I 28ff DavidsonVsTarski: ... one must have a previous understanding of the concept of truth. - But not of the conditions! Because this knowledge will be determined by the theory of truth!. Dummett: What has to be introduced, however, is the realization of the conceptual link between meaning and truth. DummettVsDavidson: In Davidson much remains implicit, E.g. this same context, which is required of every speaker. Without the exact nature of this relation the description of the T-Theory is still not a sufficient explanation of the concept of meaning. Correspondence Th./Coherence Th.: meaning before truth - Davidson: truth before meaning (truth conditions defined later by theory) - Dummett both together!. I 142 Since the vocabulary changes and can be used differently, Davidson no longer assumes the language of a particular individual to be the starting unit, but the disposition for language usage. DummettVsQuine, VsDavidson: not idiolect, but common language prevailing. I 146 Davidson def idiolect (refined): Language, date, speaker, certain listener. If there was a language that was only spoken by one personn, we could still all learn it. DummettVsDavidson: but in this case remains unresolved: the relation between truth and meaning, more precisely, between truth conditions and use. Dummett: every participant in the conversation has his own theory of what the words mean. And these theories coincide, or nearly so. I 187 DummettVsDavidson, DummettVsQuine: It is not permissible to assume that meaning and understanding depend on the private and non-communicable knowledge of a theory. It is not natural to understand precisely the idiolect primarily as a tool of communication. It is then more likely trying to see an internal state of the person concerned as that which gives the expressions of idiolect their respective meanings. I 149 E.g. What a chess move means is not derived from the knowledge of the rules by the players, but from the rules themselves. DummettVsDavidson: If the philosophy of language is described as actually a philosophy of action, not much is gained, there is nothing language-specific in the actions. Avramides I 8 DummettVsDavidson: not truth conditions, but verification conditions. The theory of meaning must explain what someone knows who understands one language. (This is a practical ability). I 9 This ability must be able to manifest itself, namely through the use of expressions of that language. DummettVsDavidson/Avramides: a realistically interpreted theory of truth cannot have a concept of meaning. I 87 Dummett: talks about translating a class of sentences that contain a questionable word. DavidsonVsDummett: This class automatically expands to an entire language! (Holism). (s) So to speak this "class of relevant sentences" does not exist. DavidsonVsDummett/Avramides: Davidson still believes that you need a body of connected sentences, he only differs with Dummett on how to identify it. There may be sentences that do not contain the word in question, but still shed light on it. It may also be important to know in what situations the word is uttered. Solution: "Translation without end". II 108 Truth Theory/M.Th./Dummett: There is certainly a wide field in non-classical logic for which is possible to construct a m.th that supplies trivial W sets. DummettVsDavidson: whenever this can be done, the situation is exactly reversed as required for Davidson’s m.th. A trivial axiom for any expression does not itself show the understanding, but pushes the whole task of explaining to the theory of meaning, which explains what it means to grasp the proposition expressed by the axiom. Putnam I 148 Truth/Dummett: Neither Tarski’s theory of truth nor Davidson’s theory of meaning (assuming a spirit-independent world) have any relevance for the truth or falsity of these metaphysical views:. DummettVsDavidson: one has to wonder what this "knowing the theory of truth" as such consists in. Some (naturalistic) PhilosophersVsDummett: the mind thinks up the statements consciously or unconsciously. VsVs: but how does he think them, in words? Or in thought signs? Or is the mind to grasp directly without representations what it means that snow is white?. |
Dummett I M. Dummett The Origins of the Analytical Philosophy, London 1988 German Edition: Ursprünge der analytischen Philosophie Frankfurt 1992 Dummett II Michael Dummett "What ist a Theory of Meaning?" (ii) In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 Dummett III M. Dummett Wahrheit Stuttgart 1982 Dummett III (a) Michael Dummett "Truth" in: Proceedings of the Aristotelian Society 59 (1959) pp.141-162 In Wahrheit, Michael Dummett Stuttgart 1982 Dummett III (b) Michael Dummett "Frege’s Distiction between Sense and Reference", in: M. Dummett, Truth and Other Enigmas, London 1978, pp. 116-144 In Wahrheit, Stuttgart 1982 Dummett III (c) Michael Dummett "What is a Theory of Meaning?" in: S. Guttenplan (ed.) Mind and Language, Oxford 1975, pp. 97-138 In Wahrheit, Michael Dummett Stuttgart 1982 Dummett III (d) Michael Dummett "Bringing About the Past" in: Philosophical Review 73 (1964) pp.338-359 In Wahrheit, Michael Dummett Stuttgart 1982 Dummett III (e) Michael Dummett "Can Analytical Philosophy be Systematic, and Ought it to be?" in: Hegel-Studien, Beiheft 17 (1977) S. 305-326 In Wahrheit, Michael Dummett Stuttgart 1982 Avr I A. Avramides Meaning and Mind Boston 1989 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 |
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Negation | Field, Hartry | II 308 "Reject"/Field: perhaps there is a sense of "reject" in which you reject everything and also the disjunction. "Reject"/Stronger/Lower/Field: this sense must be weaker than the sense of "accepting negation". But it must again be stronger than "not accepting". Solution: Def "reject p": as "accept that it is not the case that determines p". FieldVs: this proves my thesis in the section that moderate non-classical logic needs a det-operator. But the actual thesis was that he needs it just as much as classical logic does. Vs: later argued that the det-operator for classical logic is not fundamental, thesis: fundamental are rather non-classical degrees of belief. ((s) But this is about non-classical probability theory, not about non-classical logic). Because one explains acceptance with high and rejections with low degrees of belief. |
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Logic | Field, Hartry | I 36 "Wide view"/Field: thesis: not all logical truths are logically knowable. I 38 Essay 4: modal conservatism cannot be accepted in non-axiomatic logic if modality is understood narrowly. Thesis: this is not an argument against non-axiomatizable logic, because the broad conception is nothing incomprehensible to me. II 290 Def radically non-classical logic/Field: thesis: that it is possible to deny certain instances of the sentence of the excluded middle without contradictions. Def moderate non-classical logic/Field: that some instances of the sentence of the excluded middle are not claimable. II 291 Moderate non-classical logic/vagueness/Field: thesis: we should neither accept nor deny the disjunction "rich/non-rich"! |
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