In his essay on 'Broad on Induction and Probability' (first published in 1959, reprinted in this volume), Professor G. H. von Wright writes: "If Broad's writings on induction have remained less known than some of his other contributions to philosophy . . . , one reason for this is that Broad never has published a book on the subject. It is very much to be hoped that, for the benefit of future students, Broad's chief papers on induction and probability will (...) be collected in a single volume . . . . " The present volume attempts to perform this service to future students of induction and probability. The suggestion of publishing a volume of this kind in Synthese Library was first made by Professor Donald Davidson, one of the editors of the Library, and was partly prompted by Professor von Wright's statement. In carrying out this suggestion, the editors of Synthese Library have had the generous support of Professor Broad who has among other things supplied a new Addendum to 'The Principles of Problematic Induction' and corrected a number of misprints found in the first printings of this paper. The editors gratefully acknow ledge Professor Broad's help and encouragement. A bibliography of Professor Broad's writings (up to 1959) has been compiled by Dr. C. Lewy and has appeared in P. A. Schilpp, editor, The Philosophy of C. D. Broad (The Library of Living Philosophers), pp. 833-852. (shrink)

In his essay on 'Broad on Induction and Probability' (first published in 1959, reprinted in this volume), Professor G. H. von Wright writes: "If Broad's writings on induction have remained less known than some of his other contributions to philosophy..., one reason for this is that Broad never has published a book on the subject. It is very much to be hoped that, for the benefit of future students, Broad's chief papers on induction and probability will be collected in a (...) single volume.... " The present volume attempts to perform this service to future students of induction and probability. The suggestion of publishing a volume of this kind in Synthese Library was first made by Professor Donald Davidson, one of the editors of the Library, and was partly prompted by Professor von Wright's statement. In carrying out this suggestion, the editors of Synthese Library have had the generous support of Professor Broad who has among other things supplied a new Addendum to 'The Principles of Problematic Induction' and corrected a number of misprints found in the first printings of this paper. The editors gratefully acknow ledge Professor Broad's help and encouragement. A bibliography of Professor Broad's writings (up to 1959) has been compiled by Dr. C. Lewy and has appeared in P. A. Schilpp, editor, The Philosophy of C. D. Broad (The Library of Living Philosophers), pp. 833-852. (shrink)

Building on the work of Sproule, Fahnestock and Secor, and Kruger, we present a specific typology of statements. In particular, we distinguish broadly logically determinate statements, descriptions, interpretations, and evaluations. We generate this typology through a series of dichotomous divisions of statements. We divide statements first into the broadly logically determinate versus contingent, the contingent into the evaluational versus natural, and the natural into the extensional versus intensional. We show that the rationales for these (...) distinctions are well motivated and philosophically important. In particular, we argue that identifying the type of a statement is relevant to showing whether or not the sources vouching for it render the statement epistemically acceptable. (shrink)

The article covers such issues as the relevance of the theory of perception as a multi-level information processing, the methodological role of the concept of representation and the relation of neurodynamic structures to subjective experience. The author critically reviews the philosophical presumptions underlying the various concepts of “local rationality,” the core of which is constituted by the belief that large ethnic cultures generate or are based on their own rationality and their own logic. Three statements are successively considered: thinking is (...) based on the inherent rules of rationality, logic is an extract of rationality, and types of rationality are geographically consistent with large ethnocultural communities. Empirical arguments are presented that demonstrate equivocality of the first two theses. In particular, firstly, it is shown that the genuine rationality of thinking lies not in following the rules that are immanent to it, but in the development of thinking and, more broadly, cognitive operations towards optimization of certain indicators of the cognitive or motor system that are important for survival and adaptation. In addition, this rationality is multivariate, and the choice between variants is often weakly determined or even random. Thus, the first statement turns out to be refuted. Secondly, by reference to the well-known experiments, it is shown that most people do not explicitly follow some declared logical rules in solving even logical or mathematical problems, and yet there is reason to consider their behavior rational. The third thesis, as shown with some limited empirical material, appears to be partially confirmed. Nevertheless, the demonstration of the doubtfulness of the first two theses makes the conclusion that different nations have different logics insufficiently substantiated. (shrink)

Agustín Rayo’s The Construction of Logical Space offers an exciting and ambitious defense of a broadly Carnapian approach to metaphysics. This essay will focus on one of the main differences between Rayo’s and Carnap’s approaches. Carnap distinguished between analytic, a priori “meaning postulates”, and empirical claims, which were both synthetic and knowable only a posteriori. Like meaning postulates, they determine the boundaries of logical space. But Rayo is skeptical that the a priori/a posteriori or analytic/synthetic distinctions can do the (...) work Carnap wanted them to, so unlike meaning postulates, ‘just is’-statements aren’t assumed to be analytic or knowable a priori. This essay will concern the epistemology of ‘just is’-statements in Rayo’s picture. If not by a priori reflection, how can we determine which ones to accept? I’ll distinguish two competing strands in Rayo’s work. The less radical, Lewisian strand holds that the question of whether to accept a ‘just is’-statement can be addressed in a neutral, non-question-begging way, by a kind of cost-benefit analysis. The more radical, Kuhnian strand holds that there can be no ‘just is’-statement-independent, rational choice of which ‘just is’-statements to accept. I argue that Rayo faces strong internal pressure to adopt the Kuhnian picture. While it is possible for Rayo to resist these Kuhnian pressures, natural strategies for doing so leave his view more similar to Carnap’s than the above gloss suggested. (shrink)

Discrepancies between the Uniform Determination of Death Act (UDDA) and the adult and pediatric diagnostic guidelines for brain death (BD) (the “Guidelines”) have motivated proposals to revise the UDDA. A revision proposed by Lewis, Bonnie and Pope (the RUDDA), has received particular attention, the three novelties of which would be: (1) to specify the Guidelines as the legally recognized “medical standard,” (2) to exclude hypothalamic function from the category of “brain function,” and (3) to authorize physicians to conduct an apnea (...) test without consent and even over a proxy’s objection. One hundred seven experts in medicine, bioethics, philosophy, and law, spanning a wide variety of perspectives, have come together in agreement that while the UDDA needs revision, the RUDDA is not the way to do it. Specifically, (1) the Guidelines have a non-negligible risk of false-positive error, (2) hypothalamic function is more relevant to the organism as a whole than any brainstem reflex, and (3) the apnea test carries a risk of precipitating BD in a non-BD patient, provides no benefit to the patient, does not reliably accomplish its intended purpose, and is not even absolutely necessary for diagnosing BD according to the internal logic of the Guidelines; it should at the very least require informed consent, as do many procedures that are much more beneficial and less risky. Finally, objections to a neurologic criterion of death are not based only on religious belief or ignorance. People have a right to not have a concept of death that experts vigorously debate imposed upon them against their judgment and conscience; any revision of the UDDA should therefore contain an opt-out clause for those who accept only a circulatory-respiratory criterion. (shrink)

I will begin this paper by stating in rough outline what I consider to be the relevance of psychical research to philosophy, and I shall devote the rest of it to developing this preliminary statement in detail.

Our modern ideals about liberty were forged in the great political and philosophical debates of the 17th and 18th centuries, but we seldom hear about women's contributions to those debates. This paper examines the ideas of early modern English women – namely Margaret Cavendish, Mary Astell, Mary Overton, ‘Eugenia’, Sarah Chapone and the civil war women petitioners – with respect to the classic political concepts of negative, positive and republican liberty. The author suggests that these writers' woman-centred concerns provide a (...) unique historical perspective on these much-discussed ideals of freedom from external interference, freedom as self-determination and freedom from domination. (shrink)

In his correspondence, John Locke described his close friend Damaris Masham as ‘a determined foe to ecclesiastical tyranny’ and someone who had ‘the greatest aversion to all persecution on account of religious matters.’ In her short biography of Locke, Masham returned the compliment by commending Locke for convincing others that ‘Liberty of Conscience is the unquestionable Right of Mankind.’ These comments attest to Masham’s personal commitment to the cause of religious liberty. Thus far, however, there has been no scholarly discussion (...) of the tolerationist ethic underlying Masham’s 1705 publication, Occasional Thoughts. In this chapter, I argue that Masham’s work appeals to three common tolerationist principles of her time: the idea that the authorities should not use coercion and penalties as ways of imposing religious beliefs on others; the view that God requires human beings to attain salvation through their own efforts, and not by blindly following the dictates of the state-established religion; and the idea that the granting of liberty of conscience helps to ensure the peace and stability of political society. I show that Masham goes further than her tolerationist contemporaries by arguing that together these principles imply that a woman’s intellectual education—or the conscious cultivation of a woman’s ability to reflect critically on her religious beliefs—is vital for the good of the commonwealth. (shrink)

Everyone is or ought to be acquainted with the thesis of Meinong's extraordinarily able and important work. It is that beside acts of judgment and ideas there is an intermediate kind of psychical state -- the act of supposing -- which resembles judgment in that its content can be affirmative or negative, but differs from it and resembles ideas in that it is unaccompanied by conviction. Meinong tries to show that it is necessary to assume such acts for a variety (...) of reasons and that they throw a light on some of the most; difficult questions in the theory of knowledge. The extreme value of the book lies not merely in the evidence brought forward for the existence of suppositions, but in the discussions to which the search for suppositions gives rise on all manner of difficult points in logic and what Meinong calls 'Gegenstandstheorie'. There is further a contribution to Ethics and Aesthetics in Meinong's attempt to show the necessity of assuming something comparable to suppositions in the realms of Feeling and Volition. (shrink)

IN a letter to the Editor of MIND, Mr. G. T. Bennett of Emmanuel College, Cambridge, points out a stupid slip which I made on page 499 of MIND, N.S., No. 124. In illustrating Mr. Johnson's analysis of the subsumptive syllogism in my review of his Logic, Part II., I took as a major premise the proposition “Everything with sides and angles is equiangular, if equilateral”. This is, of course, ridiculously false, as Mr. Bennett points out. A figure made of (...) four equal jointed rods could be pushed into many different shapes. I want to make it quite clear that this is a slip.of my own, and that nothing of the kind occurs in Mr. Johnson's book. Of course, for purposes of illustration, it is a matter of indifference whether we choose false propositions or true ones, so that no injustice has been done to Mr. Johnson's theory. But I am not going to pretend that I did not think this proposition to be true at the moment when I wrote it down. I am sorry to have been so careless, and I should be still more sorry if anyone should have ascribed the carelessness to Mr. Johnson himself and not to his reviewer. I must thank Mr. Bennett for pointing out the mistake. (shrink)

Many philosophers take purportedly logical cases of ground ) to be obvious cases, and indeed such cases have been used to motivate the existence of and importance of ground. I argue against this. I do so by motivating two kinds of semantic determination relations. Intuitions of logical ground track these semantic relations. Moreover, our knowledge of semantics for first order logic can explain why we have such intuitions. And, I argue, neither semantic relation can be a species of ground even (...) on a quite broad conception of what ground is. Hence, without a positive argument for taking so-called ‘logical ground’ to be something distinct from a semantic determination relation, we should cease treating logical cases as cases of ground. (shrink)

Natural languages are riddled with context-sensitivity. One and the same string of words can express many different meanings on occasion of use, and yet we understand one another effortlessly, on the fly. How do we do so? What fixes the meaning of context-sensitive expressions, and how are we able to recover the meaning so effortlessly? -/- This book offers a novel response: we can do so because we draw on a broad array of subtle linguistic conventions that determine the interpretation (...) of context-sensitive items. Contrary to the dominant tradition, which maintains that the meaning of context-sensitive language is underspecified by grammar and that interpretation relies on non-linguistic cues and speakers' intentions, this book argues that meaning is determined entirely by discourse conventions, rules of language that have largely been missed and the effects of which have been mistaken for extra-linguistic effects of an utterance situation on meaning. The linguistic account of context developed here sheds new light on the nature of linguistic content and the interaction between content and context. At the same time, it provides a novel model of context that should constrain and help evaluate debates across many subfields of philosophy where appeal to context has been common, often leading to surprising conclusions such as epistemology, ethics, value theory, metaphysics, metaethics, and logic. (shrink)

The book is a collection of papers and aims to unify the questions of syntax and semantics of language, which are included in logic, philosophy and ontology of language. The leading motif of the presented selection of works is the differentiation between linguistic tokens (material, concrete objects) and linguistic types (ideal, abstract objects) following two philosophical trends: nominalism (concretism) and Platonizing version of realism. The opening article under the title “The Dual Ontological Nature of Language Signs and the Problem of (...) Their Mutual Relations” provides a broad introduction into the problem area connected with this differentiation, while the logic-formal characteristics of the distinction are framed in the work entitled “On the Type-Token Relationships” (Chapter 1). The basic part of the book deals with issues relating to syntax (Chapters 2-4) and semantics of language (Chapters 5-6), as well as pertaining to syntactic-semantic pragmatic questions (Chapters 7-13). Throughout the book, language, categorial language, is characterized syntactically as generated by classical categorial grammar (Chapter 2) and formalized on two opposing levels: as language of expression-tokens (level of tokens) and language of expression-types (level of types). The author’s considerations contained in Chapters 2 and 4 lead to the important philosophical conclusion that in formal-logical syntactic studies on language the assumption that expression-types constitute the primary language layer while expression-tokens make the secondary one, can be neglected; thus, this speaks in favour of the opposing standpoint—the concretistic one—in the ontology of language syntax. In the works “Meaning and Interpretations”, Parts I and II (Chapters 5 and 6), it is underlined, however, that such semantic concepts as: meaning, denotation and interpretation are defined on the types level, yet their formal definitions require making use of notions of the tokens level. The semantic notions introduced in the above-mentioned articles are also used in the following works of the present selection, under the titles: “Three Principles of Compositionality” and “On Metaknowledge and Truth” (Chapters 7 and 8). They formalize two principles of compositionality that are well known in the literature on the subject, deriving from Frege, i.e. those of meaning and of denotation; they are related to the syntactic principle of compositionality which was introduced by the author. All the three principles are, at the same time, three conditions of homomorphism of categorial language algebra into three kinds of non-standard models of language (one syntactic and two semantic ones: intensional and extensional), which allows introducing three definitions of truthfulness into these models. The next two works in the collection, entitled: “On Language Adequacy” and “What is the Sense in Logic and Philosophy of Language” (Chapters 9 and 10) concern adequacy of categorial language syntax along with its dual semantics: intensional and extensional, and categorial compatibility of any of its syntactic categories with two corresponding semantic categories: intensional and extensional, based on the compatibility the syntactic category of each language expression with the ontological category assigned to its denotatum. The well-known problem of categorial compatibility for first-order quantifiers finds its solution in the paper “Categories of First-Order Quantifiers” (Chapter 11). In the work “Logic and Ontology of Language” (Chapter 12), being in a sense a summary of the considerations presented in the preceding chapters of the book, language is treated as an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. Application—like throughout the book—of tools of classical logic and set theory has resulted in emergence of a general formal logical theory of syntax, semantics and pragmatics of language, which takes into account duality in the understanding of linguistic expressions as tokens (concretes) and types (abstract objects). In terms that take into account a functional approach to language itself, there comes out an ontological neutrality of logic with respect to existential assumptions relating to the ontological nature of linguistic expressions and their extra-linguistic ontological counterparts. The issues connected with applying logic while explaining the manner of using linguistic tokens and linguistic types to determine notions of language communication are raised and illustrated in the last chapter of the work, bearing the title “A Logical Conceptualization of Knowledge on the Notion of Language Communication”. (shrink)

This paper discusses two broadly logical issues related to Protagoras’ measure doctrine (M) and the self-refutation argument (SRA). First, I argue that the relevant interpretation of (M) has it that every individual human being determines all her own truths, including the truth of (M) itself. I then turn to what I take to be the most important move in the SRA: that Protagoras recognises not only that his opponents disagree with him about the truth of (M), but also that (...) they hold that (M) is false simpliciter. By recognising that his opponents do not make the relativising concession he makes for them, he is forced to accept that (M) is false. I go on to argue that several other defenders of the SRA end up with a regress which is difficult to end and might not favour anti-Protagoreans. On my reading, by recognising what his opponents believe, Protagoras is barred from adding qualifiers, and the possible regress doesn’t get off the ground. I conclude with brief discussions of how Protagoras might try to avoid the result of the SRA and the argument’s role in this part of the Theaetetus. (shrink)

1. "The map of logic." Comparatively recently, Kant's words to the effect that in the two thousand years since Aristotle logic had made "not a single step forward and, all things considered, it seems to be a fully finished and completed discipline" used to be quoted widely and not unsympathetically. Today, however, there are works about logic in which the listing of logical disciplines runs into the dozens. In this regard the attempt by the American logician N. Rescher to compile (...) a diagram or "map of logic," in which the list of the branches of logic takes up several pages, is noteworthy. Also characteristic is the following statement by one of the major modern representatives of mathematical logic, S. Kleene: "Since the discovery of non-Euclidean geometries by Lobachevsky and Bolyai , it has become clear that different systems of geometries are conceptually equally possible…. Identically, there are different logics.". (shrink)

In his recent book, Causation: A Realistic Approach , Michael Tooley discusses the following thesis, which he calls the ‘thesis of the Humean Supervenience of Causal Relations’: The truth values of all singular causal statements are logically determined by the truth values of statements of causal laws, together with the truth values of non-causal statements about particulars . represents one version of the ‘Humean’ idea that there is no more factual content to the claim that two particular events are (...) causally connected than that they occur, instantiate some law or regularity, and perhaps bear some appropriate non-causal to each other. This is an idea that is tacitly or explicitly assumed in most familiar accounts of singular causal statements. For example is assumed by many probabilistic theories of singular causal statements, by theories which attempt to analyse singular causal statements in terms of necessary and sufficient conditions, and, as I shall argue below, by David Lewis' counterfactual theory. (shrink)

The standard use of the propositional calculus ('P.C.?) in analyzing the validity of inferences involving conditionals leads to fallacies, and the problem is to determine where P.C. may be ?safely? used. An alternative analysis of criteria of reasonableness of inferences in terms of conditions of justification rather than truth of statements is proposed. It is argued, under certain restrictions, that P. C. may be safely used, except in inferences whose conclusions are conditionals whose antecedents are incompatible with the premises in (...) the sense that if the antecedent became known, some of the previously asserted premises would have to be withdrawn. (shrink)

Simple explanations are very often inadequate and can encourage faulty inferences. We examined college students’ explanations regarding illegal immigration to determine the prevalence of single-factor explanations. The form of students’ explanations was predicted by their responses on a simple three-item forced-choice multivariable causal reasoning task in which they selected the strongest evidence against a causal claim. In a further qualitative investigation of explanations by a sample of community adults, we identified positive features among those who scored high on this multivariable (...) causal reasoning task. We consider limitations of single-factor reasoning and means of encouraging more comprehensive explanations to support claims. (shrink)

Spinoza ’s letter of June 2, 1674 to his friend Jarig Jelles addresses several distinct and important issues in Spinoza ’s philosophy. It explains briefly the core of Spinoza ’s disagreement with Hobbes’ political theory, develops his innovative understanding of numbers, and elaborates on Spinoza ’s refusal to describe God as one or single. Then, toward the end of the letter, Spinoza writes: With regard to the statement that figure is a negation and not anything positive, it is obvious (...) that matter in its totality, considered without limitation [indefinitè consideratam], can have no figure, and that figure applies only to finite and determinate bodies. For he who says that he apprehends a figure, thereby means to indicate simply this, that he apprehends a determinate thing and the manner of its determination. This determination therefore does not pertain to the thing in regard to its being [esse]; on the contrary, it is its non-being [non-esse]. So since figure is nothing but determination, and determination is negation [Quia ergo figura non aliud, quam determinatio, et determinatio negatio est], figure can be nothing other than negation, as has been said. Arguably, what is most notable about this letter is the fate of a single subordinate clause which appears in the last sentence of this passage: et determinatio negatio est. That clause was to be adopted by Hegel and transformed into the slogan of his own dialectical method: Omnis determinatio est negatio. Of further significance is the fact that, while Hegel does credit Spinoza with the discovery of this most fundamental insight, he believes Spinoza failed to appreciate the importance of his discovery. The issue of negation and the possibility of self-negation stand at the very center of the philosophical dialogue between the systems of Spinoza and Hegel, and in this paper I will attempt to provide a preliminary explication of this foundational debate between the two systems. In the first part of the paper I will argue that the “determination is negation” formula has been understood in at least three distinct senses among the German Idealists, and as a result many of the participants in the discussion of this formula were actually talking past each other. The clarification of the three distinct senses of the formula will lead, in the second part of the paper, to a more precise evaluation of the fundamental debate between Spinoza and Hegel regarding the possibility of self-negation. In this part I will evaluate the validity of each interpretation of the determination formula, and motivate the positions of the various participants in the debate. (shrink)

To accommodate vague statements and predicates, I propose an infinite-valued, non-truth-functional interpretation of logic on which the tautologies are exactly the tautologies of classical two-valued logic. iI introduce a determinacy operator, analogous to the necessity operator in alethic modal logic, to allow the definition of first-order and higher-order borderline cases. On the interpretation proposed for determinacy, every statement corresponding to a theorem of modal system T is a logical truth, and I conjecture that every logical truth on the interpretation (...) corresponds to a theorem of T. the interpretation is extended to predicate logic. A borderline case of a predicate 'F’ is neither determinately F nor determinately not-F. Traditional sorites arguments are seen to fall apart early in their gradual stepwise passage from truth to falsity. (shrink)

In 2018, three journalists accused one of the Members of the Russian Parliament of harassment at workplace. Many influential persons of the Russian elite engaged themselves in the public discussion of the conflict. We studied that high-profiled discussion using a hybrid method merging human- and logic-oriented approaches in argumentation studies. The method develops ideas of the new dialectics, the argumentation logic and the logical-cognitive approach to argumentation, on which is based the algorithm for determining of dispute resolution by aggregating formal (...) and informal tools of analysis. We have reconstructed the discussion as two disputes about questions A and B. A: Did the MP violate the code of conduct by making statements or actions against the journalists? B: Are actions like the behavior of the MP harassment? The opinions of the discussion participants were grouped into the four points of view: A1 – the MP did not violate the code of conduct, A2 – the MP violated the code of conduct, B3 – the actions are not harassment, B4 – the actions are harassment. We mapped arguments in support or against each of them using OVA software, evaluated the arguments with the help of the critical questions, a tool proposed in the new dialectics, and determined the ultimate A + B resolution by applying of the algorithm that combines elements of gradual and labelling semantics from the argumentation logic and the classification of disputes from the dialectical approaches. The resolution was a subset of four arguments that ensured the victory of A1+B4. However, the substantial incompatibility of those arguments highlighted a deep disagreement, an unresolvable difference of opinion, between the parties about the permissibility of courtship. The deep disagreement, a bonus result yielded by the application of the hybrid method, excluded the interpretation of the determined resolution as convincing for the parties, but pointed out a way to smooth the difference of opinions by elaborating of legal, social and moral aspects of the problem of harassment at workplace. (shrink)

“Grammar” is Ludwig Wittgenstein's preferred term for the workings of a language: the system of rules that determine linguistic meaning. A philosophical study of language is a study of “grammar”, in this sense, and insofar as any philosophical investigation is concerned with conceptual details, which manifest themselves in language, it is a grammatical investigation. In the Tractatus Logico‐Philosophicus Wittgenstein offered a mathematical picture of language: presenting language as a calculus. Like a calculus, language was claimed to be governed by syntactic (...) rules: formation rules about the licit combination of names to form elementary propositions; formation rules about the licit combination of elementary propositions to make complex propositions; and finally, truth‐table rules, which enable us to identify logical truths and entailments. Logical grammar, for the young Wittgenstein, is only logical syntax and logical syntax can be determined without paying any attention to the meaning of the signs. (shrink)

The author discusses various concepts of observation statements, subjecting to closer examination that concept according to which an observation statement is a statement with all terms interpreted directly. The logical analysis of direct interpretation, identified with the so called ostensive definition, results in the conclusion that the denotation of predicates is determined by this procedure in a very slight degree. Consequently, observation statements affirming a predicate so interpreted of objects not identical with the standard objects referred to in (...) the ostensive definition cannot be validated. (shrink)

This article investigates the connection and dependence between the definiteness of the totalities involved in mathematical structures and the determinateness of statements about that structure. From a logical perspective, we investigate whether logical principles expressing the definiteness of totalities license the use of classical logic. From a philosophical perspective, this article provides a reconstruction of Solomon Feferman’s claim that the definiteness of the natural number conception implies the determinateness of arithmetical statements and therefore justifies the adoption of classical logic for (...) arithmetical theories. (shrink)

It is usually held that what distinguishes a good inference from a bad one is that a good inference is truth-preserving. Against this view, this paper argues that a logical inference is good or bad depending not on whether it is truth-preserving or not, but whether it belongs to a logical system the addition of which makes a deductively conservative extension of the derivation relations among the atomic statements. To so argue, the paper first contends that the meaning of the (...) logical operators of classical logic is determined not by their connections to truth, but by their inferential roles. It is claimed in conclusion that there is no genuine issue over which logic, classical or intuitionistic, is the correct logic, for they are both conservative in the relevant sense. (shrink)

It is usually held that what distinguishes a good inference from a bad one is that a good inference is truth-preserving. Against this view, this paper argues that a logical inference is good or bad depending not on whether it is truth-preserving or not, but whether it belongs to a logical system the addition of which makes a deductively conservative extension of the derivation relations among the atomic statements. To so argue, the paper first contends that the meaning of the (...) logical operators of classical logic is determined not by their connections to truth, but by their inferential roles. It is claimed in conclusion that there is no genuine issue over which logic, classical or intuitionistic, is the correct logic, for they are both conservative in the relevant sense. (shrink)

The notion of logical form and its applications are at the heart of some of the classical problems in philosophical logic and are the focus of Peter Long’s investigations in the three essays that comprise this volume. In the first, major, essay the concern is with the notion of logical form as it applies to arguments involving hypotethical statements, for example ‘If today is Wednesday then tomorrow is Thursday; today is Wednesday: therefore tomorrow is Thursday.’ Whilst such an argument is (...) cited by logical textbooks as a paradigm of one that is ‘formally valid’, it is not hard to show that the conjunction forming a hypothetical statement is not a logical constant, in which case the argument form If p then q; p: therefore q is not a logical form. But, then, how can logic claim to be the science of formal inference? The author resolves this difficulty by drawing a fundamental distinction within the notion of the form under which an argument is valid. With this distinction it becomes possible for the first time to determine the status of any formally valid argument involving hypotheticals, whether as premises or conclusion or both. The second and third essays take up the notion of logical form as it applies to such simple propositions as ‘This sheet is white’ and ‘London is north of Paris.’ When we speak of the first as giving expression to the relation of relations’s relating to its terms, what is in question is a formal relation and we call it such because the relation is expressed through these propositions having the respective forms Fa and Fab. It is shown that the confusion of formal relations with relations proper explains the assimilation of facts to complexes and is that the root of the theory of universals. _Peter Long_ has taught at the University of Leeds and University College London, and is a past Fellow of Trinity College, Cambridge. (shrink)

As far as logic is concerned, the conclusion of Michael Dummett's manifestability argument is that intuitionistic logic, as first developed by Heyting, satisfies the semantic requirements of antirealism. The argument may be roughly sketched as follows: since we cannot manifest a grasp of possibly justification-transcendent truth conditions, we must countenance conditions which are such that, at least in principle and by the very nature of the case, we are able to recognize that they are satisfied whenever they are. Intuitionistic logic (...) satisfies the semantic requirement that we should either eschew the notion of truth altogether and replace it by provability in principle, or constrain it by provability in principle (Dummett [1973] 1978). (Handout: 1-5). Some philosophers have argued that the traditional antirealist desideratum of decidability in principle is too weak, so that semantic antirealism properly construed must be committed to effective decidability. As such, it either leads to strict finitism (Wright [1982] 1993) [Handout: 6] or to a much stronger kind of logical revisionism than the one considered by intuitionists (whether or not they accept the manifestability argument): substructural logics, and in particular linear logics, rather than intuitionistic logic, satisfy the semantic requirements of strict antirealism (Dubucs and Marion 2004) [Handout: 8-9]. I shall develop two different kinds of replies. The first is concerned with the notion of meaning per se and looks to strict finitism directly, although not on the ground that it would provide a correct way of dealing with Soritic-type paradoxes (the original and primary focus of discussion in Wright [1982] 1993). The second is concerned with the justification of structural and logical rules in a natural deduction system à la Gentzen. It will deal in particular with the criticism of the structural rules of Weakening and Contraction [Handout: 10 and 11]. The first kind of reply, which Dummett has partially taken into consideration, is that if we jettison the effectively vs. in principle distinction, as applied to manifestability-type arguments, we end up with an unsatisfactory explanation of how the meaning of statements covering the practically unsurveyable or pro tempora undecided cases is fixed. The idea is that if we have a method which may be used over some small range, we have determined a way of applying the method everywhere in principle and that this is enough as far as fixing meaning is concerned. Decidability in principle is just what we need with respect to manifestation of grasp of meaning. In this perspective, antirealism shouldn't be strict and manifestability-type arguments need not be applied as far as the strict finitist would want to [Handout: 7]. It follows that there is no reason to think that practical feasibility should be built in assertibility conditions and proofs be construed dynamically as acts in the strict antirealist's acception of that term [Handout: 8]. I shall then look at one radical antirealist principle disqualifying structural rules, namely Token Preservation, arguing against Bonnay and Cozic's criticisms of Dubucs and Marion (Bonnay and Cozic 3 2007) that some conceptual support may be provided for Token Preservation, which doesn't rely on a causal misreading of the turnstile [Handout: 13, 14]. I shall then assess the merits and limits of radical antirealism and the logic of feasible proofs with respect to the original Dummettian argument in favour of semantic antirealism (provided it has indeed revisionist implications for logic), whether the radical antirealist merely stipulates what human feasibility amounts to, or dispenses with structural rules in order to argue in favour of a curb on the epistemic idealizations they unwarrantedly embed. It will be noted here that there is a great difference, conceptually speaking, between the rejection of classical logic via the curbing of the epistemic idealizations embedded in structural rules, and the rejection of classical logic via the criticism of the introduction and elimination rules which fix the meaning of the classical constants. The kind of logical revisionism envisaged by intuitionists from Heyting on is in many respects stronger than the one envisaged by advocates of linear logic, should they ground their arguments on an endorsement of strict antirealism. The crucial case of excluded middle is telling. Because of the splitting of the constants in linear logic (Handout: 12], two distinct laws of excluded middle may be formulated (Handout: 15), but the traditional arguments of Brouwer and Heyting against the classical law yield a stronger revision than the substructural revision with its admission of these two (very) weak versions of the law. (Project: a clearer conception is needed of how the introduction and elimination rules for the logical connectives in the intuitionistic calculus depend on the structural rules which the radical antirealist wishes to reject.). (shrink)

The proof of the Second Incompleteness Theorem consists essentially of proving the uniqueness and explicit definability of the sentence asserting its own unprovability. This turns out to be a rather general phenomenon: Every instance of self-reference describable in the modal logic of the standard proof predicate obeys a similar uniqueness and explicit definability law. The efficient determination of the explicit definitions of formulae satisfying a given instance of self-reference reduces to a simple algebraic problem-that of solving the corresponding fixed-point equation (...) in the modal logic. We survey techniques for the efficient calculation of such fixed-points. (shrink)

A recurring issue in any formal model representing agents' (changing) informational attitudes is how to account for the fact that the agents are limited in their access to the available inference steps, possible observations and available messages. This may be because the agents are not logically omniscient and so do not have unlimited reasoning ability. But it can also be because the agents are following a predefined protocol that explicitly limits statements available for observation and/or communication. Within the broad (...) literature on epistemic logic, there are a variety of accounts that make precise a notion of an agent's "limited access" (for example, Awareness Logics, Justification Logics, and Inference Logics). This paper interprets the agents' access set of formulas as a constraint on the agents' information gathering process limiting which formulas can be observed. (shrink)

A conversational implicature is an inference that consists in attributing to a speaker an implicit meaning that goes beyond the explicit linguistic meaning of an utterance. This paper experimentallyinvestigates scalar implicature, a paradigmatic case of implicature in which a speaker's use of a term like Some indicates that the speaker had reasons not to use a more informative one from the samescale, e.g. All; thus, Some implicates Not all. Pragmatic theorists like Grice would predict that a pragmatic interpretation is determined (...) only after its explicit, logical meaning is incorporated (e.g. whereSome means at least one). The present work aims to developmentally unpack this prediction by showing how younger, albeit competent, reasoners initially treat a relatively weak term logically beforebecoming aware of its pragmatic potential. Three experiments are presented. Experiment 1 presents a modal reasoning scenario offering an exhaustive set of conclusions; critical among these isparticipants' evaluation of a statement expressing Might be x when the context indicates that the stronger Must be x is true. The conversationally-infelicitous Might be x can be understood logically(e.g. as compatible with Must) or pragmatically (as exclusive to must). Results from five-, seven-, and nine-year-olds as well as adults revealed that a) seven-year-olds are the youngest to demonstratemodal competence overall and that; b) seven- and nine-year-olds treat the infelicitous Might logically significantly more often than adults do. Experiment 2 showed how training with the modal taskcan suspend the implicatures for adults. Experiment 3 provides converging evidence of the developmental pragmatic effect with the French existential quantifier Certains (Some). Whilelinguistically-sophisticated children (eight- and ten-year-olds olds) typically treat Certains as compatible with Tous (All), adults are equivocal. These results, which are consistent with unanticipatedfindings in classic developmental papers, reveal a consistent ordering in which representations of weak scalar terms tend to be treated logically by young competent participants and morepragmatically by older ones. This work is also relevant to the treatment of scalar implicatures in the reasoning literature. (shrink)