Find counter arguments by entering NameVs… or …VsName.
| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Frege, G. | Quine Vs Frege, G. | Quine I 425 VsFrege: tendency to object orientation. Tendency to align sentences to names and then take the objects to name them. I 209 Identity/Aristotle/Quine. Aristotle, on the contrary, had things right: "Whatever is predicated by one should always be predicated by the other" QuineVsFrege: Frege also wrong in "Über Sinn und Bedeutung". QuineVsKorzybski: repeated doubling: Korzybski "1 = 1" must be wrong, because the left and right side of the equation spatially different! (Confusion of character and object) "a = b": To say a = b is not the same, because the first letter of the alphabet cannot be the second: confusion between the sign and the object. Equation/Quine: most mathematicians would like to consider equations as if they correlated numbers that are somehow the same, but different. Whitehead once defended this view: 2 + 3 and 3 + 2 are not identical, the different sequence leads to different thought processes (QuineVs). I 264 according to Russell "Propositional Attitudes": believes, says, strives to, that, argues, is surprised, feares, wishes, etc. ... I 265 Propositional attitudes create opaque contexts into which quantification is not allowed. (>) It is not permissible to replace a singular term by an equally descriptive term, without stretching the truth value here. Nor a general term by an equally comprehensive one. Also cross-references out of opaque contexts are prohibited. I 266 Frege: in a structure with a propositional attitude a sentence or term may not denote truth values, a class nor an individual, but it works as "name of a thought" or name of a property or as an "individual term". QuineVsFrege: I will not take any of these steps. I do not forbid the disruption of substitutability, but only see it as an indication of a non-designating function. II 201 Frege emphasized the "unsaturated" nature of the predicates and functions: they must be supplemented with arguments. (Objections to premature objectification of classes or properties). QuineVsFrege: Frege did not realize that general terms can schematized without reifying classes or properties. At that time, the distinction between schematic letters and quantifiable variables was still unclear. II 202 "So that" is ontologically harmless. Despite the sad story of the confusion of the general terms and class names, I propose to take the notation of the harmless relative clause from set theory and to write: "{x:Fx} and "ε" for the harmless copula "is a" (containment). (i.e.the inversion of "so that"). Then we simply deny that we are using it to refer to classes! We slim down properties, they become classes due to the well-known advantages of extensionality. The quantification over classes began with a confusion of the general with the singular. II 203 It was later realized that not every general term could be allocated its own class, because of the paradoxes. The relative clauses (written as term abstracts "{x: Fx}") or so-that sentences could continue to act in the property of general terms without restrictions, but some of them could not be allowed to exercise a dual function as a class name, while others could. What is crucial is which set theory is to be used. When specifying a quantified expression a variable may not be replaced by an abstraction such as: "x} Fx". Such a move would require a premise of the form (1), and that would be a higher form of logic, namely set theory: (1) (Ey)(y = {x:Fx}) This premise tells us that there is such a class. And at this point, mathematics goes beyond logic! III 98 Term/Terminology/Quine: "Terms", here as a general absolute terms, in part III single-digit predicates. III 99 Terms are never sentences. Term: is new in part II, because only here we are beginning to disassemble sentences. Applying: Terms apply. Centaur/Unicorn/Quine: "Centaur" applies to any centaur and to nothing else, i.e. it applies to nothing, since there are no centaurs. III 100 Applying/Quine: Problem: "evil" does not apply to the quality of malice, nor to the class of evil people, but only to each individual evil person. Term/Extension/Quine: Terms have extensions, but a term is not the denotation of its extension. QuineVsFrege: one sentence is not the denotation of its truth value. ((s) Frege: "means" - not "denotes"). Quine: advantage. then we do not need to assume any abstract classes. VII (f) 108 Variables/Quine: "F", etc.: not bindable! They are only pseudo-predicates, vacancies in the sentence diagram. "p", "q", etc.: represent whole statements, they are sometimes regarded as if they needed entities whose names these statements are. Proposition: these entities are sometimes called propositions. These are rather hypothetical abstract entities. VII (f) 109 Frege: alternatively: his statements always denote one or the other of exactly two entities: "the true one" or "the false one". The truth values. (Frege: statements: name of truth values) Quine pro Frege: better suited to distinguish the indistinguishable. (see above: maxim, truth values indistinguishable in the propositional calculus (see above VII (d) 71). Propositions/Quine: if they are necessary, they should rather be viewed as names for statements. Everyday Language/Quine: it is best if we return to everyday language: Names are one kind of expression and statements are another! QuineVsFrege: sentences (statements) must not be regarded as names and "p", "q" is not as variables that assume entities as values that are entities denoted by statements. Reason: "p", "q", etc. are not bound variables! Ex "[(p>q). ~p]> ~p" is not a sentence, but a scheme. "p", "q", etc.: no variables in the sense that they could be replaced by values! (VII (f) 111) VII (f) 115 Name/QuineVsFrege: there is no reason to treat statements as names of truth values, or even as names. IX 216 Induction/Fregean Numbers: these are, other than those of Zermelo and of von Neumann, immune against the trouble with the induction (at least in the TT), and we have to work with them anyway in NF. New Foundations/NF: But NF is essentially abolishing the TT! Problem: the abolition of TT invites some unstratified formulas. Thus, the trouble with induction can occur again. NFVsFrege: is, on the other hand, freed from the trouble with the finite nature which the Fregean arithmetic touched in the TT. There, a UA was needed to ensure the Uniqueness of the subtraction. Subtraction/NF: here there is no problem of ambiguity, because NF has infinite classes - especially θ - without ad-hoc demands. Ad 173 Note 18: Sentences/QuineVsFrege/Lauener: do not denote! Therefore, they can form no names (by quotation marks). XI 55 QuineVsFrege/Existence Generalisation/Modal/Necessary/Lauener: Solution/FregeVsQuine: this is a fallacy, because in odd contexts a displacement between meaning and sense takes place. Here names do not refer to their object, but to their normal sense. The substitution principle remains valid, if we use a synonymous phrase for ")". QuineVsFrege: 1) We do not know when names are synonymous. (Synonymy). 2) in formulas like e.g. "(9>7) and N(9>7)" "9" is both within and outside the modal operaotor. So that by existential generalization (Ex)((9>7) and N(9>7)) comes out and that's incomprehensible. Because the variable x cannot stand for the same thing in the matrix both times. |
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 |
| Russell, B. | Hilbert Vs Russell, B. | Klaus von Heusinger, Eselssätze und ihre Pferdefüsse Uni Konstanz Fachgruppe Sprachwissenschaft Arbeitspapier 64; 1994 Heusinger I 1 Epsilon/Heusinger: brings a new representation of certain and undefined NP: these are interpreted like pronouns as context-dependent terms, which are represented by a modified epsilon operator. This is interpreted as a selection function. VsRussell/VsIota Operator: this operator is less flexible because it is subject to the Uniqueness condition. Context Dependency: is also dynamic in that the context reflects the advancing state of information. I 30 EO/Hilbert/Bernays/Heusinger: term building operator that makes the term x Fx from a formula F and a variable x. It can be understood as a generalized iota operator to which neither the condition of uniqueness nor the condition of existence applies. Iota Operator/HilbertVsRussell: has no contextual definition for Hilbert, but an explicit definition. I.e. ix Fx may be introduced if the condition of Uniqueness and existence expressed in (48i) is derivable for the formula F. Problem: this is impractical because you do not always see if the formula meets the conditions. Eta Operator/Solution/Hilbert: may be introduced as in (48ii) if there is at least one element that makes F true. Its content is interpreted as a selection function. Uniqueness Condition: has therefore been replaced by the selection principle. Problem: also this condition of existence cannot be seen in the formula. Solution/Hilbert: Epsilon Operator/EO: is defined according to (48iii) even if F is empty, so that an epsilon term is always well defined. I 38 Determination/VsRussell/Heusinger: this means that determination is not attributed to uniqueness (>Iota operator) but to the more general concept of salinity (according to Lewis). Generality/(s): whether salience (which is itself context-dependent) is more general than Uniqueness is questionable). Determination/Heusinger: is either a) a global property, such as it applies to unique and functional concepts (deictic use), or b) local: determined by the context. (anaphoric use) Both have a dynamic element. Rucker I 263 HilbertVsRussell: improved shortly after the publishing of Principia Mathematica(1) the techniques to elaborate with their help his idea of the "formal system". mathematics/Logics/Hilbert: idea to understand all relations like x = y, x = 0, and z = x + y as special predicates in predicate logic: G(x,y), N(x), and S(x,y,z). Then the axioms of mathematics can be regarded as formulae of predicate logic and the proof process becomes the simple application of the rules of logic to the axioms. I 264 this allows mechanical solution methods. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
|
| |||