Showing papers in "Journal of Philosophical Logic in 1979"
TL;DR: It’s not as easy as you might think to say something that will be unacceptable for lack of required presuppositions, and straightway that presupposition springs into existence, making what you said acceptable after all.
Abstract: EXAMPLE 1: PRESUPPOSITION’ At any stage in a well-run conversation, a certain amount is presupposed. The parties to the conversation take it for granted; or at least they purport to, whether sincerely or just “for the sake of the argument”. Presuppositions can be created or destroyed in the course of a conversation. This change is rule-governed, at least up to a point. The presuppositions at time r’ depend, in a way about which at least some general principles can be laid down, on the presuppositions at an earlier time r and on the course of the conversation (and nearby events) between r and r’. Some things that might be said require suitable presuppositions. They are acceptable if the required presuppositions are present; not otherwise. ‘me king of France is bald” requires the presupposition that France has one king, and one only; “Even George Lakoff could win” requires the presupposition that George is not a leading candidate; and so on. We need not ask just what sort of unacceptability results when a required presupposition is lacking. Some say falsehood, some say lack of truth value, some just say that it’s the kind of unacceptability that results when a required presupposition is 1acking;and some say it might vary from case to case. Be that as it may, it’s not as easy as you might think to say something that will be unacceptable for lack of required presuppositions. Say something that requires a missing presupposition, and straightway that presupposition springs into existence, making what you said acceptable after all. (Or at least, that is what happens if your conversational partners tacitly acquiesce - if no one says “But France has three kings! ” or ‘Vhadda ya mean, ‘even George’? “) That is why it is peculiar to say, out of the blue, “All Fred’s children are asleep, and Fred has children.” The first part requires and thereby creates a presupposition that Fred has children; so the second part adds nothing to what is already presupposed when it is said; so the second part has no conversational point. It would not have been peculiar to say instead “Fred has children, and all Fred’s children are asleep.”
1,763 citations
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TL;DR: A new way of handling the logical paradoxes is suggested, where instead of trying to dissolve them, or explain what has gone wrong, the authors should accept them and learn to come to live with them.
Abstract: The purpose of the present paper is to suggest a new way of handling the logical paradoxes. Instead of trying to dissolve them, or explain what has gone wrong, we should accept them and learn to come to live with them. This is argued in Sections I and II. For obvious reasons this will require the abandonment, or at least modification, of 'classical' logic. A way to do this is suggested in Section III. Sections IV and V discuss some implications of this approach to paradoxes.
680 citations
TL;DR: JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive.
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374 citations
TL;DR: Two approaches to the fallacy of begging the question (petitio pnizcipii) are compared: dialectical and dialectical in terms of dialogue.
Abstract: In their recent paper [A], J. Woods and D. Walton compare two approaches to the fallacy of begging the question (petitio pnizcipii). One is what they call the epistemicdoxastic approach: an argument is circular, and the person who uses it begs the question, if in order to know the truth of some premiss of the argument one must already know the truth of the conclusion, or some account of that general kind. The other approach is dialectical, that is, in terms of dialogue. This approach considers the fallacy as it arises in the context of contentious debate, when one participant asks the other to grant him a premiss which contains the substance of what is in dispute (see Hamblin [F] ,,p. 73). Woods and Walton claim that:
278 citations
TL;DR: One of Hintikka's aims was to show that there are simple sentences of English which contain essential uses of branching quantification, a discovery with significant implications for linguistics, for the philosophy of natural language, and perhaps even for mathematical logic.
Abstract: One of Hintikka's aims, in the paper Hintikka (1974),3 was to show that there are simple sentences of English which contain essential uses of branching quantification. If he is correct, it is a discovery with significant implications for linguistics, for the philosophy of natural language, and perhaps even for mathematical logic. Philosophically, it would influence our views of the ontological commitment inherent in specific natural language constructions, since branching quantification is a way of hiding quantification over various kinds of abstract abstract objects (functions from individuals to individuals, sets of individuals, etc.). Linguistically, the discovery of branching quantification would force us to re-examine, and perhaps re-interpret, Frege's principle of compositionality according to which the meaning of a given expression is determined by the meanings of its constituent phrases. For example, the meaning of a branching quantifier expression of logic like:
154 citations
79 citations
TL;DR: This key feature of set ups provides an easy way of falsifying the Lewis paradoxes AA ~ A B and B -* A v~ A (henceforward referred to as (P1) and (P2), respectively).
Abstract: In the terminology of Anderson and Belnap (1975), an entailment connective -~ expresses relevant entailment only if A B holds only if B is relevant to A; and an if then connective ' expresses relevant implication only if A * B holds only if B is relevant to A. It is well known that the entailment connective of Lewis' modal logic, -8, does not express relevant entailment; for A A A -8 B and A -a B v B are provable in all the Lewis systems, where A and B are any formulae. Similarly material implication, D, does not express relevant implication in view of the validity of A A D A B and A D B v ~ B. Systems of relevant entailment and relevant implication are currently the subject of intensive research. Work centres on systems neighbouring the system H' of relevant entailment due to Ackermann (1956), in particular the system R of relevant implication due to Anderson and Belnap, and the system NR of relevant entailment due to Meyer. (NR is sometimes known as R".) Routley and Meyer (1972a, 1972b, 1973) set out model theoretic semantics for various relevant logics, in particular the systems R and NR. The semantics develop earlier ideas of Routley and Routley (1972). The essence of the approach is the use in the model theory of a group of structures broader than the set of all possible worlds. These structures are named "set ups" by the Routleys. The key feature of a set up is that, unlike a world, the set of sentences determined by it may be either or both inconsistent and negation incomplete: an arbitrary formula and its negation may both hold, or both fail to hold, in some set up. The set of worlds is strictly included in the set of set ups: a world is a consistent and negation complete set up. This key feature of set ups provides an easy way of falsifying the Lewis paradoxes AA ~ A B and B -* A v~ A (henceforward referred to as (P1) and (P2), respectively). The first is falsified in an inconsistent set up in which both A and ~ A hold but B fails, and the second in an incomplete set up in which B holds but both of A and ~A fail. A feature of Ackermann-style relevant entailment systems which has
64 citations
TL;DR: Skolem’s conjecture about the consistency of the axiom of comprehension in the infinite-valued logic is proved by using some simple modifications of methods from classical proof theory and model theory: normalization of proofs in a naturaldeduction calculus and the use of maximally consistent sets of formulas.
Abstract: It is natural to suggest that the paradoxes of naive set ,theory can be avoided not by asserting only special cases of the axiom of comprehension (,!?x)~)O, E x -A@)), as in set theories like ZF formulated in classical predicate logic, but rather by retaining the unrestricted comprehension axiom while weakening the underlying logic. Various experiments have been made with such “type-free” logics by Ackermann [l] , Fitch [3] , Schtitte [6] , and others. One of the most interesting proposals is Skolem’s. After showing that versions of Russell’s paradox can be produced from the unrestricted comprehension axiom in any finite-valued Lukasiewicz predicate logic, Skolem conjectured that the axiom can however be consistently added to the infinite-valued Lukasiewicz predicate logic [7]. He also suggested that it may be possible to derive a significant amount of mathematics in a set theory based on this logic. Skolem’s conjecture about the consistency of the axiom of comprehension in the infinite-valued logic has been partially confirmed by Skolem himself and by Chang and others [2]. In this paper I shall prove Skolem’s conjecture by using some simple modifications of methods from classical proof theory and model theory: normalization of proofs in a naturaldeduction calculus and the use of maximally consistent sets of formulas. It remains to investigate the mathematical strength of the system, and I conclude the paper with some remarks on tbis subject. In outline the consistency proof proceeds as follows. Louise Hay [4] has provided a complete axiomatization of the infinite-valued predicate logic, although her formalization is not an axiomatization in the strict sense since it requires an inftitary inference rule. (It follows from work by Scarpellini [S] that this is the most one can hope for.) The result of adding the comprehension axiom to Hay’s predicate logic, with only the dyadic predicate “e” is here called H, it is therefore sufficient to prove that H is consistent. For this purpose His enlarged by adding certain Hilbert r-terms to obtain a system Hr. Every theorem of H is a theorem of Hr. Hr is then
60 citations
TL;DR: At the authors' disposal, and truth-tables tell us that (3) is a valid argument form of classical sentential calculus (CSC); hence, (2) is valid.
Abstract: at our disposal, and truth-tables tell us that (3) is a valid argument form of classical sentential calculus (CSC); hence, (2) is valid. Essentially the same procedure can be repeated for many other valid arguments; indeed, for all the valid arguments that can be so paraphrased as to fall under the scope of an extant (correct) logical system. No such procedure, however, is available to establish the invalidity of invalid arguments. Consider for example the argument
35 citations
TL;DR: This paper has considered various attempts to attribute significance to G2 and argued that two of these attempts are literally false and two are groundless.
Abstract: In this paper I have considered various attempts to attribute significance to G2.25 Two of these attempts (Beth-Cohen and the position maintaining that G2 shows the failure of Hilbert's Program), I have argued, are literally false. Two others (BCR and Resnik's Interpretation), I have argued, are groundless.
TL;DR: The present paper has grown out of a need for improved understanding of the technical aspects of the systems of tense logic that have been proposed and applied by Stuttgart people like Franz Giunthner, Christian Rohrer and myself in connection with the Deutsche Forschungsgemeinschaft research project "Die Beschreibung mit hilfe der Zeitlogik von Zeitformen und Verbalperiphrasen".
Abstract: The present paper has grown out of a need for improved understanding of the technical aspects of the systems of tense logic that have been proposed and applied by Stuttgart people like Franz Giunthner, Christian Rohrer and I myself in connection with the Deutsche Forschungsgemeinschaft (DFG) research project "Die Beschreibung mit hilfe der Zeitlogik von Zeitformen und Verbalperiphrasen im Franzosischen, Portugiesischen und Spanischen". The systems in question were presented and put to work in the following series of contributions (see the Bibliography at the end of this paper): Aqvist (1976), Aqvist and Giinthner (1977), Aqvist, Giunthner and Rohrer (1977), Aqvist, Giinthner and Rohrer (1977a), Aqvist (1977) and Aqvist (1977a). These papers are all somehow based on the Appendix to my essay Aqvist (1973), where a version of the so-called multiple indexing technique in modal logic is presented. In Aqvist (1976) this technique was used so as to yield a reconstruction of the Reichenbachian doctrine of verb tenses (see Reichenbach, 1947, Section 51) in the framework of a two-dimensional tense logic; in the five remaining papers a more powerful logic was
TL;DR: It is shown that this logic of quantum logical modalities contains all the quantum logical restrictions which come from the possible incommensurability of quantum physical objects.
Abstract: Modal logic is concerned with the concepts of necessity and possibility and a certain class of object propositions. In this paper we develop the basic concepts of a modal logic which is related to propositions about quantum physical objects. Since the object logic of quantum mechanical propositions is given by the calculi of quantum logic, the structure investigated in this paper will be called the modal logic of quantum logic. The object language and logic of quantum physical propositions is developed here within the dialogic approach to quantum logic [1]. On the basis of these object-linguistic structures we investigate the language of meta-propositions which state the material or formal truth of objectpropositions. Applying again the dialogic technique to meta-propositions the important notion of a formally true meta-proposition can be defined. Using this concept it turns out that the formal logic of meta-propositions is equivalent to the corresponding structure in ordinary logic, i.e., to the effective (intuitionistic) logic. The modalities "necessary" and "possible" are introduced here in the framework of a meta-linguistic interpretation, which considers the modalities as statements about the object-propositions under discussion [9]. On this basis it is found that meta-propositions which state the material truth of a special class of object propositions may be considered as quantum logical modalities (Section 2). A detailed investigation then shows that these quantum logical modalities are intimately related to the important quantum mechanical concepts of commensurability and objectivity. An illustration of the quantum logical modalities by relations between projection operators in Hilbert space concludes this part. In the third section we introduce the concept of a formally true modality which leads to the modal logic of quantum logic. It is shown that this logic of quantum logical modalities contains all the quantum logical restrictions which come from the possible incommensurability of quantum physical
TL;DR: The relationship between the two accounts of the truth conditions of counterfactual statements is sought to clarify particularly with respect to the logics which they determine.
Abstract: There are two accounts of the truth conditions of counterfactual statements which have been developed. According to David Lewis’s’ formulation of the possible world account “if A were the case then B would be the case” is true if there are possible worlds in which A and B are true which are more similar to the actual world than any possible world in which A is true and B is false. The other approach is the metalinguistic theory which counts a counterfactual as true if its antecedent together with certain auxiliary statements and laws of nature implies its consequent. Nelson Goodman* has developed this account and it is his version of it which we will investigate in this paper. Lewis has argued that the metalinguistic theory is compatible with his, while other? have claimed that the two approaches are fundamentally different. In this paper we seek to clarify the relationship between the two accounts particularly with respect to the logics which they determine. In order to state the two approaches with precision we will formulate them for a propositional language JZ with finitely many atoms to which the binary connective > is added. Lewis semantics for JZ are fomulated in terms of the concept of a system of spheres. A system of spheres is a three-tuple (IV, w*, $) where IV is a set of possible worlds, W* E IV is the act.ual world, and $ is a function which assigns to each ZJ G IV a subset of the power set of IV, P(W), which is totally ordered by set inclusion and which has {uj as its minimal member. Lewis suggests that we think of the members of $(u) as forming spheres centered on u. S ‘2 $(w) is said to be A-permitting if A is true at some v G S and A-necessitating if A is true at all v rZ ,S. If v belongs to a sphere around w to which u does not belong then v is said to be more similar than u to w. It will simplify our discussion to assume that if there is an A-permitting sphere in $(w) then there is a smallest A-permitting sphere in $(w).~ A Lewis model M is a system of spheres and a function 1 which assigns to each atomic sentence A of X a subset of IV, ItAll (the set of worlds at which A is true). Truth functional compounds are treated in the usual manner. Truth conditions for counterfactuals are given by
TL;DR: The main purpose of this paper is to show that the whole discussion of the previous paper can be generalized to non-metric Ockhamist tense logics and to prove the semantics of branching structures formulated in full detail by Thomason validates the formula.
Abstract: The main purpose of this paper is to show that the whole discussion of our previous paper (Nishimura, 1979) can be generalized to non-metric Ockhamist tense logics. Since the difficulty arises solely in our present version of Theorem 5, the rest of this paper is devoted to the proof that the semantics of branching structures formulated in full detail by Thomason (1970, Section 7) validates the formula
TL;DR: In many important philosophical discussions the authors need a formal theory of tensed modalities or a combined modal and tense logic, and can this semantical approach be extended to metric tense logics with modal operators or, as I prefer to call them, chronological modal logics?
Abstract: In many important philosophical discussions we need a formal theory of tensed modalities or a combined modal and tense logic. As McArther (1976, Chapter 3), McKim and Davis (1976), Thomason (1970) and the like have argued, the semantics of branching structures is indeed adequate for many non-metric tense logics with modal operators like OT in the sense that semantical completeness can be established. Can we extend this semantical approach to metric tense logics with modal operators or, as I prefer to call them, chronological modal logics? In Nishimura (1979) we have already proved that the semantics of causal structures was indeed adequate for chronological modal logics. Causal structures may be called "parallel histories", "history-time index systems with the likeness relation", etc., if the reader wants to. Thus if we were able to prove the eqiiivalence of branching structures and causal structures, the adequacy of branching structures for chronological modal logics would follow immediately. Which semantics we should adopt be a matter of taste in this case.
TL;DR: Using an unlabeled bracketing of syntactic structure and recursive definitions, the rules for other grammatical constructions do not take conjunction or disjunction into account, and in general fail either syntactically or semantically when one of their arguments is so formed.
Abstract: Although Montague claims that the system of The proper treatment of quantification in ordinary English includes some conjunction and disjunction, the rules for other grammatical constructions do not take conjunction or disjunction into account, and in general fail either syntactically or semantically when one of their arguments is so formed. Using an unlabeled bracketing of syntactic structure and recursive definitions, we have been able to rewrite the rules so that correct results are obtained.
TL;DR: Now that Martin in [3] has solved the PW problem, the stock of ancient open problems for the relevant logics has been reduced to one and the Last Problem, for therelevant logics, is the question of their decidability.
Abstract: Now that Martin in [3] has solved the PW problem, the stock of ancient open problems for the relevant logics has been reduced to one. (Fresh problems are ever upon us, to be sure, such as the question of semantical completeness for relevant quantification theories raised in [4]. But I speak here only of problems of sufficient age and venerability to have defeated a generation of scholars a sufficient but not necessary condition is that the problem should have been mentioned in [5] and the relevant logics have provided but one such.) The Last Problem, for the relevant logics, is the question of their decidability. It is, to borrow a phrase used by J. Ehrlichman in [6] (in another problematic situation) the Big Enchilada. While the honors of Old Age are due the problem, the reader who elects to try it is to be warned that it remains in the best of health, and it is not likely soon to join PW among those problems that have gone to their Reward. (The Reward is to have its solution published somewhere, with all honor, glory, and, in extreme cases, tenure due the champion that has vanquished it.) Moreover, Old Age has made the decidability problem for R, E, and their closest relatives even more crotchety. Beware, dear Reader. This problem has defeated better men than you, as your humble author will be the first to testify. Most of those who have dragged themselves away from hand-tohand combat with the Big Enchilada (and contented themselves with fresh battles on easier terrain, such as Quantum Mechanics and the General Theory of Relativity) have left in complete defeat, all their ideas having been busted and with nothing left to try. (Your bedraggled author will testify to that, too.) One Warrior, however, has had a plan. Aside from the brief but telling encounter with the decision question recounted by Kripke in [7], it is the only plan to have produced a significant advance in the status of the decidability question. Ever. The scholar with the plan is Belnap. He calls his plan 'career induction' (whence the title of this essay). The plan is to whittle away at the formulas of R, a degree at a time. Since the 0-degree formulas
TL;DR: The system C of Pottinger (1974) has as primitive logical constants = (entailment), -9 (S4 strict implication), -, (relevant implication), D (intuitionist implication), and A (absurdity); it was pointed out that the addition of either 2-A A or 2B 2A collapses -* into material implication.
Abstract: The system C of Pottinger (1974) has as primitive logical constants = (entailment), -9 (S4 strict implication), -, (relevant implication), D (intuitionist implication), & (intuitionist conjunction), v (intuitionist disjunction), and A (absurdity). In Section 8 of Pottinger (1974) it was pointed out that the addition of either 2-A A or 2B 2A .A B2 to C collapses -* into material implication and that the addition of either 21A * A or
TL;DR: In his paper 'What is Referential Opacity?' Bell argues that the answer to this question is to be found in Donnellan's familiar referential/attributive distinction (henceforth R/A D), and treats the latter as an ambiguity which should be represented at the level of logical structure.
Abstract: In his paper 'What is Referential Opacity?' (Journal of Philosophical Logic 2 (1973), 155-180), Bell argues that the answer to this question is to be found in Donnellan's familiar referential/attributive distinction (henceforth R/A D). Bell treats the latter as an ambiguity which should be represented at the level of logical structure. He then accounts for Quine's transparent/ opaque distinction in terms of the R/A D. That is, the (generally accepted) ambiguity in a sentence like (1) follows automatically, in Bell's view, from the presence of an ambiguity in the embedded sentence (2).
TL;DR: The generalized normal frame (gnf) is introduced to provlde semantics for orthomodular (OM) logic as supplemented by certain conditional functions the normal implications, which discusses the relationship of normal implications to other conditional-like functions that are defmed on the lattices in question.
Abstract: In [3], the generalized normal frame (gnf) is introduced to provlde semantics for orthomodular (OM) logic as supplemented by certain conditional functions the normal implications. [3] does not discuss the relationship of normal implications to other conditional-like functions that are defmed on the lattices in question; of interest are the “Sasaki conditional” (see [ 1,2] , for example), defmed:
TL;DR: It is shown that Frege's explanation of what is expressed by statements of number suggests an obvious way of representing propositions expressed by existence sentences, and a natural extension of this method to general propositions is suggested.
Abstract: All of the above seem content to leave general propositions alone, and Donnellan admits that "no obvious way of representing propositions expressed by existence sentences suggests itself."4 I will show that Frege's explanation of what is expressed by statements of number suggests an obvious way of representing propositions expressed by existence sentences. I will also suggest a natural extension of this method to general propositions. We will represent the proposition expressed by a subject-predicate sentence (Fa) by an ordered pair consisting of an object and a concept (in Frege's sense). An n-place relation sentence will be represented by an ordered pair consisting of an ordered n-tuplet of objects, and an n-place relation-concept.