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Entailment | Entailment: material relationship between statements, unlike the formal implication. I.e. the content of the partial statements is relevant for the truth value of the composed statement. See also conditional, implication paradox. |
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Implication | Russell | I 15 Implication/Principia Mathematica(1)/Russell: is not a conclusion. I 18 Conclusion: a proposition "p" is claimed, and a proposition "p implies q" is claimed. Then the proposition "q" is claimed as a consequence. >Conclusion, >Inference, >Proposition. I 33 Formal implication/Principia Mathematica/Russell: E.g. "Socrates is a man" implies "Socrates is mortal"- here only the values that make the antecedent true are important. >Antecedent, >make true, >Material conditional. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
Russell I B. Russell/A.N. Whitehead Principia Mathematica Frankfurt 1986 Russell II B. Russell The ABC of Relativity, London 1958, 1969 German Edition: Das ABC der Relativitätstheorie Frankfurt 1989 Russell IV B. Russell The Problems of Philosophy, Oxford 1912 German Edition: Probleme der Philosophie Frankfurt 1967 Russell VI B. Russell "The Philosophy of Logical Atomism", in: B. Russell, Logic and KNowledge, ed. R. Ch. Marsh, London 1956, pp. 200-202 German Edition: Die Philosophie des logischen Atomismus In Eigennamen, U. Wolf (Hg) Frankfurt 1993 Russell VII B. Russell On the Nature of Truth and Falsehood, in: B. Russell, The Problems of Philosophy, Oxford 1912 - Dt. "Wahrheit und Falschheit" In Wahrheitstheorien, G. Skirbekk (Hg) Frankfurt 1996 |
Implication | Wessel | I 124 Subjunction/Wessel .: ">": statement-forming operator, refers to states of affairs. >Operators, >States of affairs. Inference (= implication)/Wessel: 2-digit predicate, relates to linguistic structures. ((s) in "p>q" we do not conclude anything, but take note that a claim exists. Consequence relationship/Wessel: = implication (no operator but predicate). >paradoxes because content can be contradictory, even if the form is valid. Conditional: (E.g. scientific statement) would be false for the same reason (because the content does not form a connection). I 175 Formal implication/Russell/Principia Mathematica(1)/Wessel: "P (x)> x Q(x)": "for all x applies" corresponding "> a1a2a3..an" - binary quantifiers. >Quantifiers, >Quantification. I 297 Conditional/Wessel: subjunction follows from conditional statement - ((s) but not vice versa.) >Conditional. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
Wessel I H. Wessel Logik Berlin 1999 |
Inference | Sellars | Brandom II 76 Material inference/Sellars/Brandom: from a east of b" to "b west of a" - also from lightening to thunder - needs no logic. >Concepts/Sellars, >Consciousness/Sellars. Brandom II 79 Formally valid inferences can be derived from good material inferences, but not vice versa. Proof: given is a subset of somehow privileged vocabulary, so an inference is correct if the material is well and it cannot turn into a poor inference, if non-privileged vocabulary is replaced by non-privileged vocabulary. If one is only interested in logical form, one must be able to distinguish previously a part of the vocabulary as specifically logical. E.g. if you want to examine theological inferences, one must examine which substitution preserves the material quality of the inference when replacing non-theological vocabulary by non-theological. >Vocabulary, >Privileged vocabulary, >Conservativity, cf. >Material implication, >Formal implication. |
Sellars I Wilfrid Sellars The Myth of the Given: Three Lectures on the Philosophy of Mind, University of London 1956 in: H. Feigl/M. Scriven (eds.) Minnesota Studies in the Philosophy of Science 1956 German Edition: Der Empirismus und die Philosophie des Geistes Paderborn 1999 Sellars II Wilfred Sellars Science, Perception, and Reality, London 1963 In Wahrheitstheorien, Gunnar Skirbekk Frankfurt/M. 1977 Bra I R. Brandom Making it exlicit. Reasoning, Representing, and Discursive Commitment, Cambridge/MA 1994 German Edition: Expressive Vernunft Frankfurt 2000 Bra II R. Brandom Articulating reasons. An Introduction to Inferentialism, Cambridge/MA 2001 German Edition: Begründen und Begreifen Frankfurt 2001 |
Praxeology | Rothbard | Rothbard III 73 Praxeology/Rothbard: To sum up the relationship and the distinctions between praxeology and each of the other disciplines, we may describe them as follows: Why man chooses various ends: psychology. What men’s ends should be: philosophy of ethics. also: philosophy of aesthetics. How to use means to arrive at ends: technology. What man’s ends are and have been, and how man has used means in order to attain them: history. The formal implications of the fact that men use means to attain various chosen ends: praxeology. Economics: What is the relationship between praxeology and economic analysis? Economics is a subdivision of praxeology - so far the only fully elaborated subdivision. Logic/Rothbard: The suggestion has been made that, since praxeology and economics are logical chains of reasoning based on a few universally known premises, to be really scientific it should be elaborated according to the symbolic notations of mathematical logic.(1) RothbardVs: This represents a curious misconception of the role of mathematical logic, or “logistics.” In the first place, it is the great quality of verbal propositions that each one is meaningful. ((s) For logical symbols cf. >Connectives/Philosophical theories.) On the other hand, algebraic and logical symbols, as used in logistics, are not in themselves meaningful. Praxeology asserts the action axiom as true, and from this (together with a few empirical axioms—such as the existence of a variety of resources and individuals) are deduced, by the rules of logical inference, all the propositions of economics, each one of which is verbal and meaningful. Rothbard III 306 Praxeology/utility/measuring/Rothbard: The key problem in utility theory, neglected by the mathematical writers, has been the size of the unit. Under the assumption of mathematical continuity, this is not a problem at all; it could hardly be when the mathematically conceived unit is infinitely small and therefore literally sizeless. In a praxeological analysis of human action, however, this becomes a basic question. The relevant size of the unit varies according to the particular situation, and in each of these situations this relevant unit becomes the marginal unit. There is none but a simple ordinal relation among the utilities of the variously sized units. >Utility/Rothbard, >Marginal utility/Rothbard, >Marginal utility/Jevons. Rothbard III 308 The error in reasoning on the basis of "indifference" is the failure to appreciate the fact that a problem important in the field of psychology may have no significance in the realm of praxeology, to which economics belongs. Psychology deals with the problem of how or why the individual forms value scales, and for this question it is relevant to consider whether the individual is decisive or inclined to be "indifferent" between various alternatives. >Indifference curve/Rothbard. Praxeology, however, is a logical science based on the existence of action per se; it is interested in explaining and interpreting real action in its universal sense rather than in its concrete content. Its discussion of value scales is therefore a deduction from the nature of human action and not a speculative essay on the internal workings of the mind. It is consequently irrelevant for praxeology whether a man, in having to decide between alternatives A and B, makes a choice firmly and decisively, or whether he decides by tossing a coin. This is a problem for psychology; praxeology is concerned only with the fact that he chooses (…). Behaviorism/Rothbard: Neither is praxeology based on behaviorist psychology. In fact, in so far as praxeology touches on psychology, its principles are the reverse of those of behaviorism. >Behaviorism/Philosophy. 1. Cf. G.J. Schuller, "Rejoinder," American Economic Review, March, 1951, p. 188. For a reply, see Murray N. Rothbard, "Toward a Reconstruction ofUtility and Welfare Economics" in Mary Sennholz, ed. on Freedom and Free Enterprise: Essays in Honor of Ludwig von Mises (Princeton, N.J.: D. Van Nostrand, 19 5 6), p. 227. Also see Boris Ischboldin, "A Critique of Econometrics," Review ofsocial Economy, September, 1960, pp. 110—27; and Vladimir Niksa, "The Role of Quantitative Thinking in Modern Economic Theory," Review ofSocial Economy, September, 19 59, pp. 151-73. |
Rothbard II Murray N. Rothbard Classical Economics. An Austrian Perspective on the History of Economic Thought. Cheltenham, UK: Edward Elgar Publishing. Cheltenham 1995 Rothbard III Murray N. Rothbard Man, Economy and State with Power and Market. Study Edition Auburn, Alabama 1962, 1970, 2009 Rothbard IV Murray N. Rothbard The Essential von Mises Auburn, Alabama 1988 Rothbard V Murray N. Rothbard Power and Market: Government and the Economy Kansas City 1977 |
Skepticism | Nozick | II 168 Skepticism/Nozick: depends on that we acquire our knowledge indirectly. II 198 Skepticism/Nozick: common form: claiming that someone could believe something even though it is wrong. II 199 Punchline: the truth of Condition (3) "If p would be false, S would not believe it" is compatible with the fact that a person believes p, although p is false. - Justification: condition (3) is not an entailment (Nozick: = formal implication). >Entailment. Condition (3) does not mean that in all situations, where not-p is applied, S does not believe that p. Condition (3) can be true even if there is a possible situation where non-p and S believes that p. >Situations, >Possible worlds. Condition (3) speaks of the situation in which p is false. Not every situation where p is false, is the situation that would prevail if p is wrong. Possible World: condition (3) speaks of the next ~ p-world to our actual world. - It speaks of the not-p-neighborhood. >Actual world, >Most similar world, >Similarity metrics. E.g. Dream, E.g. demon E.g. brains in the tank - but only if p is false: - So only in the next non-p-worlds. Even if we were in the tank, condition (3) could not apply. >Brains in a vat. II 204 Punchline: I do not know that I am not in the vat. - But I know that I write this. Because for this we have a connection, a trace. II 209 Skepticism/NozickVsSkepticism: The skepticism is right that we have no connection to some facts, but it is wrong, that we could not connect to many other facts - including those that imply that we are not brains in a vat, so facts which we believe but do not know. >Belief, >Knowledge. II 242f Skepticism/NozickVsSkepticism/(s): Conclusion: 1. I know that skepticism is wrong. 2. If the skepticism were true, I would not believe that I know much. 3. Because the assertion of skepticism that I do not know much, does not consist in the possibility of confusion with an illusory world, but simply in a world where you do not know much. 4. That I do not know that I am not a brain in a vat, is an isolated special case. 5. Even if I knew very little, I would still know that I am sitting on a chair 6. Even if that would be wrong, it would not follow that I am a brain a vat. |
No I R. Nozick Philosophical Explanations Oxford 1981 No II R., Nozick The Nature of Rationality 1994 |
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Lorenzen, P. | Wessel Vs Lorenzen, P. | I 345/346 Laws/Wessel: always have the logical form of a formal implication (although not all true formal implications are laws) ((x)(P(x) > Q(x)). As conclusions from this alone we never get formulas of the form Q(a), where a is an individual constant. Modality/Lorenzen/Wessel: it is assumed that a certain group of people has accepted a certain system of statements W as true. From these people all statements are then also recognized as true, which logically follow from these statements. Lorenzen regards this as meaningful only for future statements. Knowledge/Lorenzen/Wessel: for Lorenzen it results that everything we know is necessary regarding this knowledge. Tradition: For example if we know that there are five peas in a pea pod and that it contains protein. So only the second is necessary knowledge. According to Lorenzen, both statements are necessary knowledge. (WesselVs). Modality/WesselVsCarnap: too narrow a view. Modality/WesselVsLorenzen: too broad a view. That all knowledge should be necessary is a "fatalistic consequence". I 347 Modality/Wessel: is not a kind of truth value, as is often mistakenly assumed! Carnap: identifies truth and logical necessity, Lukasiewicz: has a third truth value "possible" Lorenzen: uses "possible" and "possibly true" synonymously. WesselVsLorenzen. |
Wessel I H. Wessel Logik Berlin 1999 |
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