Find counter arguments by entering NameVs… or …VsName.
| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Boole, G. | Frege Vs Boole, G. | Berka I 57 Classical Logic/Berka: bivalent extensional logic: mostly created by Frege. Frege: clear distinction between variables and constants, laws and rules, created the concepts of logic functions (propositional functions) and quantifiers, the semantics of sense and meaning, also the first axiomatic system of classical logic. Russell: was the first to recognize Frege’s importance. Notation/Russell: was rather a follower of Peano. FregeVsBoole: pro clear distinction between statements and class logic. Sets the AL as a foundation. Truth Functions/Frege: their theory is of central importance for the propositional Calculus. Truth Value Tables: already known by Boole, Schröder, and Peirce. Systematically elaborated first by Post (1921)(1), Lukasiewicz (1921)(2), and Wittgenstein (1921)(3). First transferred to the PL by Foster (1931)(4), later by Wright (1957)(5). 1. E. L. Post, Introduction to a general theory of elemantary propositions, American Journal of Mathematics 43 (1921) , 163-185 2. J. Lukasiewicz, Logica dwuwartosciowa, PF 23 (1921), 189-205 3. L. Wittgenstein, Logisch-Philosophische Abhandlung, Ann. Naturphil. 14 (1921), 185-262 4. A. L. Forster, Formal Logic in finite terms Ann. Math. 32 (1931) 407-430 5. G. H. von Wright, Logical Studies, London 1957 Frege IV 92 SchröderVsBoole: Vs"Universe of Discourse" (> Quine: "You can still hatch enough..."). Sectors Calculus/Sector Calculus/Manifold/Schröder/Frege: division of an area into sectors, so that no point is at the same time in two sectors. (Boxes). ((s) no overlap). Most important relation between sectors: the containment of one in the others: "classification" (both can simply coincide). This corresponds to the relationship part/whole. IV 93 Instead of "sectors" we can also say "classes". Instead of manifold: "main sector". Manifold/Schröder/Frege/(s): classes of classes. ("main sector" box which comprises one or more boxes). Classes/Individuals/Schröder/Frege: Schröder also refers to an individual as class, but which only contains this single element, the individual. But also a class with several elements (individuals) can be considered a "thought thing" and thus can be presented as an individual. FregeVsSchröder: the difference between individual and class becomes fluent here. IV 9 FregeVsBoole: he tries to "embed abstract logic into the guise of algebraic signs". Frege against: tries to establish a uniform formula language of mathematics and logic. IV 13 FregeVsBoole: discards his concept of "universal class" ("universe", "universe of discourse" coined by de Morgan). SchröderVsBoole: the zero class is contained in every class. I.e. also in the class of the classes that are identical with the universal class. I.e. zero classes (in Boole designated with "0") and universal classes (in Boole designated with "1") are equal. So we have both: 1 = 1 and 0 = 1, and that is not possible. Schröder: the universal class cannot contain classes as elements among themselves, which in turn contain elements of the same manifold. ((s) anticipation of the theory of types). |
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 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Operationalism | Field Vs Operationalism | III 3 Nominalism/Field: I use some means which the nominalist rejects: E.g. finitism and operationalism reject the way in which I formulate physical theories: FieldVsFinitism/FieldVsOperationalism: I will say that between two points (E.g. of a light beam) there is always a third point (FinitismVsField). The objections (VsField) stem from considerations that have nothing to do with the nature of the physical entities. Physics/Field: I make strong assumptions about the nature and structure of physical objects (also about subatomic particles). Also about postulated unobservables. ((s) In return, he avoids strong assumptions about the mathematics that deals with it). III 36 Region/Field: do we need it together with the sp.z. points? Not necessarily, we can quantify on any small open region instead of on points. That’s still nominalistic. But we must not do without points. III 37 Finitism/Field: the purist desire to make do without points is a quasi-finitistic one, not nominalistic. FieldVsFinitism. Region/Field: reverse question: can nominalism have something against regions? Is there a problem with them? III 114 Solution: Individuals Calculus/Goodman/Field: if we accept Goodman’s individuals calculus, there is no problem with regions: we simply regard them as sums of points. Then, namely with the introduction of points, the concept of region is simultaneously introduced (as the sum of points). Empty Region/Individuals Calculus/Sum/Goodman/Field: it then also follows that there can be no empty region. III 37 Region/Goodman/Field: (as sum) does not need not be connected or measurable. There are very "unnatural" collections of points that can count as regions. Point/Field: even without individuals Calculus entities can be assumed that can be regarded as a "sum" of points. Then points can be seen as a special case of the regions (very small ones). That’s nominalistically acceptable. |
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 |
| Tradition | Sellars Vs Tradition | I 57 Meaning/Sellars: false: to regard it as a relation between a word and a non-linguistic entity. There is then the danger that one perceives this relation as a type of association. ((s) >tags, Myth of the museum). Meaning/relation/SellarsVsTradition: misleading that predicates would associated with objects. E.g. it is wrong that the semantic statement, ""red" means "rot" in German" would assert "red" would associated with red things. This would mean that this semantic statement would so to speak be a defining symbol of a longer statement on associative connections. That is not the case. (Here: difference of use and mention). (> Association). I 62 Report/act/Sellars: who supplies a report, does something. (SellarsVsTradition). Epistemology/tradition: a proposition token can play the role of a report, a) without that this is a public language implementation, and b) without speaker/listener! Sellars: here the accuracy of confirmations is supposed to correspond to the correctness of actions. This is not true, moreover, not every Ought is a Doing-Ought. I 65 Knowledge/SellarsVsTradition: Observational knowledge does not stand on its own two feet! It presupposes language acquisition. (Elsewhere: we cannot perceive a tree, without the concept of a tree.) But at the time of earlier perceptions you do not necessarily have to have had the concept. Long history of acquiring linguistic habits. Myth of the Factual/Sellars: thesis: that observation is constructed by self-authenticating, not linguistic episodes whose authority is transferred to linguistic and quasi linguistic full executions. I 84 Thinking/language/tradition: Thesis: Thoughts are possible without verbal ideas. I 88 SellarsVsTradition: Categories of intentionality are semantical. I 86 Theory/classic explanation/science/tradition/Sellars: the construction of a theory is to develop a system of postulates that is tentatively correlated with the observation language. SellarsVsTradition: this creates an extremely artificial and unrealistic picture of the actual procedure of scientists. I 87 Theory/Sellars: the basic assumptions of a theory are not normally formed by an uninterpreted calculus, but by a model (Def model/Sellars: the description of a domain of known objects that behave in the usual way). A model is distinguished primarily by the fact that it is provided with a comment which restricts or limits the analogies. The descriptions of the basic behaviors comply with the Postulates of the logistical image of theorizing. SellarsVs logistical image of theorizing: most explanations did not come readily from the theorists' minds. There is a continuous transition between science and everyday life. The distinction between theory language and observation language belongs to the logic of the concepts of inner episodes. |
Sellars I Wilfrid Sellars The Myth of the Given: Three Lectures on the Philosophy of Mind, University of London 1956 in: H. Feigl/M. Scriven (eds.) Minnesota Studies in the Philosophy of Science 1956 German Edition: Der Empirismus und die Philosophie des Geistes Paderborn 1999 Sellars II Wilfred Sellars Science, Perception, and Reality, London 1963 In Wahrheitstheorien, Gunnar Skirbekk Frankfurt/M. 1977 |
| Type Theory | Quine Vs Type Theory | III 315 Type Theory/TT/Quine: U1, U2 ... etc. logical types. Meaningless are expressions like "x e x", etc. "e2 may only stand between variables of successive type." III 316 With that we avoid confusion of constants. Example: we do not identify the number 12, which contains the class A of the Apostles, with the number 12, which contains a certain class consisting of a dozen classes. Because one is of the type U2, the other of type U3. Every type has a new number 12. ((s) Elsewhere: therefore VsType Theory: infinitely many numbers 1,2,3, etc.). Number/Existence/Ontology/Quine: that there are these numbers no longer depends on whether there are so many individuals. Type Theory/TT/Russell/Quine: Reason: we can derive an incorrect sentence without the separation of types: by simplifying the scheme (A) to (A'): (A’) (Ey)(x)(x ε y . ↔ Fx) If we then introduce the predicate «[1] ε [1]» for "F": we get the Russell antinomy/Russell paradoxy/logical form: (1) (Ey)(x)[x ε y . ↔ ~x ε x)] (2) (x)(x ε y . ↔ ~(x ε x)] (1) y (3) y ε y . ↔ ~(y ε y) (2) (4) (Ey)[y ε y . ↔ ~y ε y)]. Solution/Zermelo/VsType Theory/Quine: simpler: some predicates have classes as extension, others don't. (A') is thus considered as valid for some, but not all sentences. E.g. the predicate "[1] ε [1]" has no class as an extension. Zermelo: here (A') is assumed for the case in which the sentence has the form of a conjunction "x ε z. Gx" instead of "Fx". Then (A') becomes: (Ey)(x)( x ε y . ↔ . x ε z . Gx). Zermelo calls this the Def axiom schema of specification. To any given class z this law supplies other classes that are all sub-classes of z. But by itself it supplies at first no non-empty classes z. (...) III 318 Layers/Layered/Zermelo: (...) Sets/Classes/von Neumann/Quine: (...) Classes are not sets... III 319 Axioms/Stronger/Weaker/Quine: (...) you can seek strength or weakness. VII (e) 91 QuineVsType Theory: unnatural and uncomfortable disadvantages: 1) Universal class: because the TT only allows uniform types as members of a class, the universal class V leads to an infinite series of quasi universal classes, each for one type. 2) Negation: ~x ceases to comprise all non-elements of x, and only comprises those non-elements that do not belong to the next lower level! VII (e) 92 3) Zero class: even that accordingly leads to an infinite number of zero classes. ((s) for each level its own zero class). ((s) Absurd: we cannot distinguish different zero classes.) 4) Boolean class algebra: is no longer applicable to classes in general, but is reproduced at each level. 5) Relational Calculus: accordingly. to be re-established at each level. 6) Arithmetic: the numbers cease to be uniform! at each level (type) appears a new 0, new 1, new 2, and so on! Quine: instead counterproposal: QuineVsType Theory: Solution: Instead: variables with unlimited range, the concept of hierarchical formulas only survives in one point where we write numbers for variables and, without any reference to type theory, we replace R3 by the weaker: R3' If φ is stratified and does not contain "x", then (Ex)(y) ((y ε x) ↔ φ) is a theorem. Negation: ~x then contains everything that is not part of x. Zero class: there is only one zero class. Universal class: there is similarly only one universal class that contains absolutely everything, including itself. Relation, arithmetic, numbers: everything works out again comes in this way. VII (e) 93 Only difference between R3 and R3': R3' lacks a guarantee for the existence of such classes as: y^ (y ε y), y^~(y ε y), etc. In the case of some non-hierarchical formulas the existence of appropriate classes is still to be demonstrated through absurd consequences: R3' results in: (Ex)(y) ((y ε x) ↔ ((z ε y) l (y ε w))) and by inserting this results in subsitution inference (1) (Ex)(y) ((y ε x) ↔ ((z ε y) l (y ε z))) through the other rules What asserts the existence of a class y^ ((z ε y) l (y ε z)) whose generating formula is not hierarchical. But probably we cannot prove its existence. (From these follows inter alia Russell's paradox). Within a system, we can explicitly use such contradictions to take their existence ad absurdum. That (1) can be demonstrated, in turn, shows that the derivation strength of our system "NF" (New Foundations, Quine) exceeds the Principia Mathematica(1). 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 |
| Wittgenstein | Hintikka Vs Wittgenstein | Wittgenstein I 32 Calculus/Wittgenstein/Hintikka: but Wittgenstein’s calculus is not an intra-linguistic act. Understanding a sign is a step of calculus, (quasi to a calculation). "What a sentence is, is in a sense determined by the rules of sentence structure, in another sense through the use of the sign in the language game." PU § 136. HintikkaVsWittgenstein: Problem: that we actually need to do something in the application of the Calculus. This approach has failed, and therefore Wittgenstein almost entirely dispensed with the Calculus analogy in the PU. But it is not true that he no longer considers the entire theory valid, he has only come to realize that the concept of Calculus cannot fulfill both purposes at the same time. Wittgenstein I 238 Showing/Ostensive Definition/Wittgenstein/Hintikka: in the lectures of the early 30s, the ostensive definition is downright rejected. "The ostensive definition does not lead us beyond symbolism... we cannot do anything more than to replace one symbolism it with another." HintikkaVsWittgenstein: that is, one might think, blatantly wrong, because pointing gestures can easily lead us out of the realm of the merely linguistic. WittgensteinVsVs: denies this. He explains that what we achieve with an ostensive definition is not a connection between language and reality, but a connection between written and spoken language on the one hand and sign language on the other hand. Ostensive Definition/Wittgenstein: is nothing more than a Calculus. Wittgenstein I 242 Rule/Wittgenstein/Hintikka: middle period: for the first time, the rule is introduced as a mediator. But that does not remove the questions: What is the conceptual status of such a rule? How does it fulfill its mediation mission? Here is the seed to later philosophy: main question: the issue of the rule obedience. HintikkaVsWittgenstein: of course it bothers Wittgenstein to Postulate mysterious "mediator beings". But in the middle phase the rules threaten to become such beings. |
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 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 |
| |||