Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 20 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Constants | Constants, philosophy, logic: constants are conditions which do not change, in contrast to processes, states, and also natural objects, e.g. aging. An aging human being remains constantly the same person, but not the same body. For a constant, e.g. a name for an object is given. Letters of logic are given for individual constants (a, b, c ...), but also for individual variables (x, y, z ...). Variables are not changing objects, but a new object may be used instead of a variable, e.g. 4 instead of 5. These two numbers, however, are not changing objects, but have a constant value. |
||
| Derivation | Hilbert | Berka I 113 Derivation/insertion/"evidence threads"/Hilbert: any derivation can be dissolved into evidence threads, that is, we start with the final formula by applying the schemes (α), (β), (...). I 114 N.B.: then by the dissolution of a derivative into evidence threads, one can put back the insertions into the initial formulas. >Proofs, >Provability, >Derivability. Inserting/insertion rules/variables/evidence threads/Hilbert: we can do without rules of insertion by putting back the insertions (by means of evidence threads). From the derivation of formulas which contain no formula variable, we can eliminate the formula variables altogether, so that the formally deductive treatment of axiomatic theories can take place without any formula variables. >Inserting. Hilbert: the rule that identical formulas of the propositional calculus are permitted as initial formulas is modified in such a way that each formula which results from an identical formula of the propositional calculus by insertion is permitted as the initial formula. Evidence(s): the rule of insertion is also superfluous by the fact that one can study the practical application in the course of time. That is, each case is documented, so you do not need a rule for non-current cases. Hilbert: Instead of the basic formula (x)A(x) > A(a) is now: (x)A(x) > A(t) And in place of (Ex) A (x) is now: A(t) > (Ex)A(x) t: term. Formulas are replaced by formula schemes. Axioms are replaced with axiom schemata. In the axiom schemata, the previously free individual variables are replaced by designations of arbitrary terms, and in the formula schemes, the preceding formula variables are replaced by arbitrary formulas(1). >Schemes, >Axioms, >Axiom systems. 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 |
| Descriptions | Hintikka | II 172 Description/knowledge/Russell/Hintikka: knowledge by description: here, we know propositions about the "so-and-so" without knowing who or what the "so-and-so" is. >Propositional knowledge, >Knowlege how, >Knowledge. Ad (ii): e.g. description: instead of Bismarck: "the first chancellor of the German Reich". HintikkaVs (ii) this sweeps the problem under the carpet. Problem: the use of descriptions must ultimately lead to the fact that the descriptions are translated back into names, and this is not possible here! Also: Reduction/description/names/Hintikka: not all individuals with descriptions we talk about have identities that are known to everyone. The interpretation of Russell does not rule out the fact that many different entities act as legitimate values of the variables, which in principle can also be named with names. Ad (iii) Russell/Hintikka: that was Russell's implicit solution: he redefines the range of the individual variables so that they are restricted to individuals we know by acquaintance. Existential Generalization/EG/Russell/Hintikka: the existential generalization applies only to names of individuals with whom we are familiar. Concealed Description/Russell/Hintikka: the existential generalization fails for individuals whose names have to be conceived as covert descriptions ((s) because we know them only by description). Cf. >Acquaintance. |
Hintikka I Jaakko Hintikka Merrill B. Hintikka Investigating Wittgenstein German Edition: Untersuchungen zu Wittgenstein Frankfurt 1996 Hintikka II Jaakko Hintikka Merrill B. Hintikka The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989 |
| Domains | Hintikka | II 98 Individual Domain/possible worlds/Montague/Hintikka: thesis: Montague assumes a constant domain of individuals. >Possible worlds. HintikkaVsMontague: precisely this assumption leads to problems. Especially in religious contexts. Individual/Montague: individuals are the domain of functions that function as the sense of a singular term. >Singular terms. Belief Context/opaque context/belief/propositional attitude/HintikkaVsMontague: problem: Montague does not allow a special approach (setting contexts) for contexts with propositional attitudes. E.g. "knowing who", e.g. "remembering where", e.g. "seeing what". This is a defect because Montague had been interested in propositional attitudes. >Propositional attitudes. II 176 Domain/variable/individual variable/quantification/Hintikka: my own approach (semantics of possible worlds) has been called "interpretation of the restricted domain". HintikkaVs: this misunderstands the logical situation: it is about the fact that the individuals have to be well-defined for the set of worlds with which we have to deal. N.B.: the set of worlds changes with the propositional attitudes. So the actual world, e.g. does not have to be included! Cf. >Hyperintensionality. Propositional Attitudes/Hintikka/(s): different attitudes (beliefs, doubts, seeing, etc.) demand different sets of worlds. Variables/values/Hintikka: it may be that the domain of our variables can be a superset of the set of the actual individuals (if the set of possible worlds does not contain the actual world). E.g. it may be that someone has correct beliefs about all the actual individuals, but also mistakenly believes that there are still more individuals that he only imagines. Hintikka: therefore my approach can be called with the same right one of the "extended domains". II 176 Individual domain/domain/Russell/Hintikka: Russell, on the other hand, seems to have actually represented a set of the restricted domain by restricting it to objects of acquaintance. II 196 Possible world/individual domain/HintikkaVsKripke: one should not demand that the individuals must remain the same when changing from world to world. The speech of worlds is empty if there is possible experience that could make them different. Cf. >Centered worlds. Possible worlds/Hintikka: possible worlds should be best determined as by the connected possible totals of experience. And then separation cannot be excluded. II 196 Separation/Hintikka: separation is useful in a few models of cross-world identification, re-identification in time. E.g. a computer could be dismantled and two computers could be built from it. This could be revised later. Re-identification/Hintikka: re-identification is the key to cases of separation and fusion. Separation/Hintikka: there is a structural reason why separation is so rare: if world lines are composed of infinitesimal elements as the solutions of differential equations, the separation corresponds to a singularity, and this is a rare phenomenon. Separation/Hintikka: the arguments against them are circular in a deep sense. They are based on the idea that for quantification the individual area should remain fixed (HintikkaVsKripke). Cf. >Systems S4/S5 |
Hintikka I Jaakko Hintikka Merrill B. Hintikka Investigating Wittgenstein German Edition: Untersuchungen zu Wittgenstein Frankfurt 1996 Hintikka II Jaakko Hintikka Merrill B. Hintikka The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989 |
| Donkey Sentences | Cresswell | I 171 Geach’s donkey/Cresswell: indicates a bound individual variable, instead of a description "the donkey, he has". universal quantifier: simple Category. Then: - with Lewis: "unselective quantifier" (simply binds all variables). Problem: this is more difficult than existantial quantification: has antecedens and consequens (order no longer matters). Then generalized universal quantification: generalized quantors exclude mixed quantors. Variant: if-sentence. Geach's Donkey/Cresswell: the sentence shows a bound individual variable instead of a description "The donkey he owns". Universal quantifier: If we leave ∀ in the simple category of <0, <0,1>, <0,1>>, we need two ∀'s: (22) ‹∀, ‹a donkey›, ‹λx, ‹∀, ‹man, ‹which , ‹λy, ‹y, has, x››› ‹λ, y, ‹y beats, ‹it, x››››››. Everyday translation: every donkey is an x so that every man who has x beats x. >Universal quantification, >Semantic categories/Cresswell. Problem: more difficult than in the case of existence quantification: here there is antecedence and consequence (order does not matter any longer) - then generalized universal quantifier: The generalized ∀ would have to be for (22) in the category ‹0, ‹0,1›, ‹0,1›, ‹0,1 ›› and (21) (Geach's donkeys) would be (23) ‹∀, ‹‹λxy ‹a man, ‹which, ‹λz ‹has zy››› , x›, ‹λxy ‹a donkey y››, ‹λxy, ‹beats x ‹it y››››››. Problem: how to deal with it. Universal quantifier: the semantics for ∀ is: ‹w,t› ε V(∀)(ω1,ω2,ω3) ↔ for each a so that ‹w,t› ε ω1(a) and ‹w,t› ε ω2(a) we have ‹w,t› ε ω3(a). >Geach's donkey, >Lambda-abstraction. |
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 |
| Existence | Cresswell | I HC 155 Existence/possible worlds/modal logic/Hughes/Cresswell/(s): here it is about properties that occur in worlds, although the items (bearers of these properties), do not exist (here as individual variables) in these worlds. >Modal properties, >Possible worlds, >Modalities, >Barcan-Formula, >Non-existence, >Individual variable, cf. >Properties/Quine. |
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 |
| I, Ego, Self | Castaneda | Frank I 159 ff I/Castaneda: "volatile egos": like "here", "now", irreducible. - They are entirely epistemological, only for re-presentation, not empirical. Limited identity: only consubstantiation (sameness between coexisting sets of characteristics): not diachronic (transsubstatiation), therefore not all properties are identical, no substitutability, no strict identity with person. "I" is criteria-less, content-neutral. - "I" can only be represented by the impersonal and situation independent quasi-indicator "he". I-design/Castaneda: Vs "I" as "Something". >Guise theory, >Quasi-Indicator. I 167ff I*/Castaneda: "I myself" in an episode of self-awareness one refers to oneself - (corresponding for he*). I 186 "I" is no demonstrative. >Demonstratives. I 170 Transcendent I/Castaneda: we experience ourselves as a not completely identical with the content of our experiencen and therefore associated to the world beyond experience. I 171 I/Self/Consciousness/Self-Awareness/SA/Logical Form/Hintikka/Castaneda: E.g. "The man who is actually a, knows that he is a". Wrong: "Ka (a = a). - Right: (Ex) (Ka (x = a)) -the individual variables occurring in "Ka (...)" are conceived as relating to a range of objects that a knows - "there is a person whom a knows, so that a knows that this person is a" - CastanedaVs: does not work with contingent assertions: "there is an object, so that a does not know it exists" - E.g. "the editor does not know that he is the editor" - (Ex) (Ka(x = a) & ~Ka(x = a))) was be a formal contradiction - better: (Exa)(Ka (x = a) & Ka (x = himself) (not expressible in Hintikka). I 226f I/Castaneda: no specific feature - different contrasts: opposites: this/that, I/she - I/he - I (meaning/acting person) - I/you - I/we -> Buber: I/it - I/you -> Saussure: network of contrasts (plural). Hector-Neri Castaneda(1966b): "He": A Study on the Logic of Self-consciousness, in : Ratio 8 (Oxford 1966), 130-157 Frank I 378 I/hall of mirrors/Castaneda: seems to need two selves: one he speaks to, one he speaks about - but simple self as different from I and body not sufficient. I 430f I/Extra sense/Castaneda: psychological role that one associates with "I" - which explains mental states that do not explain proper names or descriptions: "I'm called for on the phone": spec. mental states - PerryVsCastaneda: not sufficient, you also need to know that it is the own It! - A proposition with "he*" itself says nothing about the meaning of this expression, therefore no identification - E.g. "heaviest man in Europe" could know this without a scale if "he*" could act independently without antecedent. Solution: intermediary extra sense for Sheila's beliefs about Ivan's extra-sense-i. Hector-Neri Castaneda (1987b): Self-Consciousness, Demonstrative Reference, and the Self-Ascription View of Believing, in: James E. Tomberlin (ed) (1987a): Critical Review of Myles Brand's "Intending and Acting", in: Nous 21 (1987), 45-55 James E. Tomberlin (ed.) (1986): Hector-Neri.Castaneda, (Profiles: An International Series on Contemporary Philosophers and Logicians, Vol. 6), Dordrecht 1986 I 470 I/Castaneda: Variable, not singular term, not singular reference: instead: i is the same as j and Stan believes of j... >Singular Terms, >Variables. |
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 |
| Implication Paradox | Wessel | I 129 C.I.Lewis VsParadoxes of the implication: "strict implication": modal: instead of "from contradiction any statement": "from impossible ..." >Implication, strict, >Modalities, >Modal logic. WesselVsLewis, C.I.: circular: modal terms only from logical entailment relationship - 2.Vs: strict Implication cannot occur in provable formulas of propositional calculus as an operator. >Consequence, >Operators. I 140ff Paradoxes of implication: strategy: avoid contradiction as antecedent and tautology as consequent. >Tautologies, >Antecedent, >Consequent. I 215 Paradoxes of implication/quantifier logic: Additional paradoxes: for individual variables x and y may no longer be used as any singular terms - otherwise from "all Earth's moons move around the earth" follows "Russell moves around the earth". Solution: Limiting the range: all individuals of the same area, for each subject must be clear: P (x) v ~ P (x) - that is, each predicate can be meant as a propositional function - Wessel: but that is all illogical. >Logic, >Domain. |
Wessel I H. Wessel Logik Berlin 1999 |
| Index Words | Peirce | Berka I 29 Index/indicator/Peirce: E.g. pointing finger - the physical evidence: does not say anything, it just says "there!" >Indexicality, >Ostension, >Pointing, >Ostensive definition. Berka I 30 Conclusion/Peirce: needs in addition to symbol (for truth) and index (both together (for sentence formation) the 3rd character: the icon: because inference consists in the observation that where certain relations exist, some other relations can be found. >Conclusion, >Symbols, >Icons, >Relations. These relations must be represented by an icon - e.g. the middle term of the syllogism must actually occur in both premises.(1) >Syllogisms, >Premises. Berka I 31 E.g. the empty spaces that must be filled with the symbols (x, y, ...) are indices of symbols.(1) >Variables, >Constants, Individual variables, >Individual constants, >Logical operations, >Logical formulas. 1. Ch. S. Peirce, On the algebra of logic. A contribution to the philosophy of notation. American Journal of Mathematics 7 (1885), pp. 180-202 – Neudruck in: Peirce, Ch. S., Collected Papers ed. C. Hartstone/P. Weiss/A. W. Burks, Cambridge/MA 1931-1958, Vol. III, pp. 210-249 |
Peir I Ch. S. Peirce Philosophical Writings 2011 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Individual Constants | Individual Constants: individual constants are symbols representing a single object, as opposed to individual variables. Individual constants allow you to insert a name for the object when it occurs repeatedly within a formula or an inference. Often, an a, b, c,… is used for individual constants while x, y, z are for individual variables. Individual variables do not ensure that the same object is meant during repeated use. See also constants, variables, logic, interpretation, Substitution. |
||
| Inserting | Hilbert | Berka I 113 Derivation/inserting/"evidence threads"/Hilbert: every derivation can be dissolved into evidence threads, that is, we start with the final formula by applying the schemes (α), (β), (...). >Derivation, >Derivability. I 114 N.B.: then by the dissolution of a derivative into evidence threads, one can put back the insertions into the initial formulas. Inserting/insertion rules/variables/evidence threads/Hilbert: we can do without rules of insertion by putting back the insertions (by means of evidence threads). From the derivation of formulas which do not contain a formula variable, we can eliminate the formula variables altogether, so that the formally deductive treatment of axiomatic theories can take place without any formula variables. >Proofs, >Provability. Hilbert: the rule that identical formulas of the propositional calculus are allowed as initial formulas is modified in such a way that each formula which results from an identical formula of the propositional calculus is permitted as an initial formula. Evidence threads(s): the rule of insertion also becomes superfluous by the fact that one can study the practical application in the course of time. That is, each case is documented, so you do not need a rule for non-current cases. Hilbert: In the place of the basic formula (x)A(x) > (A(a) is now: (x)A(x) > A(t) and in the place of (Ex)A(x) is now: A(t) > (Ex)A(x) t: term. Formulas are replaced by formula schemes. Axioms are replaced by axiom schemata. In the axiom schemata, the previously free individual variables are given by designations of arbitrary terms, and in the formula schemes, the preceding formula variables are replaced by arbitrary formulas(1). >Axioms, >Axiom systems. 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 |
| Proof Theory | McDowell | ad Hughes I 119 Validity/Propositional Calculus: truth tables are not sufficient for an evaluation of formulas in the propositional calculus - because we cannot assign specific individual variable and predicate variables. >Intuitionism, >Proof, cf. >Model theory. |
McDowell I John McDowell Mind and World, Cambridge/MA 1996 German Edition: Geist und Welt Frankfurt 2001 McDowell II John McDowell "Truth Conditions, Bivalence and Verificationism" In Truth and Meaning, G. Evans/J. McDowell Hughes I G.E. Hughes Maxwell J. Cresswell Einführung in die Modallogik Berlin New York 1978 |
| Propositional Logic | Berka | Berka I 237 Propositional logic: has no subject variables - because it contains no quantifiers. >Variables, >Individual variables, >Quantifiers >Quantification, >Statements, >Propositional calculus, >Logic. |
Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Prosentential Theory | Grover, D. L. | Horwich I 315 Prosentential Theory/Camp, Grover, Belnap/CGB/Grover: (modification of Ramsey's approach) thesis: if we enrich everyday language slightly with propositional quantification (quantification over propositions), then we can express everything without a truth predicate ("true") that we can express with it. See T-predicate, truth predicate. I 324 Prosentential Theory/CGB: variables do not need to be connected with predicates in prosentences. Everyday Language: everyday language already has prosentences, e.g. "it is true", "that's true". Relative pronoun: a relative pronoun is only possible with individual variables - not with propositional variables (they have a sentence position). Solution: a solution offers the cross-reference - then a variable in the prosentence does not have to be connected to a verb. I 325 True/Ramsey: "true" does not have to attribute a property. CGB: true may be a fragment of the prosentence. I 334 Prosentential/CGB: thesis: we want to say in the spirit of Ramsey that all speech about the truth can be understood so that it only involves the prosentential use of "that's true". I 349 Prosentence/CGB: a prosentence must not be split (to take "the" as an anaphora - otherwise also "is true" stands alone and is then no longer referring, but characterizing (property-attributing CGBVs)). I 351 True: "true" becomes characterizing when "they" is construed as an independent pronoun (traditional, non-anaphoric). I 354 Prosentence: a prosentence never refers to a proposition (as an object of belief). ad I 352 (Prosentence/CGB/(s): a prosentence normally does not have an assertive force). See assertive force. |
Grover, D. L. Gro I D. Grover, A Prosentential Theory of Thruth, Princeton New Jersey 1992 Kamp/Grover/Belnap D. L. Grover, J L. Camp, N. D. Belnap Philosophical Studies 27 (1) 73 – 125 (1975) See external reference in the individual contributions. Horwich I P. Horwich (Ed.) Theories of Truth Aldershot 1994 |
| 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) >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 | Grover, D. L. | Horwich I 323 Propositional Quantification/Camp, Grover, Belnap/CGB: problem: because "T" is a predicate (if it is read as "is true") and "Tp" is a sentence, "p" must be a term of the language, that means, it must occupy a nominal position. That, in turn, means that the quantifiers bind individual variables (of a certain type), and not variables via sentences. I 324 Problem: these are no longer the Ramsey variables. Ramsey variables are the ones that bind variables that occupy sentence positions. Sellars: this is right: relative pronouns can represent formulas with bound individual variables but not with propositional variables, because they have a sentence position. Solution: we need cross-reference. Cross-reference: cross-reference is made of a variable. The variable must be able to occupy the sentence position. -> Pronoun -> "Pro-verb": e.g. "do". I 331 "Generic"/Camp, Grover, Belnap/CGB/(s): here: "generic" is dependent on the antecedent. I 332 "Thatt"/CGB: "thatt" is not a new term. It is only new grammar: e.g. Mary says: "It is hot". John says: "Thatt". There are no new feature ascribing predicates. I 334 English* (with asterisk): English* is used without a truth predicate, but with the Prosentence "It is true". "Is" cannot be modified (time, etc.), because the Prosentence cannot be split. Solution: e.g. "It-is-going-to-be-true" etc. Hyphen: the hyphen shows that the truth predicate in English* cannot be isolated. N.B.: English can be translated into English* without any sacrifices - that is enlightening. >Prosentential theory. |
Grover, D. L. Gro I D. Grover, A Prosentential Theory of Thruth, Princeton New Jersey 1992 Kamp/Grover/Belnap D. L. Grover, J L. Camp, N. D. Belnap Philosophical Studies 27 (1) 73 – 125 (1975) See external reference in the individual contributions. Horwich I P. Horwich (Ed.) Theories of Truth Aldershot 1994 |
| 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 |
| Universal Validity | Gödel | Berka I 314 Universal Validity/Goedel: universal validity leads to universal quantification: for formulas with free individual variables A(x,y,...w) this means the general validity of (x)(y)...(w) A(x,y,...w). >Universal quantification, >Quantification, >Existential quantification. Def Satisfiability/Goedel: "satisfiability" leads to >existence quantification. ((s)"there is a model".) This is then correspondingly the fulfillability of (Ex)(Ey)...(Ew) A. Then one can say: "A is universally valid" means: "~A is not fulfillable". >Satisfaction, >Satisfiability. Refutability: refutability is the provability of negation. >Negation, >Proofs, >Provability. I 310 Provability/universal validity/Goedel:... here we have proved the equivalence between "universally valid" and "provable". Over-countable/Goedel: N.B.: this equivalence contains a reduction of the over-countable to the countable for the decision problem because "generally valid" refers to the over-countable totality of the functions, while "provable" presupposes only the countable totality of the proof figures.(1) >Decision problem, >Countability. 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 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Validity | Cresswell | Hughes I 65ff Validity/Hughes/Cresswell: No structural property of formulas, no relation between formulas. - In contrast: derivability relation between formulas. >Derivability, >Formulas. Yet the set of the derived and the valid formulas in a system are identical. Hughes I 119 Validity/propositional calculus: truth tables are not sufficient for an evaluation of formulas in the propositional calculus. >Predicate calculus. Because we can not assign truth values to individual variables and predicate variables. >Truth values, >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 |
| Valuation | Cresswell | ad Hughes I 119 Validity/propositional calculus/Cresswell: truth tables are not sufficient for an evaluation of formulas in the propositional calculus. - Because we cannot assign truth values to individual variables and to predicate variables. >Individual variable, >Individual constants, >Truth values, >Interpretation of variables, >Predicate calculus. |
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 |
| |||
| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| De re | Wright, von Vs De re | Hughes I 162 Def de re/Hughes/Cresswell: a well formed formula (wff) a containing a modal operator expresses a modality de re if the range of a modal operator from a contains a free occurrence of an individual variable, otherwise a expresses a modality de dicto. WrightVsDe re/Hughes/Cresswell: (and other authors): wanted to eliminate de re in favor of de dicto. one should be able to construct a well formed formula (wff) a' to each well formed formula (wff) a, which does not contain a modality de re and whose equivalence with a can be proved. Hughes/CresswellVsWright: that does not even seem possible with propositional calculus + S5. But apparently nobody has proved that it is impossible. Wright's strategy can be called the "principle of predication" (the term does not come explicitly from him). |
Hughes I G.E. Hughes Maxwell J. Cresswell Einführung in die Modallogik Berlin New York 1978 |
| Field, H. | Putnam Vs Field, H. | Field IV 405 Internal realism/metaphysical/Putnam/Field: (ad Putnam: Reason, Truth, and History): FieldVsPutnam: the contrast between internal realism and metaphysical realism is not defined clearly enough. >Internal realism, >metaphysical realism. Metaphysical realism/Field: comprises three theses, which are not separated by Putnam. 1. metaphysical realism 1: thesis, the world is made up of a unity of mentally independent objects. 2. metaphysical realism 2: thesis, there is exactly one true and complete description (theory) of the world. Metaphysical realism 2/Field: is not a consequence of the metaphysical realism 1 ((s) is independent) and is not a theory that any metaphysical realist would represent at all. Description/world/FieldVsPutnam: how can there only be a single description of the world ((s) or of anything)? The terms that we use are never inevitable; Beings that are very different from us, could need predicates with other extensions, and these could be totally indefinable in our language. Field IV 406 Why should such a strange description be "the same description"? Perhaps there is a very abstract characterization that allows this, but we do not have this yet. wrong solution: one cannot say, there is a single description that uses our own terms. Our current terms might not be sufficient for a description of the "complete" physics (or "complete" psychology, etc.). One could at most represent that there is, at best, a true and complete description that uses our terms. However, this must be treated with caution because of the vagueness of our present terms. Theory/world/FieldVsPutnam: the metaphysical realism should not only be distinguished from his opponent, the internal realism, by the adoption of one true theory. 3. Metaphysical realism 3/Field: Thesis, truth involves a kind of correspondence theory between words and external things. VsMetaphysical Realism 3/VsCorrespondence Theory/Field: the correspondence theory is rejected by many people, even from representatives of the metaphysical realism 1 (mentally independent objects). Field IV 429 Metaphysical realism/mR/FieldVsPutnam: a metaphysical realist is someone who accepts all of the three theses: Metaphysical realism 1: the world consists of a fixed totality of mentally independent objects. Metaphysical realism 2: there is only one true and complete description of the world. Metaphysical realism 3: truth involves a form of correspondence theory. PutnamVsField: these three have no clear content, when they are separated. What does "object" or "fixed totality", "all objects", "mentally independent" mean outside certain philosophical discourses? However, I can understand metaphysical realism 2 when I accept metaphysical realism 3. I: is a definite set of individuals. Williams II 430 P: set of all properties and relations Ideal Language: Suppose we have an ideal language with a name for each element of I and a predicate for each element of P. This language will not be countable (unless we take properties as extensions) and then only countable if the number of individuals is finite. But it is unique up to isomorphism; (but not further, unique up to isomorphism). Theory of World/Putnam: the amount of true propositions in relation to each particular type (up to any definite type) will also be unique. Whole/totality/Putnam: conversely, if we assume that there is an ideal theory of the world, then the concept of a "fixed totality" is (of individuals and their properties and relations) of course explained by the totality of the individuals which are identified with the range of individual variables, and the totality of the properties and relations with the region of the predicate variables within the theory. PutnamVsField: if he was right and there is no objective justification, how can there be objectivity of interpretation then? Field/Putnam: could cover two positions: 1. He could say that there is a fact in regard to what good "rational reconstruction" of the speaker's intention is. And that treatment of "electron" as a rigid designator (of "what entity whatsoever", which is responsible for certain effects and obeys certain laws, but no objective fact of justification. Or. 2. He could say that interpretation is subjective, but that this does not mean that the reference is subjective. Ad 1.: here he must claim that a real "rational reconstruction" of the speaker's intention of "general recognition" is separated, and also of "inductive competence", etc. Problem: why should then the decision that something ("approximately") obeys certain laws or disobeys, (what then applies to Bohr's electrons of 1900 and 1934, but not for phlogiston) be completely different by nature (and be isolable) from decisions on rationality in general? Ad 2.: this would mean that we have a term of reference, which is independent of procedures and practices with which we decide whether different people in different situations with different background beliefs actually refer on the same things. That seems incomprehensible. Reference/theory change/Putnam: We assume, of course, that people who have spoken 200 years ago about plants, referred, on the whole, to the same as we do. If everything would be subjective, there would be no inter-theoretical, interlinguistic term of reference and truth. If the reference is, however, objective, then I would ask why the terms of translation and interpretation are in a better shape than the term of justification. --- Putnam III 208 Reference/PutnamVsField: there is nothing that would be in the nature of reference and that would make sure that the connection for two expressions would ever result in outcomes by "and". In short, we need a theory of "reference by description". --- Putnam V 70 Reference/FieldVsPutnam: recently different view: reference is a "physicalist relationship": complex causal relationships between words or mental representations and objects. It is a task of empirical science to find out which physicalistic relationship this is about. PutnamVsField: this is not without problems. Suppose that there is a possible physicalist definition of reference and we also assume: (1) x refers to y if and only if x stands in R to y. Where R is a relationship that is scientifically defined, without semantic terms (such as "refers to"). Then (1) is a sentence that is true even when accepting the theory that the reference is only determined by operational or theoretical preconditions. Sentence (1) would thus be a part of our "reflective equilibrium" theory (see above) in the world, or of our "ideal boundaries" theory of the world. V 71 Reference/Reference/PutnamVsOperationalism: is the reference, however, only determined by operational and theoretical preconditions, the reference of "x is available in R y" is, in turn, undetermined. Knowing that (1) is true, is not of any use. Each permissible model of our object language will correspond to one model in our meta-language, in which (1) applies, and the interpretation of "x is in R to y" will determine the interpretation of "x refers to y". However, this will only be in a relation in each admissible model and it will not contribute anything to reduce the number of allowable models. FieldVs: this is not, of course, what Field intends. He claims (a) that there is a certain unique relationship between words and things, and (b) that this is the relationship that must also be used when assigning a truth value to (1) as the reference relation. PutnamVsField: that cannot necessarily be expressed by simply pronouncing (1), and it is a mystery how we could learn to express what Field wans to say. Field: a certain definite relationship between words and objects is true. PutnamVsField: if it is so that (1) is true in this view by what is it then made true? What makes a particular correspondence R to be discarded? It appears, that the fact, that R is actually the reference, is a metaphysical inexplicable fact. (So magical theory of reference, as if referring to things is intrinsically adhered). (Not to be confused with Kripke's "metaphysically necessary" truth). ---- Putnam I (c) 93 PutnamVsField: truth and reference are not causally explanatory terms. Anyway, in a certain sense: even if Boyd's causal explanations of the success of science are wrong, we still need them to do formal logic. |
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 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 WilliamsB I Bernard Williams Ethics and the Limits of Philosophy London 2011 WilliamsM I Michael Williams Problems of Knowledge: A Critical Introduction to Epistemology Oxford 2001 WilliamsM II Michael Williams "Do We (Epistemologists) Need A Theory of Truth?", Philosophical Topics, 14 (1986) pp. 223-42 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Lesniewski, St. | Prior Vs Lesniewski, St. | I 43 Abstracts/Prior: Ontological Commitment/Quine: quantification of non-nominal variables nominalises them and thus forces us to believe in the corresponding abstract objects. Here is a more technical argument which seems to point into Quine's direction at first: Properties/Abstraction Operator/Lambda Notation/Church/Prior: logicians who believe in the real existence of properties sometimes introduce names for them. Abstraction Operator: should form names from corresponding predicates. Or from open sentences. Lambda: λ followed by a variable, followed by the open sentence in question. E.g. if φx is read as "x is red", I 44 then the property of redness is: λxφx. E.g. if Aφxψx: "x is red or x is green" (A: Here adjunction) "Property of being red or green": λx∀φxψx. To say that such a property characterizes an object, we just put the name of the property in front of the name of the object. Lambda Calculus/Prior: usually has a rule that says that an object y has the property of φ-ness iff. y φt. I.e. we can equate: (λy∀φxψx)y = ∀φyψy. ((s) y/x: because "for y applies: something (x) is...") One might think that someone who does not believe in the real existence of properties does not need such a notation. But perhaps we do need it if we want to be free for all types of quantification. E.g. all-quantification of higher order: a) C∏φCφy∑φyCAψyXy∑xAψxXx, i.e. If (1) for all φ, if y φt, then φt is something then (2) if y is either ψt or Xt, then something results in either ψ or X. That's alright. Problem: if we want to formulate the more general principle of which a) is a special case: first: b) C∏φΘφΘ() Where we want to insert in the brackets that which symbolizes the alternation of a pair of verbs "ψ" and "X". AψX does not work, because A must not be followed by two verbs, but only by two sentences. We could introduce a new symbol A', which allows: (A’ φψ)x = Aψxψx this turns the whole thing into: c) C∏φΘφΘA’ψX From this we obtain by instantiation: of Θ d) C∏φCφy∑xφxCA’ψXy∑xA’ψXx. And this, Lesniewski's definition of "A", results in a). This is also Lesniewski's solution to the problem. I 45 PriorVsLesniewski: nevertheless, this is somewhat ad hoc. Lambda Notation: gives us a procedure that can be generalized: For c) gives us e) C∏φΘφΘ(λzAψzXz) which can be instatiated to: f) C∏φCφy∑xφx(λzAψzXz)y∑x(λzAψzXz)y. From this, λ-conversion takes us back to a). Point: λ-conversion does not take us back from e) to a), because in e) the λ-abstraction is not bound to an individual variable. So of some contexts, "abstractions" cannot be eliminated. I 161 Principia Mathematica(1)/PM/Russell/Prior: Theorem 24.52: the universe is not empty The universal class is not empty, the all-class is not empty. Russell himself found this problematic. LesniewskiVsRussell: (Introduction to Principia Mathematica): violation of logical purity: that the universal class is believed to be not empty. Ontology/Model Theory/LesniewskiVsRussell: for him, ontology is compatible with an empty universe. PriorVsLesniewski: his explanation for this is mysterious: Lesniewski: types at the lowest level stand for name (as in Russell). But for him not only for singular names, but equally for general names and empty names! Existence/LesniewskiVsRussell: is then something that can be significantly predicted with an ontological "name" as the subject. E.g. "a exists" is then always a well-formed expression (Russell: pointless!), albeit not always true. Epsilon/LesniewskiVsRussell: does not only connect types of different levels for him, but also the same level! (Same logical types) E.g. "a ε a" is well-formed in Lesniewski, but not in Russell. I 162 Set Theory/Classes/Lesniewski/Prior: what are we to make of it? I suggest that we conceive this ontology generally as Russell's set theory that simply has no variables for the lowest logical types. Names: so-called "names" of ontology are then not individual names like in Russell, but class names. This solves the first of our two problems: while it is pointless to split individual names, it is not so with class names. So we split them into those that are applied to exactly one individual, to several, or to none at all. Ontology/Lesniewski/Russell/Prior: the fact that there should be no empty class still requires an explanation. Names/Lesniewski/Prior: Lesniewski's names may therefore be logically complex! I.e. we can, for example, use to form their logical sum or their logical product! And we can construct a name that is logically empty. E.g. the composite name "a and not-a". Variables/Russell: for him, on the other hand, individual variables are logically structureless. Set Theory/Lesniewski/Prior: the development of Russell's set theory but without variables at the lowest level (individuals) causes problems, because these are not simply dispensable for Russell. On the contrary; for Russell, classes are constructed of individuals. Thus he has, as it were, a primary (for individuals, functors) and a secondary language (for higher-order functors, etc.) Basic sentences are something like "x ε a". I 163 Def Logical Product/Russell: e.g. of the αs and βs: the class of xs is such that x is an α, and x is a β. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| Ramsey, F. P. | Grover Vs Ramsey, F. P. | Horwich I 319 VsRedundancy Theory/VsRamsey/Camp, Grover, Belnap/CGB/Grover: the first two objections assume that the data base is too narrow, i.e. that there are cases that are not covered by the theory. (See Redundancy Theory). I 320 1) Index words: (Here: repetition of indices): (14) John: I’m greedy - Mary: That is true Problem: here no mere repetition, or else she would say "I am,..." Problem: there is no general scheme for such cases. 2) Modification: Here, a translation is absolutely impossible: (here with indirect reference and quantification): (15) Every thing that Mark said could be true Problem: there is no verb for "could". Similar: (16) Something that Charlie said is either true or not true. (17) Everything that Judith said was true then, but none of it is still true today. Of course you can try: (15’)(p) Mark said that p > It could be the case that p) or (15’)(p) (Mark said that p > that might p exist) Vs: "being the case" and "existing" are variations of "being true". This would make the redundancy theory a triviality. In this case, Ramsey’s "direct" theory would be wrong. CGBVsRamsey: we improve the redundancy theory by we let by not only allowing propositional quantification for the target language, but also an indeterminate field of links, such as M (for "might"), "P" (for past tense), "~" for negation, etc. I 321 The reader has likely already assumed that we have introduced the negation long ago. But that’s not true. Then: (16’)(p) (Mark said that p > Mp) (17’)(Ep) (Charlie said that p & (p v ~p)) (17’)(p) (Judith said that p > (Pp & ~p)) Redundancy Theory/Ramsey/CGB: it is this variant of the theory of Ramsey, enriched by the above links and propositional quantification, which we call redundancy theory (terminology) from now on. The thesis is that "true" thus becomes superfluous. Thesis this allows translations in Ramseyan sense to be found always. VsRedundancy Theory/VsRamsey: 3) "About"/Aboutness/Accuracy of the Translation/CGB: some authors: argue that "snow is white" is about snow, and "That snow is white, is true" is about the proposition. And that therefore the translation must fail. CGB: this involves the paradox of analysis. We do not directly touch upon it. ((s) Paradox of analysis, here: you’d have to act more stupid than you are in order not to realize that both sentences are about snow; to be able to name the problem at all (as the opponents do) you need to have it solved already.) 4) PragmatismVsRedundancy Theory: even if the translation preserves the alleged content, it neglects other features which should be preserved. Case of recurrence: E.g. (3) Mary: Snow is white. John: That is true. (3’) Mary: Snow is white. John: Snow is white. Is that supposed to be a good translation?. I 322 Strawson: "true" and "not true" have their own jobs to do!. Pro-Sentence/Pronoun/Anaphora/"True"/CGB: "that is true" presupposes that there is an antecedent. But that is not yet taken into account in Ramsey’s translation (3’). So Ramsey’s translation fails in pragmatic terms. VsPropositional Quantification/PQ/VsRedundancy Theory/VsRamsey/CGB: 4) redundancy: at what price? Propositional quantification is mysterious: it is not consistent with everyday language. It is not shown that "is true" is superfluous in German, but only in a curious ad hoc extension. 5) Grammar: (already anticipated by Ramsey): variables need predicates that are connected with them, even if these variables take sentence position. CGBVsRamsey: unfortunately, Ramsey’s response is not convincing. Ramsey: (see above) "p" already contains a (variable) verb. We can assume the general sentence form as aRb here, then. I 232 (a)(R)(b): If he says aRb, then aRb). Here,"is true" would be a superfluous addition. CGBVsRamsey: We must assume an infinite number of different sentence forms ((s)> language infinite). Redundancy Theory/CGB: But that does not need to worry us. 1) Propositional quantification can be set up formally and informally proper. 2) Variables which take sentences as substituents do not need a verb that is connected to them. That this was the case, is a natural mistake which goes something like this: E.g.(4’) (p)(John says p > p). If we use pronouns that simplify the connected variable: For each sentence, if John said it, it then it. Heidelberger: (1968): such sentences have no essential predicate!. Solution/Ramsey: (4’) For each sentence, if John said that it is true, then it is true. T-Predicate/CGB: "T": reads "is true". (4’) (p) (John said that Tp > Tp) Problem: because "T" is a predicate, and "Tp" is a sentence, "p" must be a term of the language, i.e. it must take a nominal position. I.e. the quantifiers bind individual variables (of a certain type), and not variables about sentences. I 335 Disappearance Cases/Pro-Sentence: some of them can be regarded as a translation in Ramsey language. Def Ramsey Language/CGB/(s): Language in which "true" is entirely superfluous. English*/CGBVsRamsey: for the purpose of better explanation. E.g. (26) It is true that snow is white, but in Pittsburgh it rarely looks white. (27) It is true that there was unwarranted violence by the IRA, but it is not true that none of their campaigns was justified. T-Predicate/CGB: used in (25) and (26) to concede a point in order to determine afterwards by "but" that not too much emphasis should be placed on it. English*. I 336: E.g. (26’) There was unwarranted violence by the IRA, that’s true, but it is not true that none of their campaigns was justified. These are all disappearance cases. I 342 VsProsentential Theory/Spurious Objections/CGB: I 343 Index Words: Laziness pro-sentences refer to their antecedent. Therefore, the theory must be refined further when it comes to indexical expressions. Otherwise E.g. John: "I’m lazy." Mary: "That’s true." Is not to say that Mary means "I (Mary) am lazy". CGB: but that’s a common problem which occurs not only when speaking about truth: E.g. John: My son has a wart on his nose. Bill: He is the spitting image of his father. E.g. Lucille: You dance well. Fred: That’s new to me. Pragmatics/CGBVsRamsey: our approach represents it correctly, in particular, because we exclude "plagiarism". Ramsey’s theory does not. I 344 Quote/VsPro-Sentence Theory/VsCGB: The pro-sentence theory is blamed to ignore cases where truth of quotes, i.e. names of sentences, is expressed. E.g. (27) "Snow is white" is true. CGB: We could say with Ramsey, that (27) simply means that snow is white. CGBVsRamsey: that obscures important pragmatic features of the example. They become more apparent when we use a foreign language translation. E.g. (28) If "snow is white" is true, then... Why (28) instead of If it’s true that snow is white, then or If snow is white, then... CGB: There are several possible reasons for this. It may be that we want to make clear that the original sentence was said in German. Or it is possible that there is no elegant translation, or we are not sufficiently familiar with German grammar. Or E.g. "snow is white" must be true, because Fritz said it, and everything Fritz says is true. I 345 Suppose, English* had a possibility to present a sentence formally: E.g. "consider __". (29) Consider: Snow is white. This is true. CGB: why should it not work just like "Snow is white is true" in normal English? VsCGB: it could be argued that this requires a reference on sentences or expressions, because quotation marks are name-forming functors. Quotation Marks/CGB: we depart from this representation! Quotation marks are not name-forming functors. I 353 Propositional Variable/Ramsey: Occupies sentence position. (Quantification over propositions). CGBVsRamsey: Such variables are of pro-sentential nature. Therefore, they should not be connected to a T-predicate. ((s) otherwise, "true" appears twice). T-Predicate/Ramsey/Redundancy Theory/CGB: this answers the old question of whether a Ramsey language has to contain a T-predicate: see below. Our strategy is to show how formulas can be read in English*, where there is no separable T-predicate. E.g. (4’) For each proposition, if John says it is true, then it is true. CGB: in this case,propositional variables and quantificational pro-sentences do the same job. Both take sentence position and have the cross-reference that is required of them. Important argument: (4’) is just the candidate for a normal English translation of (4’). Problem: this could lead to believing that a Ramsey language needs a T-predicate, as in (4’) (p)(John said that Tp > Tp). ((s) then, "true" implicitly appears twice). I 354 But since (4’) is perfect English, there is no reason to assume that the T-predicate is re-introduced by that. Or that it contains a separately bound "it" (them). |
Grover I D. L. Grover Joseph L. Camp Nuel D. Belnap, "A Prosentential Theory of Truth", Philosophical Studies, 27 (1975) pp. 73-125 In Theories of Truth, Paul Horwich Aldershot 1994 Horwich I P. Horwich (Ed.) Theories of Truth Aldershot 1994 |
| Realism | Grover Vs Realism | Horwich I 354 Propositions/Camp.Grover,Belnap/CGBVsRealism/GroverVsRealism: Is it enough that we have found a construction for the manner of speech about truth that never makes "true" as referring to a proposition necessary to answer to the realist that we do not need any propositions as belief objects? We are not sure, but we make some suggestions. (See propositions). Belief/Problem: even if we do not need propositions for discourse about truth, they might be necessary in the case of sentences about belief and psychological attitudes. I 355 Suppose there is a viable adverbial theory to solve these problems. Propositional Attitudes/Belief/Generalization/Pro-Sentence Theory/CGB: Advantage: the pro-sentence theory allows generalizations about belief without introducing propositions! At least not if they are not already assumed in simpler sentences. E.g. (33) Everything is so that if Charley beliefs it is true, it is true. If "it is true" is used here as quantificatorical pro-sentence instead of a combination of quantificatorical pronoun and T-predicate, then (33) does not need to be regarded as analogous with 1st order quantification with individual variables over propositions. Rather, it is comparable with the propositional quantification in Ramsey with variables about sentences. roblem: it might still seem that (33) requires propositions. Solution/CGB: Substitutional Quantification/SQ/CGB: then we assume that the truth of (33) is equivalent with the truth of all its substitution instances. Important argument: then the reference to propositions does not take place at the level of individual beliefs, and then no obligation on propositions emerges from the generalization. |
Grover I D. L. Grover Joseph L. Camp Nuel D. Belnap, "A Prosentential Theory of Truth", Philosophical Studies, 27 (1975) pp. 73-125 In Theories of Truth, Paul Horwich Aldershot 1994 Horwich I P. Horwich (Ed.) Theories of Truth Aldershot 1994 |
| substit. Quantific. | Hintikka Vs substit. Quantific. | II 171 Substitutional Quantification/SQ/HintikkaVsSQ/HintikkaVsSubstitutional Quantification/Hintikka: is a mock paradise, at maximum of formal interest, there has never been a satisfactory explanation for them. Ad (i)/Russell/Hintikka: implied the equivalence of (120) and (11) in the period 1905-14). Description/Knowledge/Russell. Knowledge by description: E.g. we do not know Bismarck. We do wish that the object itself were a constituent of our proposition, but that is not possible. But we know that there is an object called Bismarck (existence). Russell: We also know about this Bismarck that he is a skillful diplomat. ((s) attribution of properties, predication, to individuation, property that goes beyond the mere naming). Solution/Russell: then we can describe the proposition that we want to assert, namely: "B was a skillful diplomat" with B being the object that Bismarck is. (logical form). Logical Form/Hintikka: (15) (Eb)(b = Bismarck & we judge that b was a skillful diplomat) "b": this variable then has current objects (objects from the real world) as values. Russell/Hintikka: this shows that he has not chosen the solution (i). However, Russell says on another occasion, admittedly: II 172 Description/Knowledge/Russell/Hintikka: knowledge by description: Here we know propositions about the "so-and-so" without knowing who or what the so-and-so is. Ad (ii): E.g. description: instead of Bismarck: "the first chancellor of the German Reich". HintikkaVs (ii) that sweeps the problem under the carpet. Problem: The use of descriptions must ultimately lead to the descriptions being re-translated into names, and that is not possible here! Furthermore: Reduction/Description/Name/Hintikka: not all individuals of which we speak with descriptions have identities that are known to everyone. The interpretation of Russell does precisely not exclude that many different entities act as legitimate values of the variables that can, in principle, also be denoted with names. Ad (iii) Russell/Hintikka: that was Russell’s implicit solution: he redefined the domain of the individual variables so that they are limited to individuals who we know by acquaintance. Existential Generalization/EG/Russell/Hintikka: applies only to names of individuals with whom we are familiar. Hidden Description/Russell/Hintikka: existential generalization fails for individuals whose names must be regarded as hidden descriptions ((s) because we only know them by description). |
Hintikka I Jaakko Hintikka Merrill B. Hintikka Investigating Wittgenstein German Edition: Untersuchungen zu Wittgenstein Frankfurt 1996 Hintikka II Jaakko Hintikka Merrill B. Hintikka The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989 |
| |||