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 |
|---|---|---|---|
| Analyticity/Syntheticity | Waismann | I XII Analytic/synthetic/Waismann: Mill and Mach claimed that mathematical propositions were of empirical origin, Kant: the arithmetic and geometrical propositions are synthetic judgments a priori. >a priori, >synthetic a priori Poincaré: although arithmetic propositions are synthetically a priori, but the geometric ones are analytical. Frege: the arithmetical ones are analytical, the geometric ones are synthetic. Russell: all mathematical propositions are analytical. >Mathematics/Russell. Today (1947) it is often said that logic is a system of tautologies and mathematics is a >part of logic. |
Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 |
| Arithmetics | Waismann | I 50 Arithmetics/Waisman: arithmetics is based on logic. In doing so, one makes strong use of terms of the set theory, or the class calculus. The assertion that mathematics is only a >"part of logic" includes two theses, which are not always clearly separated: (A) The basic concepts of arithmetic can be traced back by definition to purely logical ones. (B) The principles of arithmetic can be deduced by means of proof from purely logical propositions. >Basic concepts, >Propositions, >Definitions, Definability. |
Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 |
| Logic | d’Abro | A. d'Abro Die Kontroversen über das Wesen der Mathematik 1939 in Kursbuch 8 Mathematik 1967 33 Logic/Hilbert/d'Abro: Arithmetic is, in fact, to be regarded as a part of logic; however, when looking carefully, we see that certain fundamental concepts of arithmetic have already been employed in the formulation of the laws of logic, e.g. the concept of quantity and, in part, of the number. >Sets, >Set theory, >Numbers. So we get into a circle. To avoid this, a simultaneous development of logic and arithmetic is required. >Circularity. |
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| Logic | Frege | II 49 Grammar/Logic: subject/predicate are always a thought without a truth value, there is no extension. >Subject, >Predicate, >Extension. Tugendhat II 54 Hegel: logic is composed of concepts. FregeVsHegel: logic is not composed of concepts, but of sentences. Important: not objects can be negated, but only sentences. >Concept, >Object, >Sentence, >Negation. Thiel I 335 Logic/Frege/Thiel: Frege's concept of logic, on which he wanted to trace back the entire non-geometric mathematics, was a more broadly formulated one than that of today. For Frege, the formation of sets is a logical process, so that the transition from the statement that exactly the same objects fall under two terms A and B to the statement of equality of the conceptual scopes of A and B is a law of logic for Frege. I 335/336 Today's view: conceptual scopes are nothing more than sets, therefore the law does not belong to logic, but to set theory. >Term scope. In traditional logic, the doctrine of conceptual extents was part of logic. Today it is part of set theory, while the doctrine of "conceptual content" remains in logic. That is rather weird. |
F I G. Frege Die Grundlagen der Arithmetik Stuttgart 1987 F II G. Frege Funktion, Begriff, Bedeutung Göttingen 1994 F IV G. Frege Logische Untersuchungen Göttingen 1993 Tu I E. Tugendhat Vorlesungen zur Einführung in die Sprachanalytische Philosophie Frankfurt 1976 Tu II E. Tugendhat Philosophische Aufsätze Frankfurt 1992 T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
| Russell’s Paradox | Frege | Thiel I 335 Logic/Frege/Thiel: Frege's concept of logic, on which he wanted to trace back the entire non-geometric mathematics, was a more broadly formulated one than that of today. For Frege, the formation of sets is a logical process, so that the transition from the statement that exactly the same objects fall under two terms A and B to the statement of equality of the conceptual scopes of A and B, is a law of logic for Frege. >Term scope. I 335/336 Today's view: conceptual scopes are nothing more than sets, therefore the law does not belong to logic, but to set theory. In traditional logic, the doctrine of conceptual extents was part of logic. Today it is part of set theory, while the doctrine of "conceptual content" remains in logic. This is quite weird. Russell's Antinomy/5th Basic Law/Frege: blamed the fifth of his "Basic Laws" (i. e. axioms) for inconsistency, according to which two concepts have the same extent if and only if each object falling under one of them also falls under the others. And, more generally, two functions have the same >"value progression" (artificial word coined by him), if and only if they result in exactly the same value for each argument. In his first analysis of the accident, Frege concluded that only the replacement of the arguments in the function terms by names for the equivalent conceptual scopes or value progressions themselves led to the contradiction. He changed his Basic Law V accordingly by demanding the diversity of all arguments that can be used from these special conceptual scopes or value progressions through an antecedent preceding the expression. He did not experience any more that this attempt ("Frege's way out") turned out to be unsuitable. Thiel I 337 Russell and Whitehead felt compelled to bury the logistical program again with their ramified type theory. The existence of an infinite domain of individuals had to be postulated by a separate axiom (since it could not be proven in the system itself), and an equally ad hoc introduced and otherwise unjustifiable "reduction axis" enabled type-independent general statements, e.g. about real numbers. When the second edition of Principia Mathematica appeared, it was obvious that the regression of mathematics to logic had failed. Thus, Russell's antinomy marks the unfortunate end of logicism. >Reducibility axiom, >Type theory. |
F I G. Frege Die Grundlagen der Arithmetik Stuttgart 1987 F II G. Frege Funktion, Begriff, Bedeutung Göttingen 1994 F IV G. Frege Logische Untersuchungen Göttingen 1993 T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
| Truth Functions | Quine | I 252 Every truth function is transparent for designation. V 160 Quantifiers/truth function: are indifferent in relation to most differences but not to the difference between finite/infinite. But they are probably indifferent to differences between different infinite cardinalities. (countable/uncountable) - (> Loewenheim). VII (f) 118 Universals/ontology/Truth Functions/Quine: another, bolder way to abstract universals is to make them accessible to quantification. Thus we expand the truth-functional logic! "(p)", "(Ep)" etc. are then no longer only schematic. They can accept suitable entities as values, especially propositions or better, truth values. >Ontology, >Universals. VII (h) 156ff Language/Truth Functions/Intensionality/Opacity/Quine: any non-truth functional language leads to opaque contexts. >Intensionality. V 188 Science/Opacity/Quine: Solution: Restriction of the scientific language to truth functions and object quantification. >Opacity, >Quantification. I 115 The truths of the truth-functional part of logic are the tautologies. >Tautologies. II 17 Example "As soon as (when) it becomes night, the lamps are lit" Here "as soon as" is a connecting particle comparable with the truth functions. By chance it rather leads to permanent sentences. II 192 From today's point of view, quantifier logic is nothing more than a further development of the logic of truth functions. The truth value of a truth function can be calculated on the basis of the truth values of the arguments. Why then does quantifier logic not become decidable by truth tables? This validity criterion would be too strict, because the quantified partial expressions are not always independent from each other! However, the truth table is fully functional if all variables are independent of each other. |
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 |
| Ultimate Justification | Waismann | I 50 Ultimate justification/foundation/Mathematics/Waismann: The question of the last anchorage has not been solved with these researches, but merely pushed back further. A justification is unsuitable with the help of arithmetic; we have already reached the last clues of the arithmetic deduction. But such a possibility seems to arise when one looks beyond arithmetic: this leads to the third standpoint. >Foundation. Arithmetic/Waismann: is based on logic. In doing so, one makes strong use of terms of the set theory, or the class calculus. The assertion that mathematics is only a >"part of logic" includes two theses, which are not always clearly separated: A) The basic concepts of arithmetic can be traced back to purely logical ones by definition B) The principles of arithmetic can be deduced from evidence from purely logical propositions. >Logic, >Proof, >Empiricism. I 51 It looks like the sets of logic are tautologies. (Wittgenstein in 1921 introduced the concept of tautology). >Tautology. WaismannVsFrege: Frege was completely lacking the insight that the whole logic becomes meaningless, because he did not understand the nature of logic at all. In Frege's opinion, logic should be a descriptive science, such as mechanics. And to the question of what it describes, he replied: the relations between ideal objects, such as "and", "or", "if", etc. Platonic conception of a realm of uncreated structures. >Platonism, >G. Frege. |
Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Kant | Frege Vs Kant | I 30 HankelVsKant: the assumption of an infinite number of irrefutable original truths is inappropriate and paradoxical. (Frege pro Hankel) Axioms/FregeVsKant: should be immediately obvious. E.g. is it obvious that 135 664 + 37 863 = 173 527? And that is precisely what Kant cites for their synthetic nature! I 30 Frege: much more speaks against their unprovability. How should they be viewed other than by evidence, since they are not immediately obvious. I 41 Numbers/FregeVsKant: Kant wants to use the view of fingers and points, but that is precisely what is not possible here! A distinction between small and large numbers should not be necessary! FregeVsKant: "pure view" does not help! The things that are called views. Quantities, lengths, surface areas, volumes, angles, curves, masses, speeds I 42 Forces, light levels, currents, etc. In contrast, I cannot even admit the view of the number 100 000. The sense of the word number in logic is therefore a further advanced than that in the transcendental aesthetic. Numbers/Frege: the relationship with geometry should not be overestimated!. I 43 A geometric point is, considered by itself, is impossible to distinguish from another, individual numbers, on the other hand, are not impossible to distinguish! Each number has its peculiarity. I 120 FregeVsKant: he has underestimated the analytic judgments:. I 121 He thinks the judgement in general affirmative. Problem: what if it is about an individual object, about an existential judgement? Numbers/FregeVsKant: he thinks that without sensuality no object would be given to us, but the numbers are it, as abstract but very specific items. Numbers are no concepts. IV 61 Negation/FregeVsKant: he speaks of affirmative and negative judgments. Then you would also have to distinguish affirmative and negative thoughts. This is quite unnecessary in logic. I 119 FregeVsKant: he has underestimated the analytic judgments:. I 120 He thinks the judgement in general affirmative. Problem: what if it is about an individual object, about an existential judgement? Kant: seems to think of adjunctive properties. But E.g. in the case of a continuous function of a really fruitful definition there is certainly a more intimate connection. I 121 The implications of mathematics enrich our knowledge, therefore, they should be called synthetic according to Kant, but they are certainly also analytical! They are included in the definitions as the plant in the seed, not like the beam in the house. Numbers/FregeVsKant: he thinks that without sensuality no object would be given to us, but the numbers are it, as abstract but very specific items. Numbers are no concepts. Stepanians I 34 Mathematics/Truth/FregeVsKant: it is false to generalize geometric knowledge (by mere view) to all mathematics. Stepanians I 34 pPure View/Kant/Frege/Stepanians: (like Kant): geometrical knowledge is based on pure view and is already synthetic "in us", a priori. FregeVsMill: geometrical knowledge is not a sensation, because point, line, etc. are not actually perceived by the senses. Mathematics/Truth/FregeVsKant: it is false to generalize geometric knowledge (by mere view) to all mathematics. I 35 Numbers/KantVsFrege: are not given to us by view. I 36 Numbers/Arithmetic/FregeVsKant: purely logical definitions can be given for all arithmetical concepts. ((s) Therefore, it is a safer knowledge than the geometric one). Def Logicism/Frege/Stepanians: this is the view that was called "logicism". I.e. arithmetic is a part of logic. Arithmetic/FregeVsKant: is not synthetic but analytic. Newen I21 Discovery Context/Justification Context/Newen: the distinction has its roots in Frege’s Foundations of Arithmetic. Def Analytical/Frege: is the justification of a sentence if only general logical laws and definitions are needed in the proof. I 22 Frege/FregeVsKant: all numerical formulas are analytical. Quine X 93 Analytic/FregeVsKant: (1884): the true propositions of arithmetic are all analytic. Quine: the logic that made this possible also contained the set theory. Tugendhat II 12 "Not"/Tugendhat: Error: considering the word "not" as a reflection of the "position". (Kant calls "being" a "position"). FregeVsKant: has shown that the negation always refers to the so-called propositional content and does not stand at the same level with the assertion-moment (position). The traditional opposition of negating and affirming judgments (Kant) is therefore untenable! |
F I G. Frege Die Grundlagen der Arithmetik Stuttgart 1987 F II G. Frege Funktion, Begriff, Bedeutung Göttingen 1994 F IV G. Frege Logische Untersuchungen Göttingen 1993 Step I Markus Stepanians Gottlob Frege zur Einführung Hamburg 2001 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 Tu I E. Tugendhat Vorlesungen zur Einführung in die Sprachanalytische Philosophie Frankfurt 1976 Tu II E. Tugendhat Philosophische Aufsätze Frankfurt 1992 |
| McGee, V. | Field Vs McGee, V. | II 351 Second Order Number Theory/2nd Order Logic/HOL/2nd Order Theory/Field: Thesis (i) full 2nd stage N.TH. is - unlike 1st stage N.TH. - categorical. I.e. it has only one interpretation up to isomorphism. II 352 in which the N.TH. comes out as true. Def Categorical Theory/Field: has only one interpretation up to isomorphism in which it comes out as true. E.g. second order number theory. (ii) Thesis: This shows that there can be no indeterminacy for it. Set Theory/S.th.: This is a bit more complicated: full 2nd order set theory is not quite categorical (if there are unreachable cardinal numbers) but only quasi-categorical. That means, for all interpretations in which it is true, they are either isomorphic or isomorphic to a fragment of the other, which was obtained by restriction to a less unreachable cardinal number. Important argument: even the quasi-categorical 2nd order theory is still sufficient to give most questions on the cardinality of the continuum counterfactual conditional the same truth value in all interpretations, so that the assumptions of indeterminacy in ML are almost eliminated. McGee: (1997) shows that we can get a full second order set theory by adding an axiom. This axiom limits it to interpretations in which 1st order quantifiers go above absolutely everything. Then we get full categoricity. Problem: This does not work if the 2nd order quantifiers go above all subsets of the range of the 1st order quantifiers. (Paradoxes) But in McGee (as Boolos 1984) the 2nd order quantifiers do not literally go above classes as special entities, but as "plural quantifiers". (>plural quantification). Indeterminacy/2nd Order Logic/FieldVsMcGee: (see above chapter I): Vs the attempt to escape indeterminacy with 2nd order logic: it is questionable whether the indeterminacy argument is at all applicable to the determination of the 2nd order logic as it is applicable to the concept of quantity. If you say that sentences about the counterfactual conditional have no specific truth value, this leads to an argument that the concept "all subsets" is indeterminate, and therefore that it is indeterminate which counts as "full" interpretation. Plural Quantification: it can also be indeterminate: Question: over which multiplicities should plural quantifiers go?. "Full" Interpretation: is still (despite it being relative to a concept of "fullness") quasi-unambiguous. But that does not diminish the indeterminacy. McGeeVsField: (1997): he asserts that this criticism is based on the fact that 2nd order logic is not considered part of the real logic, but rather a set theory in disguise. FieldVsMcGee: this is wrong: whether 2nd order logic is part of the logic, is a question of terminology. Even if it is a part of logic, the 2nd order quantifiers could be indeterminate, and that undermines that 2nd order categoricity implies determinacy. "Absolutely Everything"/Quantification/FieldVsMcGee: that one is only interested in those models where the 1st. order quantifiers go over absolutely everything, only manages then to eliminate the indeterminacy of the 1st order quantification if the use of "absolutely everything" is determined!. Important argument: this demand will only work when it is superfluous: that is, only when quantification over absolutely everything is possible without this requirement!. All-Quantification/(s): "on everything": undetermined, because no predicate specified, (as usual E.g. (x)Fx). "Everything" is not a predicate. Inflationism/Field: representatives of inflationist semantics must explain how it happened that properties of our practice (usage) determine that our quantifiers go above absolutely everything. II 353 McGee: (2000) tries to do just that: (*) We have to exclude the hypothesis that the apparently unrestricted quantifiers of a person go only above entities of type F, if the person has an idea of F. ((s) i.e. you should be able to quantify over something indeterminate or unknown). Field: McGee says that this precludes the normal attempts to demonstrate the vagueness of all-quantification. FieldVsMcGee: does not succeed. E.g. Suppose we assume that our own quantifiers determinedly run above everything. Then it seems natural to assume that the quantifiers of another person are governed by the same rules and therefore also determinedly run above everything. Then they could only have a more limited area if the person has a more restricted concept. FieldVs: the real question is whether the quantifiers have a determinate range at all, even our own! And if so, how is it that our use (practices) define this area ? In this context it is not even clear what it means to have the concept of a restricted area! Because if all-quantification is indeterminate, then surely also the concepts that are needed for a restriction of the range. Range/Quantification/Field: for every candidate X for the range of unrestricted quantifiers, we automatically have a concept of at least one candidate for the picking out of objects in X: namely, the concept of self-identity! ((s) I.e. all-quantification. Everything is identical with itself). FieldVsMcGee: Even thoguh (*) is acceptable in the case where our own quantifiers can be indeterminate, it has no teeth here. FieldVsSemantic Change or VsInduction!!!. II 355 Schematic 1st Stage Arithmetic/McGee: (1997, p.57): seems to argue that it is much stronger than normal 1st stage arithmetic. G. is a Godel sentence PA: "Primitive Arithmetic". Based on the normal basic concepts. McGee: seems to assert that G is provable in schematic PA ((s) so it is not true). We just have to add the T predicate and apply inductions about it. FieldVsMcGee: that’s wrong. We get stronger results if we also add a certain compositional T Theory (McGee also says that at the end). Problem: This goes beyond schematic arithmetics. McGee: his approach is, however, more model theoretical: i.e. schematic 1st stage N.TH. fixes the extensions of number theory concepts clearly. Def Indeterminacy: "having non-standard models". McGee: Suppose our arithmetic language is indeterminate, i.e. It allows for unintended models. But there is a possible extension of the language with a new predicate "standard natural number". Solution: induction on this new predicate will exclude non-standard models. FieldVsMcGee: I believe that this is cheating (although some recognized logicians represent it). Suppose we only have Peano arithmetic here, with Scheme/Field: here understood as having instances only in the current language. Suppose that we have not managed to pick out a uniform structure up to isomorphism. (Field: this assumption is wrong). FieldVsMcGee: if that’s the case, then the mere addition of new vocabulary will not help, and additional new axioms for the new vocabulary would help no better than if we introduce new axioms simply without the new vocabulary! Especially for E.g. "standard natural number". Scheme/FieldVsMcGee: how can his rich perspective of schemes help to secure determinacy? It only allows to add a new instance of induction if I introduce new vocabulary. For McGee, the required relevant concept does not seem to be "standard natural number", and we have already seen that this does not help. Predicate/Determinacy/Indeterminacy/Field: sure if I had a new predicate with a certain "magical" ability to determine its extension. II 356 Then we would have singled out genuine natural numbers. But this is a tautology and has nothing to do with whether I extend the induction scheme on this magical predicate. FieldVsMysticism/VsMysticism/Magic: Problem: If you think that you might have magical aids available in the future, then you might also think that you already have it now and this in turn would not depend on the schematic induction. Then the only possible relevance of the induction according to the scheme is to allow the transfer of the postulated future magical abilities to the present. And future magic is no less mysterious than contemporary magic. FieldVsMcGee: it is cheating to describe the expansion of the language in terms of its extensions. The cheating consists in assuming that the new predicates in the expansion have certain extensions. And they do not have them if the indeterminist is right regarding the N.Th. (Field: I do not believe that indeterminism is right in terms of N.Th.; but we assume it here). Expansion/Extenstion/Language/Theory/FieldVsMcGee: 2)Vs: he thinks that the necessary new predicates could be such for which it is psychological impossible to add them at all, because of their complexity. Nevertheless, our language rules would not forbid her addition. FieldVsMcGee: In this case, can it really be determined that the language rules allow us something that is psychologically impossible? That seems to be rather a good example of indeterminacy. FieldVsMcGee: the most important thing is, however, that we do not simply add new predicates with certain extensions. |
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 |
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The author or concept searched is found in the following theses of the more related field of specialization.
| Disputed term/author/ism | Author |
Entry |
Reference |
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| Kant | Field I 79 Def Logicism / Field: is the thesis that mathematics is part of logic. This is VsKant: who denies that mathematics is analytic, because the calculations are synthetic. And for the calculations we need the numbers as entities. LogicismVsKant - KantVsLogicism. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 |
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