Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 4 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Given | Field | I 218 Given/Givenness/Field: it is not clear what it means for a situation to be "given". - Which is linguistics- and theory-dependent. >Language dependence, >Theory depenence, >Ontology, >Existence, >Theories, >Knowledge. Problem: there is no way to describe a situation in which the relation - "double distance". (P3) "MG Eu (u is a matter particle and u is between x and y and xuCuy and uyCzw and the spatial relationships between x, y, z and w are the same as they actually are)" diverge. Spelling: C: congruent. Problem: if we define "triple distance" according to (P3), we have to show that the distance is not at the same time twice and three times. - Then we need Substantivalism or Heavy-Duty Platonism. >Platonism, >Heavy duty platonism, >Substantivalism. |
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 |
| Platonism | Field | I 8 Platonism/Field: his only argument is the applicability of mathematics. >Mathematics/Field, >Mathematical entities. I 14 FieldVsPlatonism: Platonism has to answer the fictionalist in his language - it cannot rely on it's "initial plausibility". I 152 Def Priority Thesis/PT/Crispin Wright: Thesis: the priority of the syntactic over the ontological categories. Platonism/Wright: that allows Frege to be a Platonist. >Numbers/Frege, >Gottlob Frege. Def Gödelian Platonism/Crispin Wright: in addition: the thesis that mathematical knowledge must be explained by a quasi-perceptual relation. FregeVsGödel. WrightVsGödel: we do not need that. I 153 Def weak Priority Thesis/PT: that each syntactic singular term also works automatically in a semantical way as a singular term. l 159 Equivalence/Platonism/Nominalism/Field: Question: In which sense is a Platonist statement (e.g. "direction 1 = direction 2") and a nominalistic statement equivalent (c1 is parallel to c2)? Problem: if there are no directions, the second cannot be a sequence of the first. >Nominalism. I 186 Def Moderate Platonism/mP/Field: the thesis that there are abstract objects like numbers. - Then there are probably also relations between numbers and objects. - Moderate Platonism: these relations are conventions, derived from physical relations. Def Heavy Duty Platonism/HDP/Field: takes relations between objects and numbers as a bare fact. l 189 Strong moderation condition/(Field (pro): it is possible to formulate physical laws without relation between objects and numbers. I 192 Heavy Duty Platonism/Field: assumes size relationships between objects and numbers. FieldVs: instead only between objects. --- II 332 Platonism/Mathematics/VsStructuralism/Field: isomorphic mathematical fields do not need to be indistinguishable. >Field theory. II 334 Quinish Platonism/Field: as a basic concept a certain concept of quantity, from which all other mathematical objects are constructed. So natural numbers and real numbers would actually be sets. III 31 Number/Points/Field: no Platonist will identify real numbers with points on a physical line. - That would be too arbitrary ( "What line?") - What should be zero point - What should be 1? III 90 Platonistic/Field: are terms such as e.g. gradient, Laplace Equation, etc. III 96 1st order Platonism/Field: accepts abstract entities, but no 2nd order logic - Problem: but he needs these (because of the power quantifiers). |
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 |
| Possibility | Field | I 86 Logically possible/possibility/diamond/KripkeVsField: "it is possible that" is not a logical truth. FieldVsKripke: yes it is, this is only due to Kripke's model-theoretical definition. - It should not be read "mathematically" or "metaphysically possible". >Logical truth, >Metaphysical possibility. --- I 87 E.g. Carnap: "He is bachelor and married": is logically wrong. >Meaning postulates. FieldVsCarnap: Meaning relations between predicates should not count to logic. - Then the sentence is logically consistent. Consistency operator/Field: MEx (x is red & x is round) should not only be true, but logically true. - ((s) Also without meaning postulates.) ((s) Meaning postulate/(s): here it is about the extent of the logic.) --- I 203 Geometric Possibility/Field: instead of logical possibility: there are different geometries. >Geometry. Precondition: there are empirical axioms which differentiate the possibility from impossibility. However, the existential quantifier must be within the range of the modal operator. >Existential quantification, >Modal operator, >Scope. --- I 218 Problem of Quantities/mathematical entities/me/Field: For example, it is possible that the distance between x and y is twice as long as the one between x and w, even if the actual distance is more than twice as long. Problem: extensional adequacy does not guarantee that the defined expression is true in every non-actual situation - that is, that we must either presuppose the substantivalism or the heavy duty Platonism. That is what we do in practice. I 192 Heavy Duty Platonism/Field: assumes size relationships between objects and numbers. >Substantivalism. |
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 |
| Terminology | Field | I 18 Explanation/Field: a) Def intrinsic explanation/Field: does not contain causally irrelevant entities (namely: mathematical entities) b) Def extrinsic explanation/Field: also contains causally irrelevant entities. For example, the attribution of finite sentences for the behavior of animals. II 159 Linguistic view/Field: assumes no meanings as mind-independent entities, but assigns words of a speaker to words of an interpreter. - The relations are based on different characteristics. - I.e. to inferences that contain this word - that's what I call "meaning-characteristic". - E.g. II 226 Definiteness/determined/definition/definite/vagueness/precision/(s)"definite"/Field: we cannot define "definitively true" ("determined", "determinately") by truth - we must conceive it as a reinforcement. Solution : Operator: "Definiteness-Operator"/dft-operator: this one is independent of truth-theoretical terms - but there is no physical information which decides. II 201 Signification/Terminology/Field: here: Relations are signed - objects are denoted. - predicates signify their extension. II 211 Def Basis/Field: here: E.g. the basis for predicates whose extension depends on other predicates: - E.g. "rabbit", "dinosaur": depend on the basis: predicate "identical". - The functional dependency of the other predicates from the basic predicate "identical" allows the partial extensions of the predicate to be correlated with the partial extension of the others. Def dependent: is a predicate, if it has a basis. - Now we can define relevance. Def Relevance/Structure/Language/Gavagai/Field: a structure partially agrees with the semantics of O, iff a) each independent term t of L denoted or signified partially m(t) b) each dependent term t of L denoted or signified m(t) with b(t) relative to the correlation of m(b(t)). ((s) in b) not partial). Still unsolved: how do we know which terms have a basis and which that is? - Problem: the words should also have a physical sense. II 287 Def "weak true"/truew/Field: "It is true that p" as equivalent to "p". Def "strongly true"/trues/Field: "It is true that p" as equivalent to "There is a certain fact that p". Det-Operator/D/Field: "It is a certain fact that". - This cannot be explained with "true". III 12 Def Principle C/Conservativity/Field: Let A be a nominalistic formulated claim. N: a corpus of such nominalistic assertions. - S a mathematical theory. A* is then not a consequence of N* + S if A is not itself a consequence of N* alone. ((s) "A* only if A", that is, if A * is not determined yet, that any nominalistic formulation is sufficient). III 60 Nominalization/Field: ... this suggests that laws about T (i.e., T obeying a particular differential equation) can be reformulated as laws over the relation between f and y. That is, ultimately the predicates Scal-Cong, St-Bet, Simul, S-Cong and perhaps Scal-Less. II 230 Def strongly true: is a sentence with a vague predicate then iff it is true relative to each of the candidates of an extension. Then it is a borderline case without definition-operator (dft-operator): "Jones is bald in some, but not in all extensions". I 152 Def Priority Thesis/PT/Crispin Wright: Thesis: the priority of the syntactic over the ontological categories. Platonism/Wright: that allows Frege to be a Platonist. I 153 Def weak Priority Thesis/PT: that each syntactic singular term also works automatically in a semantical way as a singular term. I 186 Def Moderate Platonism/mP/Field: the thesis that there are abstract objects like numbers. - Then there are probably also relations between numbers and objects. - Moderate Platonism: these relations are conventions, derived from physical relations. Def Heavy Duty Platonism/HDP/Field: takes relations between objects and numbers as a bare fact. l 189 Strong moderation condition/(Field (pro): it is possible to formulate physical laws without relation between objects and numbers. I 192 Heavy Duty Platonism/Field: assumes size relationships between objects and numbers. - FieldVs: instead only between objects. III 96 1st order Platonism/Field: accepts abstract entities, but no 2nd order logic. Problem: anyway he needs these (because of the power quantifiers). II 228 Def Weakly true/vagueness/truth/truth-predicate/Field: to be able to say general things about borderline cases. Not only that somebody represents a certain limiting case. Not weakly true/deflationism: e.g. "Either bald or not-bald is true". Then the Truth-predicate itself inherits the vagueness. It is not definitely true whether or not. Def Strongly true/Field: assuming, Jones is a limiting case: then neither "bald" nor its negation (strongly) plus classical logic: then the disjunction "bald or not bald" should be true even in strong interpretation. Law of the excluded middle: if we give it up: a) weakly true: then the disjunction is not true b) strongly true: then the disjunction is without truth value. Strongly true: is less vague, does not inherit the vagueness. II 230 Def strongly true: is a sentence with a vague predicate then iff it is true relative to each of the candidates of an extension. - Then the limiting case without definite-operator: "Jones is bald in some extensions but not in all". |
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 |
| |||
| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Mundy, B. | Field Vs Mundy, B. | I 199 Representation Theorem/VsRelationism: Relationism cannot take over the representation theorems from substantivalism either, because these depend on structural regularities (regularity of spacetime structure). And this regularity of spacetime is lost in relationalism. ((s) because there should be no empty sp.t., the sp.t. itself is bound to (empirically irregularly) occurring matter). Wrong Solution/Mundy: (1983): has proven a "representation theorem" which is not based on structural regularities. But that does not help heavy duty Platonism, because it generates numerical functors only from other numerical functors. That means he does not take predicates which put matter particles (point particles) in relation to each other, but a functor k: that refers particles to real numbers. E.g. For every three-point particle a real number that represents the inner product of two vectors which have one of these points as a common starting point, and the other two as endpoints. From this he extracts (several) coordinate systems, so that we have a representation theorem of species. FieldVsMundy: this does not serve the purposes for which representation theorems were originally developed, because it does not depart from a non-numeric base. Mundy: also sees that the R should not use any functions of point particles to real numbers as the basis for its formulation of physics. Therefore, he reformulates the equation: old: k(p,q,r) = a (where a is a real number) new: ka(p,q,r) so that we have an uncountable, infinite set of 3-digit space relations, one for every real number. (Mundy, 1983, p 212, 223.) FieldVsMundy: this does not solve any problem, because it’s only a notational trick. ((s) notation, orthography, paraphrasing, renaming >Rorty: "redescription" not a mere renaming, because description (language) necessitates stronger revision than replacing individual predicates with others. Potentially different number of digits). FieldVsMundy: if you really wanted to interpreted the ka’s as 3-digit spatial relations, the a’s would have to be considered as unquantifiable indices. Then we would have uncountably many primitive predicates, and thus no theory would be possible. Index/Quantification/(s): it is impossible to quantify on indices. Indices are not quantifiable. Mundy: of course, does not treat the indices as unquantifiable, but he re-writes them: k(p,q,r) = a if he wants to quantify on a. FieldVsMundy: but a quantifiable index is simply a variable that appears in a different place. And with the re-naming we do not change the fact that we have a 4-digit relation of which one term is a real number. Conclusion: With that you cannot take advantage of the difference between moderate Platonism and heavy duty Platonism. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Sklar, L. | Field Vs Sklar, L. | I 201 Absolute Acceleration/Substantialism/S/Larry Sklar: (Sklar, 1974): thinks the problem arises (for relationism), because the S understands absolute acceleration as acceleration relative to an entity, namely an inertial frame or ITAR. Relationism/Sklar: cannot do likewise. But: possible solution/Sklar: R must deny that the predicate "is absolutely accelerated" is a relational expression! The term "A is accelerated" is incomplete. To complete it, we must answer the question: "A is accelerated relative to what?" Important argument: but the term "A is absolutely accelerated" is precisely a complete expression! As E.g. "A is red" and not incomplete like "A is north of". I 202 Absolute Acceleration/Sklar: is no relation to anything! Not even to the "center of mass of the Universe"! (>Absoluteness). And it is also no relation that an object has to substantivalistic (empty) RZ. Because these ultimate "reference objects" do not exist according to R. FieldVsSklar: does it work? The answer is difficult and ambiguous. 1) You can understand his words in a way that we allow de R the use of the 1-digit predicate "is absolutely accelerated". And accordingly, "is absolutely unaccelerated" (in absolute rest). This is a non-relational predicate in which "x is absolutely unaccelerated" is not defined in terms of a relation between x and something else (neither matter nor empty RZ) Rather it would be a primitive term or defined in terms which are themselves not relational. Then the R would be permitted to use such predicates. FieldVsSklar: unfortunately, that does not change the problem of acceleration, because the problem arises, because there are so few things in the ontology of the relationalist that are absolutely unaccelerated. The primitive predicate of acceleratedness only allows sorting out those few trajectories that are unaccelerated. Problem: You cannot define the other predicates with that, such as E.g. "has twice the acceleration as". If we had a sufficient number of unaccelerated trajectories, we could use them to define numerical acceleration (more precisely, the different invariant acceleration predicates). We could simply mimic the substantivalistic definitions by using unaccelerated trajectories instead of ITAR. 2) Sklar/Field: you can read it differently: that you do not only define one single non-relational predicate of unacceleratedness, but infinitely many, perhaps a "has the acceleration (r1, r2, r3) for each triplet of definable reals R1, R2, R3. Or even a more complex family of predicates, which would have the advantage of being independent from co-ordinates and scales. I 203 Vs: infinite ideology (predicates) makes a theory impossible. 3) Skalar/Field: he could be understood as follows: we could allow the R to introduce a primitive numerical (or "vector valued") acceleration functor. (But neither he is independent from the time scale). This is possible if one accepts the Heavy Duty Platonism (HDP). R/Field: but more attractive when it comes to the rejection of the HDP. |
Hartry Field I Field Realism, Mathematics and Modality Oxford 1989 II Field Truth and the absence of facts Wahrheit ohne Tatsachen Oxford, New York 2001 III Field Science without numbers Princeton University Press 1980 |
| |||