The problem of the many threatens to show that, in general, there are far more ordinary objects than you might have thought. I present and motivate a solution to this problem using many-one identity. According to this solution, the many things that seem to have what it takes to be, say, a cat, are collectively identical to that single cat.
As anyone who has flown out of a cloud knows, the boundaries of a cloud are a lot less sharp up close than they can appear on the ground. Even when it seems clearly true that there is one, sharply bounded, cloud up there, really there are thousands of water droplets that are neither determinately part of the cloud, nor determinately outside it. Consider any object that consists of the core of the cloud, plus an arbitrary selection of these droplets. (...) It will look like a cloud, and circumstances permitting rain like a cloud, and generally has as good a claim to be a cloud as any other object in that part of the sky. But we cannot say every such object is a cloud, else there would be millions of clouds where it seemed like there was one. And what holds for clouds holds for anything whose boundaries look less clear the closer you look at it. And that includes just about every kind of object we normally think about, including humans. Although this seems to be a merely technical puzzle, even a triviality, a surprising range of proposed solutions has emerged, many of them mutually inconsistent. It is not even settled whether a solution should come from metaphysics, or from philosophy of language, or from logic. Here we survey the options, and provide several links to the many topics related to the Problem. (shrink)
A logic of grounding where what is grounded can be a collection of truths is a “many-many” logic of ground. The idea that grounding might be irreducibly many-many has recently been suggested by Dasgupta. In this paper I present a range of novel philosophical and logical reasons for being interested in many-many logics of ground. I then show how Fine’s State-Space semantics for the Pure Logic of Ground can be extended to the many- (...) class='Hi'>many case, giving rise to the Pure Logic of Many-Many Ground. In the second, more technical, part of the paper, I do two things. First, I present an alternative formalization of plg; this allows us to simplify Fine’s completeness proof for plg. Second, I formalize plmmg using an infinitary sequent calculus and prove that this formalization is sound and complete. (shrink)
This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, (...) such as a simple proof of the completeness theorem and of the equivalence between Chang's MV algebras and Abelian lattice-ordered groups with unit - a necessary prerequisite for the incorporation of a genuine addition operation into fuzzy logic. Readers interested in fuzzy control are provided with a rich deductive system in which one can define fuzzy partitions, just as Boolean partitions can be defined and computed in classical logic. Detailed bibliographic remarks at the end of each chapter and an extensive bibliography lead the reader on to further specialised topics. (shrink)
Extensively classroom-tested, Possibilities and Paradox provides an accessible and carefully structured introduction to modal and many-valued logic. The authors cover the basic formal frameworks, enlivening the discussion of these different systems of logic by considering their philosophical motivations and implications. Easily accessible to students with no background in the subject, the text features innovative learning aids in each chapter, including exercises that provide hands-on experience, examples that demonstrate the application of concepts, and guides to further reading.
In some situations in which undesirable collective effects occur, it is very hard, if not impossible, to hold any individual reasonably responsible. Such a situation may be referred to as the problem of many hands. In this paper we investigate how the problem of many hands can best be understood and why, and when, it exactly constitutes a problem. After analyzing climate change as an example, we propose to define the problem of many hands as the occurrence (...) of a gap in the distribution of responsibility that may be considered morally problematic. Whether a gap is morally problematic, we suggest, depends on the reasons why responsibility is distributed. This, in turn, depends, at least in part, on the sense of responsibility employed, a main distinction being that between backward-looking and forward-looking responsibility. (shrink)
Quine often argued for a simple, untyped system of logic rather than the typed systems that were championed by Russell and Carnap, among others. He claimed that nothing important would be lost by eliminating sorts, and the result would be additional simplicity and elegance. In support of this claim, Quine conjectured that every many-sorted theory is equivalent to a single-sorted theory. We make this conjecture precise, and prove that it is true, at least according to one reasonable notion of (...) theoretical equivalence. Our clarification of Quine’s conjecture, however, exposes the shortcomings of his argument against many-sorted logic. (shrink)
Many advocates of the Everettian interpretation consider that theirs is the only approach to take quantum mechanics really seriously, and that this approach allows to deduce a fantastic scenario for our reality, one that consists of an infinite number of parallel worlds that branch out continuously. In this article, written in dialogue form, we suggest that quantum mechanics can be taken even more seriously, if the many-worlds view is replaced by a many-measurements view. This allows not only (...) to derive the Born rule, thus solving the measurement problem, but also to deduce a one-world non-spatial reality, providing an even more fantastic scenario than that of the multiverse. (shrink)
The Many Gods Objection (MGO) is widely viewed as a decisive criticism of Pascal’s Wager. By introducing a plurality of hypotheses with infinite expected utility into the decision matrix, the wagerer is left without adequate grounds to decide between them. However, some have attempted to rebut this objection by employing various criteria drawn from the theological tradition. Unfortunately, such defenses do little good for an argument that is supposed to be an apologetic aimed at atheists and agnostics. The purpose (...) of this paper is to offer a defensive strategy of a different sort, one more suited to the Wager’s apologetic aim and status as a decision under ignorance. Instead of turning to criteria independent of the Wager, it will be shown that there are characteristics already built into its decision theoretic structure that can be used to block many categories of theological hypotheses including MGO’s more outrageous “cooked-up” hypotheses and “philosophers’ fictions”. -/- Please note that there are editorial errors in the published version. They have been corrected in the attached. (shrink)
This book provides an incisive, basic introduction to many-valued logics and to the constructions that are "many-valued" at their origin. Using the matrix method, the author sheds light on the profound problems of many-valuedness criteria and its classical characterizations. The book also includes information concerning the main systems of many-valued logic, related axiomatic constructions, and conceptions inspired by many-valuedness. With its selective bibliography and many useful historical references, this book provides logicians, computer scientists, philosophers, (...) and mathematicians with a valuable survey of the subject. (shrink)
We argue from conceptual point of view the relationship between quantum entanglement and many-worlds interpretation of quantum mechanics, the debate is still open, but we retain the objective Bayesian interpretation of quantum probability could be an interesting approach to solve this fundamental question.
A semantic analysis of mass nouns is given in terms of a logic of classes as many. In previous work it was shown that plural reference and predication for count nouns can be interpreted within this logic of classes as many in terms of the subclasses of the classes that are the extensions of those count nouns. A brief review of that account of plurals is given here and it is then shown how the same kind of interpretation (...) can also be given for mass nouns. (shrink)
Dion is a full-bodied man. Theon is that part of him which consists of all of him except his left foot. What becomes of Dion and Theon when Dion’s left foot is amputated? In Burke 1994, employing the doctrine of sortal essentialism, I defended a surprising position last defended by Chrysippus: that Dion survives while the seemingly unscathed Theon perishes. This paper defends that position against objections by Stone, Carter, Olson, and others. Most notably, it offers a novel, conservative solution (...) to the many-thinkers problem, a solution that enables us to accept the existence of brain-containing person-parts while denying that those person-parts are thinking, conscious beings. (shrink)
According to the plurivaluationist, our vague discourse doesn’t have a single meaning. Instead, it has many meanings, each of which is precise—and it is this plurality of meanings that is the source of vagueness. I believe plurivaluationist positions are underdeveloped and for this reason unpopular. This paper attempts to correct this situation by offering a particular development of plurivaluationism that I call supersententialism. The supersententialist leverages lessons from another area of research—the Problem of the Many—in service of the (...) plurivaluationist position. The Problem reveals theoretical reasons to accept that there are many cats where we thought there was one; the supersententialist claims that we are in a similar situation with respect to languages, propositions and sentences. I argue that the parallel suggested by the supersententialist reveals unappreciated advantages and lines of defense for plurivaluationism. (shrink)
I argue that the many worlds explanation of quantum computation is not licensed by, and in fact is conceptually inferior to, the many worlds interpretation of quantum mechanics from which it is derived. I argue that the many worlds explanation of quantum computation is incompatible with the recently developed cluster state model of quantum computation. Based on these considerations I conclude that we should reject the many worlds explanation of quantum computation.
J. Michael Dunn’s Theorem in 3-Valued Model Theory and Graham Priest’s Collapsing Lemma provide the means of constructing first-order, three-valued structures from classical models while preserving some control over the theories of the ensuing models. The present article introduces a general construction that we call a Dunn–Priest quotient, providing a more general means of constructing models for arbitrary many-valued, first-order logical systems from models of any second system. This technique not only counts Dunn’s and Priest’s techniques as special cases, (...) but also provides a generalized Collapsing Lemma for Priest’s more recent plurivalent semantics in general. We examine when and how much control may be exerted over the resulting theories in particular cases. Finally, we expand the utility of the construction by showing that taking Dunn–Priest quotients of a family of structures commutes with taking an ultraproduct of that family, increasing the versatility of the tool. (shrink)
In this paper I develop a novel response to the exclusion problem. I argue that the nature of the events in the causally complete physical domain raises the “problem of many causes”: there will typically be countless simultaneous low-level physical events in that domain that are causally sufficient for any given high-level physical event. This shows that even reductive physicalists must admit that the version of the exclusion principle used to pose the exclusion problem against non-reductive physicalism is too (...) strong. The burden is on proponents of the exclusion problem to provide a reason to think that any qualifications placed on the exclusion principle will solve the problem of many causes while ruling out causation by irreducible mental events. (shrink)
Suszko's Thesis maintains that many-valued logics do not exist at all. In order to support it, R. Suszko offered a method for providing any structural abstract logic with a complete set of bivaluations. G. Malinowski challenged Suszko's Thesis by constructing a new class of logics (called q-logics by him) for which Suszko's method fails. He argued that the key for logical two-valuedness was the "bivalent" partition of the Lindenbaum bundle associated with all structural abstract logics, while his q-logics were (...) generated by "trivalent" matrices. This paper will show that contrary to these intuitions, logical two-valuedness has more to do with the geometrical properties of the deduction relation of a logical structure than with the algebraic properties embedded on it. (shrink)
A many-valued (aka multiple- or multi-valued) semantics, in the strict sense, is one which employs more than two truth values; in the loose sense it is one which countenances more than two truth statuses. So if, for example, we say that there are only two truth values—True and False—but allow that as well as possessing the value True and possessing the value False, propositions may also have a third truth status—possessing neither truth value—then we have a many-valued semantics (...) in the loose but not the strict sense. A many-valued logic is one which arises from a many-valued semantics and does not also arise from any two-valued semantics [Malinowski, 1993, 30]. By a ‘logic’ here we mean either a set of tautologies, or a consequence relation. We can best explain these ideas by considering the case of classical propositional logic. The language contains the usual basic symbols (propositional constants p, q, r, . . .; connectives ¬, ∧, ∨, →, ↔; and parentheses) and well-formed formulas are defined in the standard way. With the language thus specified—as a set of well-formed formulas—its semantics is then given in three parts. (i) A model of a logical language consists in a free assignment of semantic values to basic items of the non-logical vocabulary. Here the basic items of the non-logical vocabulary are the propositional constants. The appropriate kind of semantic value for a proposition is a truth value, and so a model of the language consists in a free assignment of truth values to basic propositions. Two truth values are countenanced: 1 (representing truth) and 0 (representing falsity). (ii) Rules are presented which determine a truth value for every proposition of the language, given a model. The most common way of presenting these rules is via truth tables (Figure 1). Another way of stating such rules—which will be useful below—is first to introduce functions on the truth values themselves: a unary function ¬ and four binary functions ∧, ∨, → and ↔ (Figure 2).. (shrink)
Following on Westerståhl’s argument that many is not Conservative , I propose an intensional account of Conservativity as well as intensional versions of EXT and Isomorphism closure. I show that an intensional reading of many can easily possess all three of these, and provide a formal statement and proof that they are indeed proper intensionalizations. It is then discussed to what extent these intensionalized properties apply to various existing readings of many.
It is shown that the superposed wave function of a measuring device, in each branch of which there is a definite measurement result, does not correspond to many mutually unobservable but equally real worlds, as the superposed wave function can be observed in our world by protective measurement.
Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy (...) logical systems - Lukasiewicz, Gödel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems. (shrink)
Consider a cat on a mat. On the one hand, there seems to be just one cat, but on the other there seem to be many things with as good a claim as anything in the vicinity to being a cat. Hence, the problem of the many. In his ‘Many, but Almost One,’ David Lewis offered two solutions. According to the first, only one of the many is indeed a cat, although it is indeterminate exactly which (...) one. According to the second, the many are all cats, but they are almost identical to each other, and hence they are almost one. For Lewis, the two solutions do not compete with each other but are mutually complementary, as each one can assist the other. This paper has two aims: to give some reasons against the first of these two solutions, but then to defend the second as a self-standing solution from Lewis’s considerations to the contrary. (shrink)
The problem of the many poses the task of explaining mereological indeterminacy of ordinary objects in a way that sustains our familiar practice of counting these objects. The aim of this essay is to develop a solution to the problem of the many that is based on an account of mereological indeterminacy as having its source in how ordinary objects are, independently of how we represent them. At the center of the account stands a quasi-hylomorphic ontology of ordinary (...) objects as material objects with multiple individual forms. (shrink)
We discuss the one?many problem as it appears in the Philebus and find that it is not restricted to the usually understood problem about the identity of universals across particulars that instantiate them (the Hylomorphic Dispersal Problem). In fact some of the most interesting aspects of the problem occur purely with respect to the relationship between Forms. We argue that contemporary metaphysicians may draw from the Philebus at least three different one?many relationships between universals themselves: instantiation, subkind and (...) part, and thereby construct three new ?problems of the one and the many? (an Eidetic Dispersal Problem, a Genus?Species Problem, and an Eidetic Combination Problem), which are as problematic as the version generally discussed. We then argue that this taxonomy sheds new and interesting light on certain discussions of higher-order universals in recent Australian analytic philosophy. (shrink)
This paper deals with Kripke-style semantics for many-valued logics. We introduce various types of Kripke semantics, and we connect them with algebraic semantics. As for modal logics, we relate the axioms of logics extending MTL to properties of the Kripke frames in which they are valid. We show that in the propositional case most logics are complete but not strongly complete with respect to the corresponding class of complete Kripke frames, whereas in the predicate case there are important (...) class='Hi'>many-valued logics like BL, Ł and Π, which are not even complete with respect to the class of all predicate Kripke frames in which they are valid. Thus although very natural, Kripke semantics seems to be slightly less powerful than algebraic semantics. (shrink)
This paper presents an extensional account of manyand few that explains data that have previously motivated intensional analyses of these quantifiers :599–620, 2000). The key insight is that their semantic arguments are themselves set intersections: the restrictor is the intersection of the predicates denoted by the N’ or the V’ and the restricted universe, U, and the scope is the intersection of the N’ and V’. Following Cohen, I assume that the universe consists of the union of alternatives to the (...) nominal and verbal predicates, where an alternative to a property ψ is one that shares a pragmatic presupposition with ψ, and a pragmatic presupposition is one that is selected by context from a set of potential presuppositions associated with the sentence. A many/few-quantified sentence is then true iff the proportion of the scope to the restrictor is greater/less than some threshold, n. In addition to explaining various problematic cases from the literature, the analysis shows how the readings of a many/few-quantified sentence can be derived from the same syntactico-semantic structure, it being unnecessary to claim lexical or structural ambiguity. The analysis also provides strong support for the idea that natural language quantification is always purely extensional. (shrink)
The paper aims to clarify Ratnākaraśānti?s epistemological theory that mental images in a cognition are false (*alīkākāravāda) in comparison with Śāntarakṣita?s criticism of the Yogācāra position. Although Ratnākaraśānti frequently uses the neither-one-nor-many argument for explaining his Yogācāra position, the argument, unlike Śāntarakṣita?s original one, does not function for refuting the existence of awareness itself as the basis of mental images. This point is examined in the first two sections of this paper by analyzing Ratnākaraśānti?s proof of the selflessness of (...) entities (dharmanairātmya) and his application of the neither-one-nor-many argument for demonstrating the falsehood of mental images. On the other hand, the last section investigates into his defense of the alīkākāravāda against Śāntarakṣita?s severe criticism of it. Here, too, we can find his tactical usage of the neither-one-nor-many argument, or more precisely, one of its variants: the neither-identical-nor-different argument. Through the above procedure, we can see how Yogācāra philosophy survived in the late period of Indian Buddhism by blending the Madhyamaka opponent?s argument with its own thought. (shrink)
As noted in 1962 by Timothy Smiley, if Aristotle’s logic is faithfully translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley’s method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle’s system if and only if its translation is valid according to modern standard many-sorted logic. As William Parry observed in 1973, this result can be proved (...) using my 1972 proof of the completeness of Aristotle’s syllogistic. (shrink)
The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value (...) and the exclusion of the opposite truth value describe the same situation.). (shrink)
In 'A Constitution of Many Minds' Cass Sunstein argues that the three major approaches to constitutional interpretation – Traditionalism, Populism and Cosmopolitanism – all rely on some variation of a ‘many-minds’ argument. Here we assess each of these claims through the lens of the Condorcet Jury Theorem. In regard to the first two approaches we explore the implications of sequential influence among courts (past and foreign, respectively). In regard to the Populist approach, we consider the influence of opinion (...) leaders. (shrink)
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. (shrink)
In this paper we propose substructural propositional logic obtained by da Costa weakening of the intuitionistic negation. We show that the positive fragment of the da Costa system is distributive lattice logic, and we apply a kind of da Costa weakening of negation, by preserving, differently from da Costa, its fundamental properties: antitonicity, inversion, and additivity for distributive lattices. The other stronger paraconsistent logic with constructive negation is obtained by adding an axiom for multiplicative property of weak negation. After that, (...) we define Kripke-style semantics based on possible worlds and derive from it many-valued semantics based on truth-functional valuations for these two paraconsistent logics. Finally, we demonstrate that this model-theoretic inference system is adequate—sound and complete with respect to the axiomatic da Costa-like systems for these two logics. (shrink)
In the paper * we discuss a distinctive versatility of the non-Fregean approach to the sentential identity. We present many-valued and referential counterparts of the systems of SCI, the sentential calculus with identity, including Suszko’s logical valuation programme as applied to many-valued logics. The similarity of different constructions: many-valued, referential and mixed, leads us to the conviction of the universality of the non-Fregean paradigm of sentential identity as distinguished from the equivalence, cf. .
Kilimanjaro is a paradigmatic mountain, if any is. Consider atom Sparky, which is neither determinately part of Kilimanjaro nor determinately not part of it. Let Kilimanjaro(+) be the body of land constituted, in the way mountains are constituted by their constituent atoms, by the atoms that make up Kilimanjaro together with Sparky, and Kilimanjaro(–) the one constituted by those other than Sparky. On the one hand, there seems to be just one mountain in the vicinity of Kilimanjaro. On the other (...) hand, both Kilimanjaro(+) and Kilimanjaro(–)—and indeed many other similar things—seem to have an equal claim to be a mountain: all of them exhibit the grounds for something being a mountain—like being an elevation of the earth’s surface rising abruptly and to a large height from the surrounding level,1 or whathaveyou—; and there seems to be nothing in the vicinity with a better claim. Hence, the problem of the many. (shrink)
Quantum Mechanics notoriously faces a measurement problem, the problem that the unitary time evolution, encoded in its dynamical equations, together with the kinematical structure of the theory generally implies the non-existence of definite measurement outcomes. There have been multiple suggestions to solve this problem, among them the so called many worlds interpretation that originated with the work of Hugh Everett III. According to it, the quantum state and time evolution fully and accurately describe nature as it is, implying that (...) under certain conditions multiple measurement outcomes that are seemingly mutually exclusive can be realized at the same time – but as different 'worlds' contained in a global, quantum mechanical structure, sometimes referred to as 'the multiverse'. The many worlds interpretation has, however, been confronted with serious difficulties over the course of its development, some of which were solved by the advent of decoherence theory. The present thesis critically investi- gates the state of play on a key remaining problem of the many worlds interpretation, the problem of the meaning and quantiﬁcation of probabilities in a quantum multiverse. Recent attempts of deriving the pivotal statistical ingredient of quantum mechanics, Born’s rule, from either principles of decision theory or from quantum mechanics alone, supplemented with a few general premises about probability are analyzed and their premises are scrutinized. It will be argued that, though both approaches yield promising results, they both ultimately fail to clearly establish the validity of Born’s rule in the context of the many worlds interpretation. It is hence suggested that further research on this problem is indicated. (shrink)
This note contains a correct proof of the fact that the set of all first-order formulas which are valid in all predicate Kripke frames for Hájek's many-valued logic BL is not arithmetical. The result was claimed in , but the proof given there was incorrect.
In this paper, we study multiplicative extensions of propositional many-place sequent calculi for finitely-valued logics arising from those introduced in Sect. 5 of Pynko (J Multiple-Valued Logic Soft Comput 10:339–362, 2004) through their translation by means of singularity determinants for logics and restriction of the original many-place sequent language. Our generalized approach, first of all, covers, on a uniform formal basis, both the one developed in Sect. 5 of Pynko (J Multiple-Valued Logic Soft Comput 10:339–362, 2004) for singular (...) finitely-valued logics (when singularity determinants consist of a variable alone) and conventional Gentzen-style (i.e., two-place sequent) calculi suggested in Pynko (Bull Sect Logic 33(1):23–32, 2004) for finitely-valued logics with equality determinant. In addition, it provides a universal method of constructing Tait-style (i.e., one-place sequent) calculi for finitely-valued logics with singularity determinant (in particular, for Łukasiewicz finitely-valued logics) that fits the well-known Tait calculus (Lecture Notes in Mathematics, Springer, Berlin, 1968) for the classical logic. We properly extend main results of Pynko (J Multiple-Valued Logic Soft Comput 10:339–362, 2004) and explore calculi under consideration within the framework of Sect. 7 of Pynko (Arch Math Logic 45:267–305, 2006), generalizing the results obtained in Sect. 7.5 of Pynko (Arch Math Logic 45:267–305 2006) for two-place sequent calculi associated with finitely-valued logics with equality determinant according to Pynko (Bull Sect Logic 33(1):23–32, 2004). We also exemplify our universal elaboration by applying it to some denumerable families of well-known finitely-valued logics. (shrink)
In this paper, I identify the source of the differences between classical logic and many-valued logics (including fuzzy logics) with respect to the set of valid formulas and the set of inferences sanctioned. In the course of doing so, we find the conditions that are individually necessary and jointly sufficient for any many-valued semantics (again including fuzzy logics) to validate exactly the classically valid formulas, while sanctioning exactly the same set of inferences as classical logic. This in turn (...) shows, contrary to what has sometimes been claimed, that at least one class of infinite-valued semantics is axiomatizable. (shrink)
There are two types of theories regarding many worlds: one is modal, while the other is temporal. The former regards reality as consisting of many possible worlds, while the latter holds that reality consists of many momentary worlds, which are usually called moments. I compare these two theories, paying close attention to the concept of transworld identity and compare trans-possible world identity with trans-momentary world identity (or transmoment identity). I characterize time from the point of many-worlds (...) view, believing this to be one of the best ways of grasping the reality of time. First, I show that there is reason to adopt the many-worlds view because transworld identity is meaningful for both of them, while it is not for space. Second, I argue that transmoment identity is different from transpossible world identity concerning reality. The former is a realistic relation, while the latter is not. Thus, I find that the reality of time is in the relation of transmoment identity. Such a view, I contend, has merit on the basis that it recognizes the reality of time in a sense that is not true of space. (shrink)
This paper investigates the One over Many, first as it was first introduced by Plato. Here, it is argued, the One over Many can be understood in at least two senses, both different from, but in a sense included in, the sense in which the One-over-Many is regarded as an argument for the existence of universals. In both of these senses, it is argued, it is possible to accept the One-over-Many while denying the existence of universals.This (...) established, I examine the argument from the One-over-Many as given within the framework of Armstrong’s theory of universals. Within this framework there is another thesis of great import, that of scientific realism. I will try to show that there exists a problematic tension, if not an outright contradiction, between this thesis and that of the argument from the One-over-Many. It seems that, as soon as you accept a scientific realism, the support provided by the argument from the One-over-Many dissolves, or, vice versa, if you claim support from the argument the results of your scientific realism seem to be contradicted. I will argue that the way to resolve this tension is to give up the argument from the One-over-Many. In particular, this will results in a weakening of Armstrong’s case for the existence of universals. In general, discussing the argument from the One-over-Many brings to the fore a feature common to all senses given to the One-over-Many, and thereby a feature affecting all theories of properties (since all theories of properties in one sense or another refer on the One-over-Many). (shrink)
In 1979, H. Lewis shows that the computational complexity of the Boolean satisfiability problem dichotomizes, depending on the Boolean operations available to formulate instances: intractable (NP-complete) if negation of implication is definable, and tractable (in P) otherwise . Recently, an investigation in the same spirit has been extended to nonclassical propositional logics, modal logics in particular [2, 3]. In this note, we pursue this line in the realm of many-valued propositional logics, and obtain complexity classifications for the parameterized satisfiability (...) problem of two pertinent samples, Kleene and Gödel logics. (shrink)
We present an extension of the mosaic method aimed at capturing many-dimensional modal logics. As a proof-of-concept, we define the method for logics arising from the combination of linear tense operators with an “orthogonal” S5-like modality. We show that the existence of a model for a given set of formulas is equivalent to the existence of a suitable set of partial models, called mosaics, and apply the technique not only in obtaining a proof of decidability and a proof of (...) completeness for the corresponding Hilbert-style axiomatization, but also in the development of a mosaic-based tableau system. We further consider extensions for dealing with the case when interactions between the two dimensions exist, thus covering a wide class of bundled Ockhamist branching-time logics, and present for them some partial results, such as a non-analytic version of the tableau system. (shrink)
The Boolean many-valued approach to vagueness is similar to the infinite-valued approach embraced by fuzzy logic in the respect in which both approaches seek to solve the problems of vagueness by assigning to the relevant sentences many values between falsity and truth, but while the fuzzy-logic approach postulates linearly-ordered values between 0 and 1, the Boolean approach assigns to sentences values in a many-element complete Boolean algebra. On the modal-precisificational approach represented by Kit Fine, if a sentence (...) is indeterminate in truth value in some world, it is taken to be true in one precisified world accessible from that world and false in another. This paper points to a way to unify these two approaches to vagueness by showing that Fine’s version of the modal-precisificational approach can be combined with the Boolean many-valued approach instead of supervaluationism, one of the most popular approaches to vagueness. (shrink)
The Doctor, like many time-travelers, often finds himself in the midst of a causal loop. Events in the future cause events in the past, which in turn cause the future events. There is a worry that a person in this situation could never have true libertarian freedom: facts about the past entail their future actions, so they couldn't do otherwise than they in fact do. -/- In this paper, I argue that there are logically coherent (though perhaps unlikely!) ways (...) of understanding the relationship between human actions and Everett's "many worlds" interpretation of quantum mechanics that could salvage The Doctor's libertarian free will. I show that the existence of a causal loop does not entail that *THE* Doctor will have to do a certain thing, only that *A* Doctor will have to do it. On this interpretation, "free will" might turn out to be the choice, not of what happens in the future, but rather of which future person we are going to be. (shrink)
Here we suggest a formal using of N.A. Vasil’ev’s logical ideas in categorical logic: the idea of “accidental” assertion is formalized with topoi and the idea of the notion of nonclassical negation, that is not based on incompatibility, is formalized in special cases of monoidal categories. For these cases, the variant of the law of “excluded n-th” suggested by Vasil’ev instead of the tertium non datur is obtained in some special cases of these categories. The paraconsistent law suggested by Vasil’ev (...) is also demonstrated with linear and tensor logics but in a form weaker than he supposed. As we have, in fact, many truth-values in linear logic and topos logic, the admissibility of the traditional notion of inference in the categorical interpretation of linear and intuitionistic proof theory is discussed. (shrink)
Franco Montagna, a prominent logician and one of the leaders of the Italian school on Mathematical Logic, passed away on February 18, 2015. We survey some of his results and ideas in the two disciplines he greatly contributed along his career: provability logic and many-valued logic.
In this paper the quantum covariant relativistic dynamics of many bodies is reconsidered. It is emphasized that this is an event dynamics. The events are quantum statistically correlated by the global parameter τ. The derivation of an event Boltzmann equation emphasizes this. It is shown that this Boltzmann equation may be viewed as exact in a dilute event limit ignoring three event correlations. A quantum entropy principle is obtained for the marginal Wigner distribution function. By means of event linking (...) (concatenations) particle properties such as the equation of state may be obtained. We further reconsider the generalized quantum equilibrium ensemble theory and the free event case of the Fermi-Dirac and Bose-Einstein distributions, and some consequences. The ultra-relativistic limit differs from the non-covariant theory and is a test of this point of view. (shrink)
Originally published by the Center for Hellenic Studies, this book investigates the extent to which the Presocratics were hamstrung by their lack of detailed conceptual framework in the case of the words "one" and "many." This investigation is based on Aristotle's analyses.
A common assumption among philosophers is that every language has at most denumerably many expressions. This assumption plays a prominent role in many philosophical arguments. Recently formal systems with indenumerably many elements have been developed. These systems are similar to the more familiar denumerable first-order languages. This similarity makes it appear that the assumption is false. We argue that the assumption is true.