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Conservativity | Field | I 4 Conservativity/Field: Conservativity includes some features of necessary truth without actually ever involving truth. >Truth transfer. I 44 Def Conservativity/Mathematics/Field: means that every internally consistent combination of nominalist statements is also consistent with the mathematics. - If we can also show that mathematics is not indispensible, we have no reason to believe in mathematical entities anymore. >Mathematical entities. I 58 Def Conservative/Conservativity/Theory/Mathematics/Field: conservative is a mathematical theory that is consistent with every internally consistent physical theory. - This is equivalent to: a mathematical theory is conservative iff for each assertion A about the physical world and each corpus N of such assertions, A does not follow from N + M, if it does not follow from N alone. ((s) A mathematical theory adds nothing to a physical theory.) M: mathematical theory N: nominalistic physical theory. >Nominalism. Def Anti-Realism/Field: (new): an interesting mathematical theory must be conservative, but it must not be true. >Anti-Realism. Conservative theory: 1) It facilitates inferences 2) It can substantially occur in the premises of the physical theories. I 59 Conservativity: necessary truth without truth simpliciter. - (i.e. it is has the properties of a necessarily true theory without existing entities.) >Truh/Field. Unlike mathematics: science is not conservative. - It must also have non-trivial nominalist consequences. >Science. I 61 Truth does not imply conservativity, nor vice versa. I 63 The fact that mathematics never leads to an error shows that it is conservative, not that it is true. - From conservativity follows that statements with physical objects are materially equivalent to statements of standard mathematics. - N.b.: they need not have the same truth value! >Truth values. I 75 Conservativity: can explain what follows, but not what does not follow. I 59 Mathematics/Truth/Field: Thesis: good mathematics is not only true, but necessarily true. - N.B.: Conservativity: necessary truth without truth simpliciter. >Bare truth. I 159 Conservative expansion does not apply to ontology. >Expansion. III XI Def Conservative/Science/Field: every inference from nominalistic premises on a nominalistic conclusion that can be made with by means of mathematics can also be made without it - with theoretical entities, unlike mathematical entities, there is no conservativity principle - i.e. conclusions that are made with the assumption of theoretical entities cannot be made without them. >Nominalism, >Theoretical entities. |
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 |
Implication | Field | II 255 Material conditional/paradoxes of the material implication/Jackson/Field: best solution: (Jackson, 1979)(1): Thesis: Contraintuitive conclusions are unacceptable here: the conclusions cannot be asserted, but nevertheless true. >Acceptability, >Truth, >Conclusions. There is a conventional implication for that if we assert "if A then B", not only the probability is high (A > B), but also the conditional probability P (A > B I A). >Probability, >Probability conditionals. N.B.: the demand that P (A > B I A) should be high is equivalent to the demand of the nonfactualist that P (B I A) is high. >Nonfactualism. "Surface logic": has to do with assertibility - "depth logic": says what is truth-maintaining. >Assertibility, >Truth transfer. II 256 Factualism: has then to distinguish between levels of total unacceptability (i.e., on the surface) and acceptability at a deep level. >Facts/Field. Deflationism: in the same way the deflationism can distinguish between nonfactualism and factualism without using the terms "true" or "fact". >Deflationism. Factualism: the factualism does not accept any contraintive conclusions. Nonfactualism: seems committed to it. 1.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 |
Implication Paradox | Logic Texts | Hoyningen-Huene II 117 Problem: Ex falso quodlibet: According to classical logic, anything can be deduced from a false premise. >ex falso quodlibet/EFQ. Hoyningen-Huene II 118 Here opinions differ. Problem: if there is no transfer of truth. Premises and conclusions are [sometimes] completely independent of each other. II 119 According to the argumentation with truth transfer, [such] conclusions are incorrect. Possible solution: Strengthening by the aspect of relevance: II 123 "Strict implication." [An inference] is incorrect because nothing can be inferred from A u ~A. Caution: A u ~A could now be reformulated as A u B! (~A = B) Here the (actually not forbidden) substitution destroys the characteristic. >Strict implication, >Relevance. II 127 Although it is incorrect for the case B = ~A, it can be useful to deduce A from A u B without scruples, even if one does not know whether B = ~A. II 128 The classical propositional logic proves to be possibly inadequate here. >Propositional logic. |
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 |
Interpretation | Taylor | Gaus I 65 Interpretation/Charles Taylor/Forbes: Charles Taylor (1971)(1), the classic plea for interpretation in the social sciences, argued that political phenomena should be regarded as analogous to obscure texts, in need of translation or interpretive explication. >Translation, >Truth transfer. As with texts, so with political phenomena: we do not understand them until we understand their meanings. >Understanding, >Meaning. Forbes: Opinion polls and other surveys (e.g. Almond and Verba, 1963)(2) may be some help, but since the relevant meanings are not just ‘subjective’ (and more or less widely shared) but also ‘intersubjective’ (and thus not normally topics for discussion or even reflection), direct answers to direct questions will often be unrevealing. The deeper meanings we seek can be brought to light only by the kind of ‘thick description’ exemplified in Clifford Geertz’s famous (1973)(3) analysis of Balinese cockfighting. Perhaps the best label today for what Taylor and Geertz represent is the title of this section, ‘intentional analysis’. It avoids the unhelpful breadth of ‘interpretation’, the novelty and obscurity of ‘thick description’, the distracting associations of ‘hermeneutics’, and the misleading suggestion, implicit in the old contrast between explanation and understanding (von Wright, 1971)(4), that the clarification of intentions is not explanatory. It puts the emphasis squarely on the purposive character of individual actions and social institutions and clearly suggests the need for careful analysis, since the relevant purposes may not be obvious or easily stated. >Meaning change, >Theory change. 1. Taylor, Charles (1985 [1971]) ‘Interpretation and the sciences of man’. In his Philosophy and the Human Sciences, Philosophical Papers, vol. 2. Cambridge: Cambridge University Press, 15–57. 2. Almond, Gabriel and Sidney Verba (1963) The Civic Culture: Political Attitudes and Democracy in Five Nations. Princeton, NJ: Princeton University Press. 3. Geertz, Clifford (1973) The Interpretation of Cultures: Selected Essays. New York: Basic. 4. Von Wright, Georg Henrik (1971) Explanation and Understanding. London: Routledge and Kegan Paul. Forbes, H. Donald 2004. „Positive Political Theory“. In: Gaus, Gerald F. & Kukathas, Chandran 2004. Handbook of Political Theory. SAGE Publications. |
EconTayl I John Brian Taylor Discretion Versus Policy Rules in Practice 1993 Taylor III Lance Taylor Central Bankers, Inflation, and the Next Recession, in: Institute for New Economic Thinking (03/09/19), URL: http://www.ineteconomics.org/perspectives/blog/central-bankers-inflation-and-the-next-recession 9/3/2019 TaylorB II Barry Taylor "States of Affairs" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 TaylorCh I Charles Taylor The Language Animal: The Full Shape of the Human Linguistic Capacity Cambridge 2016 Gaus I Gerald F. Gaus Chandran Kukathas Handbook of Political Theory London 2004 |
Modalities | Field | I 185 Modality/Field: many people believe there can be a simple exchange between modality and ontology: one simply avoids an enrichment of the ontology by modal statements. >Ontology, >Modal logic. I 255 Modalization/Mathematics/Physics/Field: "Possible Mathematics": 1. Does not allow to preserve platonic physics 2. Advantage: This avoids the indispensability argument 3. False: "It is possible that mathematics is true" - but correct: Conservativity of modality. ((s) Mathematics does not change the content of physical statements). 4. For Platonic physics one still needs to use unmodalized mathematics. 5. Field: but we can formulate physics based neither on mathematics nor on modality: comparative predicates instead of numeric functors. - (257 +) >Platonism, >Mathematics, >Physics, >Conservativity. I 272f Modal translation/mathematics/Putnam/Field: the idea is that in the modal translation acceptable sentences become true modal statements and unacceptable sentences false modal statements. Field: then there are two ways of looking at the translations: 1st as true equivalences: then the modal translation shows the truth of the Platonic theorems. (Truth preservation). >Truth transfer. I 273 2nd we can regard the modal translation as true truths: then the Platonic propositions are literally false. ((s) symmetry/asymmetry). N.B.: It does not make any difference which view is accepted. They only differ verbally in the use of the word "true". >Truth. I 274 Truth/mathematical entities/mE/Field: if a modal translation is to be true, "true" must be considered non-disquotational in order to avoid mathematical entities. - True: can then only mean: it turns out to be disquotational true in the modal translation, otherwise the existence of mathematical entities would be implied. - ((s) "Non-disquotational": = "turns out as disquotational.") (No circle). |
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 |
Nonfactualism | Adams | Field II 255 Definition "surface logic"/material conditional/paradoxes of implication/Field: the surface logic tells us which conclusions are acceptable. (This is just the logic of Adams offered by nonfactualism). >Conditional/Adams, >Acceptability. Def "depth logic"/material conditional/Field: the depths logic tells us which conclusions are truth maintaining. This is the standard logic for ">". >Truth transfer. Problem: does the depth logic do anything at all, even if our mental performance is explained by the surface logic? Solution/Field: Perhaps one can say that at the deepest level classical logic prevails and the special conventions of the assertion only come later. II 256 Factualism/Field: It must then distinguish between levels of total unacceptability (i.e., on the surface) and acceptability at a deep level (which only seems unacceptable by a superficial violation of the convention). Deflationism/Field: the deflationism between nonfactualism and factualism can be distinguished in the same way without using the terms "true" or "fact". >Deflationalism. Field II 256 Factualism/Conditional/Stalnaker/Field: (Stalnaker 1984)(1): (here, at first limited to non-embedded conditionals): here his approach provides the logic of Adams, i.e. Factualism is indistinguishable from nonfactualism in relation to which conclusions ("paradox of material implication") are considered correct. >Paradox of Implication. Deflationism/Field: can he differentiate between nonfactualism and factualism? One possibility is that if there are conditionals where the antecedent is logically and metaphysically possible, but not epistemically. Nonfactualism: thesis: in epistemic impossibility of the anteceding of a conditional, there is no question of acceptability. For the joke of conditionals consists in the assumption that their antecedents are possible epistemically. N.B.: then all conditionals with epistemically unacceptable antecedents are equally acceptable. FieldVsStalnaker: for him there is a fact due to which a conditional is true or false. And some conditionals with epistemically impossible antecedents will be true and others false! Factualism/Deflationism/Field: the test of whether someone adheres to this type of factualism is then whether he takes acceptability of such conditionals seriously. 1. R. Stalnaker (1984). Inquiry. Cambridge University Press. |
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 |
Nonfactualism | Boghossian | Wright I 267 Rules/Wittgenstein/Wright: whatever Wittgenstein's dialectics exactly achieve, in any case it enforces some kind of restriction for a realistic notion of rules and meaning. >Rules/Wittgenstein, >Rule following/Wittgenstein, >Meaning/Wittgenstein, >Meaning. I 268 And therefore also for truth, since truth is a function of meaning. I 269 Paul Boghossian: he has now presented an approach that could eliminate both concerns: I 270 Boghossian: we consider a non-factualism which is exclusively concerned with meaning (not truth): There is no property of the kind that a word means something, and consequently no such fact. >Facts, >Properties. Since the truth condition of a proposition is a function of its meaning, non-factualism necessarily implies a non-factualism with regard to the truth conditions. >Truth conditions. Then the following results: (5) For all S, P: "S has the truth condition P" is not truth conditional. According to quotation redemption: (4) For each S: "S" is not truth conditional. >Truth conditional semantics. "Fascinating Consequence"/Boghossian: of a non-factualism of the meaning: a global non-factualism. And precisely in this, a non-factualism differs from the meaning of non-factualism with respect to any other object. I 271 WrightVsBoghosian: many will protest against his implicit philosophy of truth, but nothing can be objected to the use of the word alone. Boghossian: Global Minimalism, Non-Factualism: regarding meaning, not truth: There is no property that a word means something, and consequently no fact, is a result of global nonfactualism, as opposed to all other nonfactualisms. Wright I 271 Realism/Wright: so far, the question has been asked which additional realism-relevant properties can make the truth predicate "substantive". We can now use "correctness" ("correct") for the minimum case. (Formal >correctness). The thesis of non-factualism can then be formulated in such a way that any discourse on meaning and related terms is at most capable of being correct, and does not qualify for more substantial properties. (i) It is not the case that "S has the truth condition that P" has a truth condition. As a minimalist, one has to accept this, since truth conditions attribute a semantic, i.e., substantive property, and this is denied by the proposition. >Semantic properties. Next: (ii) It is not the case that "S has the truth condition that P" is true. I 272 This follows from (i) since only one sentence with a truth condition can be true. Next: (iii) It is not the case that S has the truth condition that P This follows, according to Boghossian, "due to the quotation redemption properties of the truth predicate". >Truth predicate, >Disquotation, >Disquotationalism, >Deflationism. I 272ff Nonfactualism/Boghossian/Wright: > then every discourse can be at the most correct. (i) is not the case that "S has the truth condition that P" has a truth condition" - WrightVs: can be reworded with quotation redemption (vi) is not the case that it is not the case that S has the truth condition that P has a truth condition - but denial of truth is not inconsistent with the correctness of the assertion, however, (i) is not correct if both truth and correctness are involved, the matrix for that truth predicate (Definition) does not have to be conservative: i.e. That the value of ""A"is true" becomes false or incorrect in all cases, except where A is attributed with the value true. ((s) Non-conservativity demands truth, not just correctness, >truth transfer. "Correct": truth predicate "correct" is for minimal discourses that can be true. Negation/Logic/Truth/Correctness/Correct: If both truth and correctness are involved, there is a distinction (> negation) between the: a) real, strict negation: it transforms each true or correct sentence into a false or incorrect one, another negation form is: b) negation: it acts so that a true (or correct) proposition is constructed exactly when its argument does not reach any truth. >Negation/Boghossian. |
Bogh I Paul Boghossian Fear of Knowledge: Against Relativism and Constructivism Oxford 2007 Boghe I Peter Boghossian A manual for Creating Atheists Charlottesville 2013 WrightCr I Crispin Wright Truth and Objectivity, Cambridge 1992 German Edition: Wahrheit und Objektivität Frankfurt 2001 WrightCr II Crispin Wright "Language-Mastery and Sorites Paradox" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 WrightGH I Georg Henrik von Wright Explanation and Understanding, New York 1971 German Edition: Erklären und Verstehen Hamburg 2008 |
Nonfactualism | Wright | I 272ff Non-Factualism/Boghossian/Wright:> if we assume nonfactualism, no discourse can be more than >Correctness, >Correctness/Wright. (i) it is not the case that S has the truth condition that P has a truth condition. WrightVs: this can be reformulated with disquotation into (vi) it is not the case that it is not the case that S has the truth condition that P has a truth condition. >Disquotation, >Tarski scheme, >Truth conditions. But denying the truth is not inconsistent with correctness of the assertion. >Contradictions, >Negation, >Assertibility. But (i) is incorrect, if both truth and correctness are in the game, the matrix for the truth predicate must be non-conservative: i.e. the value of A is true in all cases, false or incorrect, except those where A has the truth value true. >truth transfer, >conservativeness. |
WrightCr I Crispin Wright Truth and Objectivity, Cambridge 1992 German Edition: Wahrheit und Objektivität Frankfurt 2001 WrightCr II Crispin Wright "Language-Mastery and Sorites Paradox" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 WrightGH I Georg Henrik von Wright Explanation and Understanding, New York 1971 German Edition: Erklären und Verstehen Hamburg 2008 |
Numbers | Field | I 153 Numbers/Frege/Crispin Wright: Frege suggests that the fact that our arithmetical language has these qualities is sufficient to establish natural numbers as a sortal concept whose instances, if they have some, are the objects. WrightVsFrege: but the objects do not have to exist. Problem: Frege thus demands that empirical concerns are irrelevant. - Then there is also no possibility of an error. >Numbers/Frege, >Existence/Frege. II 214 Numbers/BenacerrafVsReduction/Benacerraf/Field: there may be several correlations so that one cannot speak of "the" referent of number words. >Paul Benacerraf. Solution/Field: we have to extend "partially denoted" also to sequences of terms. >Denotation, >Partial denotation, >Generalization/Field. Then "straight", "prim", etc. become base-dependent predicates whose basis is the sequence of the numbers. - Then one can get mathematical truth (> truth preservation, truth transfer). - E.g. "The number two is Caesar" is neither true nor false. (without truth value). >Senseless. II 326 Def Natural numbers/Zermelo/Benacerraf/Field: 0 is the empty set and every natural number > 0 is the set that is the only element which includes the set which is n-1. Def Natural numbers/von Neumann/Benacerraf/Field: Every natural number n is the set that has the sets as elements which are the predecessors of n as elements. Fact/Nonfactualism/Field: it is clear that there is no fact about whether Zermelos or von Neumann's approach "presents" the things "correctly" - there is no fact which decides whether numbers are sets. That is what I call the Definition Structural Insight: it makes no difference what the objects of a mathematical theory are, if they are only in a right relationship with each other. |
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 |
Positivism | Putnam | I (a) 41 PutnamVsPopper/PutnamVsMach: VsPositivismus: positivism is idealistic and does not correspond to reality. I (a) 44 PutnamVsPositivismus: according to positivism truth is not trans-theoretical. It is only a trans-theoretical concept and "leads to successful prediction" >Prediction. Putnam: instead: realism must adhere to the logic of truth transfers. >Realism. I (a) 45 From the fact that two theories lead to successful predictions, it does not follow, that their conjunction leads to that. Reason: the predicate, which plays the role of truth ("leads to prediction") does not have the characteristics of truth. I (a) 49 Meaning/theory/PutnamVsCarnap/VsPositivism: the theory does not determine the significance. Otherwise the concept of gravity would change if a 10th planet would be discovered. Also, the positivists demand that the theory is dependent on all additional assumptions, otherwise the scheme of theory and prediction would collapse. I (h) 215 Truth/positivism: which degree of confirmation one accepts, is ultimately conventional and a question of purpose. Putnam: that is relativism. Relativism has no answer to the enemy that says, "in my system P is not rational". >Rationality/Putnam. |
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 |
Translation | Field | II 147ff Untranslatable/Translation/Extension/Deflationism/Field: Problem: Incorporation of untranslatable sentences. - Solution: potential extension of one's own language by accepting truth-preservation in conclusion. >Truth transfer, >Extensions, >Deflationism, >Language dependence. II 148 Names by index: "Georg-i": the George, to which Mary refered at the occasion of Z. Cf. >Situation semantics. II 149 Per sentence theory: "UTT Guru, Z": the sentence the Guru uttered at Z. - The special sentence is then superfluous. II 152 Disquotational truth: Problem: untranslatable sentences are not disquotational true. >Disquotational truth, >Disquotationalism. II 161 Def Quasi-translation/Def Quasi-meaning/FieldVsChurch/FieldVsSchiffer/Field: this is what most understand as meaning: not literal translation but reproduction as the interpreter understands the use of the corresponding words in his own language at the point of time in his actual world. >Stephen Schiffer. Comparison: is preserved in the quasi-translation at the moment, not in a literal translation. >Comparisons, >Comparability. Sententialism/Sententionalism/Field: Thesis: If we say that someone says that snow is white, we express a relation between the person and the sentence. 1. Quasi-translation and quasi-meaning instead of literal. 2. "La neige est blanche" quasi-means the same as #Snow is white# - (#) what stands between #, should be further translated (quasi-). - In quasi-translation, the quasi-meaning is preserved. >Speaker intention, >Intention-based semantics, >Truth conditions. II 273 Translation/Parameter/Field: in many cases, the relativization of the translation to a parameter is necessary to make it recognizable as a translation. - E.g. "finite": the non-standard argument tells us that there are strange models, so that "is in the extension of "finite" in M" functions as a "translation" of "finite" which maintains the inferential role of all what we say in pure mathematics. N.B.: "Is in the extension of "finite" in M" is a parameterized expression. Solution: what we are doing is to "translate" the one-digit predicate "finite" into the two-digit predicate "is in the extension of "finite" in x", along with the statements to determine the value of x on a model M with the necessary characteristics. |
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 |
Translation | Mates | I 93 Translation/formal language/Mates: a translation of everyday language in the artificial language is meaningless as long as the artificial language is not interpreted. >Interpretation, >Artificial language, >Formal language, >Formalization, >Natural language. "Minimum translation":a minimum translation translates true in true and false in false statements. >Truth preservation, >Truth transfer. I 102 Translation/meaning/sense/interpretation/Mates: to know whether something is a satisfactory translation (of a formal language), we need not only to know the meaning (reference), but also the sense - otherwise we can obtain various everyday language translations. Sense/Mates: cannot be stated in a list as meaning. >Sense. Meaning/Mates: meaning gives the non-logical constants truth conditions: E.g. 2 < 3 is true, if the smallest prime number is less than 3. >Meaning. Sense/Mates: sense provides the content: that the smallest ... is smaller. Reference/Mates: reference provides truth conditions: true, if ... >Truth conditions. Sense: content: that it is true. >Reference, >Content. I 110 Translation/variables/Mates: the translation is not affected by the substitution of the variables, but only by the substitution of the constants. >Variables, >Constants. I 111 Translation/summary/Mates: 1. meaningless without interpretation. (Assignment of objects to the individual constants) 2. If an interpretation is given, one can get a "standard translation" for every formal statement, and this by means of the definition of "true in interpretation I" - Problem: if the same interpretation is given in various ways (E.g. 2 = "smallest prime" or "sole even prime number") one can obtain several non-synonymous translations. >Way of givenness, >Intension. Two formal statements may be equivalent, without being equally good translations. >Equivalence. Conversely it is possible: that two statements are adequate but not equivalent - (only for ambiguity). >Adequacy, >Ambiguity. |
Mate I B. Mates Elementare Logik Göttingen 1969 Mate II B. Mates Skeptical Essays Chicago 1981 |
Truth | Field | III 29 Truth/truth preservation/Field: because all inferences that are thus obtained are correct every time, you should assume that you can say the theory of real numbers is true. Solution: instead of having to assume the truth of the theory of real numbers we can accept the preservation of truth (truth transfer): this is explained without truth by acceptance of conservativity. >Conservativity. Conservativity: here we also need to take only the limited version of conservativity, which follows from the consistency of set theory alone. >Conservativity/Field. |
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 |
Truth Maintenance | AI Research | Norvig I 460 Truth maintenance/AI research/Norvig/Russell: We have seen that many of the inferences drawn by a knowledge representation system will have only default status, rather than being absolutely certain. Inevitably, some of these inferred facts will turn out to be wrong and will have to be retracted in the face of new information. This process is called belief revision. Belief revision: is often contrasted with belief update, which occurs when a knowledge base is revised to reflect a change in the world rather than new information about a fixed world. Belief update combines belief revision with reasoning about time and change; it is also related to the process of filtering. Suppose that a knowledge base KB contains a sentence P - perhaps a default conclusion recorded by a forward-chaining algorithm, or perhaps just an incorrect assertion - and we want to execute TELL(KB, ¬P). To avoid creating a contradiction, we must first execute RETRACT(KB, P). Norvig I 461 Problem: For example, the implication P ⇒ Q might have been used to add Q. The obvious “solution” - retracting all sentences inferred from P - fails because such sentences may have other justifications besides P. For example, if R and R ⇒ Q are also in the KB, then Q does not have to be removed after all. Truth maintenance systems, or TMSs, are designed to handle exactly these kinds of complications. One simple approach to truth maintenance is to keep track of the order in which sentences are told to the knowledge base by numbering them from P1 to Pn. A more efficient approach JTMS is the justification-based truth maintenance system, or JTMS. In a JTMS, each sentence in the knowledge base is annotated with a justification consisting of the set of sentences from which it was inferred. The JTMS assumes that sentences that are considered once will probably be considered again, so rather than deleting a sentence from the knowledge base entirely when it loses all justifications, we merely mark the sentence as being out of the knowledge base. Norvig I 462 An assumption-based truth ATMS maintenance system, or ATMS, makes this type of context switching between hypothetical worlds particularly efficient. An ATMS represents all the states that have ever been considered at the same time. >Truth transfer/Philosophical theories. Norvig I 472 The study of truth maintenance systems began with the TMS (Doyle, 1979)(1) and RUP (McAllester, 1980)(2) systems, both of which were essentially JTMSs. Forbus and de Kleer (1993)(3) explain in depth how TMSs can be used in AI applications. Nayak and Williams (1997)(4) show how an efficient incremental TMS called an ITMS makes it feasible to plan the operations of a NASA spacecraft in real time. 1. Doyle, J. (1979). A truth maintenance system. AIJ, 12(3), 231–272 2. McAllester,D. A. (1980). An outlook on truth maintenance. Ai memo 551, MIT AI Laboratory 3. Forbus, K. D. and de Kleer, J. (1993). Building Problem Solvers. MIT Press. 4. Nayak, P. and Williams, B. (1997). Fast context switching in real-time propositional reasoning. In AAAI-97, pp. 50–56 |
Norvig I Peter Norvig Stuart J. Russell Artificial Intelligence: A Modern Approach Upper Saddle River, NJ 2010 |
Validity | Logic Texts | Salmon I 41 Validity/W.Salmon: affects arguments (= groups of statements), not individual statements. Menne I 25 Menne: We become aware of laws through experience, but that does not mean that their validity is based on experience. Hoyningen-Huene II 100 Propositional logic: Validity of conclusions of propositional logic: conditions: 1. The validity of the conclusion depends on the multiple occurrence of certain (partial) statements. II 101 2. The validity is dependent on certain junction points occurring in it. 3. The validity is independent of the sense of the (partial) statements. II 102 Def Truth transfer/Hoyningen-Huene: positive: the truth of the premises guarantees the truth of the conclusion. 4. The validity of the conclusion requires truth transfer, i.e. that a true premise conjunction never occurs together with a false conclusion. >Truth transfer, Predicate logic: II 229 Adequacy conditions 1. The validity of the conclusion depends on the multiple occurrence of predicates (which refer to the same range of individuals) and possibly the logical constants (from the same range of individuals). II 230 2. The validity depends on the quantifiers and possibly the connectives that occur. 3. The validity is independent of the sense. 4. Validity requires truth transfer. >Connective, >Sense, >Quantifier, >Logical constant. Read III 71 Validity/Read: Problems: VsClassical logic: Classical logic does not succeed in including as valid those inferences whose correctness is based on the connections between non-logical expressions. If an object is round, then it follows that it is not square. But this conclusion is not valid thanks to its form, but thanks to its content. Logical Universe: Problem: one can find inferences whose invalidity can only be seen by looking at a larger universal range of definitions. ((s) See also Problems with the introduction of new connectives: >tonk.) |
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 Sal I Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 German Edition: Logik Stuttgart 1983 Sal II W. Salmon The Foundations Of Scientific Inference 1967 SalN I N. Salmon Content, Cognition, and Communication: Philosophical Papers II 2007 Me I A. Menne Folgerichtig Denken Darmstadt 1997 Re III St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 |
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Putnam, H. | Field Vs Putnam, H. | III 113 Pure Mathematics/Putnam: should be interpreted in a way that it asserts the possible existence of physical structures that satisfy the mathematical axioms. FieldVsPutnam: pure mathematics should not be interpreted at all. I 211 Properties/Relations/Putnam: (1970): are predicative, according to them we have a few basic physical prop and rel from which all others are derived: 1st order: Allows no reference to a totality of physical objects when a new property is constructed. 2nd order: Allows reference to the totality of the properties of the 1st order. 3rd order: Allows reference to the totality of the properties of the 1st and 2nd order. - Every physical property appears on any level of the hierarchy -> functionalism. Functional properties are 2nd or higher order properties - the prop that the role has may differ from person to person. I 214 FieldVsPutnam: instead of properties provide instantiations of properties with steps. I 268 Mathematics/Ontology/Putnam: ("Mathematics without foundations", 1976b, 1975 "What is mathematical truth?"): Field: Putnam Thesis: the mathematical realist does not have to accept the "mathematical object picture". He can formulate his views in purely modal terms. And that not as an alternative, but only as another formulation of the same view. I 269 Indispensability Argument/Putnam: appear in the subsequent text. Field: If "Mathematics as a modal" logic was really an equivalent description of mathematics in terms of mathematical objects (MO), then it should also be possible to reformulate the Indispensability Argument so that there is a prima facie argument for one or the other kind of modalized mathematics and mathematical objects. FieldVsPutnam: but Section 6 and 7 show that we cannot formulate the indispensability argument like that: it requires MO and modalized mathematics does not bring them forth. VSVs: but beware: I have not studied all the possibilities. I 269 FieldVsPutnam: his mathematical realism seems puzzling: Mathematics/Ontology/Putnam: Thesis: there is a modal translation of pure mathematics: he presents a translation procedure that turns mathematical statements into modal statements, one that transforms acceptable mathematical statements (E.g. axioms of set theory) into true modal assertions that include no quantification, unless it is modalized away. (I.e. no mathematical entities (ME) in the modal statements). I 270 FieldVsPutnam: two general questions: 1) what kind modality is involved here? 2) what benefit is the translation to have? ad 1): Putnam thinks that the "object-image" (the starting position) and its modal translation are equivalent at a deeper level. FieldVs: that’s really not interesting: "mathematically possible" should coincide with "logically possible" in any reasonable view (this is stated by conservatism). ((s) contrary to the above). Important argument: if A is not mathematically possible, then "~A" is a consequence of mathematics - i.e. if A (and then also its negation) are purely non-mathematically, then "~A" is logically true. If Putnam now says that his modal translation involves a "strong and clear mathematical sense of possibility", then a mathematical possibility operator must be applied to sentences that contain ME. However, such a sentence A could also be a mixed sentence (see above, with purely mathematical and purely physical components). I 271 FieldVsPutnam: for purely mathematical sentences mathematical possibility and truth coincide! But then the "modal translations" are just as ontologically committed as the mathematical assertions. FieldVs"Mathematical Possibility"/FieldVsPutnam: we had better ignore it. Maybe it was about 2nd order logical possibility as opposed to 1st order for Putnam? I 271 FieldVsPutnam: what benefits does his modal translation have? Does it provide a truth transfer (as opposed to the transmission of mere acceptability)? And what value has it to say that the mathematical statements are both true and acceptable? Etc. Mathematics/Realism/Putnam/Field: Putnam describes himself as "mathematical realist": Difference to Field’s definition of realism: he does not consider ME as mind-independent and language-independent, but (1975): Putnam: you can be a realist without being obliged to mathematical objects. I 272 The question is the one that Kreisel formulated long ago: the question of the objectivity of mathematics and not the question the existence of mathematical objects. FieldVsPutnam: this is puzzling. I 277 Model Theory/Intended Model/Putnam/Field: this morality can be strengthened: there is no reason to consider "∈" as fixed! Putnam says that in "Models and Reality": the only thing that could fix the "intended interpretation" would be the acceptance of sentences that contain "∈" through the person or the community. Putnam then extends this to non-mathematical predicates. ((s)> Löwenheim-Skolem). FieldVsPutnam: this is misleading: it is based on the confusion of the view that the reference is determined, E.g. by causal reasoning with the view that it is defined by a description theory (description theory, (labeling theory?), in which descriptions (labels?) that contain the word "cause" should play a prominent role. (> Glymour, 1982, Devitt, 1983, Lewis 1984). |
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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