Journal of Philosophic Logic

  In J Philos Logic 34:155“192, 2005, Leitgeb provides a theory of truth which is based on a theory of semantic dependence. We argue here that the conceptual
 thrust of this approach provides us with the best way of dealing with semantic paradoxes in a manner that is acceptable to
 a classical logician. However, in investigating a problem that was raised at the end of J Philos Logic 34:155“192, 2005, we discover that something is missing from Leitgeb's original definition. Moreover, we show that once the appropriate repairs
 have been made, the resultant definition is equivalent to a version of the supervaluation definition suggested in J Philos
 72:690“716, 1975 and discussed in detail in J Symb Log 51(3):663“681, 1986. The upshot of this is a philosophical justification for the simple supervaluation approach and fresh insight into its workings.
 
 
	

  We describe a variety of sets internal to models of intuitionistic set theory that (1) manifest some of the crucial behaviors
 of potentially infinite sets as described in the foundational literature going back to Aristotle, and (2) provide models for
 systems of predicative arithmetic. We close with a brief discussion of Church's Thesis for predicative arithmetic.
 
 
	

  Classical mereology (CM) is usually taken to be formulated in a tenseless language, and is therefore associated with a four-dimensionalist
 metaphysics. This paper presents three ways one might integrate the core idea of flat plenitude, i.e., that every suitable
 condition or property has exactly one mereological fusion, with a tensed logical setting. All require a revised notion of
 mereological fusion. The candidates differ over how they conceive parthood to interact with existence in time, which connects
 to the distinction between endurance and perdurance. Similar issues arise for the integration of mereology with modality,
 and much of our discussion applies to this project as well.
 
 
	

  A curious feature of Belnap's useful four-valued logic', also known as first-degree entailment (FDE), is that the overdetermined
 value B (both true and false) is treated as a designated value. Although there are good theoretical reasons for this, it seems
 prima facie more plausible to have only one of the four values designated, namely T (exactly true). This paper follows this
 route and investigates the resulting logic, which we call Exactly True Logic.
 
 
	

  We propose a revision operator on a stratified belief base, i.e., a belief base that stores beliefs in different strata corresponding
 to the value an agent assigns to these beliefs. Furthermore, the operator will be defined as to perform the revision in such
 a way that information is never lost upon revision but stored in a stratum or layer containing information perceived as having
 a lower value. In this manner, if the revision of one layer leads to the rejection of some information to maintain consistency,
 instead of being withdrawn it will be kept and introduced in a different layer with lower value. Throughout this development
 we will follow the principle of minimal change, being one of the important principles proposed in belief change theory, particularly
 emphasized in the AGM model. Regarding the reasoning part from the stratified belief base, the agent will obtain the inferences
 using an argumentative formalism. Thus, the argumentation framework will decide which information prevails when sentences
 of different layers are used for entailing conflicting beliefs. We will also illustrate how inferences are changed and how
 the status of arguments can be modified after a revision process.
 
 
	

  The conceptual spaces approach has recently emerged as a novel account of concepts. Its guiding idea is that concepts can
 be represented geometrically, by means of metrical spaces. While it is generally recognized that many of our concepts are
 vague, the question of how to model vagueness in the conceptual spaces approach has not been addressed so far, even though
 the answer is far from straightforward. The present paper aims to fill this lacuna.
 
 
	

  In this paper I present a more refined analysis of the principles of deductive closure and positive introspection. This analysis
 uses the expressive resources of logics for different types of group knowledge, and discriminates between aspects of closure
 and computation that are often conflated. The resulting model also yields a more fine-grained distinction between implicit
 and explicit knowledge, and places Hintikka's original argument for positive introspection in a new perspective.
 
 
	

  We study a range of issues connected with the idea of replacing one formula by another in a fixed (linguistic) context. The
 replacement core of a consequence relation Š¢ is the relation holding between a set of formulas {A
 1, ..., A
 
 m
 , ...} and a formula B when for every context C(·), we have C(A
 1), ..., C(A
 
 m
 ), ...‰Š¢‰C(B). Section 1 looks at some differences between which inferences are lost on passing to the replacement cores of the classical
 and intuitionistic consequence relations. For example, we find that while the inference from A and B to , sanctioned by both these initial consequence relations, is retained on passage to the replacement core in the classical
 case, it is lost in the intuitionistic case. Further discussion of these two (and some other) logics occupies Sections 3 and
 4. Section 2 looks at the m‰=‰1 case, describing A as replaceable by B according to Š¢ when B is a consequence of A by the replacement core of Š¢, and inquiring as to which choices of Š¢ render this induced replaceability relation symmetric.
 Section 5 investigates further conceptual refinements' such as a contrast between horizontal and vertical replaceability'suggested
 by some work of R. B. Angell and R. Harrop (and a comment on the latter by T. J. Smiley) in the 1950s and 1960s. Appendix 1
 examines a related aspect of term-for-term replacement in connection with identity in predicate logic. Appendix 2 is a repository
 for proofs which would otherwise clutter up Section 3.
 
 
	

  The naive theory of vagueness holds that the vagueness of an expression consists in its failure to draw a sharp boundary between
 positive and negative cases. The naive theory is contrasted with the nowadays dominant approach to vagueness, holding that
 the vagueness of an expression consists in its presenting borderline cases of application. The two approaches are briefly
 compared in their respective explanations of a paramount phenomenon of vagueness: our ignorance of any sharp boundary between
 positive and negative cases. These explanations clearly do not provide any ground for choosing the dominant approach against
 the naive theory. The decisive advantage of the former over the latter is rather supposed to consist in its immunity to any
 form of sorites paradox. But another paramount phenomenon of vagueness is higher-order vagueness: the expressions (such as
 ˜borderline' and ˜definitely') introduced in order to express in the object language the vagueness of the object language
 are themselves vague. Two highly plausible claims about higher-order vagueness are articulated and defended: the existence
 of definitely
 ω
 ' positive and negative cases and the radical' character of higher-order vagueness itself. Using very weak logical principles
 concerning vague expressions and the ˜definitely'-operator, it is then shown that, in the presence of higher-order vagueness
 as just described, the dominant approach is subject to higher-order sorites paradoxes analogous to the original ones besetting
 the naive theory, and therefore that, against the communis opinio, it does not fare substantially better with respect to immunity to any form of sorites paradox.
 
 
	

  This paper begins an analysis of the real line using an inconsistency-tolerant (paraconsistent) logic. We show that basic
 field and compactness properties hold, by way of novel proofs that make no use of consistency-reliant inferences; some techniques
 from constructive analysis are used instead. While no inconsistencies are found in the algebraic operations on the real number
 field, prospects for other non-trivializing contradictions are left open.
 
 
	

  In a number of publications A.N. Prior considered the use of what he called ˜metric tense logic'. This is a tense logic in
 which the past and future operators P and F have an index representing a temporal distance, so that Pnα means that α was true n-much ago, and Fnα means that α will be true n-much hence. The paper investigates the use of metric predicate tense logic in formalising phenomena ormally treated by such
 devices as multiple indexing or quantification over times.
 
 
	

  In the proof-theoretic semantics approach to meaning, harmony, requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction
 proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature:
 1. GE-harmony, requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony: imposes the existence of certain transformations of derivations, known as reduction and expansion. We propose a construction of the E-rules (in GE-form) from given I-rules, and prove that the constructed rules satisfy also local intrinsic harmony.
 The construction is based on a classification of I-rules, and constitute an implementation to Gentzen's (and Pawitz') remark,
 that E-rules can be read off' I-rules.
 
 
	

  The present work is motivated by two questions. (1) What should an intuitionistic epistemic logic look like? (2) How should
 one interpret the knowledge operator in a Kripke-model for it? In what follows we outline an answer to (2) and give a model-theoretic definition of the
 operator K. This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal logic. The interest of our construction also lies in a better insight into the intuitionistic solution to Fitch's paradox,
 which is discussed in the third section. In particular we examine, in the light of our definition, DeVidi and Solomon's proposal
 of formulating the verification thesis as . We show, as our main result, that this definition excapes the paradox, though it is validated only under restrictive conditions
 on the models.
 
 
	

  This paper explores De Finetti's generalized versions of Dutch Book and Accuracy Domination theorems. Following proposals
 due to Jeff Paris, we construe these as underpinning a generalized probabilism appropriate to belief states against either a classical or a non-classical background. Both results are straightforward
 corollaries of the separating hyperplane theorem; their geometrical relationship is examined. It is shown that each point
 of Accuracy Domination for b induces a Dutch Book on b; but Dutch Books may need to be ˜scaled' in order to find a point of Accuracy-Domination. Finally, diachronic Dutch Book
 defences of conditionalization are examined in the general setting. The formulation and limitations of the generalized conditionalization
 this delivers are examined.
 
 
	

  There has been very little discussion of the appropriate principles to govern a modal logic of plurals. What debate there
 has been has accepted a principle I call (NecInc); informally if this is one of those then, necessarily: this is one of those.
 On this basis Williamson has criticised the Boolosian plural interpretation of monadic second-order logic. I argue against
 (NecInc), noting that it isn't a theorem of any logic resulting from adding modal axioms to the plural logic PFO+, and showing
 that the most obvious formal argument in its favour is question begging. I go on to discuss the behaviour of natural language
 plurals, motivating a case against (NecInc) by developing a case that natural language plural terms are not de jure rigid
 designators. The paper concludes by developing a model theory for modal PFO+ which does not validate (NecInc). An Appendix
 discusses (NecInc) in relation to counterpart theory.
 
 
	

  Rabern and Rabern (Analysis 68:105“112 2) and Uzquiano (Analysis 70:39“44 4) have each presented increasingly harder versions of ˜the hardest logic puzzle ever' (Boolos The Harvard Review of Philosophy
 6:62“65 1), and each has provided a two-question solution to his predecessor's puzzle. But Uzquiano's puzzle is different from the
 original and different from Rabern and Rabern's in at least one important respect: it cannot be solved in less than three
 questions. In this paper we solve Uzquiano's puzzle in three questions and show why there is no solution in two. Finally,
 to cement a tradition, we introduce a puzzle of our own.
 
 
	

  One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley“Meyer semantics
 involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of
 an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond
 to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions
 of conditionality. We close by briefly discussing a general conception of conditionality that may unify the three given conceptions.
 
 
	

  It is commonly held that Wittgenstein abandoned the Tractatus largely because of a problem concerning color incompatibility. In this paper, I solve the color incompatibility problem and
 argue that the central program of the Tractatus can in fact be accomplished.
 
 
	

  Various proposals have suggested that an adequate explanatory theory should reduce the number or the cardinality of the set
 of logically independent claims that need be accepted in order to entail a body of data. A (and perhaps the only) well-formed
 proposal of this kind is William Kneale's: an explanatory theory should be finitely axiomatizable but it's set of logical
 consequences in the data language should not be finitely axiomatizable. Craig and Vaught showed that Kneale theories (almost)
 always exist for any recursively enumerable but not finitely axiomatizable set of data sentences in a first order language
 with identity. Kneale's criterion underdetermines explanation even given all possible data in the data language; gratuitous
 axioms may be tacked on.' Define a Kneale theory, T, to be logically minimal if it is deducible from every Kneale theory
 (in the vocabulary of T) that entails the same statements in the data language as does T. If they exist, minimal Kneale theories
 are candidates for best explanations: they are bold' in a sense close to Popper's; some minimal Kneale theory is true if
 any Kneale theory is true; the minimal Kneale theory that is data equivalent to any given Kneale theory is unique; and no
 Kneale theory is more probable than some minimal Kneale theory. I show that under the Craig-Vaught conditions, no minimal
 Kneale theories exist.
 
 
	

  A logic for classical conditional events was investigated by Dubois and Prade. In their approach, the truth value of a conditional
 event may be undetermined. In this paper we extend the treatment to many-valued events. Then we support the thesis that probability
 over partially undetermined events is a conditional probability, and we interpret it in terms of bets in the style of de Finetti.
 Finally, we show that the whole investigation can be carried out in a logical and algebraic setting, and we find a logical
 characterization of coherence for assessments of partially undetermined events.
 
 
	

  In a definition (ˆx)((xÑ'r)†'D[x]) of the set r, the definiens D[x] must not depend on the definiendum r. This implies that all quantifiers in D[x] are independent of r and of (ˆx). This cannot be implemented in the traditional first-order logic, but can be expressed in IF logic. Violations of such independence
 requirements are what created the typical paradoxes of set theory. Poincaré's Vicious Circle Principle was intended to bar
 such violations. Russell nevertheless misunderstood the principle; for him a set a can depend on another set b only if (bÑ'a) or (b‰Š†‰a). Likewise, the truth of an ordinary first-order sentence with the Gödel number of r is undefinable in Tarki's sense because the quantifiers of the definiens depend unavoidably on r.
 
 
	

  Call an argument a ˜happy sorites' if it is a sorites argument with true premises and a false conclusion. It is a striking
 fact that although most philosophers working on the sorites paradox find it at prima facie highly compelling that the premises
 of the sorites paradox are true and its conclusion false, few (if any) of the standard theories on the issue ultimately allow
 for happy sorites arguments. There is one philosophical view, however, that appears to allow for at least some happy sorites
 arguments: strict finitism in the philosophy of mathematics. My aim in this paper is to explore to what extent this appearance
 is accurate. As we shall see, this question is far from trivial. In particular, I will discuss two arguments that threaten
 to show that strict finitism cannot consistently accept happy sorites arguments, but I will argue that (given reasonable assumptions
 on strict finitistic logic) these arguments can ultimately be avoided, and the view can indeed allow for happy sorites arguments.
 
 
	

  This essay proposes a novel semantic account of demonstratives, aimed at clarifying the sense in which demonstratives are
 semantically dependent on demonstrations. Its first two sections summarize the main views currently on the market. Section 3
 argues that they are all vitiated by the same shortcomings, and yield incorrect results of ˜truth in virtue of character'
 and entailment. Section 4 proposes a different account of the relationships between demonstratives and demonstrations, grounded
 on the idea of truth-conditionally irrelevant aspects of the meaning of certain expressions. The resulting view of demonstratives
 is consonant with the so-called ˜bare boned' account of their truth-conditional role, but is also in the position to recognize
 that the dependence of a demonstrative on a demonstration is, in some sense of the term, meaning-governed. The final section
 of this essay discusses the distinction between ˜vacuous' and ˜incomplete' uses of demonstratives, and cases involving multiple
 occurrences of these expressions.
 
 
	

  In this paper we develop a reconstruction of the Tractatus ontology. The basic idea is that objects are unsaturated and that
 Sachlagen are like molecules. Bisimulation is used for the proper individuation of the Sachlagen. We show that the ordering
 of the Sachlagen is a complete distributive, lattice. It is atomistic, i.e., each Sachlage is the supremum of the Sachverhalte below it. We exhibit three normal forms for Sachlagen: the bisimulation
 collapse, the canonical unraveling and the canonical bisimulation collapse. The first of these forms is unique modulo isomorphism,
 the second and third are simply unique. The subset ordering on normal forms of the second and third kind reflects the ordering
 of the Sachlagen.
 
 
	

  Some left-nested indicative conditionals are hard to interpret while others seem fine. Some proponents of the view that indicative
 conditionals have No Truth Values (NTV) use their view to explain why some left-nestings are hard to interpret: the embedded
 conditional does not express the truth conditions needed by the embedding conditional. Left-nestings that seem fine are then
 explained away as cases of ad hoc, pragmatic interpretation. We challenge this explanation. The standard reasons for NTV about indicative conditionals (triviality
 results, Gibbardian standoffs, etc.) extend naturally to NTV about biconditionals. So NTVers about conditionals should also
 be NTVers about biconditionals. But biconditionals embed much more freely than conditionals. If NTV explains why some left-nested
 conditionals are hard to interpret, why do biconditionals embed successfully in the very contexts where conditionals do not
 embed?
 
 
	

  Ontological pluralism is the doctrine that there are different ways or modes of being. In contemporary guise, it is the doctrine
 that a logically perspicuous description of reality will use multiple quantifiers which cannot be thought of as ranging over
 a single domain. Although thought defeated for some time, recent defenses have shown a number of arguments against the view
 unsound. However, another worry looms: that despite looking like an attractive alternative, ontological pluralism is really
 no different than its counterpart, ontological monism. In this paper, after explaining the worry in detail, I argue that considerations
 dealing with the nature of the logic ontological pluralists ought to endorse, coupled with an attractive philosophical thesis
 about the relationship between logic and metaphysics, show this worry to be unfounded.
 
 
	

  There is no consensus as to whether a Liar sentence is meaningful or not. Still, a widespread conviction with respect to Liar
 sentences (and other ungrounded sentences) is that, whether or not they are meaningful, they are useless. The philosophical contribution of this paper is to put this conviction into question. Using the framework of assertoric semantics, which is a semantic valuation method for languages of self-referential truth that has been developed by the author, we show
 that certain computational problems, called query structures, can be solved more efficiently by an agent who has self-referential resources (amongst which are Liar sentences) than by
 an agent who has only classical resources; we establish the computational power of self-referential truth. The paper concludes with some thoughts on the implications of the established result for deflationary accounts of truth.
 
 
	

  We investigate the philosophical significance of the existence of different semantic systems with respect to which a given
 deductive system is sound and complete. Our case study will be Corcoran's deductive system D for Aristotelian syllogistic
 and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that
 they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of
 syllogistic, the goal is to offer a general discussion of the relations between informal notions'in this case, an informal
 notion of deductive validity'and logical apparatuses such as deductive systems and (model-theoretic or other) semantic systems
 that aim at offering technical, formal accounts of informal notions. Specifically, we will be interested in Kreisel's famous
 ˜squeezing argument'; we shall ask ourselves what a plurality of semantic systems (understood as classes of mathematical structures)
 may entail for the cogency of specific applications of the squeezing argument. More generally, the analysis brings to the
 fore the need for criteria of adequacy for semantic systems based on mathematical structures. Without such criteria, the idea
 that the gap between informal and technical accounts of validity can be bridged is put under pressure.
 
 
	

  In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea
 that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions
 of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this
 gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague
 predicates, in particular regarding judgments about borderline cases.
 
 
	

  We prove completeness of the propositional modal logic S4 for the measure algebra based on the Lebesgue-measurable subsets of the unit interval, [0, 1]. In recent talks, Dana Scott
 introduced a new measure-based semantics for the standard propositional modal language with Boolean connectives and necessity
 and possibility operators,  and . Propositional modal formulae are assigned to Lebesgue-measurable subsets of the real interval [0, 1], modulo sets of measure
 zero. Equivalence classes of Lebesgue-measurable subsets form a measure algebra, , and we add to this a non-trivial interior operator constructed from the frame of ˜open' elements'elements in  with an open representative. We prove completeness of the modal logic S4 for the algebra . A corollary to the main result is that non-theorems of S4 can be falsified at each point in a subset of the real interval [0, 1] of measure arbitrarily close to 1. A second corollary
 is that Intuitionistic propositional logic (IPC) is complete for the frame of open elements in .