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The author or concept searched is found in the following 8 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Game-theoretical Semantics | Kamp | Cresswell I 179 Game-theoretical semantics/CresswellVsHintikka: Hintikka and Kulas (1985)(1) have not made any discoveries that would not have been made by Kamp (1983)(2) and Heim (1983)(3) as well. I 180 Example: (1) Everyone loves someone. This is about two different ranges. Λ-categorial language: (2) ((s) Everyone is so that someone is so that the former likes the latter, without quantification. > Lambda notation/Cresswell). and (3) <<λy, < everyone, <λx, 1. Hintikka J. & Kulas J. (1985): Definite Descriptions. In: Anaphora and Definite Descriptions. Synthese Language Library (Texts and Studies in Linguistics and Philosophy), Vol. 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5410-6_2. 2. Kamp, H. & Rohrer, C. (1983): Tense in texts. Meaning, use and interpretation of language 250, 269. 3. Heim, I. (1983): Formal Semantics - the Essential Readings. In: P. Portner & B. H. Partee (eds.), Blackwell. pp. 249-260. |
Kamp I Kamp From Discourse to Logic: Introduction to Modeltheoretic Semantics of Natural Language, Formal Logic and Discourse Representation Theory (Studies in Linguistics and Philosophy) 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 |
| Lambda Calculus | Bigelow | I 98 Rules/composition/composition rules/syntax/Bigelow/Pargetter: one can also go the other way and want to simplify the rules. That is what the λ-categorical language/Lambda calculus/Lambda notation/Lambda abstraction/Bigelow/Pargetter does: (see also Cresswell I and II, as well as Montague). >Lambda-Abstraction/Cresswell, >R. Montague. For example: Negation: surprisingly, one can assign a referent to it and keep it thus out of the rules: I 99 Vs: we then have another referential layer in the theory. Example Negation: we can assign a set theoretical symbol that represents the value "true" or "false". ((s) Truth value/Frege/(s): assigns a referent to the negation, a "thing": "the false". >Truth values, >Existence, >Objects, >Reference, >Sets, >Set theory. Bigelow/Pargetter: then we have a judgement function that assigns the semantic value (or referent) V(a) to a symbol a. >Valuation. 1: be "true". 0: be "false". Def semantic value: (the negation V(a)) is then the function ω~, so that ω ~ (1) = 0 ω ~ (0) = 1 is appropriate for compound expressions (internal/external negation, conjunction, etc.) >Semantic value, >Outer negation, >Negation, >Conjunction. I 100 Lambda categorical language/λ/Lambda/Rules/Bigelow/Pargetter: such languages have extremely few composition rules. We have more referring symbols for this. >Rules, >Symbols. Realism: would describe this as ontologically honest. Semantics/Bigelow/Pargetter: but the realist does not have to commit himself to one semantics instead of another. >Realism. The semantics does not decide upon ontology. >Semantics, >Ontology. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Lambda Calculus | Prior | I 45 Lamda-operator/abstraction operator/Prior: the lamda-operator is not equivalent with abstract nouns. It does not refer to properties, for it cannot replace the name variable. - ((s) Adjunction of characteristics.) No problem: "something φ-s or ψ-s" but not "the property of φ-ing-or-ψ-ing" as an abstract entity. >Abstractness, >Abstract objects, >Properties. Solution: "A v C "(either A-ing or C-ing" - is not an abstract noun, but acomplex verb that forms a sentence. The lamda-operator is necessary if one wants to formulate laws on propositions. >Operators, >Lambda notation. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| Lambda-Abstraction | Stechow | 48 Lambda notation: [λx: f. g]. - E.g. if g is a sentence: - the function f, such that for any x that satisfies f : f (x) = 1 if g is true, 0 if g is false. 161 Lambda abstraction: returns the value sequence of a function. Lambda-bound variables: have no reference. - The variable in the lambda operator is neither bound nor free. >Lambda calculus, >Variables, >Bound variable, >Free variable, >Reference, >Operators, >Functions, >Value progression. |
A. von Stechow I Arnim von Stechow Schritte zur Satzsemantik www.sfs.uniï·"tuebingen.de/~astechow/Aufsaetze/Schritte.pdf (26.06.2006) |
| Operators | Prior | I 32 Nominator/Prior: a nominator should speak of things where sentences containing them can be said to be true. >Predication, >Sentences. I 34 E.g. λp for that p. - Then the sentence: T λp (it is true that ...). Operator T: true. >Lambda notation, >Lambda calculus. I 95 Operator/Prior: φ only forms sentences from names. - ((s) Something φs, different from equivalence: forming sentences out of sentences). >Equivalence. Prior: N (necessary) cannot have names as arguments. >Proper names, >Subsententials. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| Propositional Functions | Quine | IX 178 Propositional Function/Principia Mathematica(1)/Theoretical Terms/Russell: name for attributes and relations - "f", "y"... as variables - i.e. that x has the attribute f, that x is to y in the relation y, etc. "fx",y(x,y)", etc. - ^x: to abstract propositional function from statements he just inserted variables with an accent circonflexe into the argument positions - E.g. the attribute to love: "^x loves y" E.g. to be loved: "x loves ^y" (active/passive, without classes!) (>lambda notation/(s) Third Way between Russell and Quinean classes) - Analog in class abstraction: "{x: x loves y}", "{y: x loves y}" - E.g. relation of loving: "{: x loves y}" or "{: x loves}". Abstraction: Problem: in wider contexts sometimes you have no clues as to whether a variable ^x should be understood as if it caused an abstraction of a short or a longer clause - Solution/Russell: Context Definition - statement function must not occur as a value of bound variables that are used to describe it - it must always have too high an order to be a value for such variables - characteristic back and forth between sign and object: the propositional function receives its order from the abstracting expression, and the order of the variables is the order of the values. >Variables/Quine, >Attributes/Quine IX 185 Propositional Function/Attribute/Predicate/Theoretical Terms/QuineVsRussell: overlooked the following difference and its analogues: a) "propositional functions": as attributes (or intensional relations) and b) "proposition functions": as expressions, i.e. predicates (and open statements: E.g. "x is mortal") - accordingly: a) attributes b) open statements - solution/Quine: allow an expression of higher order to refer straight away to an attribute or a relation of lower order. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
| Rules | Bigelow | I 98 Rules/composition/composition rules/syntax/Bigelow/Pargetter: you can also go the other way and want to simplify the rules. That is what makes the λ-categorical language/Lambda/Lambda Calculus/Lambda Notation/Lambda Abstraction/Bigelow/Pargetter: ((see also Cresswell I and II. and Montague). >Lambda abstraction, >Lambda calculus, >M.J. Cresswell, >R. Montague. For example: Negation: you can surprisingly assign a referent to it and keep it out of the rules. >Reference, >Negation, >Rules. I 99 Vs: we then have another referential layer in the theory. Example: Negation: we can assign a set theoretical symbol to it that represents the value "true" or "false". ((s) Truth values/s): assigns a referent to the negation, a "thing": "the False". >Truth values, >Truth values/Frege. Bigelow/Pargetter: then we have a judgement function that assigns the semantic value (or referent) V (a) to a symbol a. 1: be "true". 0: be "false". + Def semantic value: (of the negation V (a)) is then the function ω ~, so that ω ~ (1) = 0 ω ~ (0) = 1 correspondingly for compound expressions (internal/external negation, conjunction, etc.) >Outer Negation. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Syntax | Prior | I 46 Syntax/Prior: variables and constants belong to the same syntactic category. >Variables, >Constants Problem: what is the meaning of the quantifier with quantification over properties? >Quantification over properties, >Quantification, >Quantifiers. Should the following variable (to be bound by the quantifier) belong to it? >Bound Variables. Solution: if we consider lambda operators as the only operators that may bind the variables, then the quantifier can build the sentence : ∏(λxφx) (which is equivalent to the simple φ) is briefly ∏φ, everything φ-s. The quantifier builts the sentence. >Lambda calculus, >Lambda notation, >Range. Syntactic status of Lambda: symbolic crutch. Problem: e.g. Something is not the case: SN: S builds a sentence out of a one-digit compound or an adverb. >Sets, >Clauses, >Adverbs. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| 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 |
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