Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 7 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Attribution | Boer | I XVI Attribution of believe/Boer: known problem: that the logical equivalence fails here. Problem: if the words in P are replaced by others. Notation/Terminology/Boer: "≡" is the truth-functional analog of "if and only if" (iff). "Bel (A, p)": "A believes that p". --- I 21 Attribution of believe/Intentionality/Boer: Question: A) is believe intentional? B) is attribution of believe intentional? Quine/Boer: his semantic rise has caused the second question to conceal the first. Definition Intensionality/(sic, with s)/Boer: is nowadays negative, defined as non-intensionality. So we need a definition of "extensional sentence". Denotation/denoting/Boer: Assuming, denotating terms are: names, indices, demonstrativa and mass terms. Definition English +/Boer: be an extension of English by zero or more denotating expressions and predicates. --- I 22 Definition extensional reading/Boer: (provisional): E.g.: "A thing x is such that ... x ..." is unambiguous, then it is an extensional reading S iff it fulfills the following extensional principles: Definition: a strong principle of existential generalization/extensibility/Boer: for a denotating term D and variable v which does not belong to S if S has the form [... D ...], then one can conclude from S validly [an existing thing v is such that ... v ...]. Definition: replacement princinple for co-extensive predicates/Boer: ... from [for objects x1, ... xn, either P (x1, ... xn) or Q(x1, ... xn) or neither P nor Q] we can exclude any theorem which is obtained by replacing one or more occurrences of P in S by Q. Definition replacement princinple for materialistic equivalent sentences/Boer: for every sentence P and Q in English +, if P is present in S, one can deduce from S and [Either P and Q, or neither P nor Q] every sentence which is formed by the replacement of one or several occurrences of P in S by Q. Definition of the substitutionality of the identity/Boer: for each denotating term D and E of English +: if S has the form [... D ...], one can deduce from S and an equation of the form [D = E] (or [E = D] every sentence which is formed by replacing one or more occurrences of D by E in S. --- I 22 Validity/everyday language/Boer: can only be asserted relatively to a particular reading. English +/Boer: we need that to exclude the fact that the four principles are not trivially fulfilled by there being no counterexamples to the inferences in question simply because there are not enough names or predicates to formulate one. |
Boer I Steven E. Boer Thought-Contents: On the Ontology of Belief and the Semantics of Belief Attribution (Philosophical Studies Series) New York 2010 Boer II Steven E. Boer Knowing Who Cambridge 1986 |
| Designation | Quine | II 61 Naming: is a name or singular term. Designate: a predicate designates. Naming and designating are referring. They do not express meaning. VIII 27 Syncategorematic expressions such as "on" do not designate anything. Likewise, we can assume that words such as "unicorn" do not designate anything; neither something abstract nor something concrete. The same applies to "-ness" or punctuation marks. The mere ability to appear in a sentence does not make a string a name. Nominalism: interprets all words as syncategorematic! Ad XI 173 Note 18: Sentences/QuineVsFrege/Lauener: sentences do not designate! Therefore no names can be formed by them (by quotation marks). XI 173 Substitutional Quantification/Ontology/Quine/Lauener: Substitutional Quantification does not enter into an ontological obligation in so far as the names used do not have to name anything. That is, we are not forced to accept values of the variables. >Substitutional Quantification/Quine. XI 49 QuineVsSubstitutional Quantification: this is precisely what we use to disguise ontology by not getting out of the language. XI 132 Sense/designate/singular term/Quine/Lauener: it does not need a name to make sense. Example: unicorn. There is a difference between sense,meaning and reference. XII 73 Distinguishability/real numbers/Quine: N.B.: any two real numbers are always distinguishable, even if not every real number can be named! ((s) Not enough names). Because it is always x < y or y < x but never x < x. |
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 |
| Infinity Axiom | Wittgenstein | IV 83 Infinity axiom/Russell/Wittgenstein/Tractatus: 5534 would be expressed in the language in that way that there would be infinitely many names with different meanings. >"Not enough names..." Solution: if we avoid illusionary sentences (E.g. "a = a" E.g. "(Ex) x = a") (this cannot be written down in a correct term notation) - then we can avoid the problems with Russell's infinity axiom. >Infinity. |
W II L. Wittgenstein Wittgenstein’s Lectures 1930-32, from the notes of John King and Desmond Lee, Oxford 1980 German Edition: Vorlesungen 1930-35 Frankfurt 1989 W III L. Wittgenstein The Blue and Brown Books (BB), Oxford 1958 German Edition: Das Blaue Buch - Eine Philosophische Betrachtung Frankfurt 1984 W IV L. Wittgenstein Tractatus Logico-Philosophicus (TLP), 1922, C.K. Ogden (trans.), London: Routledge & Kegan Paul. Originally published as “Logisch-Philosophische Abhandlung”, in Annalen der Naturphilosophische, XIV (3/4), 1921. German Edition: Tractatus logico-philosophicus Frankfurt/M 1960 |
| Intensionality | Boer | I 21 Definition Intensionality/Boer: is nowadays negative, defined as non-intensionality. So we need a definition of "extensional sentence". Denotation/denoting/Boer: Assuming, denotating terms are: names, indices, demonstrativa and mass terms. Definition English +/Boer: be an extension of English by zero or more denotating expressions and predicates. --- I 22 Definition extensional reading/Boer: (preliminary): E.g.: "A thing x is such that ... x ..." is unique, then it is an extensional reading S iff it fulfills the following extensional principles: Definition strong principle of existential generalization/extensionality/Boer: for a denotating term D and variable v which does not belong to S if S has the form [... D ...], then one can conclude from S validly [an existing thing v is such that ... v ...]. Definition replacement principle for co-extensive predicates/Boer: ...from [for object x1,...xn, either P(x1, ... xn) or Q (x1, ... xn) or neither P nor Q], one can deduce every sentence by replacing one or more occurrences of P in S by Q. (DF). (LL). Definition substituting principle for material-equivalent propositions/Boer: for every sentence P and Q in English +, if P is present in S, one can conclude from S and [Either P and Q, or neither P nor Q] every sentence one or several occurrences of P in S by Q. Definition of the substitutability of the identity/Boer: for each denotating term D and E of English+: if S has the form [... D ...], one can deduce every sentence from S and an equation of the form [D = E] (or [E = D ] which is formed by replacing one or more occurrences of D by E in S. --- I 22 Validity/everyday language/Boer: can only be asserted relatively to a particular reading. English +/Boer: we need it to exclude the fact that the four principles are not trivially fulfilled by there being no counterexamples to the inferences in question simply because there are not enough names or predicates to formulate one. |
Boer I Steven E. Boer Thought-Contents: On the Ontology of Belief and the Semantics of Belief Attribution (Philosophical Studies Series) New York 2010 Boer II Steven E. Boer Knowing Who Cambridge 1986 |
| Interpretation | Mates | I 72 Interpretation/logic/Mates: an interpretation assigns: individual constants: individuals - one-digit predicates: properties (classes of individuals) - two-digit predicates: relations - statement letter: truth values - truth values come into play when the logical constants are interpreted. >Individual constants, >Individuals, >Properties, >Predicates, >Relations, >Truth values, >Constants. I 73 Truth values: may change when we pass from one interpretation to another, without the form of the statement being changed - the terms "true" and "valid" refer to all interpretations of a particular type. >Truth, >Validity, >Universal validity, >Proofs, >Provability. I 74 A statement is always true in relation to an interpretation. I 78 Interpretation/QL/Mates: if quantifiers have to be considered, we need a helping concept. We need two interpretations I and I"- b: is an individual constant - then b-variant - the interpretations then differ at the most in what they assign to b ("at most to b-th place"). I 81 Then has the substitution y"(namely y a/b) a specific truth value at every interpretation. >Inserting. I 83 Complete interpretation: not desirable because we also examine statements, where not names for all individual constants are available - e.g. real numbers. >Real numbers, >"Not enough names". I 91 Interpretation/translation/truth/intention/artificial language/Mates. Problem: The interpretation also has a "manner of being given". E.g. "2" as the "smallest prime" or "only even prime number" - translation: not unambigiuous - solution. helping concept: "predicate of the German language" - Problem: no systematic rules - meaning/everyday language: depends on the context. >Sense, >Everyday language. I 92 Interpretation specifies truth conditions (WB) fixed - truth condition: Then here in German. - With that it will give every statement a meaning. >Truth conditions, >Translation, >Translation indeterminacy. I 93 Interpretation/logic/Mates. would there be a complete I, then scheme: (W) X is only true if and only then at I when p - although the truth conditions are in German. |
Mate I B. Mates Elementare Logik Göttingen 1969 Mate II B. Mates Skeptical Essays Chicago 1981 |
| Properties | Wittgenstein | Hintikka I 60 Name/property/relation/Wittgenstein/Hintikka: the names of properties and relations are themselves properties and relations - the number of the names must be the same as that of the objects - ((s) Cf. the problem, that there are not enough names ...). I 207 Properties/object/Wittgenstein/Hintikka: the properties, without which an object could not exist, may not be attributed in a description of the object - ((s) elsewhere/other author: one must be able to abstract from properties. - Source?) >Predication, >Attribution, >Attributes, >Predicates. --- II 189 Properties/WittgensteinVsPlaton: looks for constituents of a mixture, such as if the properties would be constituents of things. II 285 Properties/Notation/Wittgenstein: one could e.g. characterize all objects in the room on how far they differ from a chair - this is not a statement about the objects, but about the grammar - ((s)> Chisholm: "to live opposite from...": no property. >Properties/Chisholm. |
W II L. Wittgenstein Wittgenstein’s Lectures 1930-32, from the notes of John King and Desmond Lee, Oxford 1980 German Edition: Vorlesungen 1930-35 Frankfurt 1989 W III L. Wittgenstein The Blue and Brown Books (BB), Oxford 1958 German Edition: Das Blaue Buch - Eine Philosophische Betrachtung Frankfurt 1984 W IV L. Wittgenstein Tractatus Logico-Philosophicus (TLP), 1922, C.K. Ogden (trans.), London: Routledge & Kegan Paul. Originally published as “Logisch-Philosophische Abhandlung”, in Annalen der Naturphilosophische, XIV (3/4), 1921. German Edition: Tractatus logico-philosophicus Frankfurt/M 1960 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 |
| Substitutional Quantification | Quine | V 140 Substitutional quantification/Quine: is open for other grammatical categories than just singular term but has other truth function. - Referential quantification: here, the objects do not even need to be specifiable by name. >Referential quantification, >Truth functions, >Singular terms. --- V 141 Language learning: first substitution quantification: from relative pronouns. - Later: referential quantification: because of categorical sentences. Substitution quantification: would be absurd: that every inserted name that verifies Fx also verifies Gx - absurd: that each apple or rabbit would have to have a name or a singular description. - Most objects do not have names. --- V 140 Substitutional Quantification/Referential Quantification/Truth Function/Quine: referential universal quantification: can be falsified by one single object, even though this is not specifiable by a name. - The same substitutional universal quantification: in contrast, remains true. - Existential quantification: referential: may be true due to a non-assignable value. - The same in substitutional sense: does not apply for lack of an assignable example. --- V 146f Substitutional Quantification/Quine: Problem: Blind spot: substitutional universal quantification: E.g. none of the substitution cases should be rejected, but some require abstention. - Existential quantification: E.g. none of the cases is to be approved, but some abstention is in order.- then neither agree nor abstain. (Equivalent to the alternation). --- Ad V 170 Substitutional Quantification/(s): related to the quantification over apparent classes in Quine’s meta language? --- V 175 Numbers/Classes/Quantification/Ontology/Substitutional quantification/Quine: first substitutional quantification through numbers and classes. - Problem: Numbers and classes can then not be eliminated. - Can also be used as an object quantification (referential quantification) if one allows every number to have a successor. - ((s) with substitution quantification each would have to have a name.) Class quantifier becomes object quantifier if one allows the exchange of the quantifiers (AQU/AQU/ - EQu/EQu) - so the law of the partial classes of one was introduced. --- X 124 Substitutional quantification/Quine: requires name for the values of the variables. Referential quantification/(s) speaks of objects at most. - Definition truth/Substitutional Quantification/Barcan/Quine: applying-Quantification - is true iff at least one of its cases, which is obtained by omitting the quantifier and inserting a name for the variable, is true. - Problem: almost never enough names for the objects in a not overly limited world. - E.g. No Goedel numbers for irrational numbers. - Then substitutional quantification can be wrong, because there is no name for the object, but the referential quantification can be true at the same time - i.e. both are not extensionally equal. X 124 Names/logic/substitutional quantification/Quine: Problem: never enough names for all objects in the world: e.g. if a set is not determined by an open sentence, it also has no name. - Otherwise E.g. Name a, Determination: x ε a - E.g. irrational numbers cannot be attributed to integers. - (s) > substitution class. --- XII 79f Substitutional Quantification/Quine: Here the variables are placeholders for words of any syntactic category (except names) - Important argument: then there is no way to distinguish names from the rest of the vocabulary and real referential variables. ((s) Does that mean that one cannot distinguish fragments like object and greater than, and that structures like "there is a greater than" would be possible?). XII 80 Substitutional Quantification/Quine: Problem: Assuming an infinite range of named objects. - Then it is possible to show for each substitution result of a name the truth of a formula and simultaneously to refute the universal quantification of the formula. - (everyone/all). - Then we have shown that the range has at least one unnamed object. - ((s) (> not enough names). - Therefore QuineVsSubstitutional Quantification. E.g. assuming the range contained the real name - Then not all could be named, but the unnamed cannot be separated. - The theory can always be strengthened to name a certain number, but not all - referential quantification: attributes nameless objects to itself. - Trick: (see above) every substitution result with a name is true, but makes universal quantification false. ((s) Thus an infinite number of objects secured). - A theory of real names must be based on referential quantification. |
Quine I W.V.O. Quine Word and Object, Cambridge/MA 1960 German Edition: Wort und Gegenstand Stuttgart 1980 Quine II W.V.O. Quine Theories and Things, Cambridge/MA 1986 German Edition: Theorien und Dinge Frankfurt 1985 Quine III W.V.O. Quine Methods of Logic, 4th edition Cambridge/MA 1982 German Edition: Grundzüge der Logik Frankfurt 1978 Quine V W.V.O. Quine The Roots of Reference, La Salle/Illinois 1974 German Edition: Die Wurzeln der Referenz Frankfurt 1989 Quine VI W.V.O. Quine Pursuit of Truth, Cambridge/MA 1992 German Edition: Unterwegs zur Wahrheit Paderborn 1995 Quine VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Quine VII (a) W. V. A. Quine On what there is In From a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism In From a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics In From a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis In From a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic In From a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals In From a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference In From a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality In From a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference In From a Logical Point of View, Cambridge, MA 1953 Quine VIII W.V.O. Quine Designation and Existence, in: The Journal of Philosophy 36 (1939) German Edition: Bezeichnung und Referenz In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Quine IX W.V.O. Quine Set Theory and its Logic, Cambridge/MA 1963 German Edition: Mengenlehre und ihre Logik Wiesbaden 1967 Quine X W.V.O. Quine The Philosophy of Logic, Cambridge/MA 1970, 1986 German Edition: Philosophie der Logik Bamberg 2005 Quine XII W.V.O. Quine Ontological Relativity and Other Essays, New York 1969 German Edition: Ontologische Relativität Frankfurt 2003 Quine XIII Willard Van Orman Quine Quiddities Cambridge/London 1987 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Anti-Objectivism | Field Vs Anti-Objectivism | II 318 Undecidability/VsAnti-Objectivism/AO/Field: other examples are less favorable for the anti-objectivism: E.g. Gödel. Even very simple sentences may be undecidable. E.g. (*) for all natural numbers x, B(x) where B(x) is a decidable predicate, i.e. a predicate, so that for each numeral n we can either prove B(n) or ~B(n). (Through an uncontroversial proof). Problem: you may say now that every undecidable sentence must be objectively correct (see above, must follow from the axioms). Then proof of ~B(n) would be proof of the negation of (*), as opposed to its undecidability. So, because of the assumption about B(x) B(n) must be provable for each number n, thus presumably objectively correct. This seems to show, however, that the generalization (*) is also objectively correct. (This is not undisputed, because it requires as a final step that it is objectively the case that there are no other natural numbers than those for which there are names. ((s)> "not enough names"). FieldVs extreme Anti-Objectivism: if that can be believed, however, he must adopt a more moderate position. Elementary Number Theory/ENT/Undecidability/Field: in fact, almost everyone believes that the choice between an undecidable proposition and its negation is objective, also for the generalized ENT. That would be hard to give up, because many assertions about provability and consistency are actually undecidable number-theoretic assertions, so that the anti-objectivist would have to say that they lack objectivity. Only few of them want that. Nevertheless, it is not obvious that if the ENT is granted objectivity, it would also have to be conceded to the higher regions. I 347 Anti-Objectivism/Gödel/Field/Conclusion/(s): Gödel gives no reason to assume that some undecidable propositions have certain truth values. (pro extreme anti-objectivism, by Field). VsAnti-Objectivism/Gödel/Field: It may be objected that the Gödel sentences of the candidates for our most mathematical theory should not only have a certain truth value, but that they are true! The argument goes by. Induction: all logical and non-logical premises of M are true. The rules of inference receive truth, therefore, all theorems must be true. So the theory must be consistent, therefore the Gödel sentence must be unprovable and therefore true. Gödel sentence: is true only if unprovable; if provable, it is not true. Problem: this induction can of course not be formalized in M. But one often feels that it is somehow "informally valid". If that is true, only the truth of the Gödel theorem is proved, not its particular truth. Solution: we might be able to fill the gap by establishing a principle that if we can prove something informally, it must certainly be true. (Vs: That’s plausible, but not undisputed!). In any case, the arguments for the particular truth of the Gödel theorem are weaker than those for its simple truth. |
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 |
| substit. Quantific. | Quine Vs substit. Quantific. | V 158 VsSubstitutional Quantification/SQ/Quine: the SQ has been deemed unusable for the classic ML for a false reason: because of uncountability. The SQ does not accept nameless classes as values of variables. ((s) E.g. irrational numbers, real numbers, etc. do not have names, i.e. they cannot be Gödel numbered). I.e. SQ allows only a countable number of classes. Problem: Even the class of natural numbers has uncountably many sub-classes. And at some point we need numbers! KripkeVs: in reality there is no clear contradiction between SQ and hyper-countability! No function f lists all classes of natural numbers. Cantor shows this based on the class {n:~ (n e f(n))} which is not covered by the enumeration f. refQ: demands it in contrast to a function f enumerating all classes of natural numbers? It seems so at first glance: it seems you could indicate f by numbering all abstract terms for classes lexicographically. Vs: but the function that numbers the expressions is not quite the desired f. It is another function g. Its values are abstract terms, while the f, which would contradict the Cantor theorem, would have classes as values... V 159 Insertion character: does ultimately not mean that the classes are abstract terms! ((s) I.e. does not make the assumption of classes necessary). The cases of insertion are not names of abstract terms, but the abstract terms themselves! I.e. the alleged or simulated class names. Function f: that would contradict Cantor's theorem is rather the function with the property that f(n) is the class which is denoted by the n-th abstract term g(n). Problem: we cannot specify this function in the notation of the system. Otherwise we end up with Grelling's antinomy or that of Richard. That's just the feared conflict with Cantor's theorem. This can be refute more easily: by the finding that there is a class that is not denoted by any abstract term: namely the class (1) {x.x is an abstract term and is not a member of the class it denotes}. That leaves numbers and uncountability aside and relates directly to expressions and classes of expressions. (1) is obviously an abstract expression itself. The antinomy is trivial, because it clearly relies on the name relation. ((s) x is "a member of the class of abstract expressions and not a member of this class"). V 191 Substitutional Quantification/SQ/Nominalism/Quine: the nominalist might reply: alright, let us admit that the SQ does not clean the air ontologically, but still we win something with it: E.g. SQ about numbers is explained based on expressions and their insertion instead of abstract objects and reference. QuineVsSubstitutional Quantification: the expressions to be inserted are just as abstract entities as the numbers themselves. V 192 NominalismVsVs: the ontology of real numbers or set theory could be reduced to that of elementary number theory by establishing truth conditions for the sQ based on Gödel numbers. QuineVs: this is not nominalistic, but Pythagorean. This is not about the extrapolation of the concrete and abhorrence of the abstract, but about the acceptance of natural numbers and the refutal of the most transcendent nnumbers. As Kronecker says: "The natural numbers were created by God, the others are the work of man." QuineVs: but even that does not work, we have seen above that the SQ about classes is, as a matter of principle, incompatible with the object quantification over objects. V 193 VsVs: the quantification over objects could be seen like that as well. QuineVs: that was not possible because there are not enough names. Zar could be taught RZ coordination, but that does not explain language learning. Ontology: but now that we are doing ontology, could the coordinates help us? QuineVs: the motivation is, however, to re-interpret the SQ about objects to eliminate the obstacle of SQ about classes. And why do we want to have classes? The reason was quasi nominalistic, in the sense of relative empiricism. Problem: if the relative empiricism SQ talks about classes, it also speaks for refQ about objects. This is because both views are closest to the genetic origins. Coordinates: this trick will be a poor basis for SQ about objects, just like (see above) SQ about numbers. Substitutional/Referential Quantification/Charles Parsons/Quine: Parsons has proposed a compromise between the two: according to this, for the truth of an existential quantification it is no longer necessary to have a true insertion, there only needs to be an insertion that contains free object variables and is fulfilled by any values of the same. Universal quantification: Does accordingly no longer require only the truth of all insertions that do not contain free variables. V 194 It further requires that all insertions that contain free object variables are fulfilled by all values. This restores the law of the single sub-classes and the interchangeability of quantifiers. Problem: this still suffers from impredicative abstract terms. Pro: But it has the nominalistic aura that the refQ completely lacks, and will satisfy the needs of set theory. XI 48 SQ/Ontology/Quine/Lauener: the SQ does not make any ontological commitment in so far as the inserted names do not need to designate anything. I.e. we are not forced to assume values of the variables. XI 49 QuineVsSubstitutional Quantification: we precisely obscure the ontology by that fact that we cannot get out of the linguistic. XI 51 SQ/Abstract Entities/Quine/Lauener: precisely because the exchange of quantifiers is prohibited if one of the quantifiers referential, but the other one is substitutional, we end up with refQ and just with that we have to admit the assumption of abstract entities. XI 130 Existence/Ontology/Quine/Lauener: with the saying "to be means to be the value of a bound variable" no language dependency of existence is presumed. The criterion of canonical notation does not suppose an arbitrary restriction, because differing languages - e.g. Schönfinkel's combinator logic containing no variables - are translatable into them. Ontological Relativity/Lauener: then has to do with the indeterminacy of translation. VsSubstitutional Quantification/Quine/Lauener: with it we remain on a purely linguistic level, and thus repeal the ontological dimension. But for the variables not singular terms are used, but the object designated by the singular term. ((s) referential quantification). Singular Term/Quine/Lauener: even after eliminating the singular terms the objects remain as the values of variables. XI 140 QuineVsSubstitutional Quantification: is ontologically disingenuous. |
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