Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 15 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Barcan-Formula | Cresswell | Hughes I 128 Barcan-Formula/BF/Kripke: takes for each possible world an individual domain, giving it a semantics, where in contrast to our the Barcan formula is not valid. >Accessibility), >Possible worlds. Accessibility/LewisVsKripke: with Lewis accessibility runs via individuals, therefore the Barcan formula for Lewis is valid. >Counterpart theory, >Counterpart relation, >Possible worlds/Lewis. Hughes I 150f Barcan-Formula/possible worlds/Semantik/Hughes/Cresswell : Barcan formula is invalid in semantics that assign d different domains of individuals to different possible worlds. Cf. >Possible world semantics. Hughes I 150f Barcan-Formula/Hughes/Cresswell: Vs: that everything that exists is necessary f, does not exclude that there could be things (or could have been ), not-f . Then it would not be a necessary truth that everything is f. VsVs: this proceeds from the assumption that objects not only may have other properties in different possible worlds, but that there might even be objects that do not exist in the actual world. >Extension of the > existence predicate, >Existence, >"There is". Hughes I 156 Barcan-Formula/existence/possible worlds/Hughes/Cresswell: three perspectives: a) all possible worlds have the same domain of individuals: The Barcan formula is then valid (which include T and S4) objects are the same, properties and relations change b) new things arise: Barcan formula is invalid in any case concerning T and S4 c) even more liberal: objects can be removed. >Systems S4/S5, >Individual domain. |
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 |
| Classes | Wessel | I 360f Class/Wessel: "What is a class?": Wrong question, without circularity it can only be introduced as a logical operator. >Operators. It is also circular as abstraction: requires individual domains. >Circular reasoning. Th concept of class and class logic superfluous, merely different representations of the concept of the propositional function and the classical quantifier logic. >Propositional functions, >Quantifier logic, >Sets, >Set theory. The class of Amazons exists as an empty class. Def Class: if tA is a class term, then A is a class. Problem: the left side is burdened by existence,the right side is not. Solution: instead of identity only meaning equality of terms (t €s P(s) <=> t €s Q(s)) =def As(P(s) ↔ Q(s)). Thus a definition by abstraction becomes a mere facon de parler. >Abstraction, >Class abstraction. |
Wessel I H. Wessel Logik Berlin 1999 |
| 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 |
| Epistemic Logic | Hintikka | II 11 Epistemic Logic/standard/Hintikka: there are usually extremely many alternatives that are compatible with what a person b knows. But it is not necessary to demand that all such worlds are really within the domain of permitted alternatives. >Possible worlds. II 12 Epistemic Logic/Hintikka: it is not clear how we should assess the situation A) Vs Restriction of the individual domain: since the restriction can hardly be avoided in alethic standard modal logic, this is again an argument against the possibility of alethic modal logic. B) One could affirm the idea that not all epistemic and doxastically possible worlds must be logically possible. II 17 Epistemic Logic/Hintikka: epistemic logic is usually regarded as a branch of modal logic. Semantics of possible worlds/possible world/semantics/Hintikka: the semantics of a possible world is a misleading term for the semantics of epistemic logic. Epistemic Logic/Hintikka: most of the work focuses on syntactic questions and deductive techniques. This is a mistake. Instead: One should focus on semantic (model-theoretical) questions. Epistemic Logic/laws/Hintikka: the basic laws are obtained by a simple idea: Def knowledge/Hintikka: knowledge is what enables the knowing person to concentrate on the subset W1 of the set of all worlds W. W1: W1 is then relative not only to the knowing person b, but also relative to the scenario w0 ε W. Definition b knows that S iff. S is true in all epistemic b alternatives. II 143 Uniqueness Condition/W-questions/response/Hintikka: the condition that something is a complete and unambiguous answer to a who-question (ambiguous, see above) is first that (8) has to imply (7) (6) Who is the man over there? (7) I know who the man is over there. E.g. It is Sir Norman Brook. (8) I know that the man there is Sir Norman Brook. Problem: the step from (8) to (7) is that of an existential generalization (EG). >Existential generalization. II 144 Problem: for that, we need an additional premise. E.g. (13) (Ex) Ki (Sir Norman Brook = x). (Non-mirrored quantifier, perceptually) "I know who Norman Brook is." Epistemic Logic/criterion/Hintikka: with this the epistemic logic freely provides an additional criterion for complete answers. N.B.: this applies to both methods of identification (public/perspective). Uniqueness condition: for the fact that e.g. "the man over there" is a clear and complete answer to (9): (14) (∃x) Kl (that the man there = x) That is, that the man who is pointed to is as an aquaintance of the one who asks the questions. >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 |
| Functional Calculus | Berka | Berka I 119 Extended function calculus/Hilbert: Extended function calculus is used to express the existence of the opposite of a statement. E.g. For every statement X there is a statement Y, so that at least one and only one is true. This saves the constraint of content representation. >Formalism, >Statements, >Validity, >Satisfiability. I 120 Then we can ask for a criterion for the correctness of formulas with arbitrary combinations of all- and existential quantifiers. >Universal quantification, >Existential quantification, >Quantification. Then there is the principal possibility of decidability about the provability of a mathematical theorem. >Decidability, >Provability, >Proofs. Narrow function calculus: The narrow function calculus is sufficient for the formalization of logical reasoning. >Formalization. Berka I 337 Function calculus/Hilbert/Ackermann: here (in contrast to the propositional calculus) the decision problem is still unsolved and difficult. - But for certain simple cases a procedure could be given. Simplest case: only function variable with one argument. >Decision problem, >Propositional calculus. I 337 Functional calculus: here the following circumstance has to be considered in particular: the generality or satisfiability of a logical expression may depend on how large the number of objects in the individual domain is. >Individual domain, >Domain. |
Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Infinity Axiom | Hilbert | Berka I 122 Definition Number/logical form/extended function calculus/Hilbert: the general number concept can also be formulated logically: if a predicate-predicate φ (F) should be a number, then φ must satisfy the following conditions: 1. For two equal predicates F and G, φ must be true for both or none of them. 2. If two predicates F and G are not equal in number, φ can only be true for one of the two predicates F and G. Logical form: (F)(G){(φ(F) & φ(G) > Glz (F,G) & [φ(F) & Glz (F,G) > φ(G)]}. The entire expression represents a property of φ. If we designate it with Z (φ), then we can say: A number is a predicate-predicate φ that has the property Z (φ). >Numbers, >Definitions, >Definability, >Infinity, >Axioms, >Axiom systems, >Predicates, >Properties. Problem/infinity axiom/Hilbert: a problem occurs when we ask for the conditions under which two predicate-predicates φ and ψ define the same number with the properties Z (φ) and Z (ψ). Infinity Axiom/equal numbers/Hilbert: the condition for equal numbers or for the fact that two predicate-predicates φ and ψ define the same number is that, that φ(P) and ψ(P) are true for the same predicates P and false for the same predicates. So that the relationship arises: (P)(φ(P) ↔ ψ(P)) I 122 Problem: when the object area is finite, all the numbers are made equal which are higher than the number of objects in the individual domain. >Finiteness/Hilbert, >Finitism, >Finiteness. For example, if a number is e.g. smaller than 10 to the power of 60 and if we take φ and ψ the predicates which define the numbers 10 to the power of 60+1 and 10 high 60 + 1, then both φ and ψ do not apply to any predicate P. The relation (P)(φ(P) ↔ ψ(P)) Is thus satisfied for φ and ψ, that is, φ and ψ would represent the same number. Solution/Hilbert: infinity axiom: one must presuppose the individual domain as infinite. A logical proof of the existence of an infinite totality is, of course, dispensed with(1). 1. D. Hilbert & W. Ackermann: Grundzüge der theoretischen Logik, Berlin, 6. Aufl. Berlin/Göttingen/Heidelberg 1972, §§ 1, 2. |
Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Infinity Axiom | Tarski | Berka I 474 Existence/existence acceptance/Tarski: Problem: if we (...) eliminate the existential conditions in the axioms, so the corresponding allocation disappears. Every expression will continue to correspond with a natural number, but not vice versa to any natural number an expression. >Unambiguity, Berka I 519 Axiom of infinity/Tarski: with him, we renounce the postulate according to which only the right statements in each individual domain should be provable propositions of logic.(1) 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 |
| Intensional Logic | Hintikka | II 11 Intensional Logic/non-standard/Hintikka: intensional logic uses non-standard semantics (i.e. the individual domain is not fixed). Therefore, it is not necessary to limit the domain of possible worlds of their framework. It would also be inappropriate for other reasons: In the epistemic logic the restriction would mean that everyone knows the identity of all individuals in the possible world. This would lead to omniscience. Also: Problem: this would make the situation even stranger: there must then often be epistemic alternatives to the world w0, which are not alethic (logical) alternatives! This contradicts the natural assumption that logical possibility forms the broadest class of possibilities. >Epistemic logic, >Modal logic, >Domains, >Possible worlds. |
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 |
| Non-Existence | Hintikka | II 37 Non-existent objects/unrealized possibilities/HintikkaVsQuine/Hintikka: thesis: there are non-existent objects in the actual world. >Possibilia. HintikkaVsQuine: the philosophers who reject them have thought too strongly in syntactic paths. Hintikka/thesis: one has to answer the question rather semantically (model-theoretically). >Model theory. Fiction/Ryle: test: is the paraphrase valid? >Fictions. Terence ParsonsVsRyle: Ryle's test fails in cases like e.g. "Mr. Pickwick is a fiction ". HintikkaVsParsons: the relevance of the criterion is questionable at all. >Relevance. II 38 Ontology/language/linguistically/HintikkaVsRyle: how should linguistic questions such as paraphrasability decide on the ontological status? >Ontology. Solution/Hintikka: for the question whether there are non-existent objects: model theory. E.g. Puccini's Tosca is about whether the soldiers have bullets in their rifle barrels. N.B.: even if they have some, they would be just fictional! Model Theory/Hintikka: the model theory provides a serious answer. ((s) "true in the model", means it is true in the story that the bullets are there). HintikkaVsParsons: one should not argue too strongly syntactically, i.e. not merely ask what conclusions can be drawn and which cannot. Acceptance/acceptability/inferences/Hintikka: asking for the acceptability of inferences and of language and intuitions is syntactic. Singular Terms/ontological obligation/existence/Parsons: Parsons argues that the use of singular terms requires us to use an existential generalization. And thus also requires a referent. That is, it is a commitment to an inference. HintikkaVsParsons. > II 39 Non-existent objects/substance/world/Tractatus/Hintikka: the reason why Wittgenstein postulated his "objects" as the substance of the world, ((s) which cannot be increased or diminished), is that their existence cannot be expressed.) >Existence statements. II 103 Non-existence/not well-defined/HintikkaVsMontague: the Montague semantics does not allow the question of existence or non-existence to be meaningless because an individual is not well-defined in a world. ((s) Because Montague assumes the domain of individuals to be constant). Individual Domain/solution/Hintikka: we have to allow that the individual domain is not constant. Problem: Quantification/belief context/existence/truth/Hintikka: in the following example we must presuppose existence so that the proposition can be true: (11) John is looking for a unicorn and Mary is looking for it too. ((a) the same unicorn). ((s) numbering sic, then continue with (8)) Range/quantifier/Hintikka: in the only natural reading of (11) one has to assume that the range of the implicit quantifier is such that "a unicorn" has a wider range than "searches/looks for". ((s) That is, that both are looking for the same unicorn). >Objects of thought, >Cob/Hob/Nob exmaple/Geach. Problem: how can one know whether both subjects believe in the same individual? |
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 |
| Non-Existence | Montague | Hintikka I 103 Non-existence/not well-defined/HintikkaVsMontague: Montague's semantics does not allow the question of existence or non-existence to be meaningless because an individual is not well-defined in a world. ((s) Because in Montague the domain of individuals is assumed to be constant). >Possible worlds, >Identity between worlds, >Individual domain, >Identification, cf. >Counterparts, >Counterpart relation, >Counterpart theory. Individual domain/solution/Hintikka: we have to allow that the individual domain is not constant. But there is a problem: Quantification/belief context/existence/truth/Hintikka: in the following example we must presuppose existence so that the proposition can be true: (11) John is looking for a unicorn and Mary is looking for it, too. ((s) the same unicorn). Cf. >Thought objects, >Belief objects. Range/quantifier/Hintikka: in the only natural reading of (11) one has to assume that the range of the implicit quantifier is such that "a unicorn" has a wider range than "looks for". >Range, >Quantification, >Narrow/wide range. ((s) That is, that both are looking for unicorns.) Problem: how can one know whether both subjects believe in the same individual?). >Unicorn example. I 103 Existence/W-Question/Unicorn/Hintikka: nevertheless the example (11) shows that the way of reading should not oblige us to accept the existence of unicorns. Cf. >Ontological commitment. Non-existence/epistemic context/intensional/belief/Hintikka: it is obviously possible that two people can look for the same thing, even if it does not exist. Solution: We allow that well-defined individuals do not exist in some worlds. For this, only a slight modification is necessary. Problem: with more complex sentences, all problems come back: I 104 Example: John does not know whether unicorns exist, yet he is looking for a unicorn because Mary is looking for it. Problem: here John must be able to recognize a special unicorn. (Otherwise the sentence that uses "it" would not be true), although he is considering the possible non-existence. >Anaphora, >Index Words, >Indexicality, >Identification. World line/Hintikka: in order to extent the Montague semantics, we must allow more or less unnatural world lines. >World lines, cf. >Four-dimensionalism. |
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 |
| Ramsey Sentence | Schurz | I 213 Ramsey-sentene/RS/Theoretical Terms/Schurz: Here Theoretical Terms are not eliminated completely, but existentially quantified over them. Given a theory , which we now take to be a single theorem T(τ1,...τn,) (the conjunction of all axioms of T. Theoretical terms: τ1,...τn. Moreover, there are various non-theoretical terms π which are not written on separately. Then the Ramsey theorem of T is: (5.8 1) R(T): EX1,...Xn: T(X1,...Xn) Everyday language translation: there are theoretical entities X1,..Xn which satisfy the assertions of the theory. Pointe: an empirical (not theoretical) proposition follows from T exactly if it follows from R(T). ((s) It follows from the theory if it follows from the Ramsey theorem of the theory, i.e., from the assumption that the theoretical entities exist.) Thus, it holds: (5.8 -2) E(R(T)) = E(T) Notation: E(T): empirical proposition that follows from theory T. Schurz: i.e. a theory and its Ramsey theorem have the same empirical content. >Carnap-sentence/Schurz, >Empirical content. Ramsey-sentence: Here no more theoretical terms occur! Instead of it: "theoretical" variables. Therefore many, including Ramsey, saw the Ramsey theorem as an empirical theorem (not as a theoretical one. Ramsey theorem: should thus be the sought empirically equivalent non-theoretical axiomatization of the theory. HempelVs/MaxwellVs/Schurz: this is problematic because the RS asserts the existence of certain entities that we call "theoretical". Ramsey theorem/interpretation/realism/instrumentalism/Schurz: the interpretation of the RS as theoretical or non-theoretical depends on whether one interprets 2nd level quantifiers realistically or instrumentally. (a) instrumentalist interpretation: here one assumes that the range of individuals D consists of empirically accessible individuals, and runs the variables Xi over arbitrary subsets of D. (There are no theoretical individuals here). >Instrumentalism/Schurz. Whether these extensions correspond to certain theoretical real properties or not is inconsequential. (Sneed 1971(1), Ketland 2004(2), 291) I 214 Ramsey-sentence/instrumentalism: is then model-theoretically an empirical theorem! Because the models that determine the truth value of R(T) are purely empirical models (D, e1,...em). " ei": extensions of the empirical terms, pi: empirical terms of T. Structuralism: calls these empirical models "partial" models (Balzer et al. 1987(3),57). Empirical model/Schurz: is easily extendible to a full model (D, e1,...em, t1,..tn), ti: are the extensions of the theoretical terms. Pointe: this does not yet mean that R(T) is logically equivalent to E(T). Because R(T) is a 2nd level proposition and E(T) contains 1st level propositions. >Structuralism/Schurz. Def Ramsey-eliminable: if there is a 1st level empirical proposition equivalent to a RS L, then the theortical term is called Ramsey-eliminable. (Sneed 1971(1), 53). b) Realist interpretation: (Lewis, 1970(4), Papineau 1996(5)): assumes that the existence quantified variables denote real theoretical entities. The models are then no longer simple realist models: >Realism/Schurz. 1. New theoretical individuals are added to the individual domain. New: Dt. 2. not every subset of Dt corresponds to a real property. En. Ex In the simplest case, one must assume a set Et of extensions of "genuine" theoretical properties over which 2nd level variables run. Realism/Ramsey-sentence: new: now not every empirical model of instrumentalistically interpreted RS is extensible to a model of realistically interpreted Ramsey-sentence, because the quantifiers (Exi) of R(T) can have satisfactions in the power set of Det but no satisfactions in Et. In philosophical words: an empirical model, which fulfills the RS instrumentalistically, cannot be read off whether the respective theoretical entities, whose existence is postulated by R(T), are merely useful fictions or real existing entities. Instrumentalism: Proposition: Theoretical entities are useful fictions. Realism/Ramsey Theorem: here R(T) contains more than just the empirical content of a theory, it also contains the total synthetic content: if we assume that the meaning of Theoretical Terms is not determined by anything other than this theory itself, then the assertion that T makes about the world seems to be precisely that of R(T): there are unobservable entities X1,...Xn that satisfy the total assertion of the theory T(X1,...Xn). >Carnap-sentence/Schurz. 1. Sneed, J. D. (1971). The Logical Structure of Mathematical Physics. Dordrecht: Reidel. 2. Ketland, J. (2004). "Empirical Adequacy and Ramsification", British Journal for the Philosoph y of Science 55, 287-300. 3. Balzer, W. et al (1987). An Architectonic for Science. Dordrecht: Reidel. 4. Lewis, D. (1970). "How to definie Theoretical Terms", wiederabgedruckt in ders. Philosophical Papers Vol I. Oxford: Oxford University Press. 5. Papineau, D. (1996). "Theory-dependent Terms", >Philosophy of Science 63, 1- 20. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
| Substitution | Hintikka | II 194 Substitutability of Identity/intensionality/Hintikka: a sure indicator of intensionality is the failure to preserve the identity of the individual domain. >Intentionality. If it happens that the identity fails from one possible world to another, we have a counter-example to the known law ((s) Leibniz's law): (Substitutability of identity) (x)(y) (X = y > F[x] > F[y])). ((s) identical objects have all properties in common). This is sometimes called the "bound variable form of identity". Equivalent to: (x)(y) ( x = y > neccessary (x = y)) ((s) What is identical is necessarily identical). Hintikka: this failure of the substitutability of the identity is to be distinguished from the failure for any singular terms. Here it can simply be because a singular term refers to another thing in another possible world. II 195 Identity/individuals/Hintikka: it is much less clear how the identity can fail for certain individuals in the transition to another possible world. That is, that world lines can branch (> separation). Separation/KripkeVsSeparation/substitutability of identity/SI/Hintikka: Kripke excludes separation because the substitutability of identity is valid for him. A separation would violate the transitivity of the identity according to him. After a separation, the individuals would not be identical, even if they were identical after the transition. Therefore, the substitutability of identity is inviolable to Kripke. HintikkaVsKripke: that is circular: Transitivity of Identity/Hintikka: can mean two things: A) transitivity within a world or B) transitivity between worlds. The plausibility of transitivity belongs to the former, not to the latter. Transitivity of the identity between possible worlds is simply to exclude separation. This is the circularity in Kripke's argument. Substitutability of Identity/Hintikka: many authors have noted that identity and quantification remain meaningless in intensional contexts unless we have the substitutability of identity. HintikkaVs: that is simply wrong: after the world lines are defined, we can formulate the truth conditions for sentences with arbitrary intensional expressions. And then, independently of the behavior of the world lines. Modal Logic/substitutability of identity/Hintikka: it is double ironic that the defenders of conventional modal logic want to save the substitutability of identity by saying that without it, possible worlds and intensional logic makes no sense. This is because substitutability of identity excludes separation. Fusion/Hintikka: to exclude it, we need the reverse form instead substitutability of identity we need identity of substitutability: (identity of substitutability) (x)(y) (possible (x = y) > x = y) ((s) possible identity is identity, i.e. ultimately it is necessary). Problem/Hintikka: identity of substitutability is not valid in some conventional systems of the quantified modal logic, including that of Ruth Barcan Marcus. For these systems, we must allow separation when we go from possible worlds to the actual worlds (travel home). Direction/interpretation/Hintikka: however in interpretation there is nothing to distinguish between the directions. II 196 It is only a coincidence that these systems do not contain retrospective operators (Saarinen, see above). That is, every defender of these conventional systems secretly defends the possibility of separation. That is, the rejection of substitutability of identity. 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. >Cross world identity. Re-Identification/Hintikka: re-identification is the key to cases of separation and fusion. Separation/Hintikka: there is a structural reason why it is so rare: if world lines are composed of infinitesimal elements as the solutions of differential equations, the separation of a singularity corresponds - 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 domain should remain fixed (HintikkaVsKripke). Possible World/individual area/HintikkaVsKripke: one should not demand that the individuals must remain the same when changing from world to world. The talk of worlds is empty, if there are no possible experiences that could distinguish them. |
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 |
| Terminology | Hintikka | II 15 Standard Semantics/modal logic/Hintikka: problem: the alternative worlds must be formed from the same individual domain and also from the same domain of predicates (basic term). That is, the individuals must all already exist! II 46 Def Scenario/Hintikka: a scenario is everything that is compatible with the knowledge of a knowing person b. We can also call it b's worlds of knowledge. II 56 Def relevant world/Hintikka: relevant worlds are all those which are compatible with the knowledge of a person considered here. II 189 Def Qualitative/terminology/Hintikka: terminology corresponds to a yes-no distinction. Contrast: the contrast is comparative. II 216 Def Desideratum/Hintikka: the desideratum is the piece of information that provides a complete answer to a question. E.g. (3) is the desideratum of (2). (2) Who killed Roger Ackroyd? (3) I know who killed Roger Ackroyd. II 217 (3) can be analyzed as: (4) (Ex) I know that (x killed Ackroyd) Where "x" is about people. Def Conclusive/conclusive answer/Hintikka: an answer is conclusive iff. (5) implies (4), for example, (5) I know that d has killed Ackroyd. (4) (Ex) I know that (x killed Ackroyd). Problem: normally the implication is valid, but it can be because "d" (on different occasions) does not refer to the same person. II 221 Presupposition/questions/Hintikka: the presupposition of a question is obtained by omitting the extreme epistemic operator ("I know that") from the desideratum of the question. Definition matrix of a question/Hintikka: the matrix of a question is the presupposition obtained from the desideratum without the utmost epistemic operator. Def Meaning/Hintikka: meaning is the function of possible worlds on extensions. Worlds: worlds are the arguments of functions that are meanings. Intentionality/Hintikka: if intentionality is to be defined by the necessity of explaining it through possible worlds, we must examine possible counterexamples. |
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 |
| Truth | Hilbert | Berka I 395 Truth/absolute truth/Hilbert: axioms and provable propositions are images of the thoughts which make up the method of the previous mathematics, but they are not themselves the absolute truths. >Axioms, >Axiom systems, >Axioms/Hilbert. Def absolute truth/Hilbert: absolute truths are the insights provided by my proof theory with regard to the provability and consistency of the formula systems. >Proof theory/Hilbert. Through this program, the truth of the axioms is already shown for our theory of proof(1). Berka I 486 Relative Truth/correctness in the domain/Tarski: the relative truth plays a much greater role than the (Hilbertian) concept of the absolute truth, which has so far been mentioned: Definition correct statement in the domain a/Tarski: every statement in domain a is correct, which then (in the usual sense (s)> Putnam would choose spelling with asterisks)) would be true if we limit the scope of the individuals to the given class a. That is, if we interpret the terms "individual" as "element of class a", "class of individuals" as "subclasses of class a", and so on. Class Calculation: here you would have to interpret expressions, e.g. of the type "Πxp" as "for each subclass x of class a:p" and, e.g. "Ixy" as "the subclass x of the class a is contained in the subclass y of the class a". Then we modify definition 22 and 23. As derived terms, we will introduce the concept of the statement, which in an individual domain with k elements is correct, and the assertion which is correct in each individual area(2). >Truth/Tarski, >Truth Definition/Tarski. 1. D. Hilbert: Die logischen Grundlagen der Mathematik, in: Mathematische Annalen 88 (1923), pp. 151-165. 2. A. Tarski: Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol 1, Lemberg 1935. |
Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Valuation | Bigelow | I 125 Valuation function V/Bigelow/Pargetter: its definition is complex because it has to be recursive. It assigns an interpretation or a semantic value. (To each expression of the language). >Recursion. Valuation: First, semantic values are assigned to the non-logical constants. >Semantic value. Rules are then created for semantic values from compound expressions. Logical constants: their valuation is specified by recursive rules. >Logical constants. Domain: can also be restricted, e.g. if you want to exclude the Barcan formula. >Domains. For example, restriction: for each world w you can assume a separate individual domain DW. Which, for example, consists only of the possibilia of this possible world. >Possibilia, >Possible worlds. I 126 Def partition/Bigelow/Pargetter: is a family of individual domains that do not overlap. I.e. no individual is in more than one possible world. That would correspond to Lewis's counterpart theory. >Counterpart theory. I 129 Counterfactual Conditional/Valuation/Valuation Function/Valuation Rules/Bigelow/Pargetter: V9 If a = (ß would be γ) then V (a) is the set of all possible worlds w ε w so that there is a possible world u where ß is true and γ is true and every possible world v in which ß is true and γ is false, is less accessible from w than from u. >Similarity metrics, >Counterfactual conditional. Similarity/possible worlds/similarity metrics/counterfactual conditional/Bigelow/Pargetter: Rule V9 states that a counterfactual conditional (ß would be > would be γ) is true in a possible world if the next ß-worlds are all γ-worlds. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
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| Tradition | Wessel Vs Tradition | I 16 Universality/WesselVsTradition: according to the traditional view there are individual domains in which the logical rules supposedly do not apply: e.g. states of change. In modern intuitionist mathematics, double negation is not equated with position. Wessel's Question: why do we regard these logical laws as universal and not others? Where is the boundary between universal and nonuniversal laws? Here one should not expect reasonable answers. Logical laws, by their very nature, do not allow for exceptions, I 17 and they do not depend on any peculiarities of an area. The only thing that depends on the range is which of the known laws are used. I 329 Definition/Wessel: it is always about the introduction of a new term for an already known (introduced) term. ta ‹_›def tb or a ‹_›def b. I 330 Tradition: a more general term is always restricted. (>genus, differentia specifica). Example electron: light, negative elementary particle. ta '_'def t(b lv P u Q) (b lv P u Q: "b with the property P u Q"). WesselVsTradition: a definition can also have a completely different form: ta '_' t(a1 v ...van) (e.g. "fruit", enumeration). |
Wessel I H. Wessel Logik Berlin 1999 |
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