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The author or concept searched is found in the following 14 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Analog/Digital | Goodman | III 163ff Many topology diagrams, for example, only need to have the correct number of points or joints connected by lines according to the correct scheme. Here, the points and lines act as characters in a notational language. These diagrams, as with electrical circuits, are purely digital. It does not depend on a vague idea of the analog as something similar, but solely on technical requirements. III 165 Models of this type are in reality diagrams. Or: diagrams are flat and static models. A molecular model of sticks and table tennis balls is digital. A working model of a windmill can be analog. --- IV 168 A schema can be called digital in which two characters are effectively differentiated. Analog: a schemata is analog in which a path consisting of pairs of non-differentiated characters exists between two characters in the schema. (Warning: misleading notions in connection with the expression.) IV 169 "Digital" and "analog" do not apply to isolated symbols but only to schematas. Since schematas are not images and pictures, the question of how the pictorial and the analog are related can cause us some trouble. For example, a unicorn or Lincoln picture is a card with a pattern of white and black squares. IV 170 We are now assuming a pack A, a stack of cards, some of which are pictures, some are inscriptions of letters, words, numbers, etc., and some cards are not supposed to belong to a known category. Since the cards are effectively differentiated, the schema is digital. E.g. now we add A by adding many more cards of the same size, one for each pattern, so that not only all the patterns composed of dots, but also all shades of any kind are included. In this extended pack A' each card is indistinguishable from many others. The schema is analog and even completely tight. But although A' is analog, it includes A and many other digital schemata! Such digital sub-schemata can be thought to have arisen through elimination from A'. However, a digital schema does not need to consist of characters composed of dots, but can consist of several nuanced images. IV 171 Images that are not composed of dots belong to as many digital schemes as images composed of dots. An analog scheme generally contains many digital schemata and a digital schema is included in many analog schemata. But obviously no digital schema includes an analog one. IV 174 A symbol only works as an image if it is considered a character in the complete pictorial scheme. A complete schema is pictorial only if it is analog. Verbal, if it is digital. In other words, not every analog, complete schema is pictorial and not every digital complete schema is verbal. |
G IV N. Goodman Catherine Z. Elgin Reconceptions in Philosophy and Other Arts and Sciences, Indianapolis 1988 German Edition: Revisionen Frankfurt 1989 Goodman I N. Goodman Ways of Worldmaking, Indianapolis/Cambridge 1978 German Edition: Weisen der Welterzeugung Frankfurt 1984 Goodman II N. Goodman Fact, Fiction and Forecast, New York 1982 German Edition: Tatsache Fiktion Voraussage Frankfurt 1988 Goodman III N. Goodman Languages of Art. An Approach to a Theory of Symbols, Indianapolis 1976 German Edition: Sprachen der Kunst Frankfurt 1997 |
| Formalism | Bigelow | I 176 Symbol/blackening/Bigelow/Pargetter: some authors say that symbols are mere blackening on paper (e.g. numbers) or mere noises. >Blackening of the paper. BigelowVsFormalism: Problem: on the one hand there are too many symbols then, on the other hand, too little. Too little: for very large numbers there is no corresponding blackening or noise. Too many: for smaller numbers there are too many different ways of representation, more than numbers are distinguished. E.g. "4", "four", "IV". >Stronger/weaker, >Strength of theories, >Numbers, >Numerals, >Inscriptions, >Universals. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Forms | Quine | V 107 Form/similarity/Quine: E.g. ovate: is something that is more similar in shape to each of two eggs than these are to one another. It is always between two things. (s) Idealization: applies to two arbitrarily chosen things. It cannot differ independently in one direction from both eggs - pomegranate-colored: in the middle between two concrete colors. V 165 Form/analytic geometry/Quine: are class of classes of pairs of real numbers. ((s) Two-dimensional). V 184 Form: a variety can only be recognized as a square if it is marked - against this: Colour: Scarlet red, for example, does not need to be marked. Form/Colour/Quine: Difference: the union of squares is usually not a square, while the union of several scarlet areas is scarlet red. Form/Colour/Ontology/Quine: classic solution: comes down to a double ontology: matter and space. Spatial diversity: is an aggregate of points, physical objects, particles. Certain particular at a time. Squares: are spatial manifolds. For example, a certain cross-section of a physical object will occupy almost exactly a certain square, and it will occupy an infinite number of squares that almost coincide with it almost exactly. Spatiotemporal Identity/Quine: is then no longer a problem. A square, a certain aggregate of points retains its identity for all times. V 186 Manifold/Quine: these were merely individual squares, circles, etc. These were not abstract objects like squares. Forms: would be classes of such, i.e. objects of higher abstraction - Forms/(s) i.e. are classes of classes of points. Letter forms: are classes of inscriptions. >Similarity. |
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 |
| Goedel Numbers | Quine | X 82 Goedel Numbers/Goedelization/Quine: can do without sets. XII 58 Context here: is the investigation of the nature of a possible language for evidence theory: Protosyntax/Indeterminacy/Quine: the language is here a formalized system of the proof theory of the first level, whose subject area consists only of expressions, i.e. of strings of a certain alphabet. VII (c) 59 N.B.: instead of interpreting the strings as sets of inscriptions, they can be regarded as a (mathematical) sequence (of signs). Character String/Expression: is then a finite set of pairs of a character and a number. Vs: this is very artificial and complicated. Simpler: Goedel numbers themselves (the characters disappear). Problem: Question: how clear is it here that we have just started to talk about numbers instead of expressions? It is only reasonably clear that we want to fulfill laws with artificial models that are supposed to fulfill expressions in a non-explicit sense. See also the reduction of multi-sort logic: XII 72. In connection with referential or substitutional quantification: see XII 80. X 125 It is not possible to form a Goedel number for each irrational number. >Goedel/Quine. |
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 |
| Infinity | Quine | V 165 Infinity/material/Quine: if you need an infinite number of characters (e.g. for natural numbers) you cannot say, a sign is a physical object, because then you will soon come to an end. Also forms are not used as classes of inscriptions. These are again physical realizations of forms. IX 64 Infinity/Quine: is only necessary for induction - x = {y}, y = {z}, z = {w} ... ad infinitum - this is the case if {,,,x}. XIII 96 Infinite Numbers/Quine: For example, suppose we randomly assign items to any class, the only limitation is that no object can belong to more than one class. Problem: then there will not be enough items for all classes! A class for which there is no correlate will be the class of all objects that do not belong to their correlated classes. Because its correlate should belong to it, iff it does not belong to it. Cantor: proved in 1890 that the classes of items of any kind exceed the number of items. XIII 97 The reason for this has to do with the paradoxes, if the relation, which is mentioned there, is specified correctly. It turns out that there are infinitely many different infinities. For example, there are more classes of integers than there are integers. But since there are infinitely many integers, the infinity of infinitely many classes of integers must be of a higher kind. For example, there are also more classes of classes of integers than there are classes of integers. This is an even higher infinity. This can be continued infinitely many times. The argument here depended on the class of non-elements of their own correlated classes (nonmembers of own correlated classes). Russell's Antinomy/Quine: depended on the class of nonelements of selves. Cantor's Paradox/Quine: if one takes the correlation as self-correlation, Cantor's paradox amounts to Russell's Paradox. That is how Russell came up with it. Cantor/Theorem/Quine: his theorem itself is not a paradox. Russell's Antinomy/Solution/Quine: is prevented by excluding a special case from Cantor's theorem that leads to it. (See Paradoxes) Cantor Theorem/Corollar/unspecifiable classes/Quine: the existence of unspecifiable classes follows as a corollar from Cantor's theorem. I.e. classes for which we cannot specify the containment condition. There is no other identifying move either. For example, the infinite totality of grammatically constructible expressions in a language. According to Cantor's theorem, the class of such expressions already exceeds the expressions themselves. Classes/larger/smaller/criterion/Quine: our criterion for larger and smaller classes here was correlation. Def greater/classes/quantities/Quine: one class is larger than another if not each of its elements can be paired with an element of the other class. XIII 98 Problem: according to this criterion, no class can be larger than one of its real subclasses (subsets). For example, the class of positive integers is not larger than the class of even numbers. Because we can always form pairs between their elements. This simply shows that infinite sets behave unusually. Infinite/larger/smaller/class/quantities/Quine: should we change our criterion because of this? We have the choice: a) We can say that an infinite class need not be larger than its real subclasses, or b) change the criterion and say that a class is always larger than its real parts, only that they can sometimes be exhausted by correlation with elements of a smaller class. Pro a): is simpler and standard. This was also Dedekind's definition of infinity. Infinite/false: a student once wrote that an infinite class would be "one that is a real part of itself". This is not true, but it is a class that is not larger than a (some) real part of itself. For example the positive integers are not more numerous than the even numbers. E.g. also not more numerous than the multiples of 3 (after the same consideration). And they are also not less numerous than the rational numbers! Solution: any fraction (ratio) can be expressed by x/y, where x and y are positive integers, and this pair can be uniquely represented by a positive integer 2x times 3y. Conversely, we get the fraction by seeing how often this integer is divisible by 2 or by 3. Infinite/Quine: before we learned from Cantor that there are different infinities, we would not have been surprised that there are not more fractions than integers. XIII 99 But now we are surprised! Unspecifiable: since there are more real numbers than there are expressions (names), there are unspecifiable real numbers. Names/Expressions/Quine: there are no more names (expressions) than there are positive integers. Solution: simply arrange the names (expressions alphabetically within each length). Then you can number them with positive integers. Real Numbers/Cantor/Quine: Cantor showed that there are as many real numbers as there are classes of positive integers. We have seen above (see decimals and dimidials above) that the real numbers between 0 and 1 are in correlation with the infinite class of positive integers. >Numbers/Quine. |
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 |
| Inverted Spectra | Churchland | Fodor IV 195 Qualia/Quality/Sensation/inverted spectra/Fodor/Lepore: it is conceptually possible that while you see something red, I see something green. If the change is systematic, there is nothing in the behavior that could reveal it. VsBehaviorism/VsFunctionalism: the inverted spectra appear to show that behaviorism is false. And also the functionalism. (Block/Fodor, Shoemaker). One might think that a theory of qualitative content could solve the problem. But it is precisely the qualitative content that has been interchanged. And precisely the concept of the sensitive identity becomes ambiguous. VsChurchland: his approach does not help at all. The inscriptions of the points of the dice could also be inverted. ((s) One could always describe it, but one would not know which sensations are present in the other.) --- IV 195/196 Even though this frequency combination represents this particular pink, it is conceptually possible that something has the first property, but not the second. Inverted spectra/Qualia: Problem: there seems to be no property of a sensation except its qualitative content on which the qualitative content supervenes. In particular, there appears to be no proportioned or neurophysiological property on which supervenience is guaranteed. Inverted spectra/tradition: would say that Churchland's dimensions in the Qualia color dice represent by reference to properties that they do not necessarily possess. Or, if you think that it is "metaphysically necessary" that color sensations have the psychophysical properties that they have, then one would have to say that this necessity is not brought about by any necessity between sensual concepts and psychophysical concepts. One might well know that a sensation corresponds to a point in the color dice and still does not know how it is. The dimensions do not determine the content. Why not place a semantic space next to it, add the condition that the dimensions of the semantic space must be semantic? They would have to name content states through their content. E.g. Perhaps then one could identify uncle, aunt, president, Cleopatra etc. along these dimensions? --- IV 197 E.g. Cleopatra, as a politician, is closer to the president than to marriageability. Fodor/LeporeVsChurchland: that is what we are really interested in: a robust theory of the equality of content instead of identity of content that has been lost with the analytic/synthetic distinction. Problem: Equality presupposes identity and a corresponding theory. |
Churla I Paul M. Churchland Matter and Consciousness Cambridge 2013 Churli I Patricia S. Churchland Touching a Nerve: Our Brains, Our Brains New York 2014 Churli II Patricia S. Churchland "Can Neurobiology Teach Us Anything about Consciousness?" in: The Nature of Consciousness: Philosophical Debates ed. Block, Flanagan, Güzeldere pp. 127-140 In Bewusstein, Thomas Metzinger Paderborn/München/Wien/Zürich 1996 F/L Jerry Fodor Ernest Lepore Holism. A Shoppers Guide Cambridge USA Oxford UK 1992 Fodor I Jerry Fodor "Special Sciences (or The Disunity of Science as a Working Hypothesis", Synthese 28 (1974), 97-115 In Kognitionswissenschaft, Dieter Münch Frankfurt/M. 1992 Fodor II Jerry Fodor Jerrold J. Katz Sprachphilosophie und Sprachwissenschaft In Linguistik und Philosophie, G. Grewendorf/G. Meggle Frankfurt/M. 1974/1995 Fodor III Jerry Fodor Jerrold J. Katz The availability of what we say in: Philosophical review, LXXII, 1963, pp.55-71 In Linguistik und Philosophie, G. Grewendorf/G. Meggle Frankfurt/M. 1974/1995 |
| Nominalism | Meixner | I 87 Nominalism/Meixner: the thesis that all entities are individuals. I 88 These words must then be concrete sound events or concrete inscriptions for the nominalist. The word "word" in turn must not denote a type object (also called "ontological individualism"). Radical nominalism/Meixner: Thesis: That all entities are actual individuals. Most radical nominalism/Meixner: Thesis: All entities are actual physical individuals. Materialism/Meixner: Materialism would like to represent the most radical nominalism, but it turns out that only a restricted nominalism can be represented. Reconstructive nominalism: thesis: all entities are individuals and the basic individuals (BI) are physical, but at the same time: 1. most individuals (including BI) are non-actual 2. all sets over BI are also individuals (honorific "physical"). Then universals can be regarded as individual-like entities. a) Variant of Carnap: basic individuals taken as individuals. b) David Lewis: BI on the contrary equated with maximally consistent individuals. (Sets of properties). >Actualism, >Possibilism, >D. Lewis. I 94 Nominalism: Thesis: There are no true-making entities. >Universals, >Truthmakers. Extreme nominalism: must change the language. >Everyday language, >Ontology. |
Mei I U. Meixner Einführung in die Ontologie Darmstadt 2004 |
| Number Theory | Quine | IX 81 Elementary Number Theory/Quine: this is the theory that can only be expressed with the terms "zero, successor, sum, power, product, identity" and with the help of connections from propositional logic and quantification using natural numbers. One can omit the first four of these points or the first two and the fifth. But the more detailed list is convenient, because the classical axiom system fits directly to it. Quine: our quantifiable variables allow other objects than numbers. However, we will now tacitly introduce a limitation to "x ε N". Elementary Number Theory/Quine: less than/equal to: superfluous here. "Ez(x + z = y)" - x ε N > Λ + x = x. - x,y ε N >{x} + y = {x+y}. IX 239 Relative Strength/Proof Theory/Theory/Provability/Quine: Goedel, incompleteness theorem (1931)(1). Since number theory can be developed in set theory, this means that the class of all theorems IX 239 (in reality, all the Goedel numbers of theorems) of an existing set theory can be defined in that same set theory, and different things can be proved about it in it. >Set Theory/Quine. Incompleteness Theorem: as a consequence, however, Goedel showed that set theory (if it is free of contradiction) cannot prove one thing through the class of its own theorems, namely that it is consistent, i.e., for example, that "0 = 1" does not lie within it. If the consistency of one set theory can be proved in another, then the latter is the stronger (unless both are contradictory). Zermelo's system is stronger than type theory. >Type theory, >Strength of theories, >Set theory, >Provability. 1.Kurt Gödel: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. In: Monatshefte für Mathematik und Physik. 38, 1931, S. 173–198, doi:10.1007/BF01700692 II 178 Elementary number theory is the modest part of mathematics that deals with the addition and multiplication of integers. It does not matter if some true statements will remain unprovable. This is the core of Goedel's theorem. He has shown how one can form a sentence with any given proof procedure purely in the poor notation of elementary number theory, which can be proved then and only then if it is wrong. But wait! The sentence cannot be proved and still be wrong. So it is true, but not provable. Quine: we used to believe that mathematical truth consists in provability. Now we see that this view is untenable to mathematics as a whole. II 179 Goedel's incompleteness theorem (the techniques applied there) has proved useful in other fields: Recursive number theory, or recursion theory for short. Or hierarchy theory. >Goedel/Quine. III 311 Elementary Number Theory/Quine: does not even have a complete proof procedure. Proof: reductio ad absurdum: suppose we had it with which to prove every true sentence in the spelling of the elementary number theory, III 312 then there would also be a complete refutation procedure: to refute a sentence one would prove its negation. But then we could combine the proof and refutation procedure of page III 247 to a decision procedure. V 165 Substitutional Quantification/Referential Quantification/Numbers/Quine: Dilemma: the substitutional quantification does not help elementary number theory to any ontological thrift, for either the numbers run out or there are infinitely many number signs. If the explanatory speech of an infinite number sign itself is to be understood again in the sense of insertion, we face a problem at least as serious as that of numbers - if it is to be understood in the sense of referential quantification, then one could also be satisfied from the outset uncritically with object quantification via numbers. >Quantification/Quine. V 166 Truth conditions: if one now assumes substitutional quantification, one can actually explain the truth conditions for them by numbers by speaking only of number signs and their insertion. Problem: if numerals are to serve their purpose, they must be as abstract as numbers. Expressions, of which there should be an infinite number, could be identified by their Goedel numbers. No other approach leads to a noticeable reduction in abstraction. Substitutional quantification: forces to renounce the law that every number has a successor. A number would be the last, but the substitutional quantification theorist would not know which one. It would depend on actual inscriptions in the present and future. (Quine/Goodman 1947). This would be similar to Esenin Volpin's theory of producible numbers: one would have an unknown finite bound. V 191 QuineVsSubstitutional Quantification: the expressions to be used are abstract entities as are the numbers themselves. V 192 NominalismVsVs: one could reduce the ontology of real numbers or set theory to that of elementary number theory by establishing truth conditions for substitutional quantification on the basis of Goedel numbers. >Goedel Numbers/Quine. QuineVs: this is not nominalistic, but Pythagorean. It is not about the high estimation of the concrete and disgust for the abstract, but about the acceptance of natural numbers and the rejection of most transcendent numbers. As Kronecker says: "The natural numbers were created by God, the others are human work". QuineVs: but even that is not possible, we saw above that the subsitutional quantification over classes is basically not compatible with the object quantification over objects. V 193 VsVs: one could also understand the quantification of objects in this way. QuineVs: that wasn't possible because there aren't enough names. You could teach space-time coordination, but that doesn't explain language learning. X 79 Validity/Sentence/Quantity/Schema/Quine: if quantities and sentences fall apart in this way, there should be a difference between these two definitions of validity about schema (with sentences) and models (with sentences). But it follows from the Löwenheim theorem that the two definitions of validity (using sentences or sets) do not fall apart as long as the object language is not too weak in expression. Condition: the object language must be able to express (contain) the elementary number theory. Object Language: In such a language, a scheme that remains true in all insertions of propositions is also fulfilled by all models and vice versa. >Object Language/Quine The requirement of elementary number theory is rather weak. Def Elementary Number Theory/Quine: speaks about positive integers by means of addition, multiplication, identity, truth functions and quantification. Standard Grammar/Quine: the standard grammar would express the functors of addition, multiplication, like identity, by suitable predicates. X 83 Elementary Number Theory/Quine: is similar to the theory of finite n-tuples and effectively equivalent to a certain part of set theory, but only to the theory of finite sets. XI 94 Translation Indeterminacy/Quine/Harman/Lauener: ("Words and Objections"): e.g. translation of number theory into the language of set theory by Zermelo or von Neumann: both versions translate true or false sentences of number theory into true or false sentences of set theory. Only the truth values of sentences like e.g. "The number two has exactly one element", which had no sense before translation, differ from each other in both systems. (XI 179: it is true in von Neumann's and false in Zermelo's system, in number theory it is meaningless). XI 94 Since they both serve all purposes of number theory in the same way, it is not possible to mark one of them as a correct translation. |
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 |
| Satisfaction | Goodman | Definition satisfaction/Goodman: "Satisfied" = "is denoted by" "has as fulfillment object" = "denotes" "fulfillment class" = extension >Terminology/Goodman. III 139 f Extension/Goodman: the extension of a word is not both its pronunciations and the objects - the extension is always based on a system. >Extensions. III 140 Satisfaction/Goodman: satisfaction requires no special agreement; whatever is denoted by a symbol, it fulfills it. In principle, compliance is connected with an inscription. In a given system, many things can fulfill a single inscription, and the class of these things constitutes the fulfillment class of inscriptions in this system. >Systems. Of course, the fulfillment class does not normally fulfill the inscription itself - its elements do. III 141 Inscription/Goodman: we call inscriptions without a satisfaction object "vacant". A vacant inscription belongs as much to the system as any other and it can be just as big and black. It deficit is more semantic, not of syntactic nature. An object which does not fulfill an inscription, has no description in the system. In Object-English, for example, no object and no set of objects fulfills only one predicate. |
G IV N. Goodman Catherine Z. Elgin Reconceptions in Philosophy and Other Arts and Sciences, Indianapolis 1988 German Edition: Revisionen Frankfurt 1989 Goodman I N. Goodman Ways of Worldmaking, Indianapolis/Cambridge 1978 German Edition: Weisen der Welterzeugung Frankfurt 1984 Goodman II N. Goodman Fact, Fiction and Forecast, New York 1982 German Edition: Tatsache Fiktion Voraussage Frankfurt 1988 Goodman III N. Goodman Languages of Art. An Approach to a Theory of Symbols, Indianapolis 1976 German Edition: Sprachen der Kunst Frankfurt 1997 |
| Sentences | Tarski | Horwich I 136 Sentence/Tarski: here: classes of inscriptions of the same shape - not physical things. >Inscriptions. Tarski does not work with Propositions. Horwich I 109/110 Senetence/name of sentence/Tarski: "X is true" is not grammatically correct, if we replace "X" with a sentence. It must be the name of a sentence. - It must be because at this position in the sentence there is a noun.(1) >Names of sentences, >Description levels, >Levels. 1. A. Tarski, The semantic Conceptions of Truth, Philosophy and Phenomenological Research 4, pp. 341-75 |
Tarski I A. Tarski Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983 Horwich I P. Horwich (Ed.) Theories of Truth Aldershot 1994 |
| Signs | Quine | V 160 Sign/Interpretation/Quine: must not simply be reinterpreted, otherwise each string can have any meaning - N.B.: but terms can very well be reinterpreted. ((s) not signs). >Interpretation, >Meaning. VII (c) 53 Meaning/Sign/Quine: it is unsatisfactory to say that a significant sequence is simply a series of phonemes that are uttered by a speaker of a chosen population. We do not only want the expressed sequences, but also those that may yet be expressed. IV 396 Sign/Locke: ...but for two reasons we also need signs, which in turn stand for ideas: for the exchange of our thoughts and for their recording. These are the words. Behind them stand the ideas, as it were, as guarantors of meaning. Without them, words would merely be sounds. Words: are representatives of ideas. IV 397 QuineVsLocke: one should stick to what is true for everyone when openly observed. Language is also not something private, but something social. IV 398 Language: is a social skill acquired through the observation of social use. The externalisation of empiricism leads to a behavioural approach to meaning. (Behaviorism). V 165 Infinite/Name/Signs/Quine: Problem: which signs should we use when we need infinitely many as insertions for the number variables? One cannot say that every sign is a physical object, because then they run out soon. Wrong solution: to say that these signs are forms (as classes of inscriptions). Because these are again physical realizations of forms and there is not enough of them. Form/Quine: (to denote infinitely many natural numbers) here also not in the sense of analytical geometry, so that a form would become a class of classes of pairs of real numbers, because it does not help to explain the numbers by means of number signs, which are themselves explained by means of real numbers. >Infinity, >Numbers, >Denotation. |
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 |
| Syntax | Quine | VII (a) 15 Syntax/Quine: their rules are meaningful in contrast to their notation. VI 69 Syntax/translation/indeterminacy/Quine: many of my readers have mistakenly assumed that uncertainty also extends to syntax. There was a subtle reason for this: in word and object(1) (pp. 107, 129 136) it says: VI 70 that also the specific apparatus of reification and object reference, which we make use of, is subject to indeterminacy. To this apparatus belong the pronomina, the "=", (equal sign) the plural endings and whatever performs the tasks of the logical quantifiers. But it is wrong to assume that these mechanisms belonged to syntax! >Equal sign, >Quantifiers, >Pronouns, >Indeterminacy. VI 97 Spelling/Quine: resolves the syntax and lexicon of each content sentence and merges it with the interpreter's language. It then has no more complicated syntax than the addition sign. 1. Quine, W. V. (1960). Word and Object. MIT Press VII (a) 15 Syntax/Quine/Goodman: their rules are meaningful as opposed to the notation itself. XI 114 Language/Syntax/Lauener: Language cannot be regarded purely syntactically as the set of all correctly formed expressions, because an uninterpreted system is a mere formalism. ((s) This is not truthful). XI 116 Lauener: it is a mistake to think that the language contributes the syntax but the theory contributes the empirical content. Therefore, one cannot say that an absolute theory can be formulated in different languages, or vice versa, that different (even contradictory) theories can be expressed in one language. XI 136 Mathematics/QuineVsHilbert/Lauener: Mathematics is more than just syntax. Quine reluctantly professes Platonism. XII 58 The problem of the inscrutability of the reference reaches much deeper than that of the indeterminacy of the translation: e.g. protosyntax. >Inscrutability. Protosyntax/Uncertainty/Quine: the language here is a formalized system of proof theory of the first level, whose subject area consists only of expressions, i.e. of character strings of a certain alphabet. Expressions: are types here, not tokens! (no occurrences). Each expression is the set of all its occurrences. (Summarized due to similarity of inscriptions). For example, the concatenation x^y is the set of all inscriptions that consist of two parts. These parts are tokens of x and y. Problem: it can happen that x^y is the empty set ((s) the combination does not occur) although both x and y are not empty. XII 59 The probability of this problem increases with increasing length of x and y! N.B.: this violates a law of protosyntax that says: x = z, if x^y = z^y. Solution: then you will not understand the objects as sets of inscriptions. But then you can still consider its atoms, the single characters as a set of inscriptions. Then there is no danger that the set is empty. ((s) Because the atoms have to be there, even if not every combination). N.B.: instead of interpreting the strings as sets of inscriptions, they can be regarded as a (mathematical) sequence (of characters). Character String/Expression: is then a finite set of pairs of a sign and a number. Vs: this is very artificial and complicated. Simpler: Goedel numbers themselves (the characters disappear). Problem: Question: How clear is it here that we have just started to talk about numbers instead of expressions? The only thing that is reasonably clear is that we want to fulfill laws with artificial models that are supposed to fulfill expressions in a non-explicit sense. XIII 199 Syntax/Quine: "glamour" and "grammar" were originally one and the same word. XIII 200 Later, the meaning also included magic. Grammar: (in the narrower sense) said which chains of words or phonemes were coherent and which were not. Always related to a particular language. Grammar: (wider sense): "The art of speaking" (in relation to the established use). >Grammar. Syntax/Quine: for the narrower sense we do not really need the word "grammar", but "syntax". It is about which character strings belong to the language and which do not. Problem: this is indefinite in two ways: 1. How the individuals are specified (formally, by components or phonemes) and 2. What qualifies them for the specification XIII 201 Recognizability is too indeterminate (liberal). Problem: ungrammatical forms are used by many people and are not incomprehensible. A language that excludes these forms would be the dialect of a very small elite. Problem: merely possible utterances in imaginable but not actual situations that are not themselves linguistic in nature. Solution: Def ungrammatic/William Haas/Quine: a form that would not make sense in any imaginable fictitious situation. Rules/Syntax/syntactic rules/Quine: are abstractions of the syntactic from long practice. They are the fulfillment of the first task (see above) to recognize which chains are grammatical. XIII 202 Solution: this is mainly done by recursion, similar to family trees. It starts with words that are the simplest chains and then moves on to more complex constructions. It divides the growing repertoire into categories. Parts of speech/Quine: there are eight: Nouns, pronouns, verb, adjective, adverb, preposition, conjunction, sentence. Further subdivisions: transitive/intransitive, gender, etc. But this is hardly a beginning. Nomina: even abstract ones like cognizance (of) and exception (to) are syntactically quite different, they stand with different prepositions. Recursion/syntax/Quine: if we wanted to win the whole syntax by recursion, it would have to be so narrow that two chains would never be counted as belonging to the same speech part, unless they could be replaced in all contexts salva congruitate. >Recursion. Def Replaceability salva congruitate/Geach/Quine: preserves grammaticality, never returns ungrammatical forms. VsRecursion/Problem: if speech parts were so narrowly defined, e.g. Nomina, which stand with different prepositions, they would then have to be counted among different kinds of speech parts. And these prepositions e.g. of and to, should not fall into the same category either! Then there would be too many kinds of speech parts, perhaps hundreds. Of which some would also be singletons ((s) singletons = categories with only one element). Solution: to give up recursion after having the roughest divisions. |
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 |
| Terminology | Goodman | I 88 Art: There are characteristics to define a mode of symbolization that indicates whether something is a work of art. 1. Syntactic density: syntactic density is, where certain minimal differences serve to distinguish symbols, e.g. a scale free thermometer (in contrast to a digital instrument.) 2. Semantic density: semantic density is, where symbols are available for things that differ only by minimal differences from each other, e. g. not only the scale free thermometer mentioned above, but also common German, as long as it is not syntactically dense. 3. Relative fullness: relative fullness is, where comparatively many aspects of a symbol are significant, e. g. the drawing of a mountain of Hokusai consisting of a single line, in which every property such as line, thickness, shape, etc. counts. Contrary to the same curve as a depiction of the stock market trend of a day, in which only the height of the values above the basis counts. 4. Exemplification: in the exemplification, a symbol, whether or not it is denoted, is symbolized by the fact that it serves as a sample of properties which it possesses literally or metaphorically. 5. Multiple and complex reference is also possible, where one symbol fulfils several related and interacting reference functions, some direct and others mediated by other symbols. --- III 128 Definition symbol scheme: a symbol scheme consists of characters. Definition characters: characters are certain classes of utterances or inscriptions. Characteristic of the character in a notation is that its elements can be freely interchanged without any syntactic effects (class of marks). Score requires character separation. A character in a notation is an abstraction class of character indifference among inscriptions. Definition inscriptions: inscriptions include statements. An inscription is any brand visually, auditively, etc. that belongs to a character. An inscription is atomic if it does not contain any other inscription, otherwise it is compound. For example, a letter is considered atomic, including spaces. In music, the separation in atomic/together cannot always be recognized immediately, it is more complex. The atoms are best sorted into categories: key sign, time sign, pitch sign. III 128/129 Definition mark: a mark is an individual case of a character in a notation and it includes inscriptions. Actual marks are rarely moved or exchanged. All inscriptions of a given brand are syntactically equivalent. And this is a sufficient condition that they are "genuine copies" or replicas of each other, or are spelled in the same way. No mark may belong to more than one character (disjunctiveness) a mark that is unambiguously an inscription of a single character is still ambiguous, if it has different objects of fulfillment at different times or in different contexts. Definition type (opposite: use, Peirce): the type is the general or class whose individual cases or elements are the marks. Goodman: I prefer to do without the type altogether and instead name the cases of use of the type replica. Definition case of use: the case of use the replica of a type ("genuine copy"). There is no degree of similarity necessary or sufficient for replicas. Definition genuine copy: a genuine copy of a genuine copy of a genuine copy... must always be a genuine copy of "x". If the relation of being a genuine copy is not being transitive, the whole notation loses its meaning (see below: strictly speaking, a performance may not contain a single wrong note). Score requires character separation. Definition Notation: 1. Condition is character indifference among the individual cases of each character. Character indifference is a typical equivalence relation: reflexive, symmetrical, transitive. (No inscription belongs to one character to whom the other does not belong). 2. Demand to notation: the characters must be differentiated or articulated finally. For every two characters K and K' and every mark m that does not actually belong to both, the provision that either m does not belong to K or m does not belong to K' is theoretically possible. 3. The (first) semantic requirement for notation systems is that they must be unambiguous. Definition ambiguity: ambiguity consists of a multitude of fulfillment classes for one character. Definition redundancy: redundancy consists of a multitude of characters for one fulfillment class. III 133 Definition syntactically dense: a schema is syntactically dense if it provides an infinite number of characters that are arranged in such a way that there is always a third between two. Such a scheme still has gaps. For example, if the characters are rational numbers that are either less than 1 or not less than 2. In this case, the insertion of a character corresponding to 1 will destroy the density. Definition consistently dense: if there is no insertion of other characters at their normal positions, the density is destroyed. Definition ordered syntactically: e. g. by alphabet Definition discreetly not overlapping: note how absurd the usual notion is that the elements of a notation must be discreet: first, characters of a notation as classes must be rather disjoint! Discretion is a relationship between individuals. Secondly, there is no need for inscriptions of notations to be discreet. And finally, even atomic inscriptions only need to be discreet relative to this notation. Definition disjunct/disjunctiveness: no mark may belong to more than one character. The disjunctiveness of the characters is therefore somewhat surprising since we do not have neatly separated classes of ordered spheres of inscriptions in the world, but rather a confusing mixture of marks. Semantic disjunctiveness does not imply the discreetness of the objects of fulfillment, nor do syntactic disjunctiveness of the characters imply the discreetness of the inscriptions. On the other hand, a schema can consist of only two characters that are not differentiated finally. For example, all marks that are not longer than one centimeter belong to one character, all longer marks belong to the other. III 213 Definition fullness: the symbols in the picturial schema are relatively full, and fullness is distinguished from both the general public of the symbol and the infinity of a schema. It is in fact completely independent of what a symbol denotes, as well as the number of symbols in a scheme. Definition "attenuation": for the opposite of fullness I use attenuation. Definition density: e.g. real numbers, no point delimitation possible. The opposite of dense is articulated. III 232 ff Syntactic density, semantic density and syntactic fullness can be three symptoms of the aesthetic. Syntactic density is characteristic for non-linguistic systems; sketches differ from scores and scripts. Semantic density is characteristic of representation, description and expression through which sketches and scripts differ from scores. Relative syntactic fullness distinguishes the more representational among the semantically dense systems from the diagrammatic ones, the less from the more "schematic" ones. Density is anything but mysterious and vague and is explicitly defined. It arises from the unsatisfactory desire for precision and keeps it alive. III 76ff Def scheme: a scheme implicit set of alternatives. III 128 Def symbolic scheme: a symbolic scheme consists of characters. >Symbols. III ~ 140 Def symbol system: a symbol system is a symbol diagram, which is correlated with a reference region. III 76 A description does not work in isolation, but in its belonging to a family. III 195 The text of a poem, a novel or a biography is a character in a notation scheme. As a phonetic character with comments as the satisfaction of objects it belongs to an approximately notational system. >Systems. III 195 As a character with objects as the satisfaction of objects it belongs to a discursive language. >Satisfaction. |
G IV N. Goodman Catherine Z. Elgin Reconceptions in Philosophy and Other Arts and Sciences, Indianapolis 1988 German Edition: Revisionen Frankfurt 1989 Goodman I N. Goodman Ways of Worldmaking, Indianapolis/Cambridge 1978 German Edition: Weisen der Welterzeugung Frankfurt 1984 Goodman II N. Goodman Fact, Fiction and Forecast, New York 1982 German Edition: Tatsache Fiktion Voraussage Frankfurt 1988 Goodman III N. Goodman Languages of Art. An Approach to a Theory of Symbols, Indianapolis 1976 German Edition: Sprachen der Kunst Frankfurt 1997 |
| Texts | Benjamin | Bolz II 23 Text/Benjamin: the text is not important in terms of a historical point of view in relation to its author. Text: Two Spheres: "Scripture" "Inscription"(1) 1. Sphere: work/authority 2. Sphere: unsettles the authority: The relation to the subject is meaningless, like any inscription. >Writing, >Inscriptions, >Authorship. Bolz II 24 The work itself gets a chance to speak.(2) Work Character > Model character. Bolz II 26 Text/Benjamin: New forms: Flyers, brochures, magazine articles, posters: Only this prompt language is adequately effective in the moment.(3) 1. Necessity of new art forms 2. Integration of proletarian life and language forms 3. The journalistic monopoly of the newspaper. These moments have to be recalled together in such a way that the decomposition of the traditional forms by the mass media is recognizable precisely as the prerequisite of new forms. "Theological" dialectics in the relationship of "deepest humiliation" and "restoration".(4) >Theology/Benjamin. 1. W. Benjamin, Briefe. Herausgegeben und mit Anmerkungen versehen von Gershom Sholem und Th. W. Adorno, Frankfurt/M. 1966/1978, Br. 220. 2. W. Benjamin, Gesammelte Schriften. Unter Mitwirkung von Th. W. Adorno und Gershom Sholem herausgegeben von Rolf Tiedemann und Hermann Schweppenhäuser Frankfurt/M. 1972-89. Bd II, S. 688. 3. W. Benjamin, Gesammelte Schriften. Unter Mitwirkung von Th. W. Adorno und Gershom Sholem herausgegeben von Rolf Tiedemann und Hermann Schweppenhäuser Frankfurt/M. 1972-89. Bd IV S. 85 4. Ebenda. |
Bo I N. Bolz Kurze Geschichte des Scheins München 1991 Bolz II Norbert Bolz Willem van Reijen Walter Benjamin Frankfurt/M. 1991 |
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| Intuitionism | Poincaré Vs Intuitionism | Wessel I 236 PoincaréVsIntuitionism/VsConstruktivism/Wessel: (Poincaré calls the intuitionists pragmatists): "The pragmatist should take the position of the extension, the Cantorian that of comprehension (compréhension). The objects, however, are there before the inscriptions, and the set itself would exist if there was no one who would undertake to organize it." I 237 Intuitionism/Logic/Wessel: the intuitionists reject not only the concept of the actual infinite, but they also believe that they have to limit logic: Brouwer: the law of excluded third only applies within a certain finite main system, since it is possible to come to an empirical confirmation here. BrouwerVsLogic: as foundation of mathematics. Instead: vice versa! I 238 (s) It is about the practice of the mathematician, therefore the limits of the constructive possibilities are not random or can be overcome easily by logical considerations.) Constructivism/Brouwer/Heyting: examines the construction as such, without inquiring after the nature of the objects, e.g. whether they exist! Law of Excluded Third/Intuitionism/Heyting/Wessel: (a) k is the biggest prime number such that k-1 is also one; if there is no such number, k = 1 (s) "the only prime that is adjacent to another". (b) l is the biggest prime such that l-2 is also one; if there is no such number, l = 1. Wessel: k can really be determined (k = 3), while we do not have any methods to determine l. This leads to the rejection of the law of excluded third: for if the sequence of prime twins was either finite or infinite, then (b) would define an integer. Intuitionism/Logic/Logical Operators/Wessel: because certain laws of logic do not apply here, the different logics are various complexes of operators. But the intuitionists have the same claim, to comprehend the meaning of "and", "not", "or" in the everyday language. Def Conjunction/Intuitionism/Wessel: p u q can be claimed exactly then when both p and q can be claimed. |
Wessel I H. Wessel Logik Berlin 1999 |
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The author or concept searched is found in the following theses of the more related field of specialization.
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| Niominalism | Meixner, U. | I 87 Nominalism/Meixner: the thesis: that all entities are individuals, that universals are "mere names". For the nominalist, however, these words must then be concrete sound events or concrete inscriptions. For its part, the word "word" may not designate a type object. (also called "ontological individualism"). Radical Nominalism/Meixner: thesis: that all entities are actual individuals. Most Radical Nominalism/Meixner: thesis that all entities are actual physical individuals. Materialism/Meixner: would like to represent the most radical nominalism, but it turns out that only a limited nominalism can be represented. I 88 Reconstructive Nominalism: thesis: all entities, individuals and the basic individuals (BI) are physically, but simultaneously: 1. Most individuals (also the basic individuals) are not up to date. 2. All sets via basic individuals are also individuals (honorary "physical"). Then universals can be regarded as individual-like entities. a) Variant of Carnap: Basic individuals as individuals. b) David Lewis: baisc individuals on the contrary equated with maximum consistent individuals. (sets of properties). (see Chapter XI.3 below). |
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