Find counter arguments by entering NameVs… or …VsName.
| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Boole, G. | Verschiedene Vs Boole, G. | Berka I 53 Universe/Discurse Universe/SchröderVsBoole: under "1" one should not understand such a comprehensive, as it were completely open class, as the "universe of the discussionable" (thinkable) of Boole. This is because of the fact that the zero class is included (zero set, empty set): Abstention/Schröder: notation in the book: equal sign crossed by left parenthesis. Thus he simultaneously designates the "identity of an area a ("subject area") with the area b" ("predicate area"). (>area Calculus). Spelling here: "enth". Subject area identical with the predicate area. Empty set/zero class/Schröder: the 0 should be included in each class that can be lifted out of diversity 1, so that 0 enth a applies. Therefore, 0 should be subject to each predicate. VsBoole: Problem: Under a we now understand the class of those classes of diversity which are equal to 1 (and that would certainly be allowed, because everything possible should be contained in 1). Then this class essentially comprised only one object, namely the symbol 1 itself ((s)Vs: confusion of symbol and object), or the whole of the multiplicity that constitutes its meaning, and also "nothing", thus 0. Now that 1 and 0 make up the class of those objects that are equal to 1, not only 1 = 1, but also 0 = 1 should be recognized. Problem: in a multiplicity where 0 = 1 would apply, any possibility of distinguishing between two classes or individuals would be excluded from the outset. I 54 That would be a completely empty multiplicity, which itself cannot contain any element. We exclude it. The same would also apply if we had given the universe a name like b instead of 0. That would have led to the equally absurd equation 0 = b. Refutation: 0 contains a for each class a. If a is understood to mean the class of those areas which are equal to b, then this class must contain not only b (which of all areas is equal to b alone) but also the identical 0, which is what the subsumption 0 enth a claims. Then also 0 must be such an area, which is equal to b. (in contradiction to above). 0 = b for each b! VsBoole: this shows that his universal Interpretation of 1 went too far. |
Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Boyd, R. | Putnam Vs Boyd, R. | Williams II 492 Scientific Realism/Richard Boyd/M. Williams: Boyd's defense of scientific realism is much more complex than what we have considered so far: Williams II 493 Is a substantial (explanatory) truth concept necessary? Boyd: more indirect approach than Putnam: the (approximate) truth of our theories explains the instrumental reliability of our methods. Method/Boyd: is not theory neutral! On the contrary, because they are formed by our theories, it is their truth that explains the success of the methods. Boyd/M. Williams: thus it turns a well-known argument on its head: BoydVsPositivism. Positivism/Theory: Thesis: the observing language must be theory neutral. The methodological principles likewise. IdealismVsPositivism: VsTheory Neutrality. E.g. Kuhn: the scientific community determines the "facts". Boyd/M. Williams: Boyd turns the >theory ladenness of our methodological judgments very cleverly into the base of his realism. Thesis: Methods that are as theory-laden as ours would not work if the corresponding theories were not "approximately true in a relevant way". Point: thus he cannot be blamed of making an unacceptably rigid separation between theory and observation. Ad. 1) Vs: this invalidates the first objection Ad. 2) Vs: Boyd: it would be a miracle if our theory-laden methods functioned even though the theories proved to be false. For scientific realism, there is nothing to explain here. Ad. 3) Vs: Williams II 494 M. Williams: this is not VsScientific Realism, but VsPutnam: PutnamVsBoyd: arguments like that of Boyd do not establish a causal explanatory role for the truth concept. BoydVsPutnam: they don't do that: "true" is only a conventional expression which adds no explanatory power to the scientific realism. Truth/Explanation/Realism/Boyd/M. Williams: explaining the success of our methods with the truth of our theories boils down to saying that the methods by which we examine particles work, because the world is composed of such particles that are more or less the way we think. Conclusion: but it makes no difference whether we explain this success (of our methods) by the truth of the theories or by the theories themselves! M. Williams pro Deflationism: so we do not need a substantial truth concept. Putnam I (c) 80 Convergence/Putnam: there is something to the convergence of scientific knowledge! Science/Theory/Richard Boyd: Thesis: from the usual positivist philosophy of science merely follows that later theories imply many observation sentences of earlier ones, but not that later theories must imply the approximate truth of the earlier ones! (1976). Science/Boyd: (1) terms of a mature science typically refer (2) The laws of a theory that belongs to a mature science are typically approximately true. (Boyd needs more premises). I (c) 81 Boyd/Putnam: the most important thing about these findings is that the concepts of "truth" and "reference" play a causally explanatory role in epistemology. When replacing them in Boyd with operationalist concept, for example, "is simple and leads to true predictions", the explanation is not maintained. Truth/Theory/Putnam: I do not only want to have theories that are "approximately true", but those that have the chance to be true. Then the later theories must contain the laws of the earlier ones as a borderline case. PutnamVsBoyd: according to him, I only know that T2 should imply most of my observation sentences that T1 implies. It does not follow that it must imply the truth of the laws of T1! I (c) 82 Then there is also no reason why T2 should have the property that we can assign reference objects to the terms of T1 from the position of T2. E.g. Yet it is a fact that from the standpoint of the RT we can assign a reference object to the concept "gravity" in the Newtonian theory, but not to others: for example, phlogiston or ether. With concepts such as "is easy" or "leads to true predictions" no analogue is given to the demand of reference. I (c) 85/86 Truth/Boyd: what about truth if none of the expressions or predicates refers? Then the concept "truth value" becomes uninteresting for sentences containing theoretical concepts. So truth will also collapse. PutnamVsBoyd: this is perhaps not quite what would happen, but for that we need a detour via the following considerations: I (c) 86 Intuitionism/Logic/Connectives/Putnam: the meaning of the classical connectives is reinterpreted in intuitionism: statements: p p is asserted p is asserted to be provable "~p" it is provable that a proof of p would imply the provability of 1 = 0. "~p" states the absurdity of the provability of p (and not the typical "falsity" of p). "p u q" there is proof for p and there is proof for q "p > q" there is a method that applied to any proof of p produces proof of q (and proof that this method does this). I (c) 87 Special contrast to classical logic: "p v ~p" classical: means decidability of every statement. Intuitionistically: there is no theorem here at all. We now want to reinterpret the classical connectives intuitionistically: ~(classical) is identical with ~(intuitionist) u (classical) is identified with u (intuitionist) p v q (classical) is identified with ~(~p u ~q)(intuitionist) p > q (classical) is identified with ~(p u ~q) (intuitionist) So this is a translation of one Calculus into the other, but not in the sense that the classical meanings of the connectives were presented using the intuitionistic concepts, but in the sense that the classical theorems are generated. ((s) Not translation, but generation.) The meanings of the connectives are still not classical, because these meanings are explained by means of provability and not of truth or falsity (according to the reInterpretation)). E.g. Classical means p v ~p: every statement is true or false. Intuitionistically formulated: ~(~p u ~~p) means: it is absurd that a statement and its negation are both absurd. (Nothing of true or false!). |
Putnam I Hilary Putnam Von einem Realistischen Standpunkt In Von einem realistischen Standpunkt, Vincent C. Müller Frankfurt 1993 Putnam I (a) Hilary Putnam Explanation and Reference, In: Glenn Pearce & Patrick Maynard (eds.), Conceptual Change. D. Reidel. pp. 196--214 (1973) In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (b) Hilary Putnam Language and Reality, in: Mind, Language and Reality: Philosophical Papers, Volume 2. Cambridge University Press. pp. 272-90 (1995 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (c) Hilary Putnam What is Realism? in: Proceedings of the Aristotelian Society 76 (1975):pp. 177 - 194. In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (d) Hilary Putnam Models and Reality, Journal of Symbolic Logic 45 (3), 1980:pp. 464-482. In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (e) Hilary Putnam Reference and Truth In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (f) Hilary Putnam How to Be an Internal Realist and a Transcendental Idealist (at the Same Time) in: R. Haller/W. Grassl (eds): Sprache, Logik und Philosophie, Akten des 4. Internationalen Wittgenstein-Symposiums, 1979 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (g) Hilary Putnam Why there isn’t a ready-made world, Synthese 51 (2):205--228 (1982) In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (h) Hilary Putnam Pourqui les Philosophes? in: A: Jacob (ed.) L’Encyclopédie PHilosophieque Universelle, Paris 1986 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (i) Hilary Putnam Realism with a Human Face, Cambridge/MA 1990 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (k) Hilary Putnam "Irrealism and Deconstruction", 6. Giford Lecture, St. Andrews 1990, in: H. Putnam, Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992, pp. 108-133 In Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam II Hilary Putnam Representation and Reality, Cambridge/MA 1988 German Edition: Repräsentation und Realität Frankfurt 1999 Putnam III Hilary Putnam Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992 German Edition: Für eine Erneuerung der Philosophie Stuttgart 1997 Putnam IV Hilary Putnam "Minds and Machines", in: Sidney Hook (ed.) Dimensions of Mind, New York 1960, pp. 138-164 In Künstliche Intelligenz, Walther Ch. Zimmerli/Stefan Wolf Stuttgart 1994 Putnam V Hilary Putnam Reason, Truth and History, Cambridge/MA 1981 German Edition: Vernunft, Wahrheit und Geschichte Frankfurt 1990 Putnam VI Hilary Putnam "Realism and Reason", Proceedings of the American Philosophical Association (1976) pp. 483-98 In Truth and Meaning, Paul Horwich Aldershot 1994 Putnam VII Hilary Putnam "A Defense of Internal Realism" in: James Conant (ed.)Realism with a Human Face, Cambridge/MA 1990 pp. 30-43 In Theories of Truth, Paul Horwich Aldershot 1994 SocPut I Robert D. Putnam Bowling Alone: The Collapse and Revival of American Community New York 2000 WilliamsB I Bernard Williams Ethics and the Limits of Philosophy London 2011 WilliamsM I Michael Williams Problems of Knowledge: A Critical Introduction to Epistemology Oxford 2001 WilliamsM II Michael Williams "Do We (Epistemologists) Need A Theory of Truth?", Philosophical Topics, 14 (1986) pp. 223-42 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Chisholm, R.M. | Simons Vs Chisholm, R.M. | Chisholm II 166 SimonsVsChisholm/SimonsVsBrentano: thesis: Chisholm inherited a mereological essentialism by Brentano with which I do not agree. But I will use these ideas to give a slightly different interpretation of Wittgenstein's Tractatus. Wittgenstein himself was not so clear with respect to facts as it seems. Self-Criticism: self-criticism is a mess of facts and complexes. There are worlds between the later Wittgenstein and Brentano, but there are contacts between Brentano and the Tractatus. --- Simons I 1 Extensional Mereology/Simons: extensional mereology is a classical theory. Spelling: CEM. Individuals Calculus/Leonard/Goodman: (40s): another name for the CEM is an individual Calculus. This is intended to express that the objects of the part-whole relation belong to the lowest logical type (so they are all individuals, both a whole and a part are individuals). VsCEM: 1. The CEM claims the existence of sums as individuals for whose existence we have no evidence beyond the theory. Vs: 2. The whole theory is not applicable to most things in our lives. Vs: 3. The logic of the CEM has not the resources to deal with temporal and modal terms: e.g. temporal part, substantial part, etc. Simons: these are all external critiques but there is an internal critique: that comes from the extensional mereology. Extensional Mereology: thesis: objects with the same parts are identical (analogous to set theory). Problem: 1. Flux: e.g. people have different parts at different times. I 2 2. Modality/extensional mereology: problem: e.g. a man could have other parts than he actually has and still be the same person. (s) The extensionality would then demand together with the Leibniz identity that all parts are essential. This leads to mereological essentialism. Chisholm/mereological essentialism/Simons: Chisholm represents the mereological essentialism. Thesis: no object can have different parts than it actually has. Vs: it is a problem to explain why normal objects are not modally rigid (all parts are essential). Solution/Chisholm: thesis: (appearing) things (appearances) ((s) everyday things) are logical structures made of objects for which the mereological essentialism applies. Flux/mereology/Simons: problem/(s): according to the CEM changing objects may not be regarded as identical with themselves. 1. Solution/Chisholm: thesis: the actual objects are mereologically constant and the appearances again logical constructions of unchanging objects. SimonsVsChisholm: the price is too high. 2. Common solution: the common solution is to replace the normal things (continuants) through processes that themselves have temporal parts. SimonsVs: hence, the extensionality cannot be maintained. Such four-dimensional objects fail on the modal argument. CEM/event/Simons: in the case of events the extensional mereology is applicable. It is also applicable in classes and masses. Classes/masses/Simons: these are non-singular objects for which the extensionality applies. Part/Simons: a part is ambiguous, depending on whether used in connection with individuals, classes or masses. Extensionality/mereology/Simons: if extensionality is rejected, we are dealing with continuants. I 3 Continuants/Simons: continuants may be in flux. Extensionality/Simons: if extensionality is rejected, more than one object can have exactly the same parts and therefore several different objects can be at the same time in the same place. I 175 Temporal Part/continuants/mereology/SimonsVsAll/SimonsVsChisholm: thesis: continuants can also have temporal parts! That means that they are not mereologically constant but mereologically variable. Continuants/Simons: thesis: continuants do not have to exist continuously. This provides us with a surprising solution to the problem of the Ship of Theseus. I 187 SimonsVsChisholm: if Chisholm is right, most everyday things, including our organism, are only logical constructions. I 188 Strict Connection/separateness/SimonsVsChisholm: the criterion for strict connection is unfortunately so that it implies that if x and y are strictly connected, but not in contact, they can be separated by the fact that a third object passes between them what per se is not a change, also not in their direct relations to each other. Problem: when this passing is only very short, the question is whether the separated sum of the two which was extinguished by the third object is the same that exists again when the third object has disappeared. If it is the same, we have a discontinued existing sum. Chisholm: Chisholm himself asks this question with the following example: a castle of toy bricks will be demolished and built again with the same bricks. I 189 Chisholm: thesis: it is a reason to be dissatisfied with the normal ontology, because it just allows such examples. SimonsVsChisholm: but Chisholm's own concepts just allowed us the previous example. Topology/Simons: yet there is no doubt that it is useful to add topological concepts such as touching or to be inside of something to the mereology. I 192 Def succession/Chisholm: 1. x is a direct a-successor of y to t ' = Def (i) t does not start before t’ (ii) x is an a to t and y is a y to t’ (iii) there is a z so that z is part of x to t and a part of y to t’ and in every moment between t’ and t including, z is itself an a. Simons: while there will be in general several such parts. We always choose the largest. w: is the common part in it, e.g. in altering a table. SimonsVsChisholm: problem: w is not always a table. ChisholmVsVs: claims that w is indeed a table: if we cut away a small part of the table, what remains is still a table. Problem: but if the thing that remains is a table because it was already previously there then it was a table that was a real part of a table! I 193 SimonsVsChisholm: the argument is not valid! E.g.: Shakespeare, Henry IV, Act IV Scene V: Prince Hal considers: if the king dies, we will still have a king, (namely myself, the heir). But if that person is a king, then, because he had previously been there, then he was a king who was the eldest son of a king. ((s) This is a contradiction because then there would have been two kings simultaneously.) Simons: this point is not new and was already highlighted by Wiggins and Quine (not VsChisholm). I 194 Change/transformation/part/succession/SimonsVsChisholm: it seems, however, that they are not compatible with the simple case where a at the same time wins and loses parts. E.g. then a+b should be an A-predecessor of a+c and a+c an A-successor of a+b. But that is not allowed by the definition, unless we know that a is an A all the time, so that it connects a+b and a+c in a chain. But this will not usually be the case. And if it is not the case, a will never ever be an A! SimonsVsChisholm: so Chisholm's definitions only work if he assumes a wrong principle! Succession/entia successiva/SimonsVsChisholm: problem: that each of the things that shall "stand in" (for a constant ens per se to explain the transformation) should themselves be an a in the original sense (e.g. table, cat, etc.) is counterintuitive. Solution/Simons: the "is" is here an "is" of predication and not of constitution (>Wiggins 1980, 30ff). Mereological Constancy/Simons: thesis: most things, of which we predict things like e.g. "is a man" or "is a table" are mereologically constant. The rest is easy loose speech and a play with identity. E.g. if we say that the man in front of us lost a lot of hair in the last year we use "man" very loosely. Chisholm: we should say, strictly speaking, that the man of today (stands for) who today stands for the same successive man has less hair than the man who stood for him last year. SimonsVsChisholm/WigginsVsChisholm: with that he is dangerously close to the four-dimensionalism. And especially because of the following thesis: I 195 To stand in for/stand for/entia successiva/Chisholm: thesis: "to stand in for" is not a relation of an aggregate to its parts. Sortal Concept/Simons: the question is whether sortal concepts that are subject to the conditions that determine what should count at one time or over time as a thing or several things of one kind are applicable rather to mereologically constant objects (Chisholm) or variable objects (Simons, Wiggins). SimonsVsChisholm: Chisholm's thesis has the consequence that most people mostly use their most used terms wrongly, if this is not always the case at all. I 208 Person/body/interrupted existence/identity/mereology/Chisholm/Simons: our theory is not so different in the end from Chisholm's, except that we do not accept matter-constancy as "strictly and philosophically" and oppose it to a everyday use of constancy. SimonsVsChisholm: advantage: we can show how the actual use of "ship" is related to hidden tendencies to use it in the sense of "matter-constant ship". Ship of Theseus/SimonsVsChisholm: we are not obligated to mereological essentialism. A matter-constant ship is ultimately a ship! That means that it is ready for use! Interrupted Existence/substrate/Simons: there must be a substrate that allows the identification across the gap. I 274 SimonsVsChisholm: according to Chisholm's principle, there is no real object, which is a table, because it can constantly change its microstructure ((s) win or lose atoms). Chisholm/Simons: but by this not the slightest contradiction for Chisholm is demonstrated. |
Simons I P. Simons Parts. A Study in Ontology Oxford New York 1987 Chisholm I R. Chisholm The First Person. Theory of Reference and Intentionality, Minneapolis 1981 German Edition: Die erste Person Frankfurt 1992 Chisholm II Roderick Chisholm In Philosophische Aufsäze zu Ehren von Roderick M. Ch, Marian David/Leopold Stubenberg Amsterdam 1986 Chisholm III Roderick M. Chisholm Theory of knowledge, Englewood Cliffs 1989 German Edition: Erkenntnistheorie Graz 2004 |
| Frege, G. | Waismann Vs Frege, G. | Waismann I 77 Frege: Definition of the number in two steps a) when two sets are equal. b) Definition of the term "number": it is equal if each element of one set corresponds to one element of the other set. Unique relation. Under Def "Number of a Set"/Frege: he understands the set of all sets equal to it. Example: the number 5 is the totality of all classes of five in the world. VsFrege: how shall we determine that two sets are equal? Apparently by showing such a relation. For example, if you have to distribute spoons on cups, then the relation did not exist before. As long as the spoons were not on the cups, the sets were not equal. However, this does not correspond to the sense in which the word equal is used. So it is about whether you can put the spoons on the cups. But what does "can" mean? I 78 That the same number of copies are available. Not the assignment determines the equivalence, but vice versa. The proposed definition gives a necessary, but not sufficient condition for equal numbers and defines the expression "equal number" too narrowly. Class: List ("school class") logical or term (mammals) empirical. With two lists it is neither emopirical nor logical to say that they can be assigned to each other. Example 1. Are there as many people in this room as in the next room? An experiment provides the answer. 2. Are 3x4 cups equal to 12 spoons? You can answer this by drawing lines, which is not an experiment, but a process in a Calculus. According to Frege, two sets are not equal if the relation is not established. You have defined something, but not the term "equal numbered". You can extend the definition by saying that they can be assigned. But again this is not correct. For if the two sets are given by their properties, it always makes sense to assert their "being-assignment", (but this has a different meaning, depending on the criterion by which one recognizes the possibility of assignment: that the two are equal, or that it should make sense to speak of an assignment! In fact, we use the word "equal" according to different criteria: of which Frege emphasizes only one and makes it a paradigm. Example 1. If there are 3 cups and 3 spoons on the table, you can see at a glance how they can be assigned. I 79 2. If the number cannot be overlooked, but it is arranged in a clear form, e.g. square or diamond, the equal numbers are obvious again. 3. The case is different, if we notice something of two pentagons, that they have the same number of diagonals. Here we no longer understand the grouping directly, it is rather a theorem of geometry. 4. Equal numbers with unambiguous assignability 5. The normal criterion of equality of numbers is counting (which must not be understood as the representation of two sets by a relation). WaismannVsFrege: Frege's definition does not reflect this different and flexible use. I 80 This leads to strange consequences: According to Frege, two sets must necessarily be equal or not for logical reasons. For example, suppose the starlit sky: Someone says: "I don't know how many I've seen, but it must have been a certain number". How do I distinguish this statement from "I have seen many stars"? (It is about the number of stars seen, not the number of stars present). If I could go back to the situation, I could recount it. But that is not possible. There is no way to determine the number, and thus the number loses its meaning. For example, you could also see things differently: you can still count a small number of stars, about 5. Here we have a new series of numbers: 1,2,3,4,5, many. This is a series that some primitive peoples really use. It is not at all incomplete, and we are not in possession of a more complete one, but only a more complicated one, beside which the primitive one rightly exists. You can also add and multiply in this row and do so with full rigor. Assuming that the things of the world would float like drops to us, then this series of numbers would be quite appropriate. For example, suppose we should count things that disappear again during counting or others emerge. Such experiences would steer our concept formation in completely different ways. Perhaps words such as "much", "little", etc. would take the place of our number words. I 80/81 VsFrege: his definition misses all that. According to it, two sets are logically necessary and equal in number, without knowledge, or they are not. In the same way, Einstein had argued that two events are simultaneous, independent of observation. But this is not the case, but the sense of a statement is exhausted in the way of its verification (also Dummett) Waismann: So you have to pay attention to the procedure for establishing equality in numbers, and that's much more complicated than Frege said. Frege: second part of the definition of numbers: Def Number/Frege: is a class of classes. ((s) Elsewhere: so not by Frege! FregeVs!). Example: the term "apple lying on the table comes to the number 3". Or: the class of apples lying on the table is an element of class 3. This has the great advantage of evidence: namely that the number is not expressed by things, but by the term. WaismannVsFrege: But does this do justice to the actual use of the number words? Example: in the command "3 apples!" the number word certainly has no other meaning, but after Frege this command can no longer be interpreted according to the same scheme. It does not mean that the class of apples to be fetched is an element of class 3. Because this is a statement, and our language does not know it. WaismannVsFrege: its definition ties the concept of numbers unnecessarily to the subject predicate form of our sentences. In fact, it results the meaning of the word "3" from the way it is used (Wittgenstein). RussellVsFrege: E.g. assuming there were exactly 9 individuals in the world. Then we could define the cardinal numbers from 0 to 9, but the 10, defined as 9+1, would be the zero class. Consequently, the 10 and all subsequent natural numbers will be identical, all = 0. To avoid this, an additional axiom would have to be introduced, the Def "infinity axiom"/Russell: means that there is a type to which infinitely many individuals belong. This is a statement about the world, and the structure of all arithmetic depends essentially on the truth of this axiom. Everyone will now be eager to know if the infinity axiom is true. We must reply: we do not know. It is constructed in a way that it eludes any examination. But then we must admit that its acceptance has no meaning. I 82 Nor does it help that one takes the "axiom of infinity" as a condition of mathematics, because in this way one does not win mathematics as it actually exists: The set of fractions is dense everywhere, but not: The set of fractions is dense everywhere if the infinity axiom applies. That would be an artificial reInterpretation, only conceived to uphold the doctrine that numbers are made up of real classes in the world (VsFrege: but only conditionally, because Frege does not speak of classes in the world). Waismann I 85 The error of logic was that it believed it had firmly underpinned arithmetic. Frege: "The foundation stones, fixed in an eternal ground, are floodable by our thinking, but not movable." WaismannVsFrege: only the expression "justify" the arithmetic gives us a wrong picture, I 86 as if its building were built on basic truths, while she is a calculus that proceeds only from certain determinations, free-floating, like the solar system that rests on nothing. We can only describe arithmetic, i.e. give its rules, not justify them. Waismann I 163 The individual numerical terms form a family. There are family similarities. Question: are they invented or discovered? We reject the notion that the rules follow from the meaning of the signs. Let us look at Frege's arguments. (WaismannVsFrege) II 164 1. Arithmetic can be seen as a game with signs, but then the real meaning of the whole is lost. If I set up calculation rules, did I then communicate the "sense" of the "="? Or just a mechanical instruction to use the sign? But probably the latter. But then the most important thing of arithmetic is lost, the meaning that is expressed in the signs. (VsHilbert) Waismann: Assuming this is the case, why do we not describe the mental process right away? But I will answer with an explanation of the signs and not with a description of my mental state, if one asks me what 1+1 = 2 means. If one says, I know what the sign of equality means, e.g. in addition, square equations, etc. then one has given several answers. The justified core of Frege's critique: if one considers only the formulaic side of arithmetic and disregards the application, one gets a mere game. But what is missing here is not the process of understanding, but Interpretation! I 165 For example, if I teach a child not only the formulas but also the translations into the word-language, does it only make mechanical use? Certainly not. 2. Argument: So it is the application that distinguishes arithmetic from a mere game. Frege: "Without a content of thought an application will not be possible either. WaismannVsFrege: Suppose you found a game that looks exactly like arithmetic, but is for pleasure only. Would it not express a thought anymore? Why cannot one make use of a chess position? Because it does not express thoughts. WaismannVsFrege: Let us say you find a game that looks exactly like arithmetic, but is just for fun. Would it notexpress a thought anymore? Chess: it is premature to say that a chess position does not express thoughts. Waismann brings. For example figures stand for troops. But that could just mean that the pieces first have to be turned into signs of something. I 166 Only if one has proved that there is one and only one object of the property, one is entitled to occupy it with the proper name "zero". It is impossible to create zero. A >sign must designate something, otherwise it is only printer's ink. WaismannVsFrege: we do not want to deny or admit the latter. But what is the point of this assertion? It is clear that numbers are not the same as signs we write on paper. They only become what they are through use. But Frege rather means: that the numbers are already there somehow before, that the discovery of the imaginary numbers is similar to that of a distant continent. I 167 Meaning/Frege: in order not to be ink blotches, the characters must have a meaning. And this exists independently of the characters. WaismannVsFrege: the meaning is the use, and what we command. |
Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 |
| Montague, R. | Stechow Vs Montague, R. | I 44 Types/Stechow: Definition/Linguistics/Stechow: Example for definition of a definition using the semantic ranges defined by types: e.g. for an adjective and a prepositional phrase: "in". Logical Type/Linguistics/Stechow: is a semantic feature of a category symbol. Montague/Stechow: acts as if each syntactic category has exactly one logical type and therefore writes only the categories. He has made this popular. StechowVsMontague: but this is not possible, because a syntactic category does not only correspond to a logical type. Problem: for example, the nomina Fritz, student, father these probably have different meanings: Fritz: designates something of type e, student: type ep, father: Tap e(ep). Then there must also be three different noun categories for Montague. Since we only accept one noun category, we must already write the types in the lexicon. I 104 Intensional Functional Application/IFA/Intensor/Heim/KratzerVsMontague: the intensor can be replaced by the composition principle of the intesional functional application. (Intensional Functional Application): in the metalanguage it does what the interpretation of the intensor does. This makes the calculations simpler: for example Since Montague places a node before each argument, this saves a lot of money. 105 Extensional Functional Application/FA/Montague: with him you first have to dismantle the Intensor and then the FA Intensional Functional Application/Heim/Kratzer: merges both steps. 150 Lambda Abstraction/Stechow: can already be found in Frege (1884)! 151 Quantifying in/Montague/Stechow: Example Each rule consists of a syntactic and a semantic operation. Syntactic operation/Stechow: has always been very simple: just write side by side. Montagues syntactic operation f14,2 is much more complicated: take the first argument of the function (here "every linguist") and replace the first occurrence of the pronoun "him" in the second argument by this expression. The semantics of this rule is of course exactly the semantics of our quantifier relation. I.e. we apply the meaning of the quantifier to the meaning of the λ-abstract that we form from the second expression. VsMontague: Problem: there are infinitely many rules of quantifying in, one for each natural number. This is because we can choose any index for a pronoun. Lambda Calculus/Stechow: you can do almost anything with it. The original work does not contain semantics. (Lit: Lambek, 1958). 152 Type/Not/Stechow: cannot have the type (st)t, then it is a sentence adverb. Or (s(et)(et), then it is a VP modifier. ((s) > narrow range/>wide range). |
A. von Stechow I Arnim von Stechow Schritte zur Satzsemantik www.sfs.uniï·"tuebingen.de/~astechow/Aufsaetze/Schritte.pdf (26.06.2006) |
| Russell, B. | Quine Vs Russell, B. | Chisholm II 75 Predicates/Denote/Russell: denoting expressions: proper names stand for individual things and general expressions for universals. (Probleme d. Phil. p. 82f). In every sentence, at least one word refers to a universal. QuineVsRussell: confusion! II 108 Theory of Descriptions/VsRussell/Brandl: thus the whole theory is suspected of neglecting the fact that material objects can never be part of propositions. QuineVsRussell: confusion of mention and use. Quine II 97 Pricipia mathematica, 1903: Here, Russell's ontology is rampant: every word refers to something. If a word is a proper name, then its object is a thing, otherwise it is a concept. He limits the term "existence" to things, but has a liberal conception of things which even includes times and points in empty space! Then there are, beyond the existent things, other entities: "numbers, the gods of Homer, relationships, fantasies, and four-dimensional space". The word "concept", used by Russell in this manner, has the connotation of "merely a concept". Caution: Gods and fantasies are as real as numbers for Russell! QuineVsRussell: this is an intolerably indiscriminate ontology. Example: Take impossible numbers, e.g. prime numbers that are divisible by 6. It must be wrong in a certain sense that they exist, and that is in a sense in which it is right that there are prime numbers! Do fantasies exist in this sense? II 101 Russell has a preference for the term "propositional function" against "class concept". In P.M. both expressions appear. Here: Def "Propositional Function": especially based on forms of notation, e.g. open sentences, while concepts are decidedly independent of notation. However, according to Meinong Russell's confidence is in concepts was diminished, and he prefers the more nominalistic sound of the expression "propositional function" which is now carries twice the load (later than Principia Mathematica.) Use/Mention/Quine: if we now tried to deal with the difference between use and mention as carelessly as Russell has managed to do sixty years ago, we can see how he might have felt that his theory of propositional functions was notation based, while a theory of types of real classes would be ontological. Quine: we who pay attention to use and mention can specify when Russell's so-called propositional functions as terms (more specific than properties and relations) must be construed as concepts, and when they may be construed as a mere open sentences or predicates: a) when he quantifies about them, he (unknowingly) reifies them as concepts. For this reason, nothing more be presumed for his elimination of classes than I have stated above: a derivation of the classes from properties or concepts by means of a context definition that is formulated such that it provides the missing extensionality. QuineVsRussell: thinks wrongly that his theory has eliminated classes more thoroughly from the world than in terms of a reduction to properties. II 102 RussellVsFrege: "~ the entire distinction between meaning and designating is wrong. The relationship between "C" and C remains completely mysterious, and where are we to find the designating complex which supposedly designates C?" QuineVsRussell: Russell's position sometimes seems to stem from a confusion of the expression with its meaning, sometimes from the confusion of the expression with its mention. II 103/104 In other papers Russel used meaning usually in the sense of "referencing" (would correspond to Frege): "Napoleon" particular individual, "human" whole class of such individual things that have proper names. Russell rarely seems to look for an existing entity under any heading that would be such that we could call it the meaning that goes beyond the existing referent. Russell tends to let this entity melt into the expression itself, a tendency he has in general when it comes to existing entities. QuineVsRussell: for my taste, Russell is too wasteful with existing entities. Precisely because he does not differentiate enough, he lets insignificance and missed reference commingle. Theory of Descriptions: He cannot get rid of the "King of France" without first inventing the description theory: being meaningful would mean: have a meaning and the meaning is the reference. I.e. "King of France" without meaning, and "The King of France is bald" only had a meaning, because it is the short form of a sentence that does not contain the expression "King of France". Quine: actually unnecessary, but enlightening. Russell tends commingle existing entities and expressions. Also on the occasion of his remarks on Propositions: (P.M.): propositions are always expressions, but then he speaks in a manner that does not match this attitude of the "unity of the propositions" (p.50) and of the impossibility of infinite propositions (p.145) II 105 Russell: The proposition is nothing more than a symbol, even later, instead: Apparently, propositions are nothing..." the assumption that there are a huge number of false propositions running around in the real, natural world is outrageous." Quine: this revocation is astounding. What is now being offered to us instead of existence is nothingness. Basically Russell has ceased to speak of existence. What had once been regarded as existing is now accommodated in one of three ways a) equated with the expression, b) utterly rejected c) elevated to the status of proper existence. II 107 Russell/later: "All there is in the world I call a fact." QuineVsRussell: Russell's preference for an ontology of facts depends on his confusion of meaning with reference. Otherwise he would probably have finished the facts off quickly. What the reader of "Philosophy of logical atomism" notices would have deterred Russell himself, namely how much the analysis of facts is based on the analysis of language. Russell does not recognize the facts as fundamental in any case. Atomic facts are as atomic as facts can be. Atomic Facts/Quine: but they are composite objects! Russell's atoms are not atomic facts, but sense data! II 183 ff Russell: Pure mathematics is the class of all sentences of the form "p implies q" where p and q are sentences with one or more variables, and in both sets the same. "We never know what is being discussed, nor if what we say is true." II 184 This misinterpretation of mathematics was a response to non-Euclidean geometry. Numbers: how about elementary arithmetic? Pure numbers, etc. should be regarded as uninterpreted. Then the application to apples is an accumulation. Numbers/QuineVsRussell: I find this attitude completely wrong. The words "five" and "twelve" are nowhere uninterpreted, they are as much essential components of our interpreted language as apples. >Numbers. They denote two intangible objects, numbers that are the sizes of quantities of apples and the like. The "plus" in addition is also interpreted from start to finish, but it has nothing to do with the accumulation of things. Five plus twelve is: how many apples there are in two separate piles. However, without pouring them together. The numbers "five" and "twelve" differ from apples in that they do not denote a body, that has nothing to do with misinterpretation. The same could be said of "nation" or "species". The ordinary interpreted scientific speech is determined to abstract objects as it is determined to apples and bodies. All these things appear in our world system as values of variables. II 185 It even has nothing to do with purity (e.g. of the set theory). Purity is something other than uninterpretedness. XII 60 Expression/Numbers/Knowledge/Explication/Explanation/Quine: our knowledge of expressions is alone in their laws of interlinking. Therefore, every structure that fulfills these laws can be an explication. XII 61 Knowledge of numbers: consists alone in the laws of arithmetic. Then any lawful construction is an explication of the numbers. RussellVs: (early): Thesis: arithmetic laws are not sufficient for understanding numbers. We also need to know applications (use) or their embedding in the talk about other things. Number/Russell: is the key concept here: "there are n such and suches". Number/Definition/QuineVsRussell: we can define "there are n such and suches" without ever deciding what numbers are beyond their fulfillment of arithmetic addition. Application/Use/QuineVsRussell: wherever there is structure, the applications set in. E.g. expressions and Gödel numbers: even the mention of an inscription was no definitive proof that we are talking about expressions and not about Gödel numbers. We can always say that our ostension was shifted. VII (e) 80 Principia Mathematica(1)/PM/Russell/Whitehead/Quine: shows that the whole of mathematics can be translated into logic. Only three concepts need to be clarified: Mathematics, translation and logic. VII (e) 81 QuineVsRussell: the concept of the propositional function is unclear and obscures the entire PM. VII (e) 93 QuineVsRussell: PM must be complemented by the axiom of infinity if certain mathematical principles are to be derived. VII (e) 93/94 Axiom of infinity: ensures the existence of a class with infinitely many elements. Quine: New Foundations instead makes do with the universal class: θ or x^ (x = x). 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. VII (f) 122 Propositional Functions/QuineVsRussell: ambiguous: a) open sentences b) properties. Russell no classes theory uses propositional functions as properties as value-bound variables. IX 15 QuineVsRussell: inexact terminology. "Propositional function", he used this expression both when referring to attributes (real properties) and when referring to statements or predicates. In truth, he only reduced the theory of classes to an unreduced theory of attributes. IX 93 Rational Numbers/QuineVsRussell: I differ in one point: for me, rational numbers are themselves real numbers, not so for Russell and Whitehead. Russell: rational numbers are pairwise disjoint for them like those of Peano. (See Chapter 17), while their real numbers are nested. ((s) pairwise disjoint, contrast: nested) Natural Numbers/Quine: for me as for most authors: no rational integers. Rational Numbers/Russell: accordingly, no rational real numbers. They are only "imitated" by the rational real numbers. Rational Numbers/QuineVsRussell: for me, however, the rational numbers are real numbers. This is because I have constructed the real numbers according to Russell's version b) without using the name and the designation of rational numbers. Therefore, I was able to retain name and designation for the rational real numbers IX 181 Type Theory/TT/QuineVsRussell: in the present form our theory is too weak to prove some sentences of classical mathematics. E.g. proof that every limited class of real numbers has a least upper boundary (LUB). IX 182 Suppose the real numbers were developed in Russell's theory similar to Section VI, however, attributes were now to take the place of classes and the alocation to attributes replaces the element relation to classes. LUB: (Capters 18, 19) of a limited class of real numbers: the class Uz or {x:Ey(x ε y ε z)}. Attribute: in parallel, we might thus expect that the LUB of a limited attribute φ of real numbers in Russell's system is equal to the Attribute Eψ(φψ u ψ^x). Problem: under Russell's order doctrine is this LUB ψ is of a higher order than that of the real numbers ψ which fall under the attribute φ whose LUB is sought. Boundary/LUB/QuineVsRussell: You need LUB for the entire classic technique of Calculus, which is based on continuity. However, LUB have no value for these purposes if they are not available as values of the same variables whose value range already includes those numbers whose upper boundary is wanted. An upper boundary (i.e. LUB) of higher order cannot be the value of such variables, and thus misses its purpose. Solution/Russell: Axiom of Reducibility: Def Axiom of Reducibility/RA/Russell/Quine: every propositional function has the same extension as a certain predicative one. I.e. Ey∀x(ψ!x φx), Eψ∀x∀y[ψ!(x,y) φ(x,y)], etc. IX 184 VsConstruktivism/Construction/QuineVsRussell: we have seen Russell's constructivist approach to the real numbers fail (LUB, see above). He gave up on constructivism and took refuge in the RA. IX 184/185 The way he gave it up had something perverse to it: Axiom of Reducibility/QuineVsRussell: the RA implies that all the distinctions that gave rise to its creation are superfluous! (... + ...) IX 185 Propositional Function/PF/Attribute/Predicate/TT/QuineVsRussell: overlooked the following difference and its analogs: a) "propositional functions": as attributes (or intentional relations) and b) proposition functions: as expressions, i.e. predicates (and open statements: e.g. "x is mortal") Accordingly: a) attributes b) open statements As expressions they differ visibly in the order if the order is to be assessed on the basis of the indices of bound variables within the expression. For Russell everything is "AF". Since Russell failed to distinguish between formula and object (word/object, mention/use), he did not remember the trick of allowing that an expression of higher order refers straight to an attribute or a relation of lower order. X 95 Context Definition/Properties/Stage 2 Logic/Quine: if you prefer properties as sets, you can introduce quantification over properties, and then introduce quantification over sets through a schematic context definition. Russell: has taken this path. Quine: but the definition has to ensure that the principle of extensionality applies to sets, but not to properties. That is precisely the difference. Russell/QuineVsRussell: why did he want properties? X 96 He did not notice at which point the unproblematic talk of predicates capsized to speaking about properties. ((s) object language/meta language/mention/use). Propositional Function/PF: Russell took it over from Frege. QuineVsRussell: he sometimes used PF to refer to predicates, sometimes to properties. |
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 Chisholm I R. Chisholm The First Person. Theory of Reference and Intentionality, Minneapolis 1981 German Edition: Die erste Person Frankfurt 1992 Chisholm III Roderick M. Chisholm Theory of knowledge, Englewood Cliffs 1989 German Edition: Erkenntnistheorie Graz 2004 |
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