In this paper we apply proof theoretic methods used for classical systems in order to obtain upper bounds for systems in partial logic. We focus on a truth predicate interpreted in a Kripke style way via strong Kleene; whereas the aim is to connect harmoniously the partial version of Kripke–Feferman with its intended semantics. The method we apply is based on infinitary proof systems containing an ω-rule.

Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that thisextended notion of fibring preserves completeness under certain reasonableconditions. (...) This completeness transfer result, the second main contributionof the paper, generalizes the one established in Zanardo et al. (2001) butis obtained using new techniques that explore the properties of a suitablemeta-logic (conditional equational logic) where the (possibly)non-truth-functional valuations are specified. The modal paraconsistentlogic of da Costa and Carnielli (1988) is studied in the context of this novel notionof fibring and its completeness is so established. (shrink)

Kalrnaric. We set out a system T, consisting of normal proofs constructed by means of elegantly symmetrical introduction and elimination rules. In the system T there are two requirements, called ( ) and ()), on applications of discharge rules. T is sound and complete for Kalmaric arguments. ( ) requires nonvacuous discharge of assumptions; ()) requires that the assumption discharged be the sole one available of highest degree. We then consider a 'Duhemian' extension T*, obtained simply by dropping the requirement (...) ()). T* is a proper subsystem of intuitionistic relevant logic. Our main result is that T* is a double negation consistency companion to classical logic. Thus all one needs to add to T* to obtain classical logic is the (intuitionistic) absurdity rule, and the (classical) rule of double nega-. (shrink)

A dissertation in the tradition of logical positivism includes a discussion of the functions and methods of philosophy and a critique of ethics and theology.

In this paper I argue against Michael Morris’ claim, that the Tractatus view involves holding that the possibility of truth-functional combination is prior to the possibility for sentential constituents to combine with one another. I provide an alternative interpretation in which I deny the presence of any distinction in the Tractatus between these two possibilities. I then turn to Adrian Moore’s ‘disjunctivist’ account of sentencehood, itself inspired by the Tractatus view. I argue that Moore’s account need not involve a (...) commitment to the kind of priority Morris describes, and that it need not involve a commitment to transcendental idealism. (shrink)

This paper provides a new argument for a position of Crispin Wright's: given that ethical statements can be embedded within all sorts of sentential operators and are subject to definite standards of warrantedness, they must have truth conditions. Allan Gibbard's normative logic' is the only noncognitivist logic that stands a chance of avoiding Geach's Fregean objection. But what, according to Gibbard, is the point of avoiding inconsistency in one's ethical statements? He must say that it is to (...) ensure that one's ethical statements have a property that has certain features. But the only property that has those features is truth. (shrink)

Two types of logical consequence are compared: one, with respect to matrix and designated elements and the other with respect to ordering in a suitable algebraic structure. Particular emphasis is laid on algebraic structures in which there is no top-element relative to the ordering. The significance of this special condition is discussed. Sequent calculi for a number of such structures are developed. As a consequence it is re-established that the notion of truth as such, not to speak of tautologies, (...) is inessential in order to define validity of an argument. (shrink)

Several accounts of logical truth are compared and shown to define distinct concepts. Nevertheless, conditions are given under which they happen to declare exactly the same sentences logically true. These conditions involve the variety of objects in the domain, the richness of the language, and the logical resources available. It is argued that the class of sentences declared logically true by each of the accounts depends on particularities of the actual world.

We propose a new model for forming and revising beliefs about unknown probabilities. To go beyond what is known with certainty and represent the agent’s beliefs about probability, we consider a plausibility map, associating to each possible distribution a plausibility ranking. Beliefs are defined as in Belief Revision Theory, in terms of truth in the most plausible worlds. We consider two forms of conditioning or belief update, corresponding to the acquisition of two types of information: learning observable evidence obtained (...) by repeated sampling from the unknown distribution; and learning higher-order information about the distribution. The first changes only the plausibility map, but leaves the given set of possible distributions essentially unchanged; the second rules out some distributions, thus shrinking the set of possibilities, without changing their plausibility ordering.. We look at stability of beliefs under either of these types of learning, defining two related notions, as well as a measure of the verisimilitude of a given plausibility model. We prove a number of convergence results, showing how our agent’s beliefs track the true probability after repeated sampling, and how she eventually gains in a sense knowledge of that true probability. Finally, we sketch the contours of a dynamic doxastic logic for statistical learning. (shrink)

A. J. Ayer’s Language, Truth, and Logic had been responsible for introducing the Vienna Circle’s ideas, developed within a Germanophone framework, to an Anglophone readership. Inevitably, this migration from one context to another resulted in the alteration of some of the concepts being transmitted. Such alterations have served to facilitate a number of false impressions of Logical Empiricism from which recent scholarship still tries to recover. In this paper, I will attempt to point to the ways in which (...) LTL has helped to foster the various mistaken stereotypes about Logical Empiricism which were combined into the received view. I will begin by examining Ayer’s all too brief presentation of an Anglocentric lineage for his ideas. This lineage, as we shall see, simply omits the major 19th century Germanophone influences on the rise of analytic philosophy. The Germanophone ideas he presents are selectively introduced into an Anglophone context, and directed towards various concerns that arose within that context. I will focus on the differences between Carnap’s version of the overcoming of metaphysics, and Ayer’s reconfiguration into what he calls the elimination of metaphysics. Having discussed the above, I will very briefly outline the consequences that Ayer’s radicalisation of the Vienna Circle’s doctrines had on the subsequent Anglophone reception of Logical Empiricism. (shrink)

The purpose of this paper is to present a thought experiment and argument that spells trouble for “radical” deflationism concerning meaning and truth such as that advocated by the staunch nominalist Hartry Field. The thought experiment does not sit well with any view that limits a truth predicate to sentences understood by a given speaker or to sentences in (or translatable into) a given language, unless that language is universal. The scenario in question concerns sentences that are not (...) understood but are known to be logical consequences of known and understood sentences. Ultimately, the issue turns on the notion of logical consequence that is available to various versions of deflationism. (shrink)

When, in 1979, A. J. Ayer was asked for an evaluation of his youthful Language, Truth and Logic (LTL), he replied: ‘I suppose the most important of the defects was that nearly all of it was false’. Like many of the claims in the book itself, this verdict is open to question. What was wrong with LTL was not so much that what it said was false, but that it presented philosophical issues in an excessively simple and aggressive (...) way. Yet it was just this quality that put the book and its author on the philosophical map, ensuring for them an important place in the history of twentieth-century philosophy. LTL presented a challenge to traditional ways of doing philosophy, the reverberations of which are still evident today. (shrink)

Danielle Macbeth disagrees with the view that there are logical truths in an ontological sense, and argues that we have no adequate epistemological account of our access to such features of reality. In my response I recall some main aspects of my ontological and epistemological formulation of logic as a science, and argue that neither Quine’s considerations against meaning, nor Benacerraf’s considerations against Gödel’s realism, show the untenability of an approach to logical truth in terms of logical propositions (...) that denote logical states of affairs.Danielle MacBeth discorda da tese que há verdades lógicas em um sentido ontológico e argumenta que não há um tratamento adequado de nosso acesso epistêmico à tais aspectos da realidade. Em minha réplica relembro algumas características principais de minha formulação ontológica e epistemológica da lógica como ciência, e argumento que nem as considerações de Quine contra a noção de significado, nem as considerações de Benacerraf contra o realismo de Gödel, mostram a invalidade de uma concepção de verdade lógica em termos de proposições que denotam estados de coisa lógicos. (shrink)

Analytic philosophy's characteristic downgrading of literature's putative concern with truth, and envisaging of its interest to philosophy merely in terms of material for logical analysis, was prefigured by Frege. The initial plausibility of this approach was in part a function of certain preferred models of philosophy as analysis which were themselves deeply flawed. An exploration of their weaknesses in the light of more adequate theories of language, truth and logic enables us to give proper weight both to (...) rhetorical and imaginative aspects of philosophical discourse, and to the capacity of works of literature to bear on issues of truth—and thereby contribute to philosophical understanding. (shrink)

Knowledge requires both freedom and friction . Freedom to set up our epistemic goals, choose the subject matter of our investigations, espouse cognitive norms, design research programs, etc., and friction (constraint) coming from two directions: the object or target of our investigation, i.e., the world in a broad sense, and our mind as the sum total of constraints involving the knower. My goal is to investigate the problem of epistemic friction, the relation between epistemic friction and freedom, the viability of (...) foundationalism as a solution to the problem of friction, an alternative solution in the form of a neo-Quinean model, and the possibility of solving the problem of friction as it applies to logic and the philosophy of logic within that model. (shrink)

We present the Jaina theory of sevenfold predication as a 7-valued logic, in which every logical value consists in a 3-tuple of opinions. A question-answer semantics is used in order to give an intuitive characterization of these logical values in terms of opinion polls. Two different interpretations are plausible for the latest sort of opinion, depending upon whether "non-assertability" refers to incompleteness or inconsistency. It is shown hat the incomplete version of JL_{G} is equivalent to Kleene's logic K3, (...) whereas the inconsistent version of JL_{M} is equivalent to Priest's Logic of Paradox LP. Finally, it is argued that the Indian logics depart from Western logics by conflating truth and justified belief: the different preconditions for belief ascription accounts for the difference between pluralist and skeptic logics. (shrink)

Gila Sher approaches knowledge from the perspective of the basic human epistemic situation—the situation of limited yet resourceful beings, living in a complex world and aspiring to know it in its full complexity. What principles should guide them? Two fundamental principles of knowledge are epistemic friction and freedom. Knowledge must be substantially constrained by the world (friction), but without active participation of the knower in accessing the world (freedom) theoretical knowledge is impossible. This requires a grounding of all knowledge, empirical (...) and abstract, in both mind and world, but the fall of traditional foundationalism has led many to doubt the viability of this ‘classical’ project. Sher challenges this skepticism, charting a new foundational methodology, foundational holism, that differs from others in being holistic, world-oriented, and universal (i.e., applicable to all fields of knowledge). Using this methodology, Epistemic Friction develops an integrated theory of knowledge, truth, and logic. This includes (i) a dynamic model of knowledge, incorporating some of Quine’s revolutionary ideas while rejecting his narrow empiricism, (ii) a substantivist, non-traditional correspondence theory of truth, and (iii) an outline of a joint grounding of logic in mind and world. The model of knowledge subjects all disciplines to demanding norms of both veridicality and conceptualization. The correspondence theory is robust and universal yet not simplistic or naive, admitting diverse forms of correspondence. Logic’s grounding in the world brings it in line with other disciplines while preserving, and explaining, its strong formality, necessity, generality, and normativity. (shrink)

In this paper, I argue against the view there are contingent a priori truths, and against the related view that there are contingent logical truths. I will suggest that in general, predicates ›a priori‹ and ›contingent‹ are implicitly relativized to circumstances, and argue that apriority entails necessity, whenever the two are relativized to the same circumstance. I will then criticize the idea, inspired by David Kaplan's framework, of contingent contents "knowable under a priori characters." I will also argue, against Kaplan, (...) that sentences of the form »The actual F is F« do not deserve the status of logical truths, since what they express is neither necessary nor a priori. (shrink)

© The Authors [2017]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.comGila Sher believes that our basic epistemic situation — that we aim to gain knowledge of a highly complex world using our severely limited, yet highly resourceful, cognitive capacities — demands that all epistemic projects be undertaken within two broad constraints: epistemic freedom and epistemic friction. The former permits us to employ our cognitive resourcefulness fully while undertaking epistemic projects, while the latter requires that (...) such projects always be substantially grounded in both the mind and reality. Epistemic Friction is an exploration of the latter constraint — the former being left for later work — that demonstrates the complementary nature of three projects that Sher has been working on, largely independently of one another, over the past three decades: a dynamic, neo-Quinean model of knowledge, a substantivist theory of truth, and... (shrink)

This chapter contains sections titled: Preamble Conceptual Primitivism Concerning “Determinately” Incoherentism and Indeterminate Truth Slater on Indeterminate Truth Quine, Indeterminate Truth, and the Problem of the Many Truthmaker Gaps and Indeterminate Truth The Logic of Determinacy Worldly Indeterminacy: Williamson's Conception and the Ordinary Conception Minimal Versus Robust Forms of Worldly and Linguistic Indeterminacy Truthmaker Gaps and Knowledge Epistemicism, Third Possibility Views, and Indeterminate Truth Semantic Presupposition Failure and Indeterminate Truth Truthmaking Gaps and Indeterminate (...) Truth The Queerness Objection Conclusion References. (shrink)

Monists say that the nature of truth is invariant, whichever sentence you consider; pluralists say that the nature of truth varies between different sets of sentences. The orthodoxy is that logic and logical form favour monism: there must be a single property that is preserved in any valid inference; and any truth-functional complex must be true in the same way as its components. The orthodoxy, I argue, is mistaken. Logic and logical form impose only structural (...) constraints on a metaphysics of truth. Monistic theories are not guaranteed to satisfy these constraints, and there is a pluralistic theory that does so. (shrink)

The First International Workshop brings together researchers from the theoretical ends of the logic programming and artificial intelligence communities to discuss their mutual interests. Logic programming deals with the use of models of mathematical logic as a way of programming computers, where theoretical AI deals with abstract issues in modeling and representing human knowledge and beliefs. One common ground is nonmonotonic reasoning, a family of logics that includes room for the kinds of variations that can be found (...) in human reasoning. Topics covered: Stable Semantics. Default Logic. AutoEpistemic Logic. Truth Maintenance Systems. Implementation Issues. Diagnosis. Applications. Inheritance Reasoning. Logics of Belief. Inconsistency and Non-Monotonicity. (shrink)

This English translation of the author's original work has been thoroughly revised, expanded and updated. The book covers logical systems known as type-free or self-referential . These traditionally arise from any discussion on logical and semantical paradoxes. This particular volume, however, is not concerned with paradoxes but with the investigation of type-free sytems to show that: (i) there are rich theories of self-application, involving both operations and truth which can serve as foundations for property theory and formal semantics; (ii) (...) these theories provide a new outlook on classical topics, such as inductive definitions and predicative mathematics; (iii) they are particularly promising with regard to applications. Research arising from paradoxes has moved progressively closer to the mainstream of mathematical logic and has become much more prominent in the last twenty years. A number of significant developments, techniques and results have been discovered. Academics, students and researchers will find that the book contains a thorough overview of all relevant research in this field. (shrink)

In Hard Truths, Elijah Millgram maintains that analytic philosophy rests on a mistake. 1 It is committed to bivalence – the contention that every truth bearer is either true or false. As a result of this commitment, its views about logic and metaphysics are profoundly misguided. He believes that rather than restricting ourselves to two truth values, we should recognize a plethora of partial truths – sentences, beliefs and opinions that are partly true or true in a (...) way. These are located on a multidimensional continuum between truth and falsity. Millgram never says exactly what partial truth is. The closest he comes is ‘Partial truth is the not fully articulated standard, or family of standards to which we hold [utterances, inscriptions and thoughts] in partial truth inferences’ , where partial truth inferences are those used in cases where ‘there is a recognized mismatch between representation and world – but not in any way that requires changing the representations’ . A critical issue then is what constitutes such a mismatch. I will argue that Millgram’s reasons for recognizing partial truths rest on untenable conceptions of logic, truth and language. Perhaps there are partial truths; perhaps recognizing them would enhance our logic or metaphysics. But Millgram’s arguments fail to show it. 1. Logic Recognizing that there can be some truth in sentences that as a whole are false is not unprecedented. Analyses by Ullian and Goodman 2 and, more recently, Yablo 3 reveal how a false sentence or proposition can be true about a particular item. ‘The dog barks and the cat speaks French’ is true about the dog, even though the conjunction as a whole is false. This does not undermine classical logic. Rather, such analyses reveal that truth about a particular subject matter is more fine grained than truth simpliciter. ‘True …. (shrink)

After some generalities about connections between functions and relations in Sections 1 and 2 recalls the possibility of taking the semantic values of ‐ary Boolean connectives as ‐ary relations among truth‐values rather than as ‐ary truth functions. Section 3, the bulk of the paper, looks at correlates of these truth‐value relations as applied to formulas, and explores in a preliminary way how their properties are related to the properties of “logical relations” among formulas such as equivalence, implication (...) (entailment) and contrariety (logical incompatibility), concentrating for illustrative purposes on binary logical relations such as those just listed. To avoid an excess of footnotes, some points have been deferred to an Appendix as “Longer Notes”. (shrink)

I think that one of the main objections to be made to Ayer's verifiability criterion is simply the mechanical way in which it is designed to work: supposedly, a philosopher need not study, for example, how religious assertions are used, nor what sorts of illumination their users take themselves to be shedding on the human condition; instead, Ayer imagines that we can test them in a simple way that requires us to do no exploration whatever. This, surely, is hubris; and (...) that accounts for much of the very angry and passionate reaction which Ayer's criterion provoked. (shrink)

What is the fundamental insight behind truth-functionality ? When is a logic interpretable by way of a truth-functional semantics? To address such questions in a satisfactory way, a formal definition of truth-functionality from the point of view of abstract logics is clearly called for. As a matter of fact, such a definition has been available at least since the 70s, though to this day it still remains not very widely well-known. A clear distinction can be drawn (...) between logics characterizable through: (1) genuinely finite-valued truth-tabular semantics; (2) no finite-valued but only an infinite-valued truthtabular semantics; (3) no truth-tabular semantics at all. Any of those logics, however, can in principle be characterized through non-truth-functional valuation semantics, at least as soon as their associated consequence relations respect the usual tarskian postulates. So, paradoxical as that might seem at first, it turns out that truth-functional logics may be adequately characterized by non-truth-functional semantics . Now, what feature of a given logic would guarantee it to dwell in class (1) or in class (2), irrespective of its circumstantial semantic characterization? (shrink)

ABSTRACTThis paper discusses the normativity of truth and logic. The paper has three objectives. First, I argue that logic is normative for thought in the sense of underwriting instrumental rationality. Logic is a good instrument for achieving truth, the goal of cognition. In recent work, Filippo Ferrari has argued that the normative nature of truth may vary across domains. My second aim is to extend this idea to logic, against the background of the (...) idea that logic serves to underwrite instrumental rationality. The third objective is to further develop Ferrari’s framework of normative alethic variability. I do so through a discussion of the normative problem of mixed compounds: the challenge of providing a principled account of the normativity of compounds with constituents whose respective normative profiles differ. I argue that the challenge can be met. Besides offering a solution to a major challenge, the response offered sheds new light on the normative variability framework: the truth of a single mixed compound may have different normative profiles across different ‘disagreement-realizers’. This feature of the view is rooted in a key commitment of the normative variability framework – namely, that disagreement and alethic normativity are intimately connected. (shrink)

Aristotle’s words in the Metaphysics: “to say of what is that it is, or of what is not that it is not, is true” are often understood as indicating a correspondence view of truth: a statement is true if it corresponds to something in the world that makes it true. Aristotle’s words can also be interpreted in a deflationary, i.e., metaphysically less loaded, way. According to the latter view, the concept of truth is contained in platitudes like: ‘It (...) is true that snow is white iff snow is white’, ‘It is true that neutrinos have mass iff neutrinos have mass’, etc. Our understanding of the concept of truth is exhausted by these and similar equivalences. This is all there is to truth. In his book Truth (Second edition 1998), Paul Horwich develops minimalism, a special variant of the deflationary view. According to Horwich’s minimalism, truth is an indefinable property of propositions characterized by what he calls the minimal theory, i.e., all (nonparadoxical) propositions of the form: It is true that p if and only if p. Although the idea of minimalism is simple and straightforward, the proper formulation of Horwich’s theory is no simple matter. In this paper, I shall discuss some of the difficulties of a logical nature that arise. First, I discuss problems that arise when we try to give a rigorous characterization of the theory without presupposing a prior understanding of the notion of truth. Next I turn to Horwich’s treatment of the Liar paradox and a paradox about the totality of all propositions that was first formulated by Russell (1903). My conclusion is that Horwich’s minimal theory cannot deal with these difficulties in an adequate way, and that it has to be revised in fundamental ways in order to do so. Once such revisions have been carried out the theory may, however, have lost some of its appealing simplicity. (shrink)

Kuhn's alleged taxonomic interpretation of incommensurability is grounded on an ill defined notion of untranslatability and is hence radically incomplete. To supplement it, I reconstruct Kuhn's taxonomic interpretation on the basis of a logical-semantic theory of taxonomy, a semantic theory of truth-value, and a truth-value conditional theory of cross-language communication. According to the reconstruction, two scientific languages are incommensurable when core sentences of one language, which have truth values when considered within its own context, lack truth (...) values when considered within the context of the other due to the unmatchable taxonomic structures underlying them. So constructed, Kuhn's mature interpretation of incommensurability does not depend upon the notion of truth-preserving translatability, but rather depends on the notion of truth-value-status-preserving cross-language communication. The reconstruction makes Kuhn's notion of incommensurability a well grounded, tenable and integrated notion.Author Keywords: Incommensurability; Thomas Kuhn; Taxonomic structures; Lexicons; Truth-value; Untranslatability; Cross-language communication. (shrink)

This paper sheds light on the relationship between the logic of generalized truth values and the logic of bilattices. It suggests a definite solution to the problem of axiomatizing the truth and falsity consequence relations, \ and \ , considered in a language without implication and determined via the truth and falsity orderings on the trilattice SIXTEEN 3 . The solution is based on the fact that a certain algebra isomorphic to SIXTEEN 3 generates the (...) variety of commutative and distributive bilattices with conflation. (shrink)

It is explained what it is for a statement to be logically true and it is thereby explained what it is for a statement to be formally true. It is also explained how logical truth differs from formal truth. Further, it is explained what a system of logic is. Finally, the nature of entailment is explained and, in particular, it is explained how formal entailment differs from analytic entailment.

'There is much food for thought in McGinn's discussions and each chapter is rich with a series of considerations for thinking that the currently received views on the various topics have some serious difficulties that need confronting... For those interested in metaphysics and the philosophy of logic, this book will stimulate much further thought' -Mind 'The sweep of the book is broad and the pace is brisk... There is much material here to provide the basis for many a deep (...) philosophical discussion' -Mind 'Lucid and provocative little book... clear, direct and well argued' -Times Higher Education SupplementIdentity, existence, predication, necessity, and truth are fundamental philosophical concerns. Colin McGinn treats them both philosophically and logically, aiming for maximum clarity and minimum pointless formalism. He contends that there are real logical properties that challenge naturalistic metaphysical outlooks. These concepts are not definable, though we can say a good deal about how they work. The aim of Logical Properties is to bring philosophy back to philosophical logic. (shrink)

The paper develops a precise account of a logic of truth and, in particular, the logic of truth of a given truth theory. On the basis of this account maximality considerations are employed for comparing and evaluating different classical logics of truth. It is argued that, perhaps surprisingly, maximality considerations lead to a fruitful criterion for evaluating logics of truth. The paper provides two different routes for motivating the application of maximality considerations in (...) the truth case. The first route employs the Maxim of Minimum Mutilation and suggests that we should vindicate as much of our basic truth intuition, that is, the transparency intuition, as it is consistently possible. The second route argues that maximality considerations underlie much of our logical theorizing and its application in the truth case is just one particular such instance. On this view maximality considerations do not implicitly depend on the basic truth intuition but rather explain how the intuition arises and why it is not fully reliable. (shrink)

It has been argued in the literature that the deflationists’ thesis about the dispensability of truth as an explanatory notion forces them to adopt a conservative theory of truth. I suggest that the deflationists’ claim that the notion of truth is akin to a logical notion should be taken more seriously. This claim casts some doubts on the adequacy of the conservativity requirement, while it also calls for further investigation to assess its philosophical plausibility.

This paper outlines a truth-conditional view of logical form, that is, a view according to which logical form is essentially a matter of truth-conditions. The main motivation for the view is a fact that seems crucial to logic. As _§_1 suggests, fundamental logical relations such as entailment or contradiction can formally be explained only if truth-conditions are formally represented.§2 spells out the view. _§_3 dwells on its anity with a conception of logical form that has been (...) defended in the past. _§§_4-6 draw attention to its impact on three major issues that concern, respectively, the extension of the domain of formal explanation, the semantics of tensed discourse, and the analysis of quantication. (shrink)