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The author or concept searched is found in the following 28 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Abstraction | Quine | I 286 Intensional abstraction means "the act of being a dog", "the act of baking a cake", "the act of erring". I 289 Class abstraction re-traced to singular descriptions: (iy)(x)(x from y iff ..x..) - instead of: x^(..x..) - is not possible for intensional abstraction. I 295 Abstraction of relations, propositions and properties is opaque (E.g. of the planet). I 322 Property abstraction (elimination) instead of "a = x(..x..)". New is the irreducible two-digit Operator "0": "a0x(..x..)". Variables are the only thing that remains. The pronoun has primacy. IX 12ff Class Abstraction/Quine: class abstraction "{x:Fx}" refers to "the class of all objects x with Fx". In the eliminable combination that we have in mind "ε" appears only in front of a class abstraction term and class abstraction terms appear only after "ε". The whole combination "y ε {x: Fx}" is then reduced according to a law: Concretization Law/Quine: reduces "y ε {x: Fx}" to "Fy". Existence/Ontology: thus no indication remains that such a thing as the class {x:Fx} exists at all. Introduction: it would be a mistake, e.g. to write "*(Fx)" for "x = 1 and EyFy". Because it would be wrong to conclude "*(F0) *(F1)" from "F0 F1". Therefore we have to mistrust our definition 2.1 which has "Fx" in the definiendum, but does not have it in the definiens. IX 16 Relations Abstraction/Relation Abstraction/Quine: "{xy:Fxy}" is to represent the relationship of a certain x to a certain y such that Fxy. Relation/Correctness/Quine: parallel to the element relationship there is the concept of correctness for relations. Definition concretization law for relations/Quine: is also the definition correctness/relation: "z{xy: Fxy}w stands for "Fzw". IX 52 Function Abstraction/lambda operator/Quine: before terms one must generate terms (expressions). (Frege/Church: is here also valid of statements and thus a second time class abstraction, but both group statements are under terms and classes under functions (QuineVsFrege,QuineVsChurch). Definition lambda operator/Quine: if "...x..." contains x as a free variable, λx (...x...) is that function whose value is ...x... for each argument x - therefore λx(x²) the function "the "square of" - general: "λx(...x...)" stands for "{ : y = ...x...}" - identity: λx x{: y = x } = λ. - λx {z: Fxy} = {: y = {z: Fxz}} -. "λx a" stands for "{: y = a}". The equal sign now stands between variable and a class abstraction term. IX 181 Abstraction/Order/Quine: the order of the abstracting expression must not be less than that of the free variables. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| de dicto | Chisholm | I 65 de dicto/Chisholm: either "property, to be so that p" or "the fact that p is true" - attribution de dicto: does not need demonstratives, proper names or free variables. >Attribution, >Demonstratives, >Facts. II 118 Wrong: de dicto-belief would be enough for standing in a special relationship with the object alone by the fact that it exists. >Acquaintance. Vs: we need a more stringent notion of de re belief, objects must be able to be identified. de re: I cannot believe anything about the smallest spy before I know him personally. >Individuation, >Identification. ((s) But then also under another description - at least two relations to the object). >Description. Brandl, Johannes. Gegen den Primat des Intentionalen. In: M.David/L. Stubenberg (Hg) Philosophische Aufsätze zu Ehren von R.M. Chisholm Graz 1986 |
Chisholm I R. Chisholm The First Person. Theory of Reference and Intentionality, Minneapolis 1981 German Edition: Die erste Person Frankfurt 1992 Chisholm II Roderick Chisholm In Philosophische Aufsäze zu Ehren von Roderick M. Ch, Marian David/Leopold Stubenberg Amsterdam 1986 Chisholm III Roderick M. Chisholm Theory of knowledge, Englewood Cliffs 1989 German Edition: Erkenntnistheorie Graz 2004 |
| Existential Generalization | Tarski | Berka I 469 Generalization/generalization/Tarski: makes free variables disappear. Berka I 480 Generalization/generalization/fulfillment/satisfaction/"at most distinguishing at i-th position"/Tarski: ((s) here not existential generalization) Let x be a propositional function, assuming it is already known, which sequences satisfy the function x. By considering the content of the considered operation, we will only claim of the sequence f that it satisfies the ∧kx function if the sequence itself satisfies the x function and even then not stops to satisfy it if the k-th term varies in any way. >Satisfaction/Tarski, >Satisfiability/Tarski. E.g. the function ∧2l1,2 is only satisfied by such a sequence, which verifies the formula f1 ⊂ f2 and this regardless of how the second term of this sequence varies. This is only possible when the first element is the empty class.(1) >Sequences/Tarski. 1. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol 1, Lemberg 1935 |
Tarski I A. Tarski Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Functionalism | Avramides | I 146 Functionalism/Avramidis: functionalism allows to refer to behavior with propositional attitudes, not on linguistic behavior. - It allows a subjective image of the mind. >Propositional attitudes, >Behavior, >Understanding, >Language behavior. I 147 Problem: this requires an indefinite number of further propositional attitudes. I 149 Functionalism/Lewis: we take mental concepts as theoretical terms (TT) and define our mental-theoretical terms by reference to the platitudes (commonplaces) of folk psychology. >Theoretical terms, >Folk psychology, >Everyday language, >Observation. These shall contain both, theoretical terms and the rest. - Then we transform every theoretical term into a name, replace the names with free variables. - then existential closure (of the open formulas ((s) Ramsey sentence). >Ramsey sentence, >Open formula. With that we achieve the original theory with the claim that it has a single implementation. - Then the theory has input/output concepts, but no specifically mental terminology. >Input/output. Problem/Avramides: how do we characterize input and output? BlockVsFunctionalism: either characterizes them chauvinistically or liberally. ((s) Because a purely physical characterization of the inputs and outputs would include or exclude the wrong ones.) >Philosophical chauvinism. I 153f AvramidesVsFunctionalism: if he is set to non-mentalistic characterization of the inputs and outputs, then he has to say what distinguishes mental from non-mental systems that have the same functional organization. Avramides: we always start with mentalistically characterized behavior. - Even with the marsians we say that his behavior must have an interpretation. So if normal evidence (Ned Block: not only linguistic, but mainly linguistic behavior) is part of our theory of propositional attitudes, we are committed to a symmetry between the semantic and the psychological. >Language behavior, >Ned Block. |
Avr I A. Avramides Meaning and Mind Boston 1989 |
| Generalization | Mates | I 173 Generalization/theorems/spelling/terminology/logic/Mates: E.g. (x) (y) Fxy <> (y) (x) Fx: generalized: II- ∧α∧α "j <> La"∧αj E.g. (Ex) (Ey) fxy <> (Ey) (Ex) fxy: II- VaVa "φ <> VaVa"φ E.g. (x) (P u Fx) <> (P u (x) Fx): II- ∧α (φ u ψ) <> (φ u Laψ) if a in φ does not occur freely E.g. (x) (Ey) (Fx u Gy) <> ((x) Fx u (Ey) Gy): II- ∧αVa "(φ u ψ) <> (∧αφ u Va" ψ) and when a does not occur freely in ψ and when a" does not occur freely in φ. >Variables/Mates, >Free variables, >Bound variables. |
Mate I B. Mates Elementare Logik Göttingen 1969 Mate II B. Mates Skeptical Essays Chicago 1981 |
| Generalization | Tarski | Berka I 469 Generalization/generalization/Tarski: makes free variables disappear. >Free Variables, >Bound variables. Berka I 480 Generalization/generalization/fulfillment/"at most distinguished at i-th position"/Tarski: Let x be a propositional function, assuming it is already known, which sequences satisfy the function x. By taking into account the content of the subject operation, we will only claim of the sequence f, that it satisfies the function LKx if this sequence itself satisfies the function x, and even then not stops to satisfy this sequence when the k-th term varies in any way. >Satisfaction/Tarski, >Sequences/Tarski. E.g. the function L2l1,2 is only satisfied through such a result, if the formula f1 >Functions/Tarski, >Terminology/Tarski. 1. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol 1, Lemberg 1935 |
Tarski I A. Tarski Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Interpretation | Interpretation: A) making statements about other statements, whereby the new statements of the vocabulary make use of the original statements and possibly introduce new vocabulary. If no new vocabulary is introduced, new information can be obtained by changing the syntactic elements. B) In logic, the insertion of values (objects) instead of the constants or free variables. |
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| Logic | Logic: logic is the doctrine of the admissibility or inadmissibility of relations between statements and thus the validity of the compositions of these statements. In particular, the question is whether conclusions can be obtained from certain presuppositions such as premises or antecedents. Logical formulas are not interpreted at first. Only the interpretation, i. e. the insertion of values, e.g. objects instead of the free variables, makes the question of their truth meaningful. |
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| Model Theory | Field | I 85 Model theory: semantically: "all models in which A is true are models in which B is also true": B follows from A. Proof theory: syntactically: "there is a formal derivation of B from A". I 116 Model theory/Field: if one says that a logically true sentence is true in all models, a model exists in a set of objects plus the fixing which predicates (if any) of them are true in the model, which names (if any) denote these objects, etc. Moreover it is an attribution function (for free variables). - Then the truth conditions can be recursively defined. Def logically true: here: true for each model. >Models. I 117 Kripke/Field: with Kripke a non-empty set of possible worlds is called actual. >Possible worlds, >Actual world/Lewis, >Actuality. Def possible/Kripke: a sentence of the form "MA" (diamond) will then be true in a model if and only if A is in at least one possible world true in a model. Problem/Kripke: for "MA" being logically true, A itself has to be logically true. Solution/FieldVsKripke: we do not accept a possible world. - Our model is the "actual world portion" of the Kripkean model. I 121 Proof Theory: does not provide any results that could not be obtained otherwise. I 116 Model theory/modal logic/FieldVsKripke: unlike Kripke: we choose a solution without possible worlds. - "Which sentences with the operator "logically possible" are logical true?" N.B.: Both model theories are platonistic (pure set theory). >Set theory, >Platonism. |
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 |
| Models | Models, philosophy, logic: A model is obtained when a logical formula provides true statements by inserting objects instead of the free variables. One problem is the exclusion of unintended models. See also model theory. |
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| Probability | Schurz | Def Conditional probability/Schurz: the probability of A assuming that B exists: P( A I B) = p(A u B)/p(B). (pB) must be >0. B: conditional event, antecedent. A: conditional event, consequent. In the statistical case, p(A I B) coincides with the rel.frequ. of A in the finite set of all B's. Or with the limit of rel.frequ. in an infinite random sequence of B's. >Bayesianism. Non-monotonicity/non-monotonic/conditional probability /Schurz: conditional probabilities are non-monotonic: i.e. from p(A I B) = high does not follow that p(A I B u C) = high. >Monotony. Objective probability /type/predicate/Schurz: statistical probabilities always refer to a repeatable event type, expressed in a predicate or an open formula. Subjective probability: refers to an event token, expressed in a sentence. E.g. that it will rain tomorrow: tomorrow exists only once. >Subjective probability. Subjective/objective/probability /Reichenbach: Principle for the transfer from objective to subjective probability: I 101 Principle of narrowest reference class/Reichenbach: the subjective probability of a token Fa is determined as the (estimated) conditional probability p(Fx I Rx) of the corresponding type Fx, in the narrowest reference class Rx, where a is known to lie. (i.e. that Ra holds). E.g. Whether a person with certain characteristics follows a certain career path. These characteristics act as the closest reference class. Ex Weather development: closest reference class, the development of the last days. Total date/carnap: principle of: for confirmation, total knowledge. Subjective probability: main founders: Bayes, Ramsey, de Finetti. Logical probability theory/Carnap: many authors Vs. Mathematical probability theory/Schurz: ignores the difference subjective/objective probability, because the statistical laws are the same. I 102 Disjunctivity/ probability: objective. The extension of A u B is empty subjective: A u B is not made true by any admitted (extensional) interpretation of the language. Probability/axioms/Schurz: A1: for all A: p(A) > 0. (Non-negativity). A2: p(A v ~A) = 1. (Normalization to 1) A3: for disjoint A, B: p(A v B) = p(A) + p(B) (finite additivity). I.e. for disjoint events the probabilities add up. Def Probabilistic independence/Schurz: probabilistically independent are two events A, B. gdw. p(A u B) = p(A) times p(B) . Probabilistically dependent: if P(A I B) is not equal to p(A). >Conditional probability, >Subjective probability. I 109 Def exhaustive/exhaustive/Schurz: a) objective probability: a formula A with n free variables is called exhaustive, gdw. the extension of A comprises the set of all n tuples of individuals b) subjective: gdw. the set of all models making A true (=extensional interpretations) coincides with the set of all models of the language considered possible. I 110 Def Partition/Schurz: exhaustive disjunction. >Probability theory. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Properties | Chisholm | I 20 Properties/Chhisholm: Problem: E.g. ""french" is not applicable to itself": here one cannot say that it has the property, not to itself ... otherwise paradox. >Grelling's paradox/heterology. Solution: "... has not the property ... "- not every predicate is a property - so not every sentence expresses a proposition. >Sentences, >Propositions, >Predication. I 24 Properties/Chisholm: no conjunctions: E.g. "wise and bigger than this man" is not a property - "living opposite" is not a property. I 170 Properties/Chisholm: "greater than" is no property, not even "greater than z", etc. - No predicative expression containing free variables has a property as meaning. --- II 67 Properties/Chisholm: is not a conjunctive property: E.g. e(thinking and (non-thinking or thinking) would not be a conjunctive property of the partial properties of e(thinking) - Involving: a involves b iff b is a partial property of a. II 75 Synthetic apriori/SauerVsChisholm: from the standpoint of property inclusion, there seems to be no synthetic apriori - under the one of property existence no analytic apriori - since aprioricity implies necessity, because the equivalence between necessity and existence exists in all possible worlds, there can be no Chisholm-apriori. Sauer, W. Über das Analytische und das synthetische Apriori bei Chisholm. In: M.David/L. Stubenberg (Hg) Philosophische Aufsätze zu Ehren von R.M. Chisholm Graz 1986 --- Frank I 362 Properties/Chisholm: the non-comparative form is basic: one thinks that something is red before one thinks two things are the same red. |
Chisholm I R. Chisholm The First Person. Theory of Reference and Intentionality, Minneapolis 1981 German Edition: Die erste Person Frankfurt 1992 Chisholm II Roderick Chisholm In Philosophische Aufsäze zu Ehren von Roderick M. Ch, Marian David/Leopold Stubenberg Amsterdam 1986 Chisholm III Roderick M. Chisholm Theory of knowledge, Englewood Cliffs 1989 German Edition: Erkenntnistheorie Graz 2004 Fra I M. Frank (Hrsg.) Analytische Theorien des Selbstbewusstseins Frankfurt 1994 |
| Proxy Function | Quine | VI 43 Proxy Function/Quine: is every explicit and reversibly unambiguous transformation f - E.g. if Px originally meant that x was a P, we therefore re-interpret Px so that it means that x is now f of a P -according for multi-digit predicates - the predicates then apply to the correlates fx instead to x - all sentences stay as they are - observation sentences remain correlated to the same stimuli - but the objects of the theory have changed dramatically - ((s) Example: There is a Gödel number of x.) >Predicates/Quine, >Observation Sentences/Quine VI 45 Ontology/Loewenheim/Proxy Function/Quine: the different ontologies resulting from both are unambiguously correlatable - and as a whole empirically indistinguishable. - E.g. Tabhita: is only Geach’s cat or cosmos minus cat - distinction: is relativistic: by the role that one plays relatively around the other - even the link to trained stimuli remains intact - the nodes where we assume the objects are neutral. >Ontology/Quine Lauener XI 145 Definition proxy function/Proxy Function/Quine/Lauener: a function that assigns to each object of the original theory such a one from the new theory. - E.g. The Goedel number of - to reduce one theory to another. Proxy Function/(s): maintains number of digits of the predicates (fulfillment of n-tuples of arguments by n-tuples of values). - Thus it averts the trivialization of a reduction to a theory of natural numbers (> Loewenheim). XII 72 Proxy Function/PF/Reduction/Quine: must not be reversibly unambiguous. E.g. irreversible proxy function which reduces a theory of expressions and fractions: Expressions by Goedel numbers, fractions with diagonal process. Then the same number can stand for a fraction or an expression. - That is ok, because fractures and expressions are so different that the question of identity does not arise, therefore, the original theory does not benefit from the differences. -> multi-sort logic - if, in contrast, all elements of the initial theory are distinguishable. (E.g. pure arithmetic of rational or real numbers) you need a reversibly unambiguous proxy function. >Reduction/Quine XII 74 Apparent Class/Quine: is given by open formula - E.g. a proxy function can be construed as an apparent class, if it is a function as an open formula with two free variables. - (> apparent quantification). |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 Q XI H. Lauener Willard Van Orman Quine München 1982 |
| Redundancy Theory | Quine | VII (i) 164 Redundancy Theory/Quine: it is doubtful whether the connection of "Fa" with "Fa is true" is analytic. XIII 214 Redundancy Theory/QuineVsRedundancy Theory/truth/Quine: the truth has been said to disappear, because the truth of the sentence is simply the sentence. ("Disapearance theory of truth") This is wrong: the quotation marks must not be taken lightly. We can only say that the adjective "true" is dispensable if it is applied to sentences that explicitly lie before us. Truth-predicate/true/generalization/Quine: is necessary to say that all sentences of a certain form are wrong. Or For example, a sentence that is not literal (not literally passed down) is true or false. Or E.g. that the slander paragraphs cannot be applied to true sentences or E.g. that you will tell the truth, the whole truth and nothing but the truth. N.B.: if you translate such sentences into the predicate logic, the subject of the truth- predicate is not a quotation, but a variable. These are the cases where the truth-predicate is not superfluous. Disquotation/truth/definition/Quine: the disquotational approach may still be useful when it comes to defining truth. Truth-Definition/truth/Quine: it identifies all discernible truths that the truth of the sentence is communicated by the sentence itself. But that is not a strict definition; it does not show us who could eliminate the adjective "true" XIII 215 from all contexts in which it can occur grammatically. It only shows us where we can eliminate it in contexts with quotations. Paradox/Quine: we have seen above (see liar paradox) that definability can contain a self-contradiction. It is remarkable how easily definable we found truth in the present context. How easy it can be and at the same time possibly fatal. Solution/Tarski: Separation object language/meta language. Recursion/Tarski/Quine: shows how the truth-term is first applied to atomic sentences and then to compositions of any complexity. Problem: Tarski could not yet define truth because of the variables. Sentences with variables can be true in some cases and false in others. (Open Sentences). Only closed sentences (where all variables are bound by quantifiers) can be true or false. Fulfillment/Recursion/Tarski/Quine: what Tarski recursively defines is fulfillment of a sentence by an object; is not truth. These objects are then the possible values of the free variables. After that, truth trivially results as a waste product. Def Truth/Fulfillment/Tarski: a closed sentence is true if it is fulfilled by the sequence of length 0, so to speak. Liar Paradox/Tarski/Quine: Tarski's construction is masterly and coherent, but why doesn't it ultimately solve the paradox? This is shown by the translation into symbolic logic when the sentence is formulated in object language (see paradoxes above, last section). Paradox/logical form/liar/Quine: the word "true" has the context "x is true" in the explicit reconstruction where "x" is the subject of quantifiers. Problem: the recursive definition of truth and fulfillment does not show how to "fulfill x". XIII 216 or "x is true" is eliminated. Solution: this only works if "x is true" or "fulfilled" is predicated by an explicitly given open or closed sentence. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Satisfaction | Davidson | Glüer II 18 ff "True" is semantic when derived. "Fulfilled" is primarily semantic., >Truth, >Truth theory, >Semantics. I 103 Predicates/Fodor: satisfaction by a subjective state: e.g. "Is this a short-billed hedgehog or a porcupine? - Thought about animals that meet certain general criteria (exactly the ones we use in the decision). I 104 DavidsonVsFodor: these states do not exist - instead: History of learning the word. >Causal theory of knowldge, >Learning, >Translation/Davidson. Glüer II 24 Def satisfaction/Tarski/Glüer: Relation between (ordered) sequences of objects and open sentences. Here the recursive method works: for elementary propositions it is defined which objects they fulfil and rules are given according to which for all compositions of open propositions it can be determined which objects they satisfy. Statements are determined as a special case of open sentences. They either contain no free variables, or they were closed with the help of quantifiers. II 25 With true statements, satisfaction is simple: for whether an ordered sequence of objects satisfies a proposition depends only on the free variable it contains. >Open sentence. Closed proposition/fulfillment: e.g. "The moon is round" does not contain any free variables. Thus the kind of the objects of the respective sequence is completely irrelevant and it can be determined by definition whether such a proposition is true, if it is satisfied by all sequences - or by none. Satisfaction/Quantifiers/Quantification: it is somewhat more complicated for quantified statements: For example "All stars are round" or "There is at least one star that is round", also here the fulfillment is defined in such a way that either all sequences fulfill one sentence or none. Thus it becomes clear that it would be absurd to associate truth of closed propositions with the fulfillment by no sequence of objects. Example A sentence like "All stars are round" is true if there are certain objects that fulfill "X is round": all stars. Def Truth/Tarski/Glüer: a statement is true if it is fulfilled by all objects, otherwise it is false". (Statement: special case of the satisfaction relation). >Statements. |
Davidson I D. Davidson Der Mythos des Subjektiven Stuttgart 1993 Davidson I (a) Donald Davidson "Tho Conditions of Thoughts", in: Le Cahier du Collège de Philosophie, Paris 1989, pp. 163-171 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (b) Donald Davidson "What is Present to the Mind?" in: J. Brandl/W. Gombocz (eds) The MInd of Donald Davidson, Amsterdam 1989, pp. 3-18 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (c) Donald Davidson "Meaning, Truth and Evidence", in: R. Barrett/R. Gibson (eds.) Perspectives on Quine, Cambridge/MA 1990, pp. 68-79 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (d) Donald Davidson "Epistemology Externalized", Ms 1989 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson I (e) Donald Davidson "The Myth of the Subjective", in: M. Benedikt/R. Burger (eds.) Bewußtsein, Sprache und die Kunst, Wien 1988, pp. 45-54 In Der Mythos des Subjektiven, Stuttgart 1993 Davidson II Donald Davidson "Reply to Foster" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 Davidson III D. Davidson Essays on Actions and Events, Oxford 1980 German Edition: Handlung und Ereignis Frankfurt 1990 Davidson IV D. Davidson Inquiries into Truth and Interpretation, Oxford 1984 German Edition: Wahrheit und Interpretation Frankfurt 1990 Davidson V Donald Davidson "Rational Animals", in: D. Davidson, Subjective, Intersubjective, Objective, Oxford 2001, pp. 95-105 In Der Geist der Tiere, D Perler/M. Wild Frankfurt/M. 2005 D II K. Glüer D. Davidson Zur Einführung Hamburg 1993 |
| Satisfaction | Putnam | I (c) 91 Satisfaction/Tarski: satisfaction is the terminus for reference. Putnam: there is a relation between words and things, more precisely, between formulas and finite sequences of things. Tarski: "The sequence of length only existing of x, satisfies the formula "electron (y)" iff x is an electron". The sequence Abraham: Isaac meets the formula "x is the father of y". If there are more binary relations one does not speak of Reference. > Correspondence Theory, -> picture theory. Putnam: Tarski's theory is not suitable for the correspondence theory because satisfaction is explained by a list (instead > meaning postulates: "electron" refers to electrons, etc.). "True" is the zero digit case of fulfillment: a formula is true if it has no free variables and if it meets the zero sequence. I (c) 92 Zero Digit Relation: e.g. Tarski: "true" is the zero digit case of satisfaction: that means, a formula is true if it has no free variables and if the zero sequence is met. Zero Sequence: converges to 0. Example 1, 1/4, 1/9, 1/16, ... I (c) 92 Satisfaction/Putnam: criterion T can be extended to the criterion E: (E) an adequate definition of fulfilled-in-S must generate all instances of the following scheme as theorems: "P(x1 ... xn) is only fulfilled by the sequence y1. ..yn when P (y1 .... yn). Reformulated: "electron (x)" is then and only then fulfilled by y1 when y1 is an electron. This is determined by truth and reference (not by provability) and is therefore even preserved in intuitionistic interpretation. PutnamVsField: Field's objection fails: for the realists the Tarski schema is correct. FieldVsTarski: this is similar to a "definition" of chemical valence by enumeration of all elements and their valence. The causal involvement in our explanations is lacking. PutnamVsField: truth and reference are not causally explanatory terms, we still need them for formal logic, even if scientific theories are wrong. |
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 |
| Satisfaction | Tarski | Glüer II 24f Recursive method/recursion: fails with quantifiers. >Recursive Method, >Quantifiers. E.g. "No tree is large and small" cannot be analyzed as two complete elementary propositions. Most complex sentences formed with variables, connectives, predicates, must be interpreted as links of open sentences. But open sentences have no truth value. >Open sentence, >Truth value. Therefore, Tarski introduces the term "satisfaction": Def satisfaction: relation between (ordered) sequences of objects and open sentences. Here works the recursive method: for elementary sentences it is defined which objects 2 they satisfy, and there are rules specified for all compositions of open sentences by which can be determined which objects they satisfy. Statements are determined as a special case of open sentences. Either they do not contain free variables, or they have been closed by means of quantifiers. >Free variables, >Open sentence. For true statements satisfaction is simple: because whether an ordered sequence of objects satisfies a sentence depends only on the free variables it contains. >Sequences/Tarski. E.g. "The moon is round" contains no free variables. Thus, the nature of the objects of the respective sequence is irrelevant and it can be determined by definition, whether such a proposition is true when it is satisfied by all the consequences - or by none. It is slightly more complicated for quantified statements: E.g. "All stars are around" or "There is at least one star, which is round." Here, too, the fulfillment is defined such that either all sequences satisfy a sentence, or none. So it is clear that it would be absurd to associate truth of closed sentences with fulfillment by any sequence of objects. A sentence like "All stars are round" is true if there are certain objects that satisfy "X is round": all stars. Tarski: a statement is true if it is satisfied by all objects, otherwise false." --- Berka I 399 Part definition/satisfy/Tarski. E.g. Johann and Peter satisfy the propositional function "X and Y are brothers" if they are brothers.(1) 1. A.Tarski, „Grundlegung der wissenschaftlichen Semantik“, in: Actes du Congrès International de Philosophie Scientifique, Paris 1935, Bd. III, ASI 390, Paris 1936, pp. 1-8 --- Horwich I 119 Fulfillment/Tarski: here we replace the free variables of propositional functions by the names of objects and see if we can get true statements - but that does not work when we use fulfillment to define truth. Solution: recursive procedure: rules for the conditions under which objects satisfy a composite propositional function. >Propositional functions. For whole sentences, there is also fulfillment: then a sentence is either satisfied by no object or by all. Satisfaction: has as a relation always one more spot - E.g. "is greater than": is a function between a relation and pairs of objects. Therefore, there are many fulfillment terms. Solution: "infinite sequence". Then satisfaction is a binary relation between functions and sequences of objects. The reason for this indirect truth definition is that compound sentences are composed of several propositional functions, not always of complete sentences. So there is no recursive definition. >Recursive definition, >Recursion. Horwich I 139 Satisfaction/antinomy/Tarski: for the fulfillment, we can also construct an antinomy: E.g. the statements function X does not satisfy X. - Now we look at the question of whether this term, which is surely a propositional function satisfied itself or not.(2) 2. A. Tarski, The semantic Conceptions of Truth, Philosophy and Phenomenological Research 4, pp. 341-75 --- Skirbekk I 146 Semantics: refers to statements, Satisfaction, designation: refers to objects. Skirbekk I 156 Truth/Tarski: we get the truth definition simply because of the definition of satisfaction: Def satisfaction/Tarski: satisfaction is a relationship between any object and propositional functions. An object satisfies a function when the function becomes a true statement, when the free variables replace with the name of object. Snow satisfies the propositional function "x is white". Vs: that is circular, because "true" occurs in the definition of fulfillment. Solution: satisfaction itself must be defined recursively. If we have the satisfaction, it relates by itself on the statements themselves. A statement is either satisfied by all objects, or by none.(3) 3. A.Tarski, „Die semantische Konzeption der Wahrheit und die Grundlagen der Semantik“ (1944) in. G: Skirbekk (Hg.) Wahrheitstheorien, Frankfurt 1996 |
Tarski I A. Tarski Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983 D II K. Glüer D. Davidson Zur Einführung Hamburg 1993 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 Horwich I P. Horwich (Ed.) Theories of Truth Aldershot 1994 Skirbekk I G. Skirbekk (Hg) Wahrheitstheorien In Wahrheitstheorien, Gunnar Skirbekk Frankfurt 1977 |
| Satisfiability | Tarski | Berka I 482 Satisfiability/Tarski: depends only on those terms of the sequence from which (with respect to their indices) correspond to the free variables of propositional functions. >Sequences/Tarski, >Propositional functions. In the case of a statement (without free variables) the satisfiability does not depend on the properties of the links. >Statements. Each infinite sequence of class satisfies a given true statement - (because it does not contain free variables). >Free variables, >Bound variables. False statement: satisfied by no sequence - variant: satisfiability by finite sequences: according to this view, only the empty sequence satisfies a true statement (because this one has no variables). Berka I 483 Satisfiability/sequences/statements/Tarski: (here: by finite sequences): E.g. the statement (not propositional function) L1U2l1,2. i.e. "PxlNPxllNIxlxll" according to Definition 22 (satisfiability) satisfies the propositional function L1,2 those and only those sequences f of classes for which f1 Being satisfied/satisfiability/Tarski: previously ambiguous because of relations of different linking numbers or between object and classes, or areas of different semantic categories - therefore actually an infinite number of different satisfiability-concepts - Problem: then no uniform method for construction of the concept of the true statement - solution: recourse to the class calculus: Satisfiability by succession of objects.(1) >Truth definition, >Truth theory, >Class calculus. 1. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol. 1, Lemberg 1935 |
Tarski I A. Tarski Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Substitution | Quine | VII (b) 29 Substitutability/substitution/QuineVsLeibniz: the strength of this requirement varies with the richness of the language - we need both, single- and multi-digit predicates, truth functions (not, and, or, etc.), classes, classes of classes, descriptions, singular terms. >Classes, >Descriptions, >Truth functions, >Predicates, >Richness, >Expressiveness, >Singular terms. This language is then extensional: any two predicates that match extensionally (are true for the same object) are substitutable salva veritate - but that does not secure cognitive synonymy. >Extensionality, >Extension. --- VII (c) 56 Substitutability/Quine: question salvo quo? Something is always changed. --- IX 9 Replace/substitution/Quine: if in a statement that has been substituted for "Fx" free variables other than "x" occurr, then they may not be such that fall under the scope of quantifiers that occur in the scheme in which the substitution was made. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Substitution (Insertion) | Gödel | I Berka 306 Inserting/replacing/substitution/Goedel: individual variables (free and bound) may be replaced by any other, provided there occurs no overlap of the range of equally naming variables.(1) >Range, >Scope, >Variables, >Individual variables, >Substitution, >Substitutability, >Formulas, >Free variables, >Bound variables. 1. K. Gödel: Die Vollständighkeit der Axiome des logischen Funktionenkalküls, in: Mh, Math. Phys. 37 (1930), pp. 349-360. |
Göd II Kurt Gödel Collected Works: Volume II: Publications 1938-1974 Oxford 1990 |
| Terminology | Hilbert | Berka I 58 Normal form/Berka: the normal form is another method to replace truth tables. An excellent (canonical) normal form was introduced by Hilbert/Ackermann (1928). Berka I 112 Definition convertible/Hilbert/Berka: a formula is convertible into another means when the equivalence of the two is derivable. Definition pranex/Hilbert: pranex is a formula in which all quantifiers are at the beginning and the ranges extend to the end. Definiton deduction-equal/Hilbert: two formulas are deduction-equal, if each is derivable from the other. Each formula is deduction-equal to each such formula, which results from it by replacing any free individual variable (IV) with a bound variable which has not previously occurred, and the universal quantifier belonging to the introduced bound variables (in any order) are placed at the beginning. ("Exchange of free variables against bound ones"). This can also be done in reverse order. Definition Skolem's normal form/Hilbert: the Skolem's normal form is a prenexic formula (that is, all quantifiers at the beginning, range to the end), where there is nowhere among the previous quantifiers a universal quantifier before an existential quantifier. Each formula is deduction-equal to a Skolem normal form. (s) Each formula can be transformed into a Skolem normal form. Note (I 116) This Skolem normal form is the "proof-theoretic" one. Definiton fulfillment theoretic Skolem normal form/Hilbert: the fulfillment of the theoretic Skolem normal form is dual to the proof-theoretic Skolem normal form, i.e. the universal quantifiers and existence quantifiers exchange their roles. >Duality. Insert/Hilbert/(s): inserting is used here for free variables. Rename/Hilbert/(s): renaming is used here for bound variables(1). 1. D. Hilbert & P. Bernays: Grundlagen der Mathematik, I, II, Berlin 1934-1939 (2. Aufl. 1968-1970). |
Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Thinking | Castaneda | Frank I 171ff Pure Thought/Pure Thinking/Castaneda/Pape: there is no pure self-conscious thinking, I always think of myself as having a certain localizable experience content as identical. (> Hume: "I" is applicable only on perceptions). >Self-consciousness, >Self-knowledge, >Self-identification, >Self, >I, Ego, Self, >I, Ego, Self/Hume, >Sensualism. Hector-Neri Castaneda(1966b): "He": A Study on the Logic of Self-consciousness, in : Ratio 8 (Oxford 1966), 130-157 I 385f Thinking/World/Castaneda: if the thought content is purely universal and abstract thinking, how can we get in touch with something special? - Chisholm allowed not only that singular terms are only composed of expressions that denote pure universals, he goes so far as to eliminate singular terms entirely analytically, by free variables with the performative role to express self-ascription. >Self-attribution, >Attribution, >Attribution/Chisholm, >Person/Chisholm, >Singular terms. |
Cast I H.-N. Castaneda Phenomeno-Logic of the I: Essays on Self-Consciousness Bloomington 1999 Fra I M. Frank (Hrsg.) Analytische Theorien des Selbstbewusstseins Frankfurt 1994 |
| Truth Predicate | Putnam | I (c) 90 Zero Digit Relation: e.g. Tarski: "true" is the zero digit case of satisfaction: that means, a formula is true if it has no free variables and the zero sequence is met. Zero Sequence: the zero sequence converges to 0. Example 1, 1/4, 1/9, 1/16, ... >Satisfaction, >Satisfiability. I (c) 97 Truth/logic/Putnam: the meaning of "true" and the connectives are not determined by their formal logic. -> Holism/Quine: the distinction between the whole theory and meanings of each statement is useless. I (e) 145 "True"/Tarski/Putnam: all writers: the meaning of "true" is detected by any definition that meets the criterion W. The meaning can still be explained by non-semantic vocabulary (descriptive words of the object language and logical vocabulary). >Object language, >Vocabulary, >Junctions, >Connectives, >Logical constants. |
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 |
| Truth Value Gaps | Quine | I 307 Truth Value Gap/Non-existence/Quine: We interpreted "exists" as (Ex)(y=x) which applies to everything just like "x=x". But also with this procedure anomalies result. It seems strange that "Pegasus exists" should be wrong if "(x)(x exists)" is true and "Pegasus" takes a purely descriptive position. Something is wrong if Pegasus is granted the purely descriptive position. >Descriptive position. I 308 The sense should be that the term concerned is used exclusively to indicate an object about which the rest of the sentence can say something. We can call this "truth value gaps" (the expression comes from Strawson). With open sentences we have not been disturbed by the fact that they have no truth value, but they can already be recognized by the way they are written. Here the gaps are disturbing precisely because they are not recognizable. Perhaps best with trivalent logic ("undecidable")? QuineVs: one does not assume that the difficulties come from a pedantic distinction between what is true and what is neither true nor false. If one were to summarize both categories under the rubric of the false, nothing would be gained. For they are distinguished from one another by the fact that one category contains the negations of all their elements, while the other does not contain a single negation of their elements. I 318 Singular descriptions "the", e.g. "the setting of the sun" Iota operator "i" (inverted, without dot) (ix)(...x...) "This x, for that applies" Here no synonymy is claimed by additional information (as in § 33). The logical theory made possible by the canonical framework treats ambiguous terms and indicator words as if they had fixed objects of reference. I 319 Let us now compare the identity statement "y = (ix)(...x...)" with the quantification: (1) (x)(...x...if and only if x = y) can be read briefly as "...y...and exclusively y". If either (1) or the reformulation applies to an object y, both are probably true. Nevertheless, both may differ in their conditions of falsity with respect to truth values! Because one can understand these gaps in such a way that "y = (ix)(...x...)" in relation to each object y has no truth value, if it applies to none, while "...y....and exclusively y" is simply wrong in relation to any object, if it doesn't apply to any. So we can simply put our aversion to gaps into action and equate "y = (ix)( ...x...) with "...y... and exclusively y" and accordingly fill the truth value gaps of "y = (ix)(...x..)" with the truth value incorrectly. This step enables us to make the singular identifications disappear at all. I 327 Definition/singular terms/truth value gaps/Quine: if we interpret definitions as instructions for the transformation of singular terms, we can avoid the annoyance of truth value gaps: I 328 The definition of the singular descriptions is then simple as follows: Def Singular Description: Write "y = (ix)(...x...)" and "(ix)(...x...) exists" as notation variants of "...y...and exclusively y." And with recourse to §37: Write "(ix)(...x...) " as abbreviation of (7) (Ey)[y = (ix)(...x...) and y ], (In this representation, we have " y " as any open sentence.) If we apply the three parts of the above definition successively and repeatedly, they are sufficient to make "(ix)(...x...)" accessible again to any position where free variables may occur. I 389/90 Conditional: the indicative conditional is unproblematic. In unquantified form "if p then q" it is perhaps best expressed as containing a truth value gap (§ 37) if its antecedence is false.(See also EFQ (ex falso quodlibet): ex falso quodlibet). I 449 In the case of the indicative conditional, the initial problems are the truth value gaps and the ambiguity of the truth conditions. They are solved by being able to dispense with the indicative conditional in favor of a truth function. I 447 StrawsonVsRussell: Strawson has misnamed Russell's theory of descriptions because of their treatment of truth value gaps. III 282 Truth Value Gap/Quine: comes from everyday language, in logic we have to fill it. And be it arbitrary. Every sentence should have a truth value (true or false). >Everyday language. XI 39 Canonical Notation/Quine/Lauener: closes truth value gaps. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Variables | Cresswell | Hughes I 118 Variables/free/bound/Hughes/Cresswell: it is all about occurrences of variables. - Therefore one and the same variable can be in one and the same formula both bound also occur as free. (> mention / >use /> word /object, >Word/object, >Free variables, >Bound variables. A token of x can be free and once again bound in the same formula. Hughes I 120 Free variables/inserting/propositional calculus/Hughes/Cresswell: when evaluating a formula, we must assume that the other possibly occurring free variables are constant. >Valuation. |
Cr I M. J. Cresswell Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988 Cr II M. J. Cresswell Structured Meanings Cambridge Mass. 1984 Hughes I G.E. Hughes Maxwell J. Cresswell Einführung in die Modallogik Berlin New York 1978 |
| Variables | Geach | I 198f Variable/description/proxy/GeachVsCarnap: in its rules for descriptions, e.g. ""___ ___ (ix)(...x...)___ ___" etc. the strokes do not function, as Carnap believes as vacancies (substitutes) but as variables! Carnap thinks, however, if he renames them, he avoids his problems with variables. >Variables / >Constants. I 199/200 Variables/Constants/GeachVsCarnap: Carnap does not distinguish between them, as he himself says: E.g. Carnap: "If "Q" is a constant pr (determined or indeterminate), then the sentences (Prague)" (city),"Q(a)" are all equally derivable from "Q(x)". Geach: "determined or undetermined", shows that the alleged "constant pr" is used as a variable. - Solution: "For all "Q" if ..." - but then we have a variable ""Q"" that contains quotes as part of itself. I 201 Free Variables/Strawson: E.g. (A) In "x is a human", "x" is a free variable. - Here, "x" does not occur as a free variable - because "x" is "x is a human" occurs as a free variable, the theorem (A) is true. - If (A) contained a free variable, it would not be a statement, but a propositional function. >Free variable. I 203 Bound variables/use/mention/Geach: in e.g. "x is a human being", "x" is needed, therefore it is a bound variable! (Bound by the quotes) - at the same time the expression is the name of a description, even if it does not denote anything. >Bound variables. >Denotation, >Designation. Names do not denote anything. |
Gea I P.T. Geach Logic Matters Oxford 1972 |
| Variables | Mates | I 36 Variable/Mates: for them names or descriptions are used. >Names, >Descriptions, >Inserting. Values: values include all objects, which can be designated by these expressions (according to a convention). >Naming, >Denotation, >Domains. I 37 no changeable things, also no names of changeable things. >Numbers/Frege, >Variables/Frege. I 66 Variable/free/bound/Mates: E.g. "(x)F"x": here bound for the second time. Problem: simultaneously within "F"x" free. - ((S) considered without quantifier. >Bound variables, >Free variables, >Quantifiers, >Quantification. I 67 and formulas (if used) may occur bound. >Logical formulas. I 68 (s) An entire formula always occurs free of course. Cf. >Free-standing content/Brandom, cf. >Generalization/Mates. |
Mate I B. Mates Elementare Logik Göttingen 1969 Mate II B. Mates Skeptical Essays Chicago 1981 |
| Variables | Simons | I 261 Free Variable/Simons: a free variable can be replaced with parameters: = variable, from which a function depends, and which is systematically varied to recognize the dependence of the function of it. >Functions, >Free variables. |
Simons I P. Simons Parts. A Study in Ontology Oxford New York 1987 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Carnap, R. | Field Vs Carnap, R. | I 118 FieldVsCarnap: although my approach is similar to that of Carnap in Meaning and Necessity, 1) it does not refer to meaning at all. I.e. no "meaning relations between predicates" ((s)> meaning postulates). 2) my treatment of free variables does not require the introduction of "individual concepts" and is consistently anti-essentialist. (FieldVsEssentialism): no formula of the form "MB" is true in a model with view to an attribution function if it is not also true in the model in relation to any other attribution function. Nino Cocchiarella/Carnap/Field: Cocchiarella: ("On the Primary and Secondary semantics of logical necessity"): an approach similar to Carnap: FieldVsCocchiarella/FieldVsRamseyFieldVsCarnap: leads to Ramsey’s bizarre conclusion that E.g. "it is possible that there are at least 10 to the power of 10 to the power of 10 objects" is logically false if the world happens to contain fewer objects (empirical). FieldVsCarnap: 3) his idea that modal concepts are derived from semantic concepts should be modified, Field: Just the other way around! (QuineVsField). II 186 Referential Indeterminacy/Reference/Theory Change/Reference Change/Semantic Change/Field: we now have all the components for the indeterminacy of reference: Only (HR) and (HP) remain, but are mutually exclusive. (HP) Newton’s word "mass" denoted net mass. (HR) Newton’s word "mass" denoted relativistic mass. In fact there is no fact on the basis of which you could opt for one of two. Vs: it could be argued that we only lack additional information. FieldVsVs: but then it should be possible already to say what kind of information that is supposed to be. And we have already found that there can be no fact here. "Mass"/Newton/Denotation/Reference/Field: the issue is not that we do not know what Newton’s "mass" denotes, but that Newton’s word was referentially indeterminate. (Because we do not know which of the two, HP or HR should be excluded.) II 187 The truth and falsity of (4R) and (5P) cannot be explained on the basis of what Newton referred to. FieldVsReferential Semantics/FieldVsCarnap: this is excluded by this indeterminacy of reference. |
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 |
| Cresswell, M.J. | Stechow Vs Cresswell, M.J. | I 154 Lambda-Operator/λ-Operator/Stechow: the language used here corresponds pretty much to the λ categorial of Cresswell 1973. Only difference: Cresswell: does not differentiate between syntactic categories and types. The type symbols act at the same time as category symbols. StechowVsCresswell: this is impractical, because different categories can have the same type. For example intransitive verbs as well as nomina are of type ep. Here: we choose a language with meaning*types, so e, p etc. Lambda-Operator/Semantics/Linguistics/Stechow: interprets the motion index. Thus the logical properties of the operator are transferred to the interpretation of the movement. Movement: (on LF) creates a lambda operator that binds its track and thus all the same variables (pronouns) that it commands c. 1. Interpretation: of a closed expression does not depend on the choice of a certain occupancy. This is a consequence of the so-called Def Coincidence Lemma: this means that two expressions, which differ only by free variables, can be interpreted in the same way by suitable assignments. 2. The syntax of the λ language contains the principle of the Def λ conversion, which is our function conversion. The principle says that you can break down a λ operator if you use an expression of the variable type for the variables bound by the operator. This follows from the >transition lemma. (>binding). 3. Bound Renaming/Stechow: if two expressions differ only in the choice of their bound variables, they mean the same thing. ^These are the alphabetical variants. |
A. von Stechow I Arnim von Stechow Schritte zur Satzsemantik www.sfs.uniï·"tuebingen.de/~astechow/Aufsaetze/Schritte.pdf (26.06.2006) |
| Ideas | Quine Vs Ideas | III 254 Singular Term/Existence/Quine: can designate an object, or not, but in any case it has a meaning. E.g. "Cerberus" ((s) >Unicorn example). Derivation: our techniques of QL (precisely with free variables) are very favorable for conclusions in which singular terms occur. III 255 But only if we are sure that the objects really exist! Existence/Ontology/Quine: the question of existence therefore moves (for reasons of logical deduction) into the focus. a) narrow view: existence as concrete presence in space and time. I.e. "exists" is equated with "is". Advantage: then no difference needs to be placed in "being", when it is about e.g. the Parthenon or the number 7. This is at most a difference in the type of object (concrete/abstract), but certainly not in the sense of "to be". Unicorn/Quine: E.g. there is nothing the word "Cerberus" denotes, neither in the past nor in the present nor in the future. III 256 But this is not about a "shadowy existence" for fear the word might lose its meaning. Unicorn/Meaning/Quine: if the word were without meaning, not only the poets would suffer; it would also be impossible, e.g., to express the simple fact of the non-existence of Cerberus. ((s) difference reference/meaning - Terminology/Quine: speaks of designating instead of reference). Idea/QuineVsIdea: false solution: speaking of Cerberus as an "idea": that would be doubling the existence: one in Athens and one in imagination. Or one in mythology, and one in the world. QuineVs: there is only one world) Solution/Quine: Parthenon "refers to the Parthenon and only the Parthenon, while" Parthenon idea" refers to Parthenon idea and only Parthenon idea. "Cerberus idea" does not denote Cerberus! Idea/Psychology/Quine: from the standpoint of practical psychology an idea could perhaps be explained as a tendency to certain reaction schemes to words. We can be as generous as we want with that. But to equate "Parthenon" with "Parthenon idea" would simply mean confusing one thing with another. And wanting to secure the existence of a thing like Cerberus through identification with an idea would be the same confusion. IV 399 QuineVsIdeas: the idea of the idea is of evil, because its use (just like a virtus dormitiva in Moliere) creates the illusion to have explained something. IV 400 Explanation/Sense: ideas neurophysiology is in charge of the explanations. Our mentalistic concepts can likewise not gain importance by the fact that they "ultimately refer" to neural states. We learned this vocabulary on the basis of behavior, and to know something of neurological issues. You can master it completely and simultaneously have a wrong or no opinions about the brain! Brain Condition/Predicates: with our predicates (folk psychology) things can be classified together that, seen neuro-physiologically, may be worlds apart! IV 401 QuineVsIdeas: reliance on the "ideas" has other drawbacks: 1) It leads to a mistaken image of communication as a transport of ideas from one mind to another. IV 402 2) It leads to a false theory of language acquisition, according to which it would simply obtained to link words with previously existing ideas at some point. Questions of learning are degraded to idle questions about the causal connection of ideas. 3) The wrong tendency to handle the different parts of speech as semantically identical is reinforced. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| substit. Quantific. | Quine Vs substit. Quantific. | V 158 VsSubstitutional Quantification/SQ/Quine: the SQ has been deemed unusable for the classic ML for a false reason: because of uncountability. The SQ does not accept nameless classes as values of variables. ((s) E.g. irrational numbers, real numbers, etc. do not have names, i.e. they cannot be Gödel numbered). I.e. SQ allows only a countable number of classes. Problem: Even the class of natural numbers has uncountably many sub-classes. And at some point we need numbers! KripkeVs: in reality there is no clear contradiction between SQ and hyper-countability! No function f lists all classes of natural numbers. Cantor shows this based on the class {n:~ (n e f(n))} which is not covered by the enumeration f. refQ: demands it in contrast to a function f enumerating all classes of natural numbers? It seems so at first glance: it seems you could indicate f by numbering all abstract terms for classes lexicographically. Vs: but the function that numbers the expressions is not quite the desired f. It is another function g. Its values are abstract terms, while the f, which would contradict the Cantor theorem, would have classes as values... V 159 Insertion character: does ultimately not mean that the classes are abstract terms! ((s) I.e. does not make the assumption of classes necessary). The cases of insertion are not names of abstract terms, but the abstract terms themselves! I.e. the alleged or simulated class names. Function f: that would contradict Cantor's theorem is rather the function with the property that f(n) is the class which is denoted by the n-th abstract term g(n). Problem: we cannot specify this function in the notation of the system. Otherwise we end up with Grelling's antinomy or that of Richard. That's just the feared conflict with Cantor's theorem. This can be refute more easily: by the finding that there is a class that is not denoted by any abstract term: namely the class (1) {x.x is an abstract term and is not a member of the class it denotes}. That leaves numbers and uncountability aside and relates directly to expressions and classes of expressions. (1) is obviously an abstract expression itself. The antinomy is trivial, because it clearly relies on the name relation. ((s) x is "a member of the class of abstract expressions and not a member of this class"). V 191 Substitutional Quantification/SQ/Nominalism/Quine: the nominalist might reply: alright, let us admit that the SQ does not clean the air ontologically, but still we win something with it: E.g. SQ about numbers is explained based on expressions and their insertion instead of abstract objects and reference. QuineVsSubstitutional Quantification: the expressions to be inserted are just as abstract entities as the numbers themselves. V 192 NominalismVsVs: the ontology of real numbers or set theory could be reduced to that of elementary number theory by establishing truth conditions for the sQ based on Gödel numbers. QuineVs: this is not nominalistic, but Pythagorean. This is not about the extrapolation of the concrete and abhorrence of the abstract, but about the acceptance of natural numbers and the refutal of the most transcendent nnumbers. As Kronecker says: "The natural numbers were created by God, the others are the work of man." QuineVs: but even that does not work, we have seen above that the SQ about classes is, as a matter of principle, incompatible with the object quantification over objects. V 193 VsVs: the quantification over objects could be seen like that as well. QuineVs: that was not possible because there are not enough names. Zar could be taught RZ coordination, but that does not explain language learning. Ontology: but now that we are doing ontology, could the coordinates help us? QuineVs: the motivation is, however, to re-interpret the SQ about objects to eliminate the obstacle of SQ about classes. And why do we want to have classes? The reason was quasi nominalistic, in the sense of relative empiricism. Problem: if the relative empiricism SQ talks about classes, it also speaks for refQ about objects. This is because both views are closest to the genetic origins. Coordinates: this trick will be a poor basis for SQ about objects, just like (see above) SQ about numbers. Substitutional/Referential Quantification/Charles Parsons/Quine: Parsons has proposed a compromise between the two: according to this, for the truth of an existential quantification it is no longer necessary to have a true insertion, there only needs to be an insertion that contains free object variables and is fulfilled by any values of the same. Universal quantification: Does accordingly no longer require only the truth of all insertions that do not contain free variables. V 194 It further requires that all insertions that contain free object variables are fulfilled by all values. This restores the law of the single sub-classes and the interchangeability of quantifiers. Problem: this still suffers from impredicative abstract terms. Pro: But it has the nominalistic aura that the refQ completely lacks, and will satisfy the needs of set theory. XI 48 SQ/Ontology/Quine/Lauener: the SQ does not make any ontological commitment in so far as the inserted names do not need to designate anything. I.e. we are not forced to assume values of the variables. XI 49 QuineVsSubstitutional Quantification: we precisely obscure the ontology by that fact that we cannot get out of the linguistic. XI 51 SQ/Abstract Entities/Quine/Lauener: precisely because the exchange of quantifiers is prohibited if one of the quantifiers referential, but the other one is substitutional, we end up with refQ and just with that we have to admit the assumption of abstract entities. XI 130 Existence/Ontology/Quine/Lauener: with the saying "to be means to be the value of a bound variable" no language dependency of existence is presumed. The criterion of canonical notation does not suppose an arbitrary restriction, because differing languages - e.g. Schönfinkel's combinator logic containing no variables - are translatable into them. Ontological Relativity/Lauener: then has to do with the indeterminacy of translation. VsSubstitutional Quantification/Quine/Lauener: with it we remain on a purely linguistic level, and thus repeal the ontological dimension. But for the variables not singular terms are used, but the object designated by the singular term. ((s) referential quantification). Singular Term/Quine/Lauener: even after eliminating the singular terms the objects remain as the values of variables. XI 140 QuineVsSubstitutional Quantification: is ontologically disingenuous. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 |
| Tarski, A. | Field Vs Tarski, A. | Brendel I 68 T-Def/FieldVsTarski: does not do justice to physicalistic intuitions. (Field 1972). Semantic concepts and especially the W concept should be traceable to physical or logical-mathematical concepts. Tarski/Brendel: advocates for a metalinguistic definition himself that is based only on logical terms, no axiomatic characterization of "truth". (Tarski, "The Establishment of Scientific Semantics"). Bre I 69 FieldVsTarski: E.g. designation: Def Designation/Field: Saying that the name N denotes an object a is the same thing as stipulating that either a is France and N is "France" or a is Germany and N is "Germany"... etc. Problem: here only an extensional equivalence is given, no explanation of what designation (or satisfiability) is. Bre I 70 Explanation/FieldVsTarski/Field: should indicate because of which properties a name refers to a subject. Therefore, Tarski’s theory of truth is not physicalistic. T-Def/FieldVsTarski/Field/Brendel: does not do justice to physicalistic intuitions - extensional equivalence is no explanation of what designation or satisfiability is. Field I 33 Implication/Field: is also in simpler contexts sensibly a primitive basic concept: E.g. Someone asserts the two sentences. a) "Snow is white" does not imply logically "grass is green". b) There are no mathematical entities such as quantities. That does not look as contradictory as Fie I 34 John is a bachelor/John is married FieldVsTarski: according to him, a) and b) together would be a contradiction, because he defines implication with quantities. Tarski does not give the normal meaning of those terms. VsField: you could say, however, that the Tarskian concepts give similar access as the definition of "light is electromagnetic radiation". FieldVsVs: but for implication we do not need such a theoretical approach. This is because it is a logical concept like negation and conjunction. Field II 141 T-Theory/Tarski: Thesis: we do not get an adequate probability theory if we just take all instances of the schema as axioms. This does not give us the generalizations that we need, for example, so that the modus ponens receives the truth. FieldVsTarski: see above Section 3. 1. Here I showed a solution, but should have explained more. Feferman/Field: Solution: (Feferman 1991) incorporates schema letters together with a rule for substitution. Then the domain expands automatically as the language expands. Feferman: needs this for number theory and set theory. Problem: expanding it to the T-theory, because here we need scheme letters inside and outside of quotation marks. Field: my solution was to introduce an additional rule that allows to go from a scheme with all the letters in quotation marks to a generalization for all sentences. Problem: we also need that for the syntax,... here, an interlinking functor is introduced in (TF) and (TFG). (see above). II 142 TarskiVsField: his variant, however, is purely axiomatic. FieldVsTarski/FefermanVsTarski: Approach with scheme letters instead of pure axioms: Advantages: 1) We have the same advantage as Feferman for the schematic number theory and the schematic set theory: expansions of the language are automatically considered. 2) the use of ""p" is true iff. p" (now as a scheme formula as part of the language rather than as an axiom) seems to grasp the concept of truth better. 3) (most important) is not dependent on a compositional approach to the functioning of the other parts of language. While this is important, it is also not ignored by my approach. FieldVsTarski: an axiomatic theory is hard to come by for belief sentences. Putnam I 91 Correspondence Theory/FieldVsTarski: Tarski’s theory is not suited for the reconstruction of the correspondence theory, because fulfillment (of simple predicates of language) is explained through a list. This list has the form "Electron" refers to electrons "DNS" refers to DNS "Gene" refers to genes. etc. this is similar to (w) "Snow is white" is true iff.... (s)> meaning postulates) Putnam: this similarity is no coincidence, because: Def "True"/Tarski/Putnam: "true" is the zero digit case of fulfillment (i.e. a formula is true if it has no free variables and the zero sequence fulfills it). Def Zero Sequence: converges to 0: E.g. 1; 1/4; 1/9; 1/16: ... Criterion W/Putnam: can be generalized to the criterion F as follows: (F for fulfillment): Def Criterion F/Putnam: (F) an adequate definition of fulfilled in S must generate all instances of the following scheme as theorems: "P(x1...xn) is fulfilled by the sequence y1...yn and only if P(y1...yn). Then we reformulate: "Electron (x)" is fulfilled by y1 iff. y1 is an electron. PutnamVsField: it would have been formulated like this in Tarskian from the start. But that shows that the list Field complained about is determined in its structure by criterion F. This as well as the criterion W are now determined by the formal properties we desired of the concepts of truth and reference, so we would even preserve the criterion F if we interpreted the connectives intuitionistically or quasi intuitionistically. Field’s objection fails. It is right for the realist to define "true" à la Tarski. |
Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 Bre I E. Brendel Wahrheit und Wissen Paderborn 1999 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 |
| Tarski, A. | Brendel Vs Tarski, A. | I 49 Truth-Def/Tarski/Brendel: contains no object constants and only one relation expression for class inclusion. Testimony/Property/Name/Model Theory/Brendel: compared to Tarski we need some changes: 1. Statements no longer result from the fact that free variable n AF are bound by universal quantification, but e.g. that object constants are assigned property or relation expressions. Example "Hans loves Paula". 2. Property/Model Theory: here you also have to specify for each property what it means that I 50 a sequence of objects satisfies this property or relation. 3. Naming/Model Theory: a semantic relation of the naming of objects by object constants must be formulated. Interpretation/Model Theory/Brendel: (instead of fulfillment) new: now the constants as well as the variables and the property and relation expressions can be used as descriptive signs. This is done by a function of assignment. (Assignment function). Variables/Model Theory: new: now also variables are interpreted semantically. Therefore also formulas with free variables are truthful statements. Truth-Def/Modell Theory/BrendelVsTarski: new: now also a recursive truth definition about the structure of statements is possible. Example for the language L with countable infinite property and relation expressions ...+.... I 51 Model Theory/T-Def/BrendelVsTarski: this model theoretical truth definition is more general than Tarski's definition, since it cannot only make statements about set-theoretical entities. Semantic: but it is also because "truth" is defined by "interpretation in an area of objects", i.e. a function is described that connects linguistic entities with non-linguistic ones. I 58 Semantic Truth/T-Concept/Brendel: should be ontologically neutral in relation to truth value-bearers. VsRealism: should the T-concept force a realistic position, it could not function as minimal consensus of all knowledge conceptions. VsTarski: he is often accused of his T-concept being based on an uncritical realism. (Because of the existence of state of affairs as truth makers.) TarskiVsVs: no realism is implied, but only that if a statement is rejected, then also the assertion of the truth of this statement. (Tarski 1944, 169). I 59 JenningsVsTarski: his T-term is ambivalent: a) semantic, as relation between statements and the state of affairs b) that only an equivalence of two statements (e.g. "snow is white" and, "sn..."is true") (Jennings 1987). I.e. the assertiveness conditions are the same. But then the semantic dimension is abandoned! Brendel: Thesis: we should keep the semantic T-concept, which however is not ontologically neutral. |
Bre I E. Brendel Wahrheit und Wissen Paderborn 1999 |
| Various Authors | Burge Vs Various Authors | Wol I 272 Names/Burge: Vs theory of individual constants: large number of indexes for each of the really existing people and objects. Moreover, the truth theorists would have to go to great lengths to really consider all the Johns who a speaker knows. Variant of I. theory: proper names only if they are used to analyze constants interpreted as complete, but otherwise as indefinite constants. Burge pro: that way, one might regard proper names as free variables. That would work. Problem: the conventional predicative element would be disregarded. One could not give a semantic representation according to which a name could be applied to some objects, but not to others. That would give up the consistent view of modified and unmodified incidents. The advantage of our conception of the names as predicates is that we do not need to distinguish the objects to which they apply truth theoretically. It is picked out as a singular term by the reference of the speaker. The infinity of possible objects is represented by the variable. |
Burge I T. Burge Origins of Objectivity Oxford 2010 Burge II Tyler Burge "Two Kinds of Consciousness" In Bewusstein, Thomas Metzinger Paderborn/München/Wien/Zürich 1996 |
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The author or concept searched is found in the following theses of the more related field of specialization.
| Disputed term/author/ism | Author |
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| Predication | Wright, von G.H. | Hughes/CresswI 162 Principle of Predication/PdP/von Wright/Hughes/Cresswell: Thesis: according to this principle, all properties belong to one of the following two species: (a) Formal properties: those whose belonging ((s) or not belonging) to an object is always necessary or impossible. (b) Material properties: whose belonging to an object is always contingent. Therefore, if f is a formal property, it applies: (x)Lfx v L~fx) Material Property: (x)Mfx. M~fx). Principle of Predication (PdP): (x)(Lfx v L~fx) v (x)(Mfx . M~fx) We can generalize that into a scheme: Pr (a)(La v L~a) v (a)(Ma . M~a) whereby a is an invariant and a is any well formed formula containing no free variables other than a. Hughes/Cresswell: the principle of predication is not a thesis even in PK+S5, but it could be added to it without contradiction to a PK+S5+Pr system. |
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