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The author or concept searched is found in the following 6 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Calculability | Church | Thiel I 249 Calculability/Church/Thiel: how close did one get to a concept of "general calculability"? There is the concept of "Turing calculability" of "l-definability in Church, the "canonical systems" in Post. Each function, which is in one of these classes, is also demonstrable in the others. Church: Church has then assumed the presumption that an adequate specification of the general concept of calculability is achieved. ("Church thesis"). >"Church-Thesis". But it means that this is an "non-mathematical" presumption, and is not capable of any mathematical proof. An intuitive term. Whether such a specification is "adequate" cannot be answered by mathematical means. >Adequacy. I 250 Apart from finiteness and constructivity, there remain other questions: none of the definitions for the offered functional classes is finite: (e.g. μ-recursive functions). >Recursion, >Finiteness, >Definitions, >Definability. The attempt to describe effective executability with classical means remains questionable, but if we interpret the existence quantifier constructively, we have already presupposed the concept of constructivity. >Existential quantification, >Quantifiers, >Effectiveness. Thiel I 251 Calculability/Herbrand/Thiel: Due to Herbrand's demands, some of the classical laws of logic lose their validity. >J. Herbrand. For example, the end of ~ (x) A (x) to (Ex) ~ A (x) is not permissible: For example, that not all real numbers are algebraic, does not yet help us to a transfinite real number. For example, from the fact that the statements: "The decimal fraction development of pi contains an uninterrupted sequence of 1000 ones" and "The decimal fraction development of pi does not contain an uninterrupted sequence of 100 ones" both cannot be true (since the second statement follows from the first statement), one cannot conclude that the negation of the first statement or the last statement in the parenthesis is true. I 252 This counter-example, however, shows that the classic conclusion of ~ (a u b) to ~ a v ~ b is not permissible if the adjunction sign is to be used for the expression of a decidable alternative. In particular, as can be seen in the substitution of b by ~ a, we cannot conclude from ~ (a u ~ a) to ~ a v ~~ a, although this is a special case of the classical unrestrictedly valid tertium non datur. >Law of the excluded middle, >Logical constants, >Substitutability. |
Chur I A. Church The Calculi of Lambda Conversion. (Am-6)(Annals of Mathematics Studies) Princeton 1985 T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
| Church-Turing Thesis | Lorenzen | Berka I 266 Church thesis/Lorenzen: the thesis is an equation of "constructive" with "recursive". >Constructivism, >Recursion, >Recursivity. LorenzenVsChurch: this is a too narrow view: thus it no longer permits the free use of the quantification over the natural numbers. >Quantification, >Numbers, >Infinity. I 267 Decision-making problem/ChurchVsLorenzen: (according to Lorenzen): Advantage: greater clarity: when limiting to recursive statements, there can never be a dispute as to whether one of the admitted statements is true or false. The definition of recursiveness guarantees precisely the decision-definition, that is, the existence of a decision-making process. >Decidability, >decision problem.(1) 1. P. Lorenzen, Ein dialogisches Konstruktivitätskriterium, in: Infinitistic Methods, (1961), 193-200 |
Lorn I P. Lorenzen Constructive Philosophy Cambridge 1987 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Cognitivism/ Noncognitivism | Searle | ((s) This entry is not about cognitivism in ethics). I 60ff Cognitive Science (computer model of the mind): the relation of the mind to the brain is like that of a program to the hardware. >Computer model. SearleVsCognition: is the brain like a computer? This not the question. The question is: is the mind like a program? No, it is not. Simulation is, however, possible. The mind has an intrinsical mental content and is therefore not a program. I 226 Church Thesis: simulation on a computer is possible if it is divisible into steps. Searle: if the mind were like weather there would be no problem. >">Simulation, >Church thesis. I 242 SearleVsCognitivism: syntax (or 0 and 1) has no causal powers (unlike e.g. viruses, photosynthesis, etc.). People follow rules consciously: that would be a causal explanation. The computer has no intentional causation. I 251/52 VsCognition: cognition has a much too high level of abstraction. The brain does not process information, but carries out chemical processes. Do not confuse the model with reality. >Information processing/Psychology. See also >cognitivism/ethics. |
Searle I John R. Searle The Rediscovery of the Mind, Massachusetts Institute of Technology 1992 German Edition: Die Wiederentdeckung des Geistes Frankfurt 1996 Searle II John R. Searle Intentionality. An essay in the philosophy of mind, Cambridge/MA 1983 German Edition: Intentionalität Frankfurt 1991 Searle III John R. Searle The Construction of Social Reality, New York 1995 German Edition: Die Konstruktion der gesellschaftlichen Wirklichkeit Hamburg 1997 Searle IV John R. Searle Expression and Meaning. Studies in the Theory of Speech Acts, Cambridge/MA 1979 German Edition: Ausdruck und Bedeutung Frankfurt 1982 Searle V John R. Searle Speech Acts, Cambridge/MA 1969 German Edition: Sprechakte Frankfurt 1983 Searle VII John R. Searle Behauptungen und Abweichungen In Linguistik und Philosophie, G. Grewendorf/G. Meggle Frankfurt/M. 1974/1995 Searle VIII John R. Searle Chomskys Revolution in der Linguistik In Linguistik und Philosophie, G. Grewendorf/G. Meggle Frankfurt/M. 1974/1995 Searle IX John R. Searle "Animal Minds", in: Midwest Studies in Philosophy 19 (1994) pp. 206-219 In Der Geist der Tiere, D Perler/M. Wild Frankfurt/M. 2005 |
| Completeness | Lorenzen | Berka I187 Completeness/intuitionistic predicate calculus/Berka: the completeness with regard to the semantics of Kripke and Lorenzen has been proved several times, but always with classical means. Cf. >Kripke Semantics. An intuitionist completeness proof has not yet been found. On the contrary. Kreisel (1962)(2) proved that the intuitionist predicate calculus follows intuitionistically from the intuitionist Church thesis. >Church thesis, >Intuitionism, >Predicate calculus. 2. G. Kreisel. On Weak Completeness of Intuitionistic Predicate Logic. J.Symbolic Logic Volume 27, Issue 2 (1962), 139-158. |
Lorn I P. Lorenzen Constructive Philosophy Cambridge 1987 |
| Computer Model | Searle | I 225ff Church Thesis: computer simulation is possible if it is divisible into steps. Searle: there is no problem if the mind were like weather. >Mind, >Simulation, >Analogy, >Computation, >Computer model, >Brain emulation/Bostrom. |
Searle I John R. Searle The Rediscovery of the Mind, Massachusetts Institute of Technology 1992 German Edition: Die Wiederentdeckung des Geistes Frankfurt 1996 Searle II John R. Searle Intentionality. An essay in the philosophy of mind, Cambridge/MA 1983 German Edition: Intentionalität Frankfurt 1991 Searle III John R. Searle The Construction of Social Reality, New York 1995 German Edition: Die Konstruktion der gesellschaftlichen Wirklichkeit Hamburg 1997 Searle IV John R. Searle Expression and Meaning. Studies in the Theory of Speech Acts, Cambridge/MA 1979 German Edition: Ausdruck und Bedeutung Frankfurt 1982 Searle V John R. Searle Speech Acts, Cambridge/MA 1969 German Edition: Sprechakte Frankfurt 1983 Searle VII John R. Searle Behauptungen und Abweichungen In Linguistik und Philosophie, G. Grewendorf/G. Meggle Frankfurt/M. 1974/1995 Searle VIII John R. Searle Chomskys Revolution in der Linguistik In Linguistik und Philosophie, G. Grewendorf/G. Meggle Frankfurt/M. 1974/1995 Searle IX John R. Searle "Animal Minds", in: Midwest Studies in Philosophy 19 (1994) pp. 206-219 In Der Geist der Tiere, D Perler/M. Wild Frankfurt/M. 2005 |
| Finiteness | Hilbert | Thiel I 245 Finite/Hilbert: in the sense of Hilbert, it is only a question of how statements about infinite objects can be justified by means of "finite" methods. >Infinity, >Circularity, cf. >Recursion, >Recursivity. Hilbert found the finiteness in the "operational" method, especially of the combinatorics, arithmetics, and elemental algebra already exemplarily realized. They were "genetically" (constructively) built up into the second third of the 19th century, while the construction of geometry was a prime example for the axiomatic structure of a discipline. >Constructivism, >Geometry, >Number theory, >Arithmetics, >Axioms, >Axiom systems. I 246 Each finite operation is an area that is manageable for the person who is acting. This area can change during the process. I 247 The fact that the arithmetic functions required for Goedel's proof are even primitively recursive is remarkable in that not all effectively computable functions are primitively recursive, and the primitive recursive functions are a true subclass of the computable functions. >K. Gödel, >Completeness/Gödel, >Incompleteness/Gödel. I 248 An effectively computable, but not primitive, recursive function is e.g. explained by the following scheme for the calculation of their values (not proved) (x 'is the successor of x): ψ(0,n) = n' ψ(m',0) = ψ(m,1) ψ(m',n')= ψ(m,ψ(m',n)). (I 247) If one wants to approach the general concept of comprehensibility, one has to accept the so-called μ operator as a new means of expression. Thiel I 249 Computability/Church/Thiel: how close is this to a concept of "general computability"? There is the concept of "Turing computability", the concept of the "l definability" in Church and the "canonical systems" in Post. >Calculability, >A. Turing, >E. Post. Each function, which is in one of these classes, is also demonstrable in the others. Church has then uttered the presumption that with this an adequate clarification of the general concept of computability is achieved. >Church Thesis. But it means that this is a "non-mathematical" presumption, and is not capable of any mathematical proof. It is an intuitive term: whether such a specification is "adequate" cannot be answered with mathematical means. >Proofs, >Provability, >Adequacy. I 250 Apart from finiteness and constructivity, there remain other questions: none of the definitions for the offered functional classes is finite: e.g. μ-recursive functions. The attempt to describe effective executability with classical means remains questionable, but if we interpret the existence quantifier constructively, we have already assumed the concept of constructivity. >Quantification, >Quantifiers, >Existential quantification. |
T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
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| Church, A. | Lorenzen Vs Church, A. | Berka I 266 Church thesis/Lorenzen: the thesis is an equating of "constructive" with "recursive". (S) so all structures are recursively possible? Or: there is only one recursive structure. (Slightly different meaning). LorenzenVsChurch: view to narrow: it allows no longer the free use of the quantification of the natural numbers. I 267 Decision Problem/ChurchVsLorenzen: (according to Lorenzen): Advantage: greater clarity: when limited to recursive statement forms there can never arise dispute whether one of the approved statements is true or false. The definition of recursivity guarantees precisely the decision definiteness, that means the existence of a decision process.(1) 1. P. Lorenzen, Ein dialogisches Konstruktivitätskriterium, in: Infinitistic Methods, (1961), 193-200 |
Lorn I P. Lorenzen Constructive Philosophy Cambridge 1987 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
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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 |
|---|---|---|---|
| Church-Thesis | Searle, J.R. | I 225 Church Thesis: Simulation on computer possible if divisible into steps - Searle: when the mind is such as the weather, no problem. |
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