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| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Attributes | Logic Texts | Read III 210 Attributive Adjectives / Read: what is large for a mouse is not large for an elephant - e.g. "great", "few", "high", "good", "beautiful". >Sorites, >Vagueness. Vagueness: Max Black: Vagueness is not ambiguity and also not generality. It can be difficult to draw a line between what is a chair and what is not. This is where vagueness comes in and threatens the sorites. Read III 211 Tarski: separation of the language levels: Suppose we wanted to say that "15 is little" is neither true nor false. According to the T-scheme, "15 is little" is not false" is equivalent to "15 is little". So ""A" is neither true nor false" is equivalent to "15 is both little and not little". This is a contradiction. >Double negation, >Negation, >Description levels, >Levels (Order). Application/Penumbra/Read: to call it a penumbra means that it is not wrong to apply it here. It is then not wrong to say that 15 is little, and not wrong to say that 15 is not little for the same reason. So it seems that it is not wrong to say that 15 is both little and not little, which is a contradiction. >Contradiction. Vagueness/Read: the world itself is not vague. There are no vague objects. |
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 |
| Negation | Cresswell | II 73 Double Negation/possible worlds/Proposition/indirect speech/Cresswell: Solution: if propositions are nothing but sets of possible worlds. Then not-not-a means the same as a - (because of the complement formation of the set). >Double negation, >Possible worlds. Indirect speech: problem: if propositions should be something else than sets of possible worlds: then it may be that the speaker has said nothing at all. Then the double negation is something else. ((s) "He has not said anything to this" does not mean that he rejects a.) >Indirect speech. II 73 Problem: but then the truth value differs against the logic. >Truth values. Solution/Cresswell: Hyperintensionality: hyperintensional propositions express (despite the same intension of a and not-not-a) different propositions. ((s) Then intension is unequal proposition). >Hyperintensionality. Solution/Cresswell: Structural ambiguity: "saying" is sometimes applied to whole sentence, sometimes to parts. VsHyperintensionality: before, the meaning of "not" was clear, it is now unclear. II 74f Double Negation/Cresswell: another problem: we can add to maximum consistent sets of propositions further inconsistent propositions. - The sets are then equal with respect to the consistent propositions and differ only in the inconsistent ones. >maximum consistent. N.B.: if there are only possible worlds (no impossible world), a and ~~a are equal. Impossible world: if they are admitted, there is a difference between position and double negation. - that is because "~" is then no real negation. >Impossible world. |
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 |
| Negation | Geach | I 16ff Negation/Geach: the problem with compound expressions is always the negation (with "all", "some"). >All/Geach, >Each/every/Geach, >Sentences, >Quantification, cf. >Someone/Geach. I, 45ff Negation/Geach: in the subject-predicate-sentence: negation is only possible from the predicate, not from the subject. Modernity: quantification: also the negation of "there is" is possible. New: also subject negation is possible: E.g. "not everyone is ..." I 75 Negation/Russell: cannot be applied as a primitive term to propositions, therefore: All x are F: Negation: some x are not F ". Negation: not via a sentence: "Do not open the door" is on the same level as "Open the door". Negation is not "logical secondary". >Negation/Frege, >Thought/Frege. Asymmetry: only with identifying predicates: e.g. the same man/not the same man - subject negation: "not everyone is ..." - predicate negation: Socrates is not ... ". Negation is not parasitic to affirmation. - There is no added meaning. - Otherwise there would be a summation with double negation. >Double negation. I 260 Negation/assertion/Geach: propositions can be put forward without asserting them. For example, "p > q" therefore we need a negation which is not polar to the assertion. >Proposition, >Assertion. |
Gea I P.T. Geach Logic Matters Oxford 1972 |
| Negation | Nozick | II 234 double negation: "not-(not-q)" is weaker than "q" - it is the same as "may" ("might") - not the same as "would". >Stronger/weaker, cf. >Strength of theories, >Double negation, >Multi-valued logic, >Truth values, >Truth. |
No I R. Nozick Philosophical Explanations Oxford 1981 No II R., Nozick The Nature of Rationality 1994 |
| Possibility | Aristotle | Berka I 137 Possibility/Aristotle: 1 unilateral: what is not necessary. ("normal" definition today). 2 two-sided: what is neither necessary nor required (not impossible). (This is leading to problems). "Pure chance"/Aristotle ... follows from the "two-sided" possibility: For a certain P: it is possible that p, and it is possible that non-P. >Contingency, >Necessity, >Negation, >Double negation. |
Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Situation Semantics | Barwise | Cresswell II 169 Situation semantics/Barwise/Perry/Cresswell: (Barwise/Perry, 1983)(1): here it is explicitly denied that logically equivalent sentences in contexts with propositional attitudes are interchangeable. (1983(1), 175, 1981b(4), 676f) - e.g. double negation in the attribution of propositional attitudes. >Equivalence, >Double negation. Solution: partial character of situations. - Not everything has to be given - or the speaker may have to suspend judgment. ("do not ..."). >Situations. Def sentence meaning/Barwise/Perry: a relation between situations. Cresswell I 63 Situation SemanticsVsPossible World Semantics/knowledge/meaning/Barwise/Perry/BarweiseVsCresswell/ PerryVsCresswell/Cresswell: the possible worlds are too big to explain what the speaker knows when he/she utters a meaningful sentence. Possible worlds: are complete possible situations. >Possible worlds, >Possible World Semantics. Situation semantics: we need a more partial type of entity. ((s) partial, not complete). CresswellVsSituation Semantics: (Cresswell 1985a(2), 168 ff, 1985b(3), Chapter 7) Solution/Cresswell: Thesis: The situations only have to be partial in the sense that they are small worlds. Def Abstract Situation/Barwise/Perry: (1983(1), 57 ff): abstract situations are theoretical constructs used for an adequate semantic modeling of reality consisting of real situations. Cresswell: I ignore this distinction here. The semantics of possible worlds is better here, even if one differentiates between reality and theoretical representation. >Possible World Semantics. What we need to compare are abstract situations and worlds. I 64 Situation-SemanticsVsPossible World Semantics/BarwiseVsCresswell: there are often two propositions, one of which is believed by the person, but the other is not, but both are still true in the same worlds - for example, all logical and mathematical truths - but they are not all known, otherwise there could be no progress. I 65 CresswellVs: the situations should play roles that cannot be played at the same time. Solution: Semantics of possible worlds: the roles are played by entities of different kinds. Solution: Context with space-time specification. >Context. False sentences: describe non-actual situations. I 66 Sentences describe situations in a context - context is itself a situation that provides the listener with time, place, etc. Interpretation/Barwise: Meaning of sentences in a context. >Interpretation, >Sentence meaning. Meaning/CresswellVsSituation Semantics/CresswellVsBarwise/CresswellVsPerry: Meaning: = set of worlds in which they are true. Problem: Meanings are often equated with proposition, and then there are problems in playing roles that they cannot play at the same time. I 67 On the other hand, some of the other things that Barwise and Perry ask for from situations behave like worlds! For example: Mollie barks e*: = in I, Mollie, yes. That describes a situation e iff e* < e. ((s) Subset of situations where Mollie barks otherwise? Or where Mollie exists and someone barks?). Def Generation property/terminology/Cresswell: (generation property): sentences that describe a situation have a situation property ((s) that is part of a set of situations). A sentence ? has the generation property in terms of a context u, iff there is a situation e*, so that u[[φ]] e iff e* < e. ((s) If there is a sentence that is more general than the sentence "Mollie barks in the space-time situation I" Or: Generation property is the property that embeds the sentence in the context, because proposition as sets of worlds must not be limited to a single situation.) The sentence φ has the generation property (simpliciter) iff it has it in every context. Atomic sentence/Barwise/Perry: Thesis: all atomic sentences have the generation property. >Atomic sentences. Cresswell: if situations are to be understood as proposition, all sentences should have the generation property. And that is because the generating situation e* can be understood as the proposition expressed by the sentence ? in context u. In fact, we do not need the other situations at all! We can say that e* is the only situation described by φ in u. But that doesn't matter, because each e* determines the only class of e's, so e* < e, and each class generated by an e* determines that e* uniquely. 1. Jon Barwise & John Perry (1983). Situations and Attitudes. Cambridge, Mass.: MIT Press. Edited by John Perry 2. M. J. Cresswell (1985a) Situations and Attitudes. Philosophical Review 94 (2):293 3. M. J. Cresswell (1985b). Structured meanings. MIT Press 4. Jon Barwise & John Perry (1981). Semantic Innocence and Uncompromising Situations. Midwest Studies in Philosophy (1981), 6 : 387 https://doi.org/10.1111/j.1475-4975.1981.tb00447.x |
Barw I J. Barwise Situations and Attitudes Chicago 1999 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 |
| Truth | Leibniz | Holz I 44 Truth of reason/Truth of facts/Leibniz: Truth of reason: certain simple and original ideas, such as those of identity, are immediately seen as modes or forms of our sense-perception as categories of the givenness of beings. They are not mediated by perception, but are the determinateness of perception itself. >Perception/Leibniz. I 54 Def Truth/Leibniz/Holz: truth appears as a statement relation, in which the identity of different things is determined against each other. Def Experience/Leibniz/Holz: experience is the return of something different to their connection in such a relation. Discovery of the truth of different things, namely subject and predicate in synthetic sentences of experience. Truth/Leibniz/Holz: truth is not really in the identity of the subject A = A, but in the return of the predication to the identity of a certain predicate with a certain subject in which it is contained, thereby distinguishing the subject from other subjects. The truth of a proposition states that it can be traced back to an identical proposition (axiom). I 57 Truth/Leibniz: truth appears only mediated, in the medium of its opposite, of appearance (> Appearance/Hegel). Truth of facts/truth of reason/Leibniz: I gain the certainty of the facts, the vérités de fait only by means of their representation on the level of reason - the vérités de raison. This can show me the material truth but only as the not wrong. ((s) Double negation: is weaker.) In the reversal of the method of proof in truths of facts, the variety of experience and the unity of reason stand opposite to each other like a mirror image. I 63 Truth of facts/Leibniz: the truth of facts must exist, if anything should be said at all about the infinite manifoldness, and knowledge should thus be gained. Truth of reasons/Leibniz: truth of reasons is necessary, their opposite is impossible. Truth of facts/Leibniz: truth of facts is contingent, their opposite is possible. Holz: the difference between the two must not be misunderstood, otherwise Russell would be right: I 64/65 Russell: It is nonsense to say of a true proposition that it is not true in the sense of another, apotictically true proposition. ((s), for example, that a truth of reason contradicts a truth of facts). Holz: the difference lies in the argument. For the proof of truth of facts, we must examine the preceding chain of connections and because of the infinite divisibility of the bodies an infinite number of sentences. This can only do the infinite mind of God. >Order/Leibniz. Truth of reason/Leibniz: is the generic term for truths of reasons and truths of facts! The truth attribute of both lies in the fact that in the subject concept all its possible predicates are contained. "Praedicatum inest subiecto". Inclusion of the predicate in the subject: A is contained in Ax or Ax = A + B + ... X. I 66 This inclusion of the predicate is the foundation of truth. This is, according to structure, a reason of reason. >Predicate/Leibniz. Def truth/Leibniz/Holz: is then the constitution of that state in which identity comes to a being or a fact when it enters into a distinction between subject/predicate/definiendum/definiens. This state is where the fact appears as the concept of the fact. Truth is a reflexion relationship. I 68 "Overarching general"/Leibniz/Holz: the truth of reason is the genre which comprises two (and only two) species, namely the truth of reason itself and its opposite, the truths of facts. For the formal logician, this remains a systematic contradiction: Leibniz makes a distinction between necessary and contingent truths. Nevertheless, he comprehends both of them analytically! Holz: in fact, the relationship is not a formal logical one, but a dialectical one. > Josef König: "The Overarching General" as the basic logical figure of Leibniz's metaphysics, is necessary for the inexpressable multiplicity of the world, which can nevertheless be subjected to an order of reason. I 73 Complete concept/Leibniz: the complete concept contains all possible conditions and determinations for the existence of a particular being, is thus identical with the concept of the world as a whole. Only perceptible to an infinite mind. Overarching general: for the infinite mind, the distinction between truths of reason and truths of facts is again invalid. For him, everything is a truth of reason, or, one can say as well, everything is a truth of facts for him! For the finite mind, however, the truth of reason is the opposite of the truth of facts. Overarching general: the one involves its opposite. Truth/Cognition/Metaphysics/Leibniz/Holz: This again has the astounding consequence that Leibniz can only speak sensibly of two kinds of truth (truths of facts/truths of reason) when he comprehends the idea of the infinite mind (for which the two coincide) only as a metaphysical auxiliary construction. >Truth of reason, >Truth of facts. |
Lei II G. W. Leibniz Philosophical Texts (Oxford Philosophical Texts) Oxford 1998 Holz I Hans Heinz Holz Leibniz Frankfurt 1992 Holz II Hans Heinz Holz Descartes Frankfurt/M. 1994 |
| Vagueness | Field | II 227 Vagueness/revision of the logic/Field: some authors: to allow double negation, to prohibit explicit contradictions, thus also not to allow negations of the law of the excluded middle (l.e.m.). >Negation, >Double negation, >Contradictions, >Stronger/Weaker, >Excluded middle. Then old version: if Jones is a limiting case for "Jones is bald", we cannot claim either "bald" or "not-bald", so we can now. New: neither claim: E.g. "Jones is bald or not bald" nor "It is not the case that Jones is either bald or not bald." On the other hand: Field: with definite-operator (definite): "It is not the case that Jones is either definitely bald or definitely not bald". - Without law of the excluded middle: "neither bald nor not bald". II 228 Limiting case/vagueness/definite-Operator/Field: we need the definite-operator to avoid a limiting case of the a limiting case. >dft-operator, >Terminology/Field. II 228 Def Weakly true/vagueness/truth/truth-predicate/Field: to be able to say general things about borderline cases. Not only that somebody represents a certain limiting case. >Generalization. Def paradigmatic borderline case: definitely a borderline case. Not weakly true/deflationism: e.g. "Either bald or not-bald is true". Then the Truth-predicate itself inherits the vagueness. It is not definitely true whether or not. Def Strongly true/Field: assuming, Jones is a limiting case: then neither "bald" nor its negation (strongly) plus classical logic: then the disjunction "bald or not bald" should be true even in strong interpretation. Law of the excluded middle: if we give it up: a) weakly true: then the disjunction is not true b) strongly true: then the disjunction is without truth value. Strongly true: is less vague, does not inherit the vagueness. Correctness: which interpretation is the correct one is only dependent on utility. >Correctness. Per weak truth: allows infinite conjunction and disjunction. This corresponds more to the theory of validity. - Only the weak Truth-concept is supplied by the disquotation scheme. Deflationism: deflationism additionally requires the definite-operator to declare the predicate strongly true. >Deflationism. II 230 Inflationism/Vagueness/FieldVsInflationism: Problem: the I. needs a thing that is "neither bald nor not bald". Inflationism: explains e.g. "weakly true" compositional. >Inflationism. Supervaluation/Sorites/Inflationism: "candidate of an extension". >Supervaluation. Def strongly true: is a sentence with a vague predicate then iff it is true relative to each of the candidates of an extension. - Then the limiting case without definite-operator: "Jones is bald in some extensions but not in all". II 233 Vagueness/Ontology/Field: Thesis: vgueness is a deficiency of language, not of the world. >Language dependence. II 234 Vagueness/radical non-classical logic/Field: here we do not need a definite-operator or distinction between strong/weak truth: e.g. Jones is a limiting case iff it is not the case that he is either bald or not bald. Deflationism/Field: seems to save a lot of trouble, because there is no definite-operator, one would have to understand. Vs: that deceives: the trouble is only postponed: here the logical rules for "not", etc. are much more complicated. ... + ... II 228 Weakly true:...++... |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
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