Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 10 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Biconditional | Biconditional: notation ↔; a statement that is true if the two sides have the same truth value ("true" or "false"). The biconditional (also bisubjunction) is part of the object language. Contrary to that is equivalence (⇔) which belongs to meta language. A biconditional that is always true is an equivalence. |
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| Conditional | Mates | I 71 Def Inference/Mates: exists when the associated subjunction (Ante/Suc) is valid. >Validity. I 84 Def Inference/Mates: is a statement j of a set G of statements, iff there is no interpretation where all statements of G are true and j is false. >Interpretation. Def Consistent: is a set G of statements if there is an interpretation where no statements of G are true. (Here, consistency = satisfiable) >Consistency, >Contradictions, >Satisfaction, >Satisfiability. Def satisfiability: a set G of statements is satisfiable if there is an interpretation in which all statements of G are true (= consistent). >Truth. Problem: this does not enable us to decide whether a statement is valid, which is an inference, or what a consistent set is. >Decidability/Mates, >Decidability. |
Mate I B. Mates Elementare Logik Göttingen 1969 Mate II B. Mates Skeptical Essays Chicago 1981 |
| Conditional | Wessel | I 124 Entailment/Wessel: = implication (not an operator, but a 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 context). I 138 Logical Entailment/Wessel: statement about the context (of two statements), not about two objects. - in the rules of entailments no semantic terms must occur - tA: "the statement A" (term or name) - I 140 Entailment/Sense/Wessel: If A I- B, then not only with regard to the truth value, but also in terms of sense. - But not merely assertion that "linked by sense". Context is guaranteed by occurrence of the same variables or the "same material of terms and statements. >Content, >Material conditional. I 286 Use/Mention: logical entailment: A I- B: talks about statements (i.e. precisely not content). Conditional: A -> B: talks about content and about what is being talked about in the statements (e.g. current, magnetic field). "A is true" - precisely does not mean "the current flows". I 279 Conditional/Wessel (s): empirical if-then, no logical necessity conditional operator I- not truth-functional. >Operators, >Truth functions. I 283 Conditional/Wessel: e.g. from empirical studies, from statements about entailment, from axioms, from definitions, from other statements according to rules of inference. I 294 Conclusions on the conditional cannot be made from a conjunction (empirical) - E.g. Potsdam >100,000 inhabitants and state capital, i.e. if P >.... false. I 297 Conditional/Wessel: subjunction follows from a conditional statement. - ((s) but not vice versa.) I 308 Existence Load/Wessel: cannot be determined like this in conditionals, because not truth-functional. |
Wessel I H. Wessel Logik Berlin 1999 |
| Correctness | Mates | I 16 Correctness Criterion/Correct/Mates: the criterion needs "true" and "possible": "impossible to reach false conclusion from true premises. >Conditional, >Premises, >Truth, cf. >Validity. I 18 Correctness does not provide any information about the truth value of the conclusion. >Truth values, >Conclusion. I 19 Def correct: is a conclusion if the associated subjunction is analytical. >Subjunction, >Analyticity/Syntheticity. Def analytical: is a statement that cannot be wrong - or if it cannot be the conclusion of an incorrect conclusion. >Conclusion. I.e. a conclusion with mathematical truth as a conclusion cannot be incorrect - Point: this demonstrates that you cannot equate concepts like "correct conclusion" and "proof" - proof requires more. >Proofs, >Provability. I 128 Def correct derivation/Mates: carried out according to rules (to be specified). >Derivation, >Derivability. |
Mate I B. Mates Elementare Logik Göttingen 1969 Mate II B. Mates Skeptical Essays Chicago 1981 |
| Equivalence | Wessel | I 50 Bisubjunction/(biconditional)/Wessel: a biconditional is an operator that makes one formula out of two. >Formulas, >Logical formulas, >Operators. >Contrary to this: Equivalence: an equivalence isno Operator, but a sentence which asserts the equivalence of two formulas. >Assertions, The formulas are not even in the equivalence but quoted: "Formula A" ⇔ "formula B". >Statements, >Mention, >Quotation, >Levels/order. |
Wessel I H. Wessel Logik Berlin 1999 |
| Functional Explanation | Bigelow | I 323 Definition Functional Explanation/Function/Bigelow/Pargetter: with a functional explanation we describe existing patterns by reference to future events or states. It is possible that these may never occur. >Induction. Why: we explain, e.g. why we have teeth by pointing out their function. Problem: to explain the function of causally inactive patterns or elements. I 324 Problem: because the future conditions may not even arise, we do not describe any real properties. Properties/Bigelow/Pargetter: properties of a system are derived from its causal history, not from its function! Therefore, they do not depend on the function of the system! >Properties, >Function. Backward causation/Bigelow/Pargetter: is simply excluded with this. Function/Explanation/Bigelow/Pargetter: therefore, the function of a system is correspondingly redundant. The function can of course be mentioned, but description is more than mentioning possible effects. >Evolution, >Darwinism. Functional Explanation/Science/Bigelow/Pargetter: there are three approaches that we consider to be generally correct. They all have in common that functions have no significant explanatory power. I 325 E.g. Evolution/Bigelow/Pargetter: the theories of functional explanation do not allow to explain evolution by saying that a pattern has formed because it fulfils a certain function. Functional Explanation/Bigelow/Pargetter: Thesis: our theory will be a realistic one. I 332 Functional Explanation/function/Bigelow/Pargetter: thesis: we want a theory that is forward oriented. Functions can and should be explained by reference to future events and states. Analogous to the explanation of dispositions. Analog: our explanation has an analog: the explanation of the evolution-theoretical concept of survival (fitness). (Lit. Pargetter 1987)(1). VsDarwinism/VsDarwin/Bigelow/Pargetter: frequent objection: the "survival of the able" is an empty tautology. >Survival. BigelowVsVs: the objection is based on the assumption that fitness could only be determined retrospectively. He also assumes that the fact that some individuals survive is exactly what constitutes efficiency. (circular). BigelowVsAetiologic theory: is based on the same misunderstanding. It then claims that also the property of having a function is a retrospective property constituted by the history of survival. Thus, the concept of function is deprived of its explanatory potential. I 333 Circularity/Bigelow/Pargetter: this objection is often erroneously raised VsDarwinism. Fitness/solution/Bigelow/Pargetter: however, it is not defined retrospectively, but is analogous to a disposition. Subjunction/subjunctive/conditional/fitness/Bigelow/Pargetter: Fitness is a subjunctive property: it determines what would happen if these or that circumstances were to occur. >Subjunction. This subjunctive property supervenes on the morphological character of the individual or species. There is no circularity. >Supervenience, >Circularity. Biological function/Bigelow/Pargetter: the same applies to them as to fitness. They are two sides of the same coin. Fitness/Bigelow/Pargetter: means looking forward. 1. Pargetter, R. (1987). Fitness. Pacific Philosophical Quarterly 68. pp.44-56. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| 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 |
| Logic | Quine | II 47ff Bivalence: Problem: Sorites. II 53 Bivalence is still a basic feature of our scientific world. - In the liberal sense there is no problem - Frege: each general term is true or not - all terms are vague by ostension. >Sorites. II 168 Logic, old: deals with properties - new: with relations - Quine: feels implications. II 169 Logic, old: failed with relative terms: drawing figures/drawing circles (Carroll) - new: no problem with that: implication lies precisely in the relative term. II 173 Existence: "all x are y" controversy: does this imply the existence of "x"? medieval logic: yes - Modern Times: No (thus gains in symmetry and simplicity). --- VII (e) 82 Logic/Quine: triple: propositions - classes - relations - logical terms: we only need three "ε" ("element of") - Sheffer stroke and universal quantifier. --- VII (f) 119 ff Class logic/Quine: emerges from quantifier logic if we bind scheme letters (predicate letters) "F" etc. - ((s) 2nd order Logic ). --- IX 8 Logic/Quine: main task: to prove the validity of schemes - 2nd order logic: this is about the validity of the formula schemes of quantifier logic - E.g. substitutability of bi-subjunction: "x1 ..." xn[((AB) and CA) > CB]. --- X 110 Logic/Quine: if you determine the totality of logical truths, you have established the logic. X 110 Different logic/Quine: there is no differing procedure of taking evidence, but rejection of part of the logic as untrue. X 111 "Everything could be different"/translation/different logic/interchanging/and/or/key position/ Gavagai/Quine: assuming a heterodox logic, in which the laws of the adjunction now apply to the conjunction, and vice versa - there is a mere change of phonetics or the designation. - ((s) If he says adjunction, he uses our conjunction.) - Quine: we force our logic on him by translating his different way of expressing himself. It is pointless to ask which one is the right conjunction. - There is also no essence of the conjunction beyond the sounds and signs and the laws for its use. >Gavagai/Quine, >Connectives/Quine, >Schmatic Letters/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 |
| Operators | Wessel | I 1 logical operators/Wessel: e.g. and, not, or, all, some, "the fact that", "the non-fact that". >Connectives, >Logical constants. Terms/Wessel: e.g "the fact that metals conduct electricity ’"H2O", "brother and sister", "divisible by three" ... No terms are: and, all, in, or, "the earth revolves around the sun". I 131 Operator/Wessel: must not occur more than once in provable formulas of propositional logic. >Propositional logic, >Proofs, >Provability, >Logical formulas. ((s)Operator/(s): (e.g. subjunction) does not lead to paradoxes, because it is not "predicated of something" like predicates (implication). ((s) Operator / (s): rather purely formal - in contrast: predicate: content). >Predicates, >Predication. |
Wessel I H. Wessel Logik Berlin 1999 |
| Universal Quantification | Millikan | I 232 All/negation/"not all"/Millikan: the "not" in "not all A are φ" is not immunizing. If it were, then the fact that e.g. "All Blubbs are gull" is meaningless and would entail that "not all Blubbs are gull" would be true. So: from the fact that "not all unicorns are white" is not true, should not follow that "all unicorns are white" is true. Solution: if the word "unicorn" has no meaning (no mapping rule, not to be confused with intension, which the word has very well) then the sentence "All unicorns are white" should also have no meaning! Representation/non-existence: in a representative sentence, "All A's are φ" should never be true if there are no A's. Universal Quantification/Existential Quantification/Millikan: "All A's are φ" would always imply "Some A's are φ". ((s) For representative sentences). Representation/all/Millikan: but is it such that such sentences with "all" always represent? E.g. "Painfully disappointed, Johnny never returned", e.g. "the boy who delivers the newspaper is not very tall": Here "not" does not operate above the logical predicate that is contained in the grammatical subject. Suppose, it would also be like this in "All A's are φ". "Not all A's are φ" is equivalent to "Some A are not-φ". So if there is any positive sentence embedded here, then it should also be embedded in the grammatical subject "All A's" E.g. "All red cows are friendly": becomes "Not all red cows are friendly". What is equivalent to... I 233 ..."Some red cows are not friendly". The grammatical subject contains an embedded sentence here ""Some" cows are red". And that must also have embedded the original sentence! So if "All A's are f" implies "Some are ..." then the way "not" works here is perfectly compatible with the way it works on other representative sentences and does not need any special comment. Representation/Millikan: Question: are such sentences representations then? Often yes, but sometimes not! Stabilization function: what could be the stabilization function of "All A's are φ"? It must at least be that a disposition is evoked in the listener to produce certain types of inferences. For example, from "x is an A" to "x is φ" and from "x is not φ" to "x is not A". And from "no B is φ" to "no B is an A". >Terminology/Millikan. Problem: beyond these elementary functions the functions of "All A's are φ" seem to be separated. A) Nominal use/all/Millikan: licensed here "All A's are f" is a subjunction (subjunctive inference) of this type: E.g. "Suppose x is an A, then x would be φ" and B) "Suppose x should not be φ, then x would better be not an A". Representation: E.g.: "All students who cheat are exmatriculated". Now everyone is so frightened that no one cheats at all. That is, the students are adapted to this world, simply by the fact that the sentence produces dispositions to inferences which map dispositions in this world. Intentional Icons: one might think that the dispositions are correct intentional icons because they map potential dispositions. I 234 MillikanVs: but the use is not representative here, but rather nomical! Here nothing has to be mapped so that the eigenfunction is fulfilled, but a disposition is produced. ((s) The disposition is not mapped). Nomical use/"not"/Millikan: nomical use, however, is very special and always must be marked somehow. Here, e.g. through the use of the future tense. There remain two questions regarding "all": 1. Why are we tempted to believe that "all A are φ" is true, not despite, but precisely because of the fact that there are no A's? E.g. "All day-active bats are herbivores" is true, because there are no day-active bats. 2. How do sentences of the form "All A are φ" map the world at all? If we consider here only the normal and the nominal use, there is no common explanation, only a jointly focused eigenfunction. Namely, a disposition to produce inferences. If there are no A's, it is not a problem to conclude the disposition from A to φ is simply not activated. Also, the inferences from "x is not " to "x is not an A" and... I 235 ...from "no B is φ" to "no B is an A" become true. (Here, however, A must have a meaning, that is to say, in this case, a complex term.) E.g. "All bad apples have been removed from the basket". Here one can conclude that only good apples are in the basket. Whether bad apples have been in it before, does not have any consequences. |
Millikan I R. G. Millikan Language, Thought, and Other Biological Categories: New Foundations for Realism Cambridge 1987 Millikan II Ruth Millikan "Varieties of Purposive Behavior", in: Anthropomorphism, Anecdotes, and Animals, R. W. Mitchell, N. S. Thomspon and H. L. Miles (Eds.) Albany 1997, pp. 189-1967 In Der Geist der Tiere, D Perler/M. Wild Frankfurt/M. 2005 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Aristotle | Nozick Vs Aristotle | II 145 Relation/Law/Incident/Language/Interpretation/Nozick: Wittgenstein needed people to teach the language with its instances. Nozick: but it cannot be people who teach a natural law with its instances. Causal laws also apply for people, inter alia, and were valid before people existed. The consent of people to something depends on causality and cannot determine causality itself. (FN 22). Law/Nozick: therefore seems to have no own ontological status, because it cannot reach for incidents itself. Nevertheless, if a natural law only determines a pattern, it is merely descriptive. Without ontological status it cannot support counterfactual conditionals beyond actual events and how could laws then be used to explain something? Explanation/Nozick: how does a higher level pattern explain a lower level one? Is every explanation implicitly only a repetition? Explanation/Law/NozickVsAristotle: explanatory laws need not be necessary truths, but do they need to be anything at all? If events proceed according to laws, what is the connection between the event and the law? It can of course not be causal. ((s) recourse). But even any logical connection must be interpreted in turn. Can a lawlike statement interpret itself? I.e. can a law give instructions for the interpretation? Problem: these instructions would have to be interpreted again II 146 If the interpretation was to be fixed, the law would have to include something analogous to reflexive self-reference. This itself is mysterious. Hence, we must not treat laws as related to statements. Gödel: there is no formal system in which all the truths of number theory can be proved. Nozick: that is bad luck for a picture of all the facts from which the statements of fact can be completely derived. Determinism/Nozick: should therefore not rely on derivability from causal laws! (FN 23). NozickVsDeterminism: claims: if the initial state was repeated, the later states would also repeat themselves. Problem: in a re-collapsing universe other laws could apply for another big bang. I.e. the subjunctivist conditional, (subjunction = counterfactual conditional, unlike implication (metalinguistical)) on which determinism is based would be wrong. |
No I R. Nozick Philosophical Explanations Oxford 1981 No II R., Nozick The Nature of Rationality 1994 |
| Intuitionism | Wessel Vs Intuitionism | I 239 WesselVsIntuitionism: the limitation of negation to a specific field destroys logic as an independent science. But this can be solved in a universal system of rules. (see below). I 269 WesselVsIntuitionism: Main defect: that the universal character of logic is denied. Different logics for finite and infinite domains. Also the representatives of microphysics (quantum mechanics) propagate different domain logics. I 270 Wessel: this has to do with a wrong understanding of the object of logic: Logic/Wessel: a special science that investigates the properties of the rules of language. Science: Understands by the object of logic (erroneously) any extra-linguistic object (e.g. quantum, elementary particle, etc.). WesselVs: Dilemma: that this considered object is not directly given to the view, it must be constructed linguistically. But for this you need logic, circular. Negation/Intuitionism/Wessel: the intuitionists reject the negation of the classical calculus, but they should apply (our) non-traditional predication theory, which already takes into account the problem of undecidability. For example, the question whether a certain sequence of numbers occurs at some point in the development of the number π: here there are three possibilities: 1. it can occur (A) 2. it cannot occur (B) 3. it is impossible to determine (C) Suppose someone claims A, then two different negations are possible: 1. the assertion of B 2. the explanation that it is not right. Negation/WesselVsIntuitionism: confuses two different types of negation: the propositional (outer) and the negation in the operator of awarding predicates ( I 271 Intuitionists/Logic/Wessel: accepts, like most classic logicians, the bisubjunction ~(s< P) ↔ (s We now compare some formulas, using the character combinations that are actually meaningless: -i p, ?p etc. -i p: shall be ~(s <--) u ~( I 272 In the class logic the de Morgan laws apply, the IntuitionismVsDe Morgan: Vs 3. and 4. law . 3. ~(p u q) > ~p v ~q 4 ~(~p v ~q) > p u q. Intuitionism/Wessel: is a hidden epistemic logic: "It is provable that p is provable or that ~p is provable". WesselVs: but first you have to have logical basic systems that are not dependent on empiricism! Epistemic predicates ("provable") must not be confused with logical operators! The classic paradoxes occur for the most part also in intuitionistic logic. I 273 There is evidence to show that there must be a number, but not the number itself! Example + One need not be a follower of intuitionism to prefer evidence that constructively provide the number. I 274 MT5. There is a group of formulae provable in the IPC (intuitionist propositional calculus) for which the following applies: some of their P-R are provable in PT and others are not...e.g. p > ~p > ~p p > ~q > (q > _p) ++ I 275 MT6. There is a group of formulas that can be proven in the IPC (intuitionist propositional calculus) to which applies; all their P-R are not provable in PT. E.g. ~(p v q) > ~p u ~q, ~~(p u ~p) WesselVsIntuitionism: MT5 and MT6 show that the intuitionists are inconsistent: if they identify s |
Wessel I H. Wessel Logik Berlin 1999 |
| Leibniz, G.W. | Wessel Vs Leibniz, G.W. | I 221 Def Identity/Leibniz: match in all properties (traced back to Aristotle). Identity/WesselVsLeibniz: inappropriate because it suggests searching for two objects to compare and verify properties. In modern mathematics, the problem is circumvented by specifying a fixed range with precisely defined predicates. In an attempt to apply Leibniz's definition to empiricism, an attempt was made to establish the identity relation directly ontologically, without seeing its origin in the properties of language. Wrong approach: in the relative temporal stability of objects: Dilemma: from a = a results not much more than "Socrates is Socrates". Problem: one must then demand that Socrates must have had the same qualities at all times of his life. In fact, some authors have linked the negation of the possibility of change to it. I 228 Def Diversity/Leibniz: "which is not the same or where the substitution sometimes does not apply". Identity/Leibniz: substitutability salva veritate. x = y = def AP(P(x) ↔ P(y)). (s) All properties of one are also those of the other and vice versa). WesselVsLeibniz: the corresponding bisubjunction (= without def) is existentially loaded and therefore not logically true. Identity/PeirceVsLeibniz: "his principle is completely nonsense. No doubt all things are different from each other, but there is no logical necessity for that". Identity/Peirce: x = y ↔ AP(P(x) u P(y) v ~P(x) u ~P(y)) WesselVsPeirce: this is also existentially charged! Identity/Indistinguishability/Wessel: in literature there is a distinction between the principle of the identity of the indistinguishable. (x)(y)AP((P(x) ↔ P(y)) > x = y) (e) and the principle of indistinguishability of the identical (also substitution principle): (x)(y)(x = y > AP(P(x) ↔ P(y))) (n) Identity/Vagueness/WesselVsLeibniz: in vagueness the Leibniz's principle of the identity of the indistinguishable does not apply, since in non-traditional predication theory the formulae P(x) ↔ P(y) and -i P(x) ↔ -i P(y) are not equivalent. Additional demand (Wessel 1987; 1988): the same predicates must also be denied! strict identity: x = y =def AP((P(x) ↔ P(y)) u (-i P(x) ↔ -i P(y))). WesselVsWessel: but this cannot be maintained, because the corresponding bisubjunction is existentially loaded! I 229 In term theory, we will define identity with the help of the term relation. |
Wessel I H. Wessel Logik Berlin 1999 |
| Russell, B. | Wessel Vs Russell, B. | I 14 Ontology/Logic/Psychology/RussellVsLaws of Thought: it is not important that we think in accordance with laws of thought, but that the behavior of things corresponds to them. Russell: what we believe when we believe in the sentence of contradiction is not that our consciousness is constructed this way. We do not believe, for example, that we cannot think at the same time that a tree is a beech and not a beech either. We believe that if the tree is a beech, it cannot be not a beech at the same time. I 15 And even if belief in the sentence of contradiction is a thought, the sentence of contradiction itself is not a thought, but a fact concerning the things of the outside world. If what we believe would not apply to the things of the outside world, then the fact that we are forced to think like this would not guarantee that the sentence of contradiction cannot be wrong (this shows that it cannot be a law of thought). WesselVsRussell: logical laws do not concern the outside world! They do not give us any information about the outside world. The validity results only from the determination of the use of the signs! Of course, such phrases can also be formulated ontologically, but they are not ontological statements. Where else would we have the certainty that they are unrestrictedly valid? We cannot search the world endlessly. I 123 Subjunction/Material Implication/Frege/Wessel: Frege calls it "conditionality". I 123/124 Difference: between the subjunction A > B and a logical conclusion in which the only conclusion rule accepted by Frege is to conclude from A > B and A to B. ((s) modus ponens). Russell/Whitehead/Principia Mathematica(1): took over from Frege. "Essential property" of the implication: what is implied by a true statement is true. Through this property, an implication provides evidence. Def Implication/Russell/Principia Mathematica(1): p > q = def ~ p v q.(Materials Implication). WesselVsRussell: this is just inappropriate and misleading! It is purely formal! Implication/Conclusion/Wessel: the implication has a completely different logical structure than the consequence: Subjunction: > is a two-digit proposition-forming operator and p > q is synonymous with ~p v q. Conclusion (implication): "q follows logically p" or "P implies q" is a statement about statements: "From the statement p follows logically the statement q". "Follows from" is a two-digit predicate - not an operator. Conclusion (also called implication) refers to linguistic structures. Notation l-. Subjunction: > refers to facts. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
Wessel I H. Wessel Logik Berlin 1999 |
| Skepticism | Nozick Vs Skepticism | II 197 Skepticism/Nozick: we do not try to refute the skeptic. VsSkepticism: other authors: 1) when he argues against knowledge, he already presupposes that it exists. 2) to accept it would be unreasonable, because it is more likely that his extreme conclusions are wrong than that all its premises are true. NozickVs. We do not have to convince the skeptic. We want to explain how knowledge is possible, therefore it is good to find hypotheses which we ourselves find acceptable! II 198 Skepticism/Nozick: Common Variant: claims that someone could believe something even though it is wrong. Perhaps caused by a demon or because he is dreaming or because he is a brain in a vat. But how do these possibilities adopted by the skeptic show that I do not know p? (3) if p were false, S would not believe that p (as above). If (3) is a necessary condition for knowledge that shows the possibility of the skeptic that there is no knowledge. Strong variant: R: Even if p were false, S would still believe that p II 199 This conditional with the same antecedent as (3) and contradictory consequent is incompatible with (3). If (3) is true, R is false. But R is stronger than skepticism requires. Because if (3) were wrong, S could still believe that p. The following conditional is weaker than R, it is merely the negation of (3): T: Not (not p > not (S believes that p)). ((s) >Range: weaker: negation of the entire conditional stronger: the same antecedent, opposite of the consequent ((s) not necessarily negation of consequent) Here: stronger: ".... would have to believe ..." - weaker.. "... could ...") Nozick: While R does not simply deny (3), it asserts its own conditional instead. The truth of (3) is not incompatible with a possible situation (here not possible world) where the person believes p, although p is false. (3) does not cover all possibilities: (3) not p > not (S believes p) That does not mean that in all situations where not p is true, S does not believe that p. Asserting this would mean to say that not p entails not (S believes p) (or logical implication) ((s) >Entailment). But subjunction (conditional) differs from entailment: So the existence of a possible situation in which p is wrong and S still believes p does not show that (3) is false. (? LL). (3) can be true even if there is a possible situation where not p and S believes that p. (3) speaks of the situation in which p is false. Not every possible situation where p is false is the situation that would prevail if p were false. Possible World: (3) speaks of the ~p world closest to our actual world. It speaks of the non-p neighborhood. Skepticism/SK/Terminology/Nozick: SK stands for the "possibilities of the skeptic": II 200 We could dream of being misled by an evil demon or being brains in a vat. These are attempts to refute (3): (3) if p were false, S would not believe that p. But these only attempts succeed if one of these possibilities(dream, vat, demon) prevails when p is false. I.e. only in the next non-p worlds. Even if we were in the vat, (3) could be true, i.e. although - as described by skeptics - p is false and S believes p. ((s) E.g. p: "I am in the Café": false, if I'm in the vat. But I would not believe to be the vat. That is what the skeptic means. If I do not believe the truth (that I am in the vat) and do not know, then my belief is wrong. But then p means "I'm not in the vat."). NozickVsSkepticism: when the skeptic describes a situation SK that would not prevail (sic), even if p were wrong, then this situation SK (vat) does not show that (3) is wrong and does not undermine our knowledge. (see below) ((s) i.e. from the perspective VsSkepticism: the skeptic asserts that all beliefs are wrong, but that is not yet the situation that we are all in the tank). This is just the preliminary consideration, the expected one follows in the next paragraph). Condition C: to exclude skeptical hypothesis: C: not-p > SK (vat situation) does not exist ((s) That is what the skeptic denies!). That excludes every skeptical situation that fulfills C. ((s) it is only about n-p cases). Skepticism: for a vat situation to show that we do not know that p, it must be a situation that could exist if p did not exist, and thus satisfies the negation of C: Negation of C: -not (not p > SK (vat situation) does not exist) Although the vat situations of the skeptic seem to show that (3) is wrong, they do not show it: they satisfy condition C and are therefore excluded! SkepticismVs: could ask why we know that if p were wrong, SK (vat) would not exist. But usually it asks something stronger: do we know that the vat situation does not exist? And if we do not know that, how can we know that p? ((s) reverse order). This brings us to the second way in which the vat situatios could show that we do not know that p: Skeptical results Knowledge/Nozick: according to our approach, S knows that the vat situation does not exist iff II 201 (1) vat situation does not exist (2) S believes that vat situation does not exist (3) If the vat situation existed, then S would not believe that the vat situation did not(!) exist. (4) If the vat situation did not exist, then S would believe that it does not exist. (3) is the necessary condition for knowledge! It follows from it that we do not know that we are not in the vat! Skepticism/Nozick: that is what the skeptic says. But is it not what we say ourselves? It is actually a feature of our approach that it provides this result! Vat/Demon/Descartes/Nozick: Descartes would say that proof of the existence of a good God would not allow us to be in the vat. Literature then focused on whether Descartes would succeed to obtain such evidence. II 202 Nozick: could a good God not have reasons to deceive us? According to Descartes his motives are unknowable for us. Cogito/Nozick: can "I think" only be produced by something existing? Not perhaps also by Hamlet, could we not be dreamed by someone who inspires "I think" in us? Descartes asked how we knew that we were not dreaming, he could also have asked whether we were dreamed about by someone. Def Doxastically Identical/Terminology/Nozick: is a possible situation for S with the current situation, if S believed exactly the same things (Doxa) in the situation. II 203 Skepticism: describes doxastically identical situations where nearly all the believed things are wrong. (Vat). Such possible worlds are possible, because we possess our knowledge through mediation, not directly. It's amazing how different doxastically identical worlds can be. What else could the skeptic hope for? Nozick pro skepticism: we agree that we do not know that "not-vat". II 204 But that does not keep me from knowing that I'm writing this! It is true, I believe it and I would not believe it if it were not true, and if it were true, I would believe it. I.e. our approach does not lead to general skepticism. However, we must ensure that it seems that the skeptic is right and that we do not know that we are not in the vat. VsSkepticism: we must examine its "short step" to the conclusion that we do not know these things, because either this step is wrong or our approach is incoherent. Not seclusion II 204 Completed/Incompleteness/Knowledge/Nozick: Skepticism: (wrongly) assumes that our knowledge is complete under known logical implication: if we progress from something known to something entailed, we allegedly do not leave the realm of knowledge. The skeptic tries the other way around, of course: if you do not know that q, and you know that p entails q, then it should follow that you do not know that p. E.g. ((s) If you do not know that you are not in the vat, and sitting here implies not being in the vat, then you do not know that you're sitting here, if you know that the implication exists. (contraposition).) Terminology: Contraposition: knowledge that p >>: entails Then the (skeptical) principle of closure under known implication is: P: K(p >> q) & Kp > Kq. II 205 Nozick: E.g. if you know that two sentences are incompatible, and you know that the first one is true, then you know that the negation of the second one is true. Contraposition: because you do not know the second one, you do not know the first. (FN 48) Vs: you could pick on the details and come to an iteration: the person might have forgotten inferences etc. Finally you would come to KK(p >> q) & KKp Kq: amplifies the antecedent and is therefore not favorable for the skeptics. II 206 NozickVsSkepticism: the whole principle P is false. Not only in detail. Knowledge is not closed under known logical implication. (FN 49) S knows that p if it has a true belief and fulfills (3) and (4). (3) and (4) are themselves not closed under known implication. (3) if p were false, S would not believe that p. If S knows that p, then the belief is that p contingent on the truth of p. And that is described by (3). Now it may be that p implies q (and S knows that), that he also believes that q, but this belief that q is not subjunktivically dependent on the truth of q. Then he does not fulfill (3') if q were wrong, S would not believe q. The situation where q is wrong could be quite different from the one where p is wrong. E.g. the fact that they were born in a certain city implies that they were born on the earth, but not vice versa. II 207 And pondering the respective situations would also be very different. Thus the belief would also be very different. Stronger/Weaker: if p implies q (and not vice versa), then not-q (negation of consequent) is much stronger than not-p (negation of the antecedent). Assuming various strengths there is no reason to assume that the belief would be the same in both situations. (Doxastically identical). Not even would the beliefs in one be a proper subset of the other! E.g. p = I'm awake and sitting on a chair in Jerusalem q = I'm not in the vat. The first entails the second. p entails q. And I know that. If p were wrong, I could be standing or lying in the same city or in a nearby one. ((s) There are more ways you can be outside of a vat than there are ways you can be inside). If q were wrong, I would have to be in a vat. These are clearly two different situations, which should make a big difference in what I believe. If p were wrong, I would not believe that p. If q were wrong, I would nevertheless still believe that q! Even though I know that p implies q. The reason is that (3) is not closed under known implication. It may be that (3) is true of one statement, but not of another, which is implied by it. If p entails q and we truthfully believe that p, then we do not have a false belief that q. II 208 Knowledge: if you know something, you cannot a have false belief about it. Nevertheless, although p implies q, we can have a false belief that q (not in vat)! "Would not falsely believe that" is in fact not completed under known implication either. If knowledge were merely true belief, it would be closed under implication. (Assuming that both statements are believed). Because knowledge is more than belief, we need additional conditions of which at least one must be open (not completed) under implication. Knowledge: a belief is only knowledge when it covaries with the fact. (see above). Problem: This does not yet ensure the correct type of connection. Anyway, it depends on what happens in situations where p is false. Truth: is what remains under implication. But a condition that does not mention the possible falseness, does not provide us covariance. Belief: a belief that covaries with the facts is not complete. II 209 Knowledge: and because knowledge involves such a belief, it is not completed, either. NozickVsSkepticism: he cannot simply deny this, because his argument that we do not know that we are not in the vat uses the fact that knowledge needs the covariance. But he is in contradiction, because another part of his argument uses the assumption that there is no covariance! According to this second part he concludes that you know nothing at all if you do not know that they are not in the vat. But this completion can only exist if the variation (covariance) does not exist. Knowledge/Nozick: is an actual relation that includes a connection (tracking, traceable track). And the track to p is different from that to q! Even if p implies q. NozickVsSkepticism: skepticism is right in that we have no connections to some certain truths (we are not in the vat), but he is wrong in that we are not in the correct relation to many other facts (truths). Including such that imply the former (unconnected) truth that we believe, but do not know. Skepticism/Nozick: many skeptics profess that they cannot maintain their position, except in situations where they rationally infer. E.g. Hume: II 210 Hume: after having spent three or four hours with my friends, my studies appear to me cold and ridiculous. Skepticism/Nozick: the arguments of the skeptic show (but they also show only) that we do not know that we are not in the vat. He is right in that we are not in connection with a fact here. NozickVsSkepticism: it does not show that we do not know other facts (including those that imply "not vat"). II 211 We have a connection to these other facts (e.g. I'm sittin here, reading). II 224f Method/Knowledge/Covariance/Nozick: I do not live in a world where pain behavior e is given and must be kept constant! - I.e. I can know h on the basis of e, which is variable! - And because it does not vary, it shows me that h ("he is in pain") is true. VsSkepticism: in reality it is not a question that is h not known, but "not (e and not h)" II 247 NozickVsSkepticism: there is a limit for the iteration of the knowledge operator K. "knowing knowledge" is sometimes interpreted as certainly knowing, but that is not meant here. Point: Suppose a person knows exactly that they are located on the 3rd level of knowledge: K³p (= KKKp), but not k4p. Suppose also that the person knows that they are not located on the 4th level. KK³p & not k4p. But KK³p is precisely k4p which has already been presumed as wrong! Therefore, it should be expected that if we are on a finite level Knp, we do not know exactly at what level we are. |
No II R., Nozick The Nature of Rationality 1994 |
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