Find counter arguments by entering NameVs… or …VsName.
| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Principia Mathematica | Wittgenstein Vs Principia Mathematica | II 338 Identity/Relation/Notation/WittgensteinVsRussell: Russell's notation triggers confusion, because it gives the impression that the identity is a relationship between two things. This use of the equal sign, we have to differentiate from its use in arithmetics, where we may think of it as part of a replacement rule. WittgensteinVsRussell: its spelling gives erroneously the impression that there is a sentence like x = y or x = x. But one can abolish the signs of identity. II 352 Definition number/Russell/Wittgenstein: Russell's definition of number as a property of a class is not unnecessary, because it states a method on how to find out if a set of objects had the same number as the paradigm. Now Russell has said, however, that they are associated with the paradigm, not that they can be assigned. II 353 The finding that two classes are associated with one another, means, that it makes sense to say so. WittgensteinVsRussell: But how do you know that they are associated with one another? One cannot know and hence, one cannot know, if they are assigned to the same number, unless you carry out the assignment, that is, to write it down. II 402 Acquaintance/description/WittgensteinVsRussell: misleading claim that, although we have no direct acquaintance with an infinite series, but knowledge by description. II 415 Number/definition/WittgensteinVsRussell: the definition of the number as the predicate of a predicate: there are all sorts of predicates, and two is not an attribute of a physical complex, but a predicate. What Russell says about the number, is inadequate because no criteria of identity are named in Principia and because the spelling of generality is confusing. The "x" in "(Ex)fx" stands for a thing, a substrate. Number/Russell/Wittgenstein: has claimed, 3 is the property that is common to all triads. WittgensteinVsRussell: what is meant by the claim that the number is a property of a class? II 416 It makes no sense to say that ABC was three; this is a tautology and says nothing when the class is given extensionally. By contrast, it makes sense to claim that in this room there are three people. Definition number/WittgensteinVsRussell: the number is an attribute of a function which defines a class, not a property of the extension. WittgensteinVsRussell: he wanted to get ,next to the list, another "entity", so he provided a function that uses the identity to define this entity. II 418 Definition number/WittgensteinVsRussell: a difficulty in Russell's definition is the concept of the clear correspondence. Equal sign/Russell/Wittgenstein: in Principia Mathematica(1), there are two meanings of identity. 1. by definition as 1 + 1 = 2 Df. ("Primary equations") 2. the formula "a = a" uses the "=" in a special way, because one would not say that a can be replaced by a. The use of "=" is limited to cases in which a bound variable occurs. WittgensteinVsRussell: instead of (Ex):fx . (y).fy > (x=y), one writes (Ex)fx: ~ (Ex,y).fx.fy, (sic) which states that there are no two things, but only one. --- IV 47/48 So you cannot introduce objects of a formal concept and the formal concept itself, as primitive concepts. WittgensteinVsRussell: one cannot introduce the concept of function and special functions as primitive concepts, or e.g. the concept of number and definite numbers. IV 73 WittgensteinVsRussell/Tractatus: 5.452 in Principia Mathematica(1) definitions and basic laws occur in words. Why suddenly words here? There is no justification, and it is also forbidden. Logic/Tractatus: 5.453 All numbers in logic must be capable of justification. Or rather, it must prove that there are no numbers in logic. 5.454 In logic there is no side by side and there can be no classification. There can be nothing more universal and more special here. 5.4541 The solutions of logical problems must be simple, because they set the standard of simplicity. People have always guessed that there must be a field of questions whose answers are - a priori - symmetrical, and IV 74 lie combined in a closed, regular structure. In an area in which the following applies: simplex sigillum veri. ((s) Simplicity is the mark (seal) of the truth). Primitive signs/Tractatus: 5:46 the real primitive signs are not "pvq" or "(Ex).fx", etc. but the most general form of their combinations. IV 84 Axiom of infinity/Russell/Wittgenstein/Tractatus: 5.534 would be expressed in the language by the fact that there are infinitely many names with different meanings. Apparant sentences/Tractatus: 5.5351 There are certain cases where there is a temptation to use expressions of the form "a = a" or "p > p": this happens when one wants to talk of archetype, sentence, or thing. WittgensteinVsRussell: (Principia Mathematica, PM) nonsense "p is a sentence" is to be reproduced in symbols by "p > p" and to put as a hypothesis before certain sentences, so that their places for arguments could only be occupied by sentences. That alone is enough nonsense, because it does not get wrong for a non-sentence as an argument, but nonsensical. 5.5352 identity/WittgensteinVsRussell: likewise, one wanted to express "there are no things" by "~ (Ex).x = x" But even if this was a sentence, it would not be true if there IV 85 would be things but these were not identical with themselves? IV 85/86 Judgment/sense/Tractatus: 5.5422 the correct explanation of the sentence "A judges p" must show that it is impossible to judge a nonsense. (WittgensteinVsRussell: his theory does not exclude this). IV 87 Relations/WittgensteinVsRussell/Tractatus: 5.553 he said there were simple relations between different numbers of particulars (ED, individuals). But between what numbers? How should this be decided? Through the experience? There is no marked number. IV 98 Type theory/principle of contradiction/WittgensteinVsRussell/Tractatus: 6.123 there is not for every "type" a special law of contradiction, but one is enough, since it is applied to itself. IV 99 Reducibility axiom/WittgensteinVsRussell/Tractatus: (61232) no logical sentence, if true, then only accidentally true. 6.1233 One can think of a possible world in which it does not apply. But the logic has nothing to do with that. (It is a condition of the world). 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
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 |
| Russell, B. | Wittgenstein Vs Russell, B. | Carnap VI 58 Intensional logic/Russell: is not bound to certain statement forms. All of their statements are not translatable into statements about extensions. WittgensteinVsRussell. Later Russell, Carnap pro Wittgenstein. (Russell, PM 72ff, e.g. for seemingly intensional statements). E.g. (Carnap) "x is human" and "x mortal": both can be converted into an extensional statement (class statement). "The class of humans is included in the class of mortals". --- Tugendhat I 453 Definition sortal: something demarcated that does not permit any arbitrary distribution . E.g. Cat. Contrast: mass terminus. E.g. water. I 470 Sortal: in some way a rediscovery of the Aristotelian concept of the substance predicate. Aristotle: Hierarchy: low: material predicates: water, higher: countability. Locke: had forgotten the Aristotelian insight and therefore introduced a term for the substrate that, itself not perceivable, should be based on a bunch of perceptible qualities. Hume: this allowed Hume to reject the whole. Russell and others: bunch of properties. (KripkeVsRussell, WittgensteinVsRussell, led to the rediscovery of Sortals). E.g. sortal: already Aristotle: we call something a chair or a cat, not because it has a certain shape, but because it fulfills a specific function. --- Wittgenstein I 80 Acquaintance/WittgensteinVsRussell/Hintikka: eliminates Russell's second class (logical forms), in particular Russell's free-floating forms, which can be expressed by entirely general propositions. So Wittgenstein can say now that we do not need any experience in the logic. This means that the task that was previously done by Russell's second class, now has to be done by the regular objects of the first class. This is an explanation of the most fundamental and strangest theses of the Tractatus: the logical forms are not only accepted, but there are considered very important. Furthermore, the objects are not only substance of the world but also constitutive for the shape of the world. I 81 1. the complex logical propositions are all determined by the logical forms of the atomic sentences, and 2. The shapes of the atomic sentences by the shapes of the objects. N.B.: Wittgenstein refuses in the Tractatus to recognize the complex logical forms as independent objects. Their task must be fulfilled by something else: I 82 The shapes of simple objects (type 1): they determine the way in which the objects can be linked together. The shape of the object is what is considered a priori of it. The position moves towards Wittgenstein, it has a fixed base in Frege's famous principle of composite character (the principle of functionality, called Frege principle by Davidson (s)> compositionality). I 86 Logical Form/Russell/Hintikka: thinks, we should be familiar with the logical form of each to understand sentence. WittgensteinVsRussell: disputes this. To capture all logical forms nothing more is needed than to capture the objects. With these, however, we still have to be familiar with. This experience, however, becomes improper that it relates to the existence of objects. I 94ff This/logical proper name/Russell: "This" is a (logical) proper name. WittgensteinVsRussell/PU: The ostensive "This" can never be without referent, but that does not turn it into a name "(§ 45). I 95 According to Russell's earlier theory, there are only two logical proper names in our language for particularistic objects other than the I, namely "this" and "that". One introduces them by pointing to it. Hintikka: of these concrete Russellian objects applies in the true sense of the word, that they are not pronounced, but can only be called. (> Mention/>use). I 107 Meaning data/Russell: (Mysticism and Logic): sense data are something "Physical". Thus, "the existence of the sense datum is not logically dependent on the existence of the subject." WittgensteinVsRussell: of course this cannot be accepted by Wittgenstein. Not because he had serious doubts, but because he needs the objects for semantic purposes that go far beyond Russell's building blocks of our real world. They need to be building blocks of all logical forms and the substance of all possible situations. Therefore, he cannot be satisfied with Russell's construction of our own and single outside world of sensory data. I 108 For the same reason he refused the commitment to a particular view about the metaphysical status of his objects. Also: Subject/WittgensteinVsRussell: "The subject does not belong to the objects of the world". I 114 Language/sense data/Wittgenstein/contemporary/Waismann: "The purpose of Wittgenstein's language is, contrary to our ordinary language, to reflect the logical structure of the phenomena." I 115 Experience/existence/Wittgenstein/Ramsey: "Wittgenstein says it is nonsense to believe something that is not given by the experience, because belonging to me, to be given in experience, is the formal characteristics of a real entity." Sense data/WittgensteinVsRussell/Ramsey: are logical constructions. Because nothing of what we know involves it. They simplify the general laws, but they are as less necessary for them as material objects." Later Wittgenstein: (note § 498) equates sense date with "private object that stands before my soul". I 143 Logical form/Russell/Hintikka: both forms of atomic sentences and complex sentences. Linguistically defined there through characters (connectives, quantifiers, etc.). WittgensteinVsRussell: only simple forms. "If I know an object, I also know all the possibilities of its occurrence in facts. Every such possibility must lie in the nature of the object." I 144 Logical constants/Wittgenstein: disappear from the last and final logical representation of each meaningful sentence. I 286 Comparison/WittgensteinVsRussell/Hintikka: comparing is what is not found in Russell's theory. I 287 And comparing is not to experience a phenomenon in the confrontation. Here you can see: from a certain point of time Wittgenstein sees sentences no more as finished pictures, but as rules for the production of images. --- Wittgenstein II 35 Application/use/WittgensteinVsRussell: he overlooked that logical types say nothing about the use of the language. E.g. Johnson says red differed in a way from green, in which red does not differ from chalk. But how do you know that? Johnson: It is verified formally, not experimentally. WittgensteinVsJohnson: but that is nonsense: it is as if you would only look at the portrait, to judge whether it corresponds to the original. --- Wittgenstein II 74 Implication/WittgensteinVsRussell: Paradox for two reasons: 1. we confuse the implication with drawing the conclusions. 2. in everyday life we never use "if ... then" in this sense. There are always hypotheses in which we use that expression. Most of the things of which we speak in everyday life, are in reality always hypotheses. E.g.: "all humans are mortal." Just as Russell uses it, it remains true even if there is nothing that corresponds to the description f(x). II 75 But we do not mean that all huamns are mortal even if there are no humans. II 79 Logic/Notation/WittgensteinVsRussell: his notation does not make the internal relationships clear. From his notation does not follow that pvq follows from p.q while the Sheffer-stroke makes the internal relationship clear. II 80 WittgensteinVsRussell: "assertion sign": it is misleading and suggests a kind of mental process. However, we mean only one sentence. ((s) Also WittgensteinVsFrege). > Assertion stroke. II 100 Skepticism/Russell: E.g. we could only exist, for five minutes, including our memories. WittgensteinVsRussell: then he uses the words in a new meaning. II 123 Calculus/WittgensteinVsRussell: jealousy as an example of a calculus with three binary relations does not add an additional substance to the thing. He applied a calculus on jealousy. II 137 Implication/paradox/material/existence/WittgensteinVsRussell: II 137 + applicable in Russell's notation, too: "All S are P" and "No S is P", is true when there is no S. Because the implications are also verified by ~ fx. In reality this fx is both times independent. All S are P: (x) gx > .fx No S is P: (x) gx > ~ fx This independent fx is irrelevant, it is an idle wheel. Example: If there are unicorns, then they bite, but there are no unicorns = there are no unicorns. II 152 WittgensteinVsRussell: his writing presupposes that there are names for every general sentence, which can be given for the answer to the question "what?" (in contrast to "what kind?"). E.g. "what people live on this island?" one may ask, but not: "which circle is in the square?". We have no names "a", "b", and so on for circles. WittgensteinVsRussell: in his notation it says "there is one thing which is a circle in the square." Wittgenstein: what is this thing? The spot, to which I point? But how should we write then "there are three spots"? II 157 Particular/atom/atoms/Wittgenstein: Russell and I, we both expected to get through to the basic elements ("individuals") by logical analysis. Russell believed, in the end there would be subject predicate sentences and binary relations. WittgensteinVsRussell: this is a mistaken notion of logical analysis: like a chemical analysis. WittgensteinVsAtomism. Wittgenstein II 306 Logic/WittgensteinVsRussell: Russell notes: "I met a man": there is an x such that I met x. x is a man. Who would say: "Socrates is a man"? I criticize this not because it does not matter in practical life; I criticize that the logicians do not make these examples alive. Russell uses "man" as a predicate, even though we almost never use it as such. II 307 We could use "man" as a predicate, if we would look at the difference, if someone who is dressed as a woman, is a man or a woman. Thus, we have invented an environment for this word, a game, in which its use represents a move. If "man" is used as a predicate, the subject is a proper noun, the proper name of a man. Properties/predicate/Wittgenstein: if the term "man" is used as a predicate, it can be attributed or denied meaningfully to/of certain things. This is an "external" property, and in this respect the predicate "red" behaves like this as well. However, note the distinction between red and man as properties. A table could be the owner of the property red, but in the case of "man" the matter is different. (A man could not take this property). II 308 WittgensteinVsRussell: E.g. "in this room is no man". Russell's notation: "~ (Ex)x is a man in this room." This notation suggests that one has gone through the things in the room, and has determined that no men were among them. That is, the notation is constructed according to the model by which x is a word like "Box" or else a common name. The word "thing", however, is not a common name. II 309 What would it mean, then, that there is an x, which is not a spot in the square? II 311 Arithmetics/mathematics/WittgensteinVsRussell: the arithmetic is not taught in the Russellean way, and this is not an inaccuracy. We do not go into the arithmetic, as we learn about sentences and functions, nor do we start with the definition of the number. |
L. Wittgenstein I Hintikka/Hintikka Untersuchungen zu Wittgenstein, Frankfurt/M, 1996 II Wittgenstein Vorlesungen 1930-35, Frankfurt 1989 III J.R. Flor Der frühe Wittgenstein J.R. Flor der späte Wittgenstein in: Hügli(Hrsg.) Philosophie im 20. Jahrhundert, Reinbek, 1993 Der junge Wittgenstein -Der späte Wittgenstein) IV Wittgenstein Tractratus, Frankfurt 1960 V Chris Bezzel Wittgenstein zur Einführung Hamburg, 1988 VI Joachim Schulte Wittgenstein Stuttgart 2001 VII H. Tetens: Wittgensteins Tractatus, ein Kommentar Stuttgart 2009 Ca I R. Carnap Die alte und die neue Logik In Wahrheitstheorien, G. Skirbekk (Hg) Frankfurt 1996 Ca II R. Carnap Philosophie als logische Syntax In Philosophie im 20.Jahrhundert, Bd II, A. Hügli/P.Lübcke (Hg) Reinbek 1993 Ca IV R. Carnap Mein Weg in die Philosophie Stuttgart 1992 Ca IX Rudolf Carnap Wahrheit und Bewährung. Actes du Congrès International de Philosophie Scientifique fasc. 4, Induction et Probabilité, Paris, 1936 In Wahrheitstheorien, Gunnar Skirbekk Frankfurt/M. 1977 Ca VI R. Carnap Der Logische Aufbau der Welt Hamburg 1998 CA VII = PiS R. Carnap Sinn und Synonymität in natürlichen Sprachen In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Ca VIII (= PiS) R. Carnap Über einige Begriffe der Pragmatik In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Tu I E. Tugendhat Vorlesungen zur Einführung in die Sprachanalytische Philosophie Frankfurt 1976 Tu II E. Tugendhat Philosophische Aufsätze Frankfurt 1992 |
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