Find counter arguments by entering NameVs… or …VsName.
| Disputed term/author/ism | Author Vs Author |
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| Carnap, R. | Quine Vs Carnap, R. | Carnap VII 151 Intensionalist Thesis of Pragmatics/CarnapVsQuine: determining the intention is an empirical hypothesis that can be checked by observing the linguistic habits. Extensionalist Thesis/QuineVsCarnap: determining the intention is ultimately a matter of taste, the linguist is free, because it can not be verified. But then the question of truth and falsehood does not arise. Quine: the completed lexicon is ex pede Herculem i.e. we risk an error if we start at the bottom. But we can gain an advantage from it! However, if in the case of the lexicon we delay a definition of synonymy no problem arises as nothing for lexicographers that would be true or false. Carnap VII 154 Intention/Carnap: essential task: to find out which variations of a given specimen in different ways (for example, size, shape, color) are allowed in the area of the predicate. Intention: can be defined as the range of the predicate. QuineVsCarnap: might answer that the man on the street would be unwilling to say anything about non-existent objects. Carnap VII 155 CarnapVsQuine: the tests concerning the intentions are independent of existential questions. The man on the street is very well able to understand questions related to assumed counterfactual situations. Lanz I 271 QuineVsCarnap: criticism of the distinction analytic/synthetic. This distinction was important for logical empiricism, because it allows an understanding of philosophy that assigns philosophy an independent task which is clearly distinct from that of empirical sciences! Quine undermines this assumption: the lot of concepts is not independent of their use in empirical theories! I 272 There are no conceptual truths that would be immune to the transformation of such theories. Philosophy and sciences are on one and the same continuum. --- Newen I 123 Quine/Newen: is like Carnap in the spirit of empiricism, but has modified it radically. I 124 Thought/Frege: irreducible. Thought/QuineVsFrege: seeks a reductive explanation of sentence content (like Carnap). Base/QuineVsCarnap: not individual sense data, but objectively describable stimuli. Sentence Meaning/Quine/Newen: is determined by two quantities: 1) the amount of stimuli leading to approval 2) the amount of the stimuli leading to rejection. This only applies for occasion sentences. I125 Def Cognitively Equivalent/Quine/Newen: = same meaning: two sentences if they trigger the same behavior of consent or reflection. For the entire language: if it applies to all speakers. QuineVsCarnap: sentences take precedence over words. Quine I 73 QuineVsCarnap: difference to Carnap's empirical semantics: Carnap proposes to explore meaning by asking the subject whether they would apply it under different, previously described circumstances. Advantage: opposites of terms such as "Goblin" and "Unicorn" are preserved, even if the world falls short of examples that could be so sharply distinct from each other in such a way. I 74 Quine: the stimulus meaning has the same advantage, because there are stimulus patterns that would cause consent to the question "unicorn?", but not for "Goblin?" QuineVsCarnap: Carnap's approach presumes decisions about which descriptions of imaginary states are permissible. So, e.g. "Unicorn", would be undesired in descriptions to explore the meaning of "Unicorn". Difference: Quine restricts the use of unfulfilled conditionals to the researchers, Carnap makes his researcher himself submit such judgments to the informant for evaluation. Stimulus meaning can be determined already in the first stages of radical translation, where Carnap's questionnaire is not even available yet. Quine: theory has primarily to do with records, Carnap: to do with terms. I 466 For a long time, Carnap advocated the view that the real problems of philosophy are linguistic ones. Pragmatic questions about our language behavior, not about objects. Why should this not apply to theoretical questions in general? I 467 This goes hand in hand with the analyticity concept. (§ 14) In the end, the theoretical sentences generally can only be justified pragmatically. QuineVsCarnap: How can Carnap draw a line there and claim that this does not apply for certain areas? However, we note that there is a transition from statements about objects to statements about words, for example, when we skip classes when moving from questions about the existence of unicorns to questions about the existence of points and kilometers. Through the much-used method of "semantic ascent": the transition from statements about kilometers to statements about "kilometers". From content-related to formal speech. It is the transition from speech in certain terms to talk about these concepts. It is precisely the transition of which Carnap said that it undressed philosophical questions of their deceptive appearance and made them step forward in their true form. QuineVsCarnap: this part, however, I do not accept. The semantic ascent of which I speak can be used anywhere. (Carnap: "content-related" can also be called "material".) Ex If it came down to it, the sentence "In Tasmania there are Wombats" could be paraphrased like this: ""Wombat" applies to some creatures in Tasmania." IV 404 Carnap/(Logical Particles): ("The logical structure of the world"): Thesis: it is possible in principle to reduce all concepts to the immediately given. QuineVsCarnap: that is too reductionist: Disposition concepts such as "soluble" cannot be defined like this. (Even later recognized by Carnap himself). IV 416 QuineVsCarnap: Why all these inventive reconstructions? Ultimately sense stimuli are the only thing we have. We have to determine how the image of the world is constructed from them. Why not be content with psychology? V 28 Disposition/Quine: Problem: the dependence on certain ceteris paribus clauses. Potential disturbances must be eliminated. Solution: some authors: (like Chomsky) retreat to probabilities. V 29 Carnap: instead of probability: reduction sentences seen as idealizations to which corrections are made. Carnap conceives these corrections as re-definitions, i.e. they lead to analytic sentences that are true from the meaning. QuineVsCarnap: I make no distinction between analytical and other sentences. V 30 Reflexes/Holt/Quine: those that are conditioned later are not fundamentally different from innate ones. They consist of nerve paths with reduced resistance. Quine: therefore, one can conceive disposition as this path itself! ((s) I.e. pratically physical. Precisely as physical state.) Disposition/GoodmanVsQuine: a disposition expression is a change to an eventually mechanical description and therefore circular. The mechanistic terms will ultimately be implicit disposition terms. QuineVsGoodman/QuineVsCarnap: I, unlike the two, am satisfied with a theoretical vocabulary, of which some fundamental physical predicates were initially learned with the help of dipositioned speech. (Heuristic role). VII (b) 40 But his work is still only a fragment of the whole program. His space-time-point quadruples presume a world with few movements ("laziest world"). Principle of least movement is to be the guide for the construction of a world from experience. QuineVsCarnap: he seemed not to notice that his treatment of physical objects lacked in reduction! The quadruples maximize and minimize certain overall features and with increasing experience the truth values are revised in the same sense. X 127 Logical Truth/Carnap: Thesis: only the language and not the structure of the world makes them true. Truth/Logical Truth/QuineVsCarnap: is not a purely linguistic matter. Logic/QuineVsCarnap: the two breakdowns that we have just seen are similar in form and effect: 1) The logic is true because of the language only insofar as it is trivially true because of everything. 2) The logic is inseparable from the translation only insofar as all evident is inseparable from the translation. Logic/Language/Quine: the semantic ascent seems to speak for linguistic theory. QuineVs: the predicate "true" (T predicate) already exists and helps precisely to separate logic from language by pointing to the world. Logic: While talks a lot about language, it is geared towards the world and not towards language. This is accomplished by the T predicate. X 133 We learn logic by learning language. VsCarnap: but that does not differentiate logic from other areas of everyday knowledge! XI 99 QuineVsProtocol Sentence/QuineVsCarnap/Lauener: describes private, non-public autopsychological experiences. XI 129 Intention/Carnap/Lauener: (Meaning and Necessity): attempts to introduce intentions without thereby entangling himself in metaphysics. QuineVsCarnap: you cannot take advantage of a theory without paying the ontological bill. Therefore, the assumed objects must be values of the variable. Another way would be to say that certain predicates must be true for the theory to be true. But that means that it is the objects that must be the values of variables. To every value applies a predicate or its negation. ((s) >continuous determination). XI 130 Conversely, everything to which a predicate applies is a value of a variable. Because a predicate is an open sentence. XI 138 Ontology/Carnap/Lauener: Ex "x is a thing": at a higher level of universality existence assumptions no longer refer to the world, but only to the choice of a suitable linguistic framework. QuineVsCarnap: this is merely a gradual difference. XI 142 Ontology/Carnap/Lauener: (temporarily represented): Thesis: philosophical questions are always questions about the use of language. Semantic Ascent/QuineVsCarnap: it must not be misused for evasive ontological maneuvers. XI 150 Thing/Object/Carnap/Lauener: to accept things only means choosing a certain language. It does not mean believing in these things. XI 151 CarnapVsQuine: his existence criterion (being the value of a bound variable) has no deeper meaning in as far as it only expresses a linguistic choice. QuineVsCarnap: language and theory cannot be separated like that. Science is the continuation of our daily practice. XII 69 QuineVsCarnap/QuineVsUniversal Words: it is not said what exactly is the feature for the scope. Ontological Relativity/QuineVsCarnap: cannot be enlightened by internal/external questions, universal words or universal predicates. It has nothing to do with universal predicates. The question about an absolute ontology is pointless. The fact that they make sense in terms of a framework is not because the background theory has a wider scope. Absolute Ontology/Quine: what makes it pointless, is not its universality but its circularity. Ex "What is an F?" can only be answered by recourse to another term: "An F is a G." XII 89 Epistemology/Scope/Validity/QuineVsCarnap: Hume's problem (general statements + statements about the future are uncertain if understood as about sense data or sensations) is still unsolved. Carnap/Quine: his Structures would have allowed translating all sentences about the world in sense data or observation terms plus logic and set theory. XII 90 QuineVsCarnap: the mere fact that a sentence is expressed with logical, set-theoretical and observational terms does not mean that it could be proved by means of logic and set theory from observation statements. ((s) means of expression are not evidence. (inside/outside, plain, circles).) Epistemology/Quine: Important argument: wanting to equip the truths about nature with the full authority of direct experience is just as much sentenced to failure as the reduction of truths in Mathematics to the potential intelligibility of elementary logic. XII 91 Carnap/QuineVsCarnap: If Carnap had successfully carried out its construction, how could he have known if it is the right one? The question would have been empty! Any one would have appeared satisfactory if only it had represented the physical contents properly. This is the rational reconstruction. Def Rational Reconstruction/Carnap/Quine: construction of physicalistic statements from observation terms, logical and set-theoretical concepts. QuineVsCarnap: Problem: if that had been successful, there would have been many such constructions and each would have appeared equally satisfactory,if only it had represented the physicalistic statements properly. But each would have been a great achievement. XII 92 QuineVsCarnap: unfortunately, the "structure" provides no reduction qua translation that would make the physicalist concepts redundant. It would not even do that if his sketch was elaborated. Problem: the point where Carnap explains how points in physical space and time are attributed sensory qualities. But that does not provide a key for the translation of scientific sentences into such that are formed of logic, set-theoretical and observation concepts. CarnapVsCarnap: later: ("Testability and Meaning", 1936): reduction propositions instead of definitions. XII 94 Empiricism/QuineVsCarnap: empiricism has 1) abandoned the attempt to deduce the truth about nature from sensory experience. With that he has made a substantial concession. 2) He has abandoned rational reconstruction, i.e. attempt to translate these truths in observation terms and logical mathematical tools. QuineVsPeirce: Suppose we meant that the meaning of a statement consists in the difference that its truth makes for the experience. Could we then not formulate in a page-long sentence in observation language any differences that might account for the truth, and could we then not see this as a translation? Problem: this description could be infinitely long, but it could also be trapped in an infinitely long axiomatization. Important argument: thus the empiricist abandons the hope that the empirical meaning of typical statements about reality could be expressed. Quine: the problem is not too high a complexity for a finite axiomatization, but holism: XII 95 Meaning/QuineVsPeirce: what normally has experience implications ("difference in the experience") only refers to theories as a whole, not to individual experience sentences. QuineVsCarnap: also the "structure" would have to be one in which the texts, into which the logical mathematical observation terms are to be translated, are entire theories and not just terms or short sentences. Rational Reconstruction/QuineVsCarnap: would be a strange "translation": it would translate the whole (whole theories), but not the parts! Instead of "translation" we should just speak of observation bases of theories. pro Peirce: we can very well call this the meaning of empirical theories. ((s) Assigning whole theories to observations). |
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 Ca I R. Carnap Die alte und die neue Logik In Wahrheitstheorien, G. Skirbekk (Hg) Frankfurt 1996 Ca II R. Carnap Philosophie als logische Syntax In Philosophie im 20.Jahrhundert, Bd II, A. Hügli/P.Lübcke (Hg) Reinbek 1993 Ca IV R. Carnap Mein Weg in die Philosophie Stuttgart 1992 Ca IX Rudolf Carnap Wahrheit und Bewährung. Actes du Congrès International de Philosophie Scientifique fasc. 4, Induction et Probabilité, Paris, 1936 In Wahrheitstheorien, Gunnar Skirbekk Frankfurt/M. 1977 Ca VI R. Carnap Der Logische Aufbau der Welt Hamburg 1998 CA VII = PiS R. Carnap Sinn und Synonymität in natürlichen Sprachen In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Ca VIII (= PiS) R. Carnap Über einige Begriffe der Pragmatik In Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982 Lanz I Peter Lanz Vom Begriff des Geistes zur Neurophilosophie In Philosophie im 20. Jahrhundert, A. Hügli/P. Lübcke Reinbek 1993 New II Albert Newen Analytische Philosophie zur Einführung Hamburg 2005 Newen I Albert Newen Markus Schrenk Einführung in die Sprachphilosophie Darmstadt 2008 |
| Field, H. | Bigelow Vs Field, H. | I 345 Mathematics/Bigelow/Pargetter: our metaphysics allows a realistic conception of mathematics (BigelowVsField). I VII Mathematics/BigelowVsField: can be understood realistically, if it is understood as studying the universals, properties and relations, patterns and structures of things that can be at different places at the same time. I 59 Equivalence class/equ.set/Bigelow/Pargetter: sort objects with the same D-ates (determinates) into classes. THis is how they explain how two things can be more similar in one way than in another. Level 1: objects Level 2: properties of things Level 3: proportions between such properties. Proportions/Bigelow/Pargetter: are universals that can introduce subtle differences between equ.sets of properties on tier 2nd level. Equal/different/Bigelow/Pargetter: Important argument: This explains why two relations can be the same and different at the same time. E.g. Suppose one of the two relations is a mass relation (and stands in relation to other mass-relations) and the other is not a mass relation (and is not in relation to mass relations), and yet I 60 both have something in common: they are "double" once in relation to mass, and then in terms of volume. This is explainedon level 3. Numbers/Bigelow/Pargetter: this shows the usefulness of numbers in the treatment of quantities. (BigelowVsField). I 383 BigelowVsField: (a propos science without numbers): he wrongly assumes that physics begins with pure empiricism in order to then convert the results into completely abstract mathematics. Field/Bigelow/Pargetter: wants to avoid this detour. BigelowVsField: his project is superfluous if we accept that Mathematics is just a different description of the physical proportions and relations instead of a detour. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Formalism | Barrow Vs Formalism | Barrow I 57 VsFormalism: every mathematical sentence is true in any mathematical system. Therefore formalism is a very unsatisfactory theory of mathematics. Besides, you have to change all the structures even if only one axiom changes. |
B I John D. Barrow Warum die Welt mathematisch ist Frankfurt/M. 1996 B II John D. Barrow The World Within the World, Oxford/New York 1988 German Edition: Die Natur der Natur: Wissen an den Grenzen von Raum und Zeit Heidelberg 1993 B III John D. Barrow Impossibility. The Limits of Science and the Science of Limits, Oxford/New York 1998 German Edition: Die Entdeckung des Unmöglichen. Forschung an den Grenzen des Wissens Heidelberg 2001 |
| Hempel, C. | Schlick Vs Hempel, C. | I 91 Context: Schlick: The foundation of knowledge" (1934) HempelVsSchlick). HempelVsSchlick: he was a "metaphysician and poet". Proposition/reality/HempelVsSchlick: you cannot compare statements with facts! SchlickVsHempel: you can without being a metaphysician. I 92 E.g. I compare this sentence in my Baedeker "This cathedral has two towers" with reality: namely simply by looking at the cathedral. If someone has something against it, it may just be that he understands "Proposition" in another sense. Coherence theory/HempelVsSchlick/HempelVscorrespondence theorie: you can only compare propositions with each other. ((s) Not propositions with reality). Schlick: we can distinguish between cases where a written, printed or spoken proposition is compared with another written, printed or spoken proposition. Schlick: and I call that the comparison a proposition with a fact. HempelVsSchlick: statements can only be compared with other statements. ((s)> coherence, > coherence theory). SchlickVsHempel: Why? I take out the modest freedom to compare everything with everything. If propositions and facts are to be too far from each other? Too different? Should it be a mysterious property of propositions that they cannot be compared with anything? Fact/statement/Hempel: the gap between them is only a metaphysical. SchlickVsHempel: that may be so, but who believes because in such a gap? I 93 Def Proposition/Schlick: is a string along with the logical rules for their use. ((s) So almost a proposition, along with the importance of rules). Proposition meaning/Schlick: these rules culminate in "deictic" definitions that make up the meaning of the proposition. Verification/compliance/correspondence/SchlickVsHempel: to verify the proposition, I have to find out if the (meaning-) rules were followed. Why should it be impossible? E.g. I look at the cathedral and then at the proposition and realize that the symbol "two" is used in the proposition in connection with the symbol "towers" and so I will get to the same icon when applying the rules of counting the cathedral towers. Coherence theory/fact/proposition/Compare/Schlick: sometimes it is said that "in a logical sense" propositions can be compared only with other propositions. That may be so, but I do not know what is meant by a "comparison in a logical way". Comparison/HempelVsSchlick: we cannot say exactly what a comparison of statements and facts is, I 94 Because we cannot determine the structure of facts. Fact/structure/SchlickVsHempel: that we cannot determine the "structure of a fact" reminds me of the metaphysics of "things in themselves". If one does not deny the existence of facts, then why deny the possibility to determine their structure? Structure of a fact: E.g. if I count the towers of a cathedral, I become familiar with the structure of a certain fact. If you wanted to say that it is meaningless to speak of "Structures of facts" at all that would be merely a question of terminology. One proposition is also not per se meaningful, but only in conjunction with the rules for its use. Fact/propositions/Compare/Vscorrespondence theory/SchlickVsHempel: that is what the whole controversy is about, if it should be impossible to compare propositions and facts, Hempel uses the words simply in a different sense. The easiest way to deny that you can compare them would be to say that there are simply no facts! (In formal speech: the rule of the word "fact" is such that it should not be used). Or maybe the comparison is simply never applied in the sciences? I think this is true for purely logical sciences such as Mathematics, but not in experimental sciences. I 95 SchlickVsHempel: here is the psychological motivation of his criticism: it is about a vision that completely settles within the sciences. Science as a system of propositions. This should be a substitute for reality. Then "protocol statements" are used as a material, without subjecting them to an empirical test. Science/Schlick: But science is not the world! The universe of discourse is not the universe. It's one thing to ask how their whole system is constructed and why it is generally regarded as true, and another, why I even look at them as true. This is a psychological question. But none of the "cultural subordination". My trust in science and colleagues is that I found them trustful, every time I checked their allegations. I 96 Def confirmation/Schlick: the final step in the comparison between a statement and a fact. But one should not attach too much importance to the concept. I 97 Fact/proposition/compare/match/correspondence/HempelVsSchlick: his example for comparison is not quite adequate. (E.g. "The cathedral has two towers"). Hempel: I agree that one can consider propositions as empirical objects that can be compared with any other empirical object. But if we take that literally it leads to something like: I 98 E.g. "The proposition contains more parts, "the words" referred to" than the cathedral has towers". Correspondence/SchlickVsHempel: There is a different kind of comparison between proposition and fact: Comparison of symbols "two" in the sentence and the counting by looking at the cathedral. HempelVsSchlick: so by that he compares a proposition in Baedeker with the result of an action by himself. Coherence theory/Pointe: this result of the action is determined in a second proposition. And these two are compared! That is what I meant with "logical point". Revision/verification/coherence theory/HempelVsSchlick: it's about whether the propositions contradict each other. This goes even without knowing the meanings of the propositions! (> Carnap: "The logical syntax of the language", "Philosophy and logical syntax"). Example, the above two propositions, both contain an icon that is shaped like "two". |
Schlick I Moritz Schlick "Facts and Propositions" Analysis 2 (1935) pp. 65-70 In Theories of Truth, Paul Horwich 1994 Schlick II M. Schlick General Theory of Knowledge 1985 |
| Locke, J. | Verschiedene Vs Locke, J. | VsLocke Locke I 26/27 Knowledge/VsLocke: Problem: the ideas have to be fixed in words, but that does not mean recognizing yet, because the words have to be processed into statements. Locke, however, develops his idea analysis first in isolation. (Thereby lengthy repetitions arise). Locke I 42 VsLocke/VsSensualism: the critique of Locke always misses a clarification of the necessary preconditions of human knowledge in the subject itself. This is caught by Locke's introduction of reason at the end of the essay. Locke I 66 Ethics/Locke: the suspension force is of utmost importance for Locke's ethics: the "Angel" around which the freedom of rational beings revolves. Thus the possibility of a free decision for the morally good is to be justified. (Despite hedonism). VsLocke: this is not contradictory, but not very plausible. It has been criticized time and again that the motive of moral decision is not the independent value of the morally good, but the benefit determined according to desire/displeasure. Locke never clarified this despite the pressure of his contemporaries. Locke I 169 Sensualism/VsLocke: an old tradition of Locke-Criticism considers sensualism naive. (LeibnizVsLocke, KantVsLocke). Locke: Thesis: "Nothing is in the mind that was not in the senses before". LeibnizVsLocke: "except the mind itself!". Curl I 170 KantVsLocke: there are a priori forms of perception that enable us to have experiences in the first place. Language/Knowledge/VsLocke: (today): Locke misjudges the irreducible linguistic foundations of empirical perception. But in his thinking the correction is already applied in order to also include abstract and general ideas under the empirically given, from which every reconstruction of knowledge must already start. (L. Krüger). Economy/EuchnerVsLocke: Contradiction: Locke's mercantilism and its simultaneous praise of world trade. Locke I 188 Knowledge/Reality/KreimendahlVsLocke: restricts possible statements of reality to the realm of ideas and the "nominal" entities formed by them. In doing so, he questions his own empirical program. On the one hand it is correct that there can be no knowledge without mediation of ideas, which in their complex form are human art products, while on the other hand he claims that the source of all ideas is experience (circular). Experience/Locke: the combination of sensory experience and reflection ("inner experience"). Gravity/Locke: "Hoop and Ribbon" (Euchner: that was more naive than it should have been at the time). Locke II 187 Complex ideas/Locke: e.g. friend: from simple ideas: human, love, willingness, action, happiness, which in turn can be traced back to even simpler ideas. LambertVsLocke: he did not recognize the necessary connections of the terms. ArndtVsLambert: Locke was not interested in an axiomatic system. He was interested in separating the realm of "real knowledge" (Mathematics) from the empirical, in which the complex idea is based solely on the observable factual co-existence of qualities. In empiricism, no necessary connection can be observed! Locke I 62 Law of Nature/EuchnerVsDoctrine of the Law of Nature: Locke does not treat it systematically, otherwise he would have had to deal with the following problems: the world as an order of creation, to the legal order of political Structures under the aspects of natural and human law, as well as the the legal position of the individual, to the question of how the unrevealed and written down natural law can be recognized with the help of reason, and to the question of how the unrevealed and written down natural law can be recognized with the help of reason. Reasons why the principles of natural law and morality are recognised as binding and followed. |
Loc III J. Locke An Essay Concerning Human Understanding |
| Principia Mathematica | Gödel Vs Principia Mathematica | Russell I XIV Circular Error Principle/VsPrincipia Mathematica(1)/PM/Russell/Gödel: thus seems to apply only to constructivist assumptions: when a term is understood as a symbol, together with a rule to translate sentences containing the symbol into sentences not containing it. Classes/concepts/Gödel: can also be understood as real objects, namely as "multiplicities of things" and concepts as properties or relations of things that exist independently of our definitions and constructions! This is just as legitimate as the assumption of physical bodies. They are also necessary for Mathematics, as they are for physics. Concept/Terminology/Gödel: I will use "concept" from now on exclusively in this objective sense. A formal difference between these two conceptions of concepts would be: that of two different definitions of the form α(x) = φ(x) it can be assumed that they define two different concepts α in the constructivist sense. (Nominalistic: since two such definitions give different translations for propositions containing α.) For concepts (terms) this is by no means the case, because the same thing can be described in different ways. For example, "Two is the term under which all pairs fall and nothing else. There is certainly more than one term in the constructivist sense that satisfies this condition, but there could be a common "form" or "nature" of all pairs. All/Carnap: the proposal to understand "all" as a necessity would not help if "provability" were introduced in a constructivist manner (..+...). Def Intensionality Axiom/Russell/Gödel: different terms belong to different definitions. This axiom holds for terms in the circular error principle: constructivist sense. Concepts/Russell/Gödel: (unequal terms!) should exist objectively. (So not constructed). (Realistic point of view). When only talking about concepts, the question gets a completely different meaning: then there seems to be no objection to talking about all of them, nor to describing some of them with reference to all of them. Properties/GödelVsRussell: one could surely speak of the totality of all properties (or all of a certain type) without this leading to an "absurdity"! ((s) > Example "All properties of a great commander". Gödel: this simply makes it impossible to construe their meaning (i.e. as an assertion about sense perception or any other non-conceptual entities), which is not an objection to someone taking the realistic point of view. Part/whole/Mereology/GödelVsRussell: neither is it contradictory that a part should be identical (not just the same) with the whole, as can be seen in the case of Structures in the abstract sense. Example: the structure of the series of integers contains itself as a special part. I XVI/XVII Even within the realm of constructivist logic there are certain approximations to this self-reflectivity (self-reflexivity/today: self-similarity) of impredicative qualities, namely e.g. propositions, which as parts of their meaning do not contain themselves, but their own formal provability. There are also sentences that refer to a totality of sentences to which they themselves belong: Example: "Each sentence of a (given) language contains at least one relational word". This makes it necessary to look for other solutions to the paradoxes, according to which the fallacy does not consist in the assumption of certain self-reflectivities of the basic terms, but in other assumptions about them! The solution may have been found for the time being in simple type theory. Of course, all this refers only to concepts. Classes: one should think that they are also not created by their definitions, but only described! Then the circular error principle does not apply again. Zermelo splits classes into "levels", so that only sets of lower levels can be elements of sets of higher levels. Reducibility Axiom/Russell/Gödel: (later dropped) is now taken by the class axiom (Zermelo's "axiom of choice"): that for each level, for any propositional function φ(x) the set of those x of this level exists for which φ(x) is true. This seems to be implied by the concept of classes as multiplicities. I XVIII Extensionality/Classes: Russell: two reasons against the extensional view of classes: 1. the existence of the zero class, which cannot be well a collection, 2. the single classes, which should be identical with their only elements. GödelVsRussell: this could only prove that the zero classes and the single classes (as distinguished from their only element) are fictions to simplify the calculation, and do not prove that all classes are fictions! Russell: tries to get by as far as possible without assuming the objective existence of classes. According to this, classes are only a facon de parler. Gödel: but also "idealistic" propositions that contain universals could lead to the same paradoxes. Russell: creates rules of translation according to which sentences containing class names or the term "class" are translated into sentences not containing them. Class Name/Russell: eliminate by translation rules. Classes/Principia Mathematica/Russell/Gödel: the Principia Mathematica can do without classes, but only if you assume the existence of a concept whenever you want to construct a class. First, some of them, the basic predicates and relations like "red", "colder" must be apparently considered real objects. The higher terms then appear as something constructed (i.e. something that does not belong to the "inventory of the world"). I XIX Ramsey: said that one can form propositions of infinite length and considers the difference finite/infinite as not so decisive. Gödel: Like physics, logic and Mathematics are based on real content and cannot be "explained away". Existence/Ontology/Gödel: it does not behave as if the universe of things is divided into orders and one is forbidden to speak of all orders, but on the contrary: it is possible to speak of all existing things. But classes and concepts are not among them. But when they are introduced as a facon de parler, it turns out that the extension of symbolism opens the possibility of introducing them in a more comprehensive way, and so on, to infinity. To maintain this scheme, however, one must presuppose arithmetics (or something equivalent), which only proves that not even this limited logic can be built on nothing. I XX Constructivist posture/constructivism/Russell/Gödel: was abandoned in the first edition, since the reducibility axiom for higher types makes it necessary that basic predicates of arbitrarily high type exist. From constructivism remains only 1. Classes as facon de parler 2. The definition of ~, v, etc. as valid for propositions containing quantifiers, 3. The stepwise construction of functions of orders higher than 1 (of course superfluous because of the R-Axiom) 4. the interpretation of definitions as mere typographical abbreviations (all incomplete symbols, not those that name an object described by the definition!). Reducibility Axiom/GödelVsRussell: this last point is an illusion, because of the reducibility axiom there are always real objects in the form of basic predicates or combinations of such according to each defined symbol. Constructivist posture/constructivism/Principia Mathematica/Gödel: is taken again in the second edition and the reducibility axiom is dropped. It is determined that all basic predicates belong to the lowest type. Variables/Russell/Gödel: their purpose is to enable the assertions of more complicated truth functions of atomistic propositions. (i.e. that the higher types are only a facon de parler.). The basis of the theory should therefore consist of truth functions of atomistic propositions. This is not a problem if the number of individuals and basic predicates is finite. Ramsey: Problem of the inability to form infinite propositions is a "mere secondary matter". I XXI Finite/infinite/Gödel: with this circumvention of the problem by disregarding the difference between finite and infinite a simpler and at the same time more far-reaching interpretation of set theory exists: Then Russell's Apercu that propositions about classes can be interpreted as propositions about their elements becomes literally true, provided n is the number of (finite) individuals in the world and provided we neglect the zero class. (..) + I XXI Theory of integers: the second edition claims that it can be achieved. Problem: that in the definition "those cardinals belonging to each class that contains 0 and contains x + 1 if it contains x" the phrase "each class" must refer to a given order. I XXII Thus whole numbers of different orders are obtained, and complete induction can be applied to whole numbers of order n only for properties of n! (...) The question of the theory of integers based on ramified type theory is still unsolved. I XXIII Theory of Order/Gödel: is more fruitful if it is considered from a mathematical point of view, not a philosophical one, i.e. independent of the question of whether impredicative definitions are permissible. (...) impredicative totalities are assumed by a function of order α and ω . Set/Class/Principia Mathematica(1)/Russell/Type Theory/Gödel: the existence of a well-ordered set of the order type ω is sufficient for the theory of real numbers. Def Continuum Hypothesis/Gödel: (generalized): no cardinal number exists between the power of any arbitrary set and the power of the set of its subsets. Type Theory/VsType Theory/GödelVsRussell: mixed types (individuals together with predications about individuals etc.) obviously do not contradict the circular error principle at all! I XXIV Russell based his theory on quite different reasons, similar to those Frege had already adopted for the theory of simpler types for functions. Propositional functions/statement function/Russell/Gödel: always have something ambiguous because of the variables. (Frege: something unsaturated). Propositional function/p.f./Russell/Gödel: is so to speak a fragment of a proposition. It is only possible to combine them if they "fit together" i.e. are of a suitable type. GödelVsRussell: Concepts (terms) as real objects: then the theory of simple types is not plausible, because what one would expect (like "transitivity" or the number two) to be a concept would then seem to be something that stands behind all its different "realizations" on the different levels and therefore does not exist according to type theory. I XXV Paradoxes in the intensional form/Gödel: here type theory brings a new idea: namely to blame the paradoxes not on the axiom that every propositional function defines a concept or a class, but on the assumption that every concept results in a meaningful proposition if it is claimed for any object as an argument. The objection that any concept can be extended to all arguments by defining another one that gives a false proposition whenever the original one was meaningless can easily be invalidated by pointing out that the concept "meaningfully applicable" does not always have to be meaningfully applicable itself. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
Göd II Kurt Gödel Collected Works: Volume II: Publications 1938-1974 Oxford 1990 |
| Putnam, H. | Field Vs Putnam, H. | III 113 Pure Mathematics/Putnam: should be interpreted in a way that it asserts the possible existence of physical structures that satisfy the mathematical axioms. FieldVsPutnam: pure Mathematics should not be interpreted at all. I 211 Properties/Relations/Putnam: (1970): are predicative, according to them we have a few basic physical prop and rel from which all others are derived: 1st order: Allows no reference to a totality of physical objects when a new property is constructed. 2nd order: Allows reference to the totality of the properties of the 1st order. 3rd order: Allows reference to the totality of the properties of the 1st and 2nd order. - Every physical property appears on any level of the hierarchy -> functionalism. Functional properties are 2nd or higher order properties - the prop that the role has may differ from person to person. I 214 FieldVsPutnam: instead of properties provide instantiations of properties with steps. I 268 Mathematics/Ontology/Putnam: ("Mathematics without foundations", 1976b, 1975 "What is mathematical truth?"): Field: Putnam Thesis: the mathematical realist does not have to accept the "mathematical object picture". He can formulate his views in purely modal terms. And that not as an alternative, but only as another formulation of the same view. I 269 Indispensability Argument/Putnam: appear in the subsequent text. Field: If "Mathematics as a modal" logic was really an equivalent description of Mathematics in terms of mathematical objects (MO), then it should also be possible to reformulate the Indispensability Argument so that there is a prima facie argument for one or the other kind of modalized Mathematics and mathematical objects. FieldVsPutnam: but Section 6 and 7 show that we cannot formulate the indispensability argument like that: it requires MO and modalized Mathematics does not bring them forth. VSVs: but beware: I have not studied all the possibilities. I 269 FieldVsPutnam: his mathematical realism seems puzzling: Mathematics/Ontology/Putnam: Thesis: there is a modal translation of pure Mathematics: he presents a translation procedure that turns mathematical statements into modal statements, one that transforms acceptable mathematical statements (E.g. axioms of set theory) into true modal assertions that include no quantification, unless it is modalized away. (I.e. no mathematical entities (ME) in the modal statements). I 270 FieldVsPutnam: two general questions: 1) what kind modality is involved here? 2) what benefit is the translation to have? ad 1): Putnam thinks that the "object-image" (the starting position) and its modal translation are equivalent at a deeper level. FieldVs: that’s really not interesting: "mathematically possible" should coincide with "logically possible" in any reasonable view (this is stated by conservatism). ((s) contrary to the above). Important argument: if A is not mathematically possible, then "~A" is a consequence of Mathematics - i.e. if A (and then also its negation) are purely non-mathematically, then "~A" is logically true. If Putnam now says that his modal translation involves a "strong and clear mathematical sense of possibility", then a mathematical possibility operator must be applied to sentences that contain ME. However, such a sentence A could also be a mixed sentence (see above, with purely mathematical and purely physical components). I 271 FieldVsPutnam: for purely mathematical sentences mathematical possibility and truth coincide! But then the "modal translations" are just as ontologically committed as the mathematical assertions. FieldVs"Mathematical Possibility"/FieldVsPutnam: we had better ignore it. Maybe it was about 2nd order logical possibility as opposed to 1st order for Putnam? I 271 FieldVsPutnam: what benefits does his modal translation have? Does it provide a truth transfer (as opposed to the transmission of mere acceptability)? And what value has it to say that the mathematical statements are both true and acceptable? Etc. Mathematics/Realism/Putnam/Field: Putnam describes himself as "mathematical realist": Difference to Field’s definition of realism: he does not consider ME as mind-independent and language-independent, but (1975): Putnam: you can be a realist without being obliged to mathematical objects. I 272 The question is the one that Kreisel formulated long ago: the question of the objectivity of mathematics and not the question the existence of mathematical objects. FieldVsPutnam: this is puzzling. I 277 Model Theory/Intended Model/Putnam/Field: this morality can be strengthened: there is no reason to consider "∈" as fixed! Putnam says that in "Models and Reality": the only thing that could fix the "intended interpretation" would be the acceptance of sentences that contain "∈" through the person or the community. Putnam then extends this to non-mathematical predicates. ((s)> Löwenheim-Skolem). FieldVsPutnam: this is misleading: it is based on the confusion of the view that the reference is determined, E.g. by causal reasoning with the view that it is defined by a description theory (description theory, (labeling theory?), in which descriptions (labels?) that contain the word "cause" should play a prominent role. (> Glymour, 1982, Devitt, 1983, Lewis 1984). |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
| Structuralism | Field Vs Structuralism | II 328 Numbers/Structuralism/Field: it is sometimes expressed in a way that 2 is simply a point in a structure. (Resnik 1981, Shapiro 1989). Vagueness/Field: This view corresponds to the view that vagueness is in the world instead of in our language! ((s)> epistemic view). FieldVs: it seems to work well not only for numbers like "2", but also for the expressions that we use to describe Structures in which there are no symmetries. Symmetry/Field: brings a problem into play here. E.g. Brandom: √-1/Root -1/Complex Numbers/Field: Problem: every complex number other than 0 (Ex -1) has two roots. (actually BrandomVsFrege, BrandomVsLogicism). "Number i": this term has introduced as a standard for one of the two, (-i is then of course the other one). Problem: even if we assume that we have somehow defined which objects are the complex numbers, which subset of them are the real numbers, and which functions of them are addition and multiplication, then our use of these expressions still leaves undetermined to which of the two roots of -1 our expression "i" refers. ((s) Because of the symmetry, it is impossible to make out a difference). Complex Numbers/Interior/Exterior/Theory/Field: within the theory of complex numbers there is no way to distinguish i and -i. There is no predicate A(x) that does not itself contain "i" and that is true of one but not of the other. Complex Numbers/Field: Of course, the practical applications are no help in distinguishing them either!. Problem: even if you say that "i" is simply a point in the system of complex numbers, the indeterminacy continues, because the complex number plane contains two structurally identical positions for the roots of -1, without distinguishing properties. 4) Incompleteness"/Mathematics/Numbers/Field: numbers are more or less incomplete objects: E.g. 2 has properties such as being the predecessor of 3 and being a prime, but no property that determines whether it is a quantity!. FieldVsStructuralism: This fourth way of seeing it is certainly not the best way to capture the "structuralist insight". II 332 Platonism/Mathematics/VsStructuralism/Field: isomorphic mathematical domains must not be indistinguishable. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 |
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The author or concept searched is found in the following theses of the more related field of specialization.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Platonism | Field, Hartry | I 44 To succeed in VsPlatonism, we must also show, thesis: that mathematics is dispensable in science and metalogic. Then we have reason not to literally have to believe in mathematics. (>Indispensability argument). I 45 If that succeeds, we can get behind the agnosticism. I 186 Def moderate platonism/mP/Field: the thesis that there are abstract objects like numbers. Then one probably also believes that there are relations of physical size between objects and numbers. (But only derived): Example "mass in kilogram" is then relation between a given physical object and the real number 15,2. Example "distance in meters" is a relation between two objects ((s) on one side) and the real number 7,4. The difference to high-performance platonism (HPP) lies in the attitude to these relations: Moderate Platonism: Thesis: These are conventional relations derived from more fundamental relations existing between physical objects alone. Def High Performance Platonism/Field: denies that and takes the relations between objects and numbers as a bare fact that cannot be explained in other terms. Inflated one could explain this as "platonistic participation". II 332 Standard Platonism: Thesis: Mathematical theories such as set theory or the theory of real numbers are about different mathematical domains, or at least about certain structures, because there is no need to assume that isomorphic domains (i.e. domains with the same structure) would be mathematically indistinguishable. Thus, "regions" should not be assumed as sets. II 333 Def "Platonism of perfection": (plenitude): postulates a set of mathematical objects. Thesis: Whenever we have a consistent purely mathematical theory, there are mathematical objects that fulfill the theory under a standard-fulfillment relation. Platonism of perfection: but also suggests that we can consider all quantifiers about mathematical entities in this way, I 334 that they are implicitly limited by a predicate to which all other predicates of mathematical entities are subordinated: The "overarching" predicate: is then different between the different mathematical theories. These theories then no longer conflict. II 335 Universe/Standard Platonism/Field: (Thesis: "Only one universe exists"). Problem/PutnamVsPlatonism: how do we even manage to pick out the "full" (comprehensive) universe and confront it with a sub-universe, and accordingly the standard element relationship as opposed to a non-standard element relationship? (Putnam 1980). (Here placed from the perspective of "Universe"). Putnam: Thesis: We simply cannot do that. |
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