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Canonicalness | Bigelow | I 137 Canonical models/Bigelow/Pargetter: deal with maximally consistent sets of sentences to provide completeness proofs. >Models, >Completeness, >Proofs, >Provability. Canonical models were discovered only after Hughes/Cresswell 1968(1), they were described in the later work (Hughes/Cresswell 1984)(2). Definition completeness theorem/Bigelow/Pargetter: is a theorem that proves that if a proposition in a certain semantics is guaranteed true this proposition can be proved as a theorem. How can we prove this? How can we prove that each such proposition is a theorem? Solution: we prove the contraposition of the theorem: Instead: If a is assuredly true in semantics, a is a theorem We prove If a is not a theorem, it is not assuredly true in semantics. >Semantics. Then we prove this by finding an interpretation according to which it is false. >Interpretation, >Valuation. Def canonical model/Bigelow/Pargetter: provides an interpretation which guarantees that every non-theorem is made wrong in at least one possible world. >Possible worlds. I 138 We begin that there will be a sentence a, for which either a or ~a is a theorem. This can be added to the axioms to give another consistent set of sentences. Maximum consistent set of sentences/Bigelow/Pargetter: it can be proved that for the axiom systems which we deal with, there is always a maximally consistent set of sentences. >Maximum consistent. That is, a consistent set of sentences to which no further sentence can be added without making the set inconsistent. That is, for each sentence g is either γ in the set or ~ γ. W: be the set of all maximally consistent extensions of the axiom system with which we have begun. >Expansion. 1. Hughes, G. E. and Cresswell, M.C. (1968) An introduction to modal logic. London: Methuen. 2. Hughes, G. E. and Cresswell, M.C. (1984) A companion to modal logic. London: Methuen. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
Completeness | Bigelow | I 134 Completeness/Bigelow/Pargetter: completeness occurs when our explicit semantics guarantees all and only the extroverted asserted theorems. That is, our semantics does not read anything into our language, which is not already there. >Semantics/Bigelow. Def "extroverted axiomatics"/Terminology/Bigelow/Pargetter: an axiomatics that is developed in an already existing language. >Axioms, >Axiom systems. I 135 Completeness/correspondence theory/Bigelow/Pargetter: the existence of completeness proofs provides a kind of correspondence theory. >Correspondence theory, >Proofs, >Provability. Completeness: for us, we can show that all the propositions that are true to our semantics in all possible worlds can be derived. >Derivation, >Derivability, >Possible worlds. I 137 Def completeness theorem/Bigelow/Pargetter: is a theorem that proves that if a proposition in a certain semantics is assuredly true, this proposition can be proved as a theorem. How can we prove this? How can we prove that each such proposition is a theorem? Solution: we prove the contraposition of the theorem: Instead: If a is assuredly true in semantics, a is a theorem. We prove: If a is not a theorem, it is not assuredly true in semantics. We prove this by finding an interpretation according to which it is false. >Falsification, >Verification, >Verifiability. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
Conditional | Fraassen | I 118 Conditional/truth value/Fraassen: the truth value of the conditional is partly context-dependent. >Truth values, >Context. But science does not imply that the context is either way somehow - therefore science implies counterfactual conditionals at most in the limiting case where a conditional has the same truth value in all contexts - in this case the theory plus antecedent (conditions) strictly implies the consequent. Then also the laws of attenuation and contraposition apply - but then they are useless for our task to provide an explanation. >Explanations. |
Fr I B. van Fraassen The Scientific Image Oxford 1980 |
Explanation | Schurz | I 30 Explanation/Schurz: Explanation concerns only facts that have already occurred. Otherwise it refers to a prediction. Both have the form of deductive or probabilistic arguments. >Facts, >States of affairs, >Prediction, >Probability, >Deduction. I 92 Notation: II- : "follows logically". Explanation scheme/logical form/explanation/Schurz: strict all proposition & singular proposition II- singular proposition. All A are K and a is A II- a is K. Falsification scheme/falsification/logical form/Schurz: FS I: singular proposition falsifies strict universal sentence. singular sentence II- negation of strict universal sentence a is A and not K II- not all A are K FS II: existence sentence falsifies strict all proposition There is an A that is not a K II- not all A are K. >Universal sentence. I 225 Explanation/law/Schurz: More important than explanation of events is explanation of laws by higher-level theories. Problem: irrelevance and redundancy. Therefore Hempel considered laws only implicitly. Logical form: "T U A / G" (U: union). T: is a set of laws or axioms of theories, all of which are essentially quantified and some of which are essentially general. A: (antecedent) is a (possibly empty) set of sing propositions or localized existential propositions. G: an essentially general proposition. Ex Theoretical explanation of planetary orbits Ex Theoretical explanation of Piaget's law of development. I 227 Causality/explanation/causal explanation/Schurz: problem: Ex "If A, then E will be the case": is L equivalent with its contraposition. "If Not E, then Not A was the case". Problem: "Not E" cannot be a cause of Not A! >Causal explanation/Schurz. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
Imagination | Nagel | I 82ff Of course, we can be wrong in some of our judgments about what is inconceivable and what is not. It is possible that a statement whose falsity we could not imagine still may be untrue. Mere external information about how we got there to hold the statement to be true is not enough. We may also have imagined something right, but later find out that we have described our actions incorrectly. I 87ff Imagination: not even temporarily can we "bracket" the basic thought that the contraposition is valid and replace it with the purely psychological observation that we consider the falsity of this statement unimaginable (DescartesVs). I 88 NagelVsDescartes: demon: the idea of confused thoughts also contains the disentangled thought. >Descartes. |
NagE I E. Nagel The Structure of Science: Problems in the Logic of Scientific Explanation Cambridge, MA 1979 Nagel I Th. Nagel The Last Word, New York/Oxford 1997 German Edition: Das letzte Wort Stuttgart 1999 Nagel II Thomas Nagel What Does It All Mean? Oxford 1987 German Edition: Was bedeutet das alles? Stuttgart 1990 Nagel III Thomas Nagel The Limits of Objectivity. The Tanner Lecture on Human Values, in: The Tanner Lectures on Human Values 1980 Vol. I (ed) St. M. McMurrin, Salt Lake City 1980 German Edition: Die Grenzen der Objektivität Stuttgart 1991 NagelEr I Ernest Nagel Teleology Revisited and Other Essays in the Philosophy and History of Science New York 1982 |
Lawlikeness | Schurz | I 237 Laws of nature/natural laws/Schurz: Laws of nature do not refer to specific physical systems but express what is valid for any systems in all physically possible universes. E.g. Newton's nuclear axioms (E.g. total force = mass times acceleration, E.g. force = counterforce, E.g. gravitational force is proportional to the product of masses). Only if they are used system conditions, which explicitly list the present forces, we get a concretely solvable differential equation. There are only a few fundamental ones and they are found only in physics. However, most of the laws of physics are: Def system laws/Schurz: involve concrete contingent system conditions. Therefore they are not physically necessary but contingent. Example law of fall, example law of pendulum, example law of planets etc. Law-likeness/law-like/Schurz: a) in the broad sense: the law-like character of spatiotemporally limited general propositions is gradual. In this sense not only the laws of nature but also all system laws are law-like. Counterfactual conditionals: if we would agree to them are an indication of law-likeness. Problem: the counterfactual conditional also characterizes spatiotemporally bounded laws Ex "All ravens are black". Counterfactual conditionals/Schurz: on the other hand: we would not say Ex "If this apple had not been in the basket, it would not be green." >Counterfactual conditionals, >Laws of nature, >Laws. I 237 Similarity-metris/Possible Worlds/Counterfactual Conditional/RescherVsLewis/Schurz: (Lewis 1973b(1)): for philosophy of science, Lewis' logical semantics for counterfactual conditionals yields little, because the substantive interpretation of the similarity metric between Possible Worlds presupposes that we already know a distinction between laws and contingent facts. (Stegmüller 1969(2), 320-334). I 238 Law-like/law-like/Schurz: b) in the narrower sense: = physical necessity (to escape the vagueness resp. graduality of the broad term). Problem: Not all spatiotemporally unrestricted laws are law-like in the narrow sense. Universal but not physically necessary: Ex "No lump of gold has a diameter of more than one kilometer". Universality: is not a sufficient, but a necessary condition for law-likeness. E.g. the universal proposition "All apples in this basket are red" is not universal, even if one replaces it by its contraposition: Ex "All non-red objects are not apples in this basket". (Hempel 1965(3), 341). Strong Hume-thesis/Hume/Schurz: universality is a sufficient condition for law-likeness. SchurzVs: this is wrong Weak-Hume thesis/Schurz: universality is a necessary condition for law-likeness. >Causality/Hume. Stronger/weaker/(s): the claim that a condition is sufficient is stronger than that it is necessary. BhaskarVWeak Hume-thesis. Solution/Carnap/Hempel: Def Maxwell conditional/law-like: laws of nature or nomological predicates must not contain an analytic reference to particular individuals or spacetime points (spacetime points). This is much stronger than the universality condition. >Stronger/weaker. Ex "All emeralds are grue": is spatiotemporally universal, but does not satisfy Maxwell's condition. >Grueness. I 239 Laws of nature/Armstrong: Thesis: Laws of nature are implication relations between universals. Therefore no reference to individuals. >Laws of nature/Armstrong, >Causality/Armstrong. Maxwell-Conditioning/Wilson/Schurz: (Wilson 1979): represent a physical symmetry principle: i.e. laws of nature must be invariant under translation of their time coordinates and translation or rotation of their space coordinates. From this, conservation laws can be obtained. Symmetry principles/principles/Schurz: physical symmetry principles are not a priori, but depend on experience! >Symmetries/Feynman, >Symmetries/Kanitscheider. Maxwell-condition/Schurz: is too weak for law-like character: e.g. "no lump of gold has a diameter of more than 1 km" also this universal theorem fulfills it. Law-likeness/Mill/Ramsey/Lewis/Schurz: proposal: all those general propositions which follow from those theories which produce the best unification of the set of all true propositions. (Lewis 1973b(1), 73). Vs: problem: it remains unclear why one should not add the proposition Bsp "No lump of gold has a diameter of more than 1 km". Because many true singular propositions also follow from it. Solution/Schurz: we need a clear notion of physical possibility. Problem: we have no consistent demarcation of natural laws and system laws. 1. Lewis, D. (1973b). Counterfactuals. Oxford: Basil Blackwell 2. Stegmüller, W. (1969). Probleme und Resultate der Wissenschaftstheorie und Analytischen Philosophie. Band I:Wissenschaftliche Erklärung und Begründung. Berlin: Springer. 3. Hempel, C. (1965). Aspects of Scientific Explanation and other Essays in the Philosophy of Science, New York: Free Press. |
Schu I G. Schurz Einführung in die Wissenschaftstheorie Darmstadt 2006 |
Loewenheim | Quine | X 79 Validity/Sentence/Quantity/Schema/Quine: if quantities and sentences fall apart in this way, there should be a difference between these two definitions of validity (via schema with sentences) or models (with quantities). But it follows from the Loewenheim theorem that the two definitions of validity (via sentences or quantities) do not fall apart as long as the object language is not too weakly (poorly) expressive. Condition: the object language must be able to express (include) the elementary number theory. Object Language: in such a language, a scheme that remains true for all sentence implementations is also fulfilled by all models and vice versa. The demand of elementary number theory is quite weak. Def Elementary Number Theory/eZT/Quine: is about positive integers using addition, multiplication, identity, truth functions and quantification. >Number Theory/Quine. Standard Grammar/Quine: the standard grammar would express the addition, multiplication and identity functions by appropriate predicates. That is how we get the two sentences: (I) If a scheme remains true for all implentations of sentences of the elementary number theory sets, then it is fulfilled by all models. X 80 (II) If a scheme is fulfilled by each model, then e is true for all settings of sets. Quine: Sentence (I) goes back to Loewenheim 1915: Sentence of Loewenheim/Quine: every scheme that is ever fulfilled by a model is fulfilled by a model 'U,‹U,β,α...', where U contains only the positive integers. Loewenheim/Hilbert/Bernays: intensification: the quantities α, β,γ,...etc. may each be determined by a sentence of the elementary number theory: So: (A) If a scheme is fulfilled by a model at all, it is true when using sentences of the elementary number theory instead of its simple schemes. Prerequisite for the implentations: the quantifiable variables must have the positive integers in their value range. However, they may also have other values. (I) follows from (A) that: (A) is equivalent to its contraposition: if a schema is wrong in all the implementations of s of sentences of the elementary number theory, it is not fulfilled by any model. If we speak here about its negation instead of the schema, then "false2" becomes "true" and "from no model" becomes "from every model". This gives us (I). The sentence (II) is based on the theorem of the deductive completeness of the quantifier logic. II 29 Classes: one could reinterpret all classes in its complement, "not an element of ..." - you would never notice anything! Bottom layer: each relative clause, each general term determines a class. >Classes/Quine. V 160 Loewenheim/Quine: there is no reinterpretation of characters - but rather a change of terms and domains - the meanings of the characters for truth functions and for quantifiers remain constant. The difference is not that big and can only play a role with the help of a new term: "ε" or "countable". For quantifiers and truth functions only the difference finite/infinte plays a role. Uncountable is not a matter of opinion. Solution: it is all about which term is fundamental: countable or uncountable. |
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 |
Logic | Wright | I 60ff Semantic anti-realism/evidence: in contrast to Putnam might be satisfied now with a "one-way": (EC, epistemic limitation): (EC) If P is true, then there is evidence that it is so. Evidence/WrightVsPutnam: truth is limited by evidence. This leads to a revision of the logic. >Evidence, >Truth. If there is no evidence, Putnam must actually allow by contraposition of EC that it is not the case that P is true, from which follows per negation equivalence that the negation of P must be regarded as true. >Contraposition, >Negation, >Equivalence. I 61 Semantic Anti-Realism: refuses to concede the unlimited validity of the principle of bivalence (true/false). >Bivalence, >Truth value. Semantic Anti-Realism/Wright: there is this scope for reconciliation: who represents EC, is obliged by the negation equivalence, to permit (A): A If no evidence for P is present, then there is evidence for its negation. Wright: this is synonymous to an admission that there is evidence, in principle, both for the confirmation as well as for the rejection of P: But that conceals a suppressed premise: (B) Either there is evidence for P or there is none. This is a case of the excluded third. I 62 Classic, is the conditional (A) an equivalent of the disjunction (C): (C) Either there is evidence for P or there is evidence for its negation. Problem: that it is precisely the case of the excluded third, that is not to be assertible (not assertible): It would not be sufficient to simply reject the principle of the bivalence (true/false). If (B) Either there is evidence for P or there is no unlimited assertible, the embarrassment will occur: the logic must be revised for all cases where evidence is not guaranteed. >Assertibility. I 87f Revision of Logic/Wright: may be required when the Liar or anything alike comes into play. Here one can assume a "weak" biconditional: Definition biconditional, weak: A <> B is weakly valid if it is impossible that one of the two statements may be true, if the other is not, even if A, under certain circumstances has a different valuation from B or no truth value, while B has one. Definition biconditional, strong: A <> B is highly valid if A and B always get necessarily the same valuation. Then it also apllies for discourse areas in which the disquotation scheme and the equivalence scheme are called into doubt that both are still weakly valid. >Discourse. Revision of Logic/Negation: within an apparatus with more than two truth values there can be no objection against the introduction of an operator "Neg", which is subject to the determination that Neg A is false if A is true, but is true in all other cases. >Operations. Then, if A <> B is weakly valid, that also aplies to Neg A <> Neg B. Then there is no obstacle against the derivation of the negation equivalence: Neg (P) is true <> Neg ("P" is true). --- I 89 WrightVs: however, this will not succeed. Not even as an assertion of weak validity when "assertible" is used for "true." >Validity. |
WrightCr I Crispin Wright Truth and Objectivity, Cambridge 1992 German Edition: Wahrheit und Objektivität Frankfurt 2001 WrightCr II Crispin Wright "Language-Mastery and Sorites Paradox" In Truth and Meaning, G. Evans/J. McDowell Oxford 1976 WrightGH I Georg Henrik von Wright Explanation and Understanding, New York 1971 German Edition: Erklären und Verstehen Hamburg 2008 |
Paradoxes | Prior | Cresswell II 110 Paradox/liar/Cretans/Prior/Cresswell: thesis: the Cretan must, so that he can have expressed anything , have said more than one sentence. ((s) Otherwise the sentence refutes itself and thus logically expresses nothing). Cresswell II 180ff Paradox/Cohen/Prior/Cresswell: (Cohen 1957, p. 225)(1), (Prior 1962)(2). Cohen: E.g. When the policeman testifies that everything that the prisoner says is wrong, and the prisoner explains that something that the policeman testified is true, then something that the police officer testified is wrong and something that the prisoner explains, true. Notation: d1: "the policeman testified that:" d2:" the prisoner explains". Logical form: (d1 p(d2p> ~ p) u d2Ep(d1 p up))> (Ep (d1P u ~ p) u Ep (d2p up)) Liar/Prior: d: "was told by a Cretan": dp (dp> ~ p)> (Ep (dp up) and Ep (dp u ~ p)) (ii) dp (dp> ~ p)> Ep Eq(p unequal q) u dp u dq). (ii) states that the Cretans must have said at least two things. --- Prior I 81 Prior/(s): tautology p > pq. Prior reads it like this: p E.g. Say, q: adverb. E.g. CpAKpqKpNq: if it is the case that p, then either it is the case that p-and-q or it is the case that p-but-not-q. Moore's paradox: the same device can be used for it, I believe that it is raining, but of course it does not rain. Philosophers have found it remarkably difficult to explain what is wrong with it - but that happens all the time. Prior I 2 Moore's Paradox/Prior: we only need normal truth and error (error or dishonesty as the only options). >Truth, >Truthfulness, >Error. Prior I 85 Preface paradox/Prior: thesis that something is in the book, is not the case, can only be claimed outside of the book. >Levels/order, >Description levels. Variant: book with only one sentence: something in this book is wrong: sequence of theorems: 1. then something is wrong 2. the say that something is wrong in the book is true 3. which in turn is true 4. then something is wrong in the book and something is true. ((s) But only a statement). Prior: But then at least two different things are said in the book - by contraposition: if nothing is wrong in the book, except that it is said that something is wrong in the book, then this is not said in the book. Prior I 88 Preface paradox/Prior: in the book there is something wrong just cannot be the only assertion - but self-reference is not the problem. >Self-reference. Prior I 96f Preface Paradox/Prior: Parallel/Cohen E.g. If John has a brown cow which is then and only then pregnant if any animal of John is not pregnant, then any animal of John is not pregnant - Proof: e.g. hypothesi : when an animal of John is not pregnant, the cow is pregnant so if the cow is not pregnant, the other animal is pregnant - and therefore (because the cow is only pregnant, when another animal is not, then an animal of John is not pregnant. - He must have at least two animals - Prior: oddly enough, not essential that the pregnant animal must be a brown cow, just so: for x, x means that the sky is blue and x is true, iff grass is green. Both elements are quite irrelevant for each other - Even for the preface paradox. Prior I 98 Preface paradox/PriorVsTarski: my concept of truth here non-Tarski: truth is not property of sentences, but of propositions. - That means, Quasi properties of quasi-objects. - Rather adverbs than adjectives. - E.g. truthfully and incorrectly. >Sentences, >Propositions, >Truth/Tarski, >Truth Definition/Tarski. 1. L.J. Cohen (1957). The Diversity of Meaning. London, 1962. 2. Arthur Prior (1960). On a family of paradoxes. Notre Dame Journal of Formal Logic 2 (1):16-32 |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 Cr I M. J. Cresswell Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988 Cr II M. J. Cresswell Structured Meanings Cambridge Mass. 1984 |
Proof of God’s Existence | Bolzano | Simons I 321 Cosmological proof of God/unconditioned existence/Bolzano/Simons: (circumvents the problem of being founded by referring to classes. >Classes. A) there is something real, e.g. my thoughts that it is like that. B) Suppose there is some thing A that is absolutely essential in its existence, then we already have it C) Suppose A is conditional. Then form the class of all conditional real things A, B, C, ... This is also possible if this class is infinite D) the class of all conditioned real things is itself real. Is it conditional or unconditional? If it is absolute, we already have it E) Suppose it is conditional: every conditioned presupposes the existence of something else, whose existence it determines. Thus even the class of all conditional things, if conditioned, presupposes the existence of something that determines it. F) This other thing must be unconditioned, for if it were conditioned, it would belong to the class of all conditioned things G) Therefore, there is something unconditional, e.g. a god. Simons: this makes no use of being founded: C) leaves the possibility of an infinite chain open. >Foundation, >Justification, >Reasons, >Ultimate justification, >Conditions. 1. RussellVsBolzano/Simons: one might have doubts about the "class of all unconditioned things". >Paradoxes, >Russell's paradox, >Sets, >Set theory. Solution/Bolzano: it's about the real things from which we can assume spatial-temporal localization. >Localization. 2. SimonsVsBolzano: Step F) I 322 Why should the class of all conditioned things not be conditioned by something within? This would be conditioned itself, etc. but any attempt to stop the recourse would again appeal to being founded. ((s) The thing that conditions would be within the class of conditioned things, it would be conditioned and conditional at the same time). >Regress. Solution/Simons: we need additionally a conditioning principle. Definition Conditioning Principle/Simons: if a class C is such that each dependent element of it has all the objects on which it depends within X, then X is not dependent. (Simons pro). Simons: this allows infinite chains of dependencies. A kind of infinite dependence already arises e.g. when two objects are mutually dependent. >Dependence, >Causal dependence, >Ontological dependence. If the conditioning principle applies, why should the class X be still externally conditioned? Ad Bolzano: Suppose we accept his argument until e). Then it can go on like this: H) if the class of all conditioned things is conditioned, then there is an element of it that is dependent on something that is not an element of that class. (Contraposition to the conditioning principle) >Contraposition. I) Then such an (unconditioned) object is not an element of the class of all conditioned things, and is thus unconditional. J) Therefore, there is in any case something unconditioned. SimonsVsAtomism: that is better than anything that an atomism achieves. >Atomism. Conditioning principle/Simons: is the best extension of the strong rigid dependency (//), i.e. (N) (a // x ↔ (Ey) [x ε a u a // x] u ~ x ε a) >Rigidity. SimonsVsBlack: with the strong instead of the weak dependency, we can counter Black. >Stronger/weaker, >Strength of theories. I 323 God/Mereology/Ontology/Simons: in any case, the strong rigid dependence does not prove the existence of God. Only the existence of an unconditional, which Bolzano cautiously calls "a God". >God, >Existence, >Ontology. Independence/Simons: does not include divinity. >Independence, >Existence statement. |
Simons I P. Simons Parts. A Study in Ontology Oxford New York 1987 |
Similarity | Logic Texts | II 60 Similarity/form/content/logic/Hoyningen-Huene: equality and diversity are part of the logical form, not of the content. --- Read III 105 Similarity analysis: a number of logical principles that are classically valid, fails here. For example, the Def Contraposition: that "If B, then not-A" from "if A, then not-B" follows. The similar world in which it rains can very well be one in which it rains only lightly. But the most similar world, in which it rains violently, cannot be one in which it does not rain at all. III 105f Similarity: But worlds in which Lewis is 2.02, 2.01, 2.005 meters tall are progressively similar to the real world, yet this sequence has no limit. >Similarity metrics/Lewis. III 111 Vs Similarity Theory: It makes all conditional sets with true if-and then-sentences true. But in this respect it is in error: many such conditional sentences are false. >Conditional, >Truth condition, >Truth-conditional semantics. |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 Re III St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 |
Similarity Metrics | Logic Texts | Read III 104ff Similarity Metrics/Stalnaker: smallest possible revision - i.e. the most similar world. Selection function: f(A, w) - "If you get a one, you will receive a scholarship" is true if the world in which you receive a scholarship is most similar to the world in which you are getting a one. Possible world view: deviates from the probability function if the fore-link is wrong". - Because all combinations can be realized in a possible world. >Possible world, >Similarity. III 105 Similarity Metrics/possible world/conditional sentence/Read: some classical logical principles fail here: e.g. contraposition that "if B, then not-A" follows from "if A, then not B" - the similar world in which it rains, can be very well one in which it rains only lightly. But the most similar world in which it rains violently cannot be one in which it does not rain at all. >Conditional. III 106 Another principle that fails: the reinforcement of the if-sentence: "If A, then B. So if A and C, then B." - For example, when I put sugar in my tea, it will taste good. So when I put sugar and diesel oil in my tea, it will taste good. In the most similar world in which I put diesel oil like sugar in my tea, it tastes horrible - further: the results of the conditionality principle are invalid: - If A, then B. So if A and C, then B - and if A, then B. If B, then C. So if A, then C - Reason: the conditional sentence has become a modal connection. We must know that these statements are strong enough in any appropriate modal sense - to ensure that the most similar A and C world is the most similar A-world, we must know that C is true everywhere. III 108 Similarity metrics/the conditionally excluded middle/Read: the sentence of the conditionally excluded middle: one or other member of a pair of conditional sentences must be true. This corresponds to the assumption that there is always a single most similar world. - (Stalnaker pro). >Conditionally excluded middle. LewisVsStalnaker: e.g. Bizet/Verdi - All combinations are false. Stalnaker: instead of the only similar one at least one similar world. LewisVs: the set of possible world in which Lewis is 2 m + e tall, whereby e decreases appropriately, this has no boundary. Solution/Lewis: instead of the selection function: similarity relation: Lewis proposes, that "if A then B" is true in w if there is either no "A or non-B"-world, or any "A and B"-world that is more similar than any "A and not-B"-World. III 110 Bizet/Verdi-example: where there is no unique most similar world, the "would" conditional sentences are wrong because there is no most similar world for any of the most appropriate similar worlds in which they are compartiots, where Bizet has a different nationality. >Bizet/Verdi case. E.g. If you get a one, you will receive a scholarship: will be true, if there is for every world in which you get a one and do not receive scholarship, is a more similar world in which you get both (without conditional sentence of the excluded middle). III 115 Similarity metrics/similarity analysis/possible world/ReadVsLewis: problem: e.g. (assuming John is in Alaska) If John is not in Turkey, then he is not in Paris. - This conditional sentence is true according to the "similarity statement", because it only asks, whether the then-sentence is true in the most similar world. >Conditional, >Counterfactual conditional. |
Logic Texts Me I Albert Menne Folgerichtig Denken Darmstadt 1988 HH II Hoyningen-Huene Formale Logik, Stuttgart 1998 Re III Stephen Read Philosophie der Logik Hamburg 1997 Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983 Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001 Re III St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 |
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Bolzano, B. | Simons Vs Bolzano, B. | I 321 Cosmological proof of God’s existence/unconditional existence/Bolzano/Simons: avoids the problem of foundedness by referring to classes. a) There is something real e.g. my thoughts that it is so. b) Suppose there is any thing, e.g. A that is unconditional in its existence, then we have it already. c) Suppose A is conditional. Then the class of all conditional real things forms A, B, C, ... This is also possible if this class is infinite. d) The class of all conditional real things is itself real. Is it conditional or unconditional? If it is unconditional, we have it already. e) Suppose it is conditional: each conditional presupposes the existence of something else, the existence of which it requires. So even the class of all conditioned things, if conditional, requires the existence of something that it presupposes. f) This other thing has to be unconditional because if it were conditional, it would belong to the class of all conditional things. g) Therefore, there is something unconditional, e.g. a God. Simons: this does not use foundedness: c) leaves the possibility of an infinite chain open. RussellVsBolzano/Simons: one could have doubts about the "class of all unconditional things" (> paradoxes). Solution/Bolzano: it is exactly about the real things of which we can assume spatiotemporal localization. 2. SimonsVsBolzano: step f) I 322 Why should the class of all conditional things not be required by something within? This itself would be conditional, etc. but any attempt to stop the recourse would again appeal to foundedness. ((s) The conditional would be within the class of conditional things, it would be conditional and conditioning at the same time.) Solution/Simons: we need a conditioning principle in addition. Def Conditioning Principle/Simons: if a class C is such that each dependent member of her has all of the objects on which it depends within X, then X is not dependent (Simons pro). Simons: this allows infinite chains of dependencies. A kind of infinite dependence appears already if e.g. two objects mutually require each other. If the conditioning principle applies, why should the class X then be even conditioned from the outside? Ad Bolzano: suppose we accept his argument up to e). Then it can go on like this: h) If the class of all conditional things is conditional, then there is an element of it which is dependent on something that is not a member of this class (contraposition to the conditioning principle). i) Then such an (unconditional) object is no member of the class of all conditional things and therefore unconditional. j) Therefore, something unconditional definitely exists. SimonsVsAtomism: that is better than anything the atomism accomplishes. Conditioning Principle/Simons: the conditioning principle is the best extension of strong rigid dependence (7), that means that: (N) (a 7 x ≡ (Ey)[x ε a u a 7 x] u ~ x ε a) SimonsVsBlack: we can face Black with the strong rather than with the weak dependence. I 323 God/mereology/ontology/Simons: in any case, the strong rigid dependence does not prove the existence of God. Only the existence of something unconditional that Bolzano prudently called "a god". Independence/Simons: independence includes by no means divinity. |
Simons I P. Simons Parts. A Study in Ontology Oxford New York 1987 |
Hume, D. | Verschiedene Vs Hume, D. | Hacking I 68 Causality/W.C.BroadVsHume: VsRegularity: For example we can see that the siren of Manchester howls every day at the same time, whereupon the workers of Leeds let the work rest for one hour. But no causation. Hacking I 70 CartwrightVsHume: the regularities are characteristics of the procedures with which we establish theories. (>Putnam). Hume I 131 Def Atomism/Hume/Deleuze: is the thesis that relations are external to conceptions. (KantVs). VsHume: Critics accuse him of having "atomized" the given. Theory/DeleuzeVsVs: with this one believes to have pilloried a whole system. As if it were a quirk of Hume. What a philosopher says is presented as if it were done or wanted by him. I 132 What do you think you can explain? A theory must be understood from its conceptual basis. A philosophical theory is an unfolded question. Question and critique of the question are one. I 133 It is not about knowing whether things are one way or the other, but whether the question is a good question or not. Apron I 238 Lawlikeness/lawlike/Schurz: b) in the narrower sense: = physical necessity (to escape the vagueness or graduality of the broad term). Problem: not all laws unlimited in space-time are legal in the narrower sense. Universal, but not physically necessary: Example: "No lump of gold has a diameter of more than one kilometre". Universality: is therefore not a sufficient, but a necessary condition for lawfulness. For example, the universal statement "All apples in this basket are red" is not universal, even if it is replaced by its contraposition: For example "All non-red objects are not apples in this basket". (Hempel 1965, 341). Strong Hume-Thesis/Hume/Schurz: Universality is a sufficient condition for lawlikeness. SchurzVs: that is wrong. Weak Hume-Thesis/Schurz: Universality is a necessary condition for lawfulness. ((s) stronger/weaker/(s): the claim that a condition is sufficient is stronger than the claim that it is necessary.) BhaskarVsWeak Hume-Thesis. BhaskarVsHume. Solution/Carnap/Hempel: Def Maxwell Condition/lawlikeness: Natural laws or nomological predicates must not contain an analytical reference to certain individuals or spacetime points. This is much stronger than the universality condition. (stronger/weaker). Example "All emeralds are grue": is universal in space-time, but does not meet the Maxwell condition. ((s) Because observed emeralds are concrete individuals?). I 239 Natural Law/Law of Nature/Armstrong: are relations of implication between universals. Hence no reference to individuals. (1983) Maxwell condition/Wilson/Schurz: (Wilson 1979): it represents a physical principle of symmetry: i.e. laws of nature must be invariant under translation of their time coordinates and translation or rotation of their space coordinates. From this, conservation laws can be obtained. Symmetry Principles/Principle/Principles/Schurz: physical symmetry principles are not a priori, but depend on experience! Maxwell Condition/Schurz: is too weak for lawlikeness: Example "No lump of gold..." also this universal statement fulfills them. Stegmüller IV 243 StegmüllerVsHume: usually proceeds unsystematically and mixes contingent properties of the world with random properties of humans. Ethics/Morality/Hume: 1. In view of scarce resources, people must cooperate in order to survive. 2. HumeVsHobbes: all people have sympathy. If, of course, everything were available in abundance, respect for the property of others would be superfluous: IV 244 People would voluntarily satisfy the needs in the mutual interest according to their urgency. Moral/Ethics/Shaftesbury/ShaftesburyVsHume: wants to build all morality on human sympathy, altruism and charity. (>Positions). HumeVsShaftesbury: illusionary ideal. Ethics/Moral/Hume: 3. Human insight and willpower are limited, therefore sanctions are necessary. 4. Advantageous move: intelligence enables people to calculate long-term interests. IV 245 The decisive driving force is self-interest. It is pointless to ask whether the human is "good by nature" or "bad by nature". It is about the distinction between wisdom and foolishness. 5. The human is vulnerable. 6. Humans are approximately the same. |
Hacking I I. Hacking Representing and Intervening. Introductory Topics in the Philosophy of Natural Science, Cambridge/New York/Oakleigh 1983 German Edition: Einführung in die Philosophie der Naturwissenschaften Stuttgart 1996 Carnap V W. Stegmüller Rudolf Carnap und der Wiener Kreis In Hauptströmungen der Gegenwartsphilosophie Bd I, München 1987 St I W. Stegmüller Hauptströmungen der Gegenwartsphilosophie Bd I Stuttgart 1989 St II W. Stegmüller Hauptströmungen der Gegenwartsphilosophie Bd 2 Stuttgart 1987 St III W. Stegmüller Hauptströmungen der Gegenwartsphilosophie Bd 3 Stuttgart 1987 St IV W. Stegmüller Hauptströmungen der Gegenwartsphilosophie Bd 4 Stuttgart 1989 |
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 I R. Nozick Philosophical Explanations Oxford 1981 No II R., Nozick The Nature of Rationality 1994 |
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Dissimilarity | Wiggins, D. | Simons I 213 "relative identity" / Geach ("Theory R"), ("sortal theory") for sortals F and G, it is possible to find two objects a and b, so that a and b both are F and G, a is the same F as B, but not the same G - On the other hand: b) Grice / George Myro (both unpublished): VsWiggins thesis, that things that are ever different, are always different. I 216 Wiggins: his thesis is: a not = b and a 2I b > ~ (a sup tb) ((s) 2I above) This can be simplified and brought into contraposition: WP (Wiggins principle) a sup t b > a ot b |
Simons I P. Simons Parts. A Study in Ontology Oxford New York 1987 |
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