The basic notions in Prior's Ockhamist and Peircean logics of branching-time are the notion of moment and that of history. In the tree semantics, histories are defined as maximal linearly ordered sets of moments. In the geometrical approach, both moments and histories are primitive entities and there is no set theoretical dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank 1 base of a non-Archimedean topology on the set (...) of histories. In this paper, it will be shown that the topological approach, and hence the other approaches, can be reconstructed in a framework in which the basic notions are those of history and of relative closeness relation among histories. (shrink)

In Ockhamist branching-time logic [Prior 67], formulas are meant to be evaluated on a specified branch, or history, passing through the moment at hand. The linguistic counterpart of the manifoldness of future is a possibility operator which is read as `at some branch, or history (passing through the moment at hand)'. Both the bundled-trees semantics [Burgess 79] and the $\langle moment, history\rangle$ semantics [Thomason 84] for the possibility operator involve a quantification over sets of moments. The Ockhamist frames are (3-modal) (...) Kripke structures in which this second-order quantification is represented by a first-order quantification. The aim of the present paper is to investigate the notions of modal definability, validity, and axiomatizability concerning 3-modal frames which can be viewed as generalizations of Ockhamist frames. (shrink)

A completeness theorem is established for logics with congruence endowed with general semantics (in the style of general frames). As a corollary, completeness is shown to be preserved by fibring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under fibring and to be included in the class of logics with congruence. Thus, completeness is shown to be preserved by fibring logics with equivalence and general semantics. (...) An example is provided showing that completeness is not always preserved by fibring ligics endowed with standard (non general) semantics. A categorial characterization of fibring is provided using coproducts and cocartesian liftings. (shrink)

Temporal logic is one of the many areas in which a possible world semantics is adopted. Prior's Ockhamist and Peircean semantics for branching-time, though, depart from the genuine Kripke semantics in that they involve a quantification over histories, which is a second-order quantification over sets of possible worlds. In the paper, variants of the original Prior's semantics will be considered and it will be shown that all of them can be viewed as first-order counterparts of the original semantics.

The branching-time logic called Peircean by Arthur Prior is considered and given an infinite axiomatization. The axiomatization uses only the standard deduction rules for tense logic.

In the tree-like representation of Time, two histories are undivided at a moment t whenever they share a common moment in the future of t. In the present paper, it will first be proved that Ockhamist and Peircean branching-time logics are unable to express some important sentences in which the notion of undividedness is involved. Then, a new semantics for branching-time logic will be presented. The new semantics is based on trees endowed with an indistinguishability function, a generalization of the (...) notion of undividedness. It will be shown that Ockhamist and Peircean semantics can be viewed as limit cases of the semantics developed in this paper. (shrink)

The basic notions in Prior’s Ockhamist and Peircean logics of branching-time are the notion of moment and that of history (or course of events). In the tree semantics, histories are defined as maximal linearly ordered sets of moments. In the geometrical approach, both moments and histories are primitive entities and there is no set theoretical (and ontological) dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank 1 base of (...) a non-Archimedean topology on the set of histories. In this paper, it will be shown that the topological approach, and hence the other approaches, can be reconstructed in a framework in which the basic notions are those of history and of relative closeness relation among histories. (shrink)

This paper deals with structures ${\langle{\bf T}, I\rangle}$ in which T is a tree and I is a function assigning each moment a partition of the set of histories passing through it. The function I is called indistinguishability and generalizes the notion of undividedness. Belnap’s choices are particular indistinguishability functions. Structures ${\langle{\bf T}, I\rangle}$ provide a semantics for a language ${\mathcal{L}}$ with tense and modal operators. The first part of the paper investigates the set-theoretical properties of the set of indistinguishability (...) classes, which has a tree structure. The significant relations between this tree and T are established within a general theory of trees. The aim of second part is testing the expressive power of the language ${\mathcal{L}}$ . The natural environment for this kind of investigations is Belnap’s seeing to it that (stit). It will be proved that the hybrid extension of ${\mathcal{L}}$ (with a simultaneity operator) is suitable for expressing stit concepts in a purely temporal language. (shrink)

The semantical structures called T x W frames were introduced in (Thomason, 1984) for the Ockhamist temporal-modal language, $[Unrepresented Character]_{o}$ , which consists of the usual propositional language augmented with the Priorean operators P and F and with a possibility operator ◇. However, these structures are also suitable for interpreting an extended language, $[Unrepresented Character]_{so}$ , containing a further possibility operator $\lozenge^{s}$ which expresses synchronism among possibly incompatible histories and which can thus be thought of as a cross-history 'simultaneity' operator. (...) In the present paper we provide an infinite set of axioms in $[Unrepresented Character]_{so}$ , which is shown to be strongly complete for T x W-validity. Von Kutschera (1997) contains a finite axiomatization of T x W-validity which however makes use of the Gabbay Irreflexivity Rule (Gabbay, 1981). In order to avoid using this rule, the proof presented here develops a new technique to deal with reflexive maximal consistent sets in Henkin-style constructions. (shrink)

The semantical structures called T×W frames were introduced in (Thomason, 1984) for the Ockhamist temporal-modal language, ℒO, which consists of the usual propositional language augmented with the Priorean operators P and F and with a possibility operator ⋄. However, these structures are also suitable for interpreting an extended language, ℒSO, containing a further possibility operator ⋄s which expresses synchronism among possibly incompatible histories and which can thus be thought of as a cross-history ‘simultaneity’ operator. In the present paper we provide (...) an infinite set of axioms in ℒSO, which is shown to be strongly complete forT ×W-validity. Von Kutschera (1997) contains a finite axiomatization of T×W-validity which however makes use of the Gabbay Irreflexivity Rule (Gabbay, 1981). In order to avoid using this rule, the proof presented here develops a new technique to deal with reflexive maximal consistent sets in Henkin-style constructions. (shrink)

This paper investigates logical aspects of combining linear orders as semantics for modal and temporal logics, with modalities for possible paths, resulting in a variety of branching time logics over classes of trees. Here we adopt a unified approach to the Priorean, Peircean and Ockhamist semantics for branching time logics, by considering them all as fragments of the latter, obtained as combinations, in various degrees, of languages and semantics for linear time with a modality for possible paths. We then consider (...) a hierarchy of natural classes of trees and bundled trees arising from a given class of linear orders and show that in general they provide different semantics. We also discuss transfer of definability from linear orders to trees and introduce a uniform translation from Priorean to Peircean formulae which transfers definability of properties of linear orders to definability of properties of all paths in trees. (shrink)

The transition semantics presented in Rumberg :77–108, 2016a) constitutes a fine-grained framework for modeling the interrelation of modality and time in branching time structures. In that framework, sentences of the transition language \ are evaluated on transition structures at pairs consisting of a moment and a set of transitions. In this paper, we provide a class of first-order definable Kripke structures that preserves \-validity w.r.t. transition structures. As a consequence, for a certain fragment of \, validity w.r.t. transition structures turns (...) out to be axiomatizable. The result is then extended to the entire language \ by means of a quite natural ‘Henkin move’, i.e. by relaxing the notion of validity to bundled structures. (shrink)

In this paper we present BTC, which is a complete logic for branchingtime whose modal operator quantifies over histories and whose temporal operators involve a restricted quantification over histories in a given possible choice. This is a technical novelty, since the operators of the usual logics for branching-time such as CTL express an unrestricted quantification over histories and moments. The value of the apparatus we introduce is connected to those logics of agency that are interpreted on branching-time, as for instance (...) Stit Logics. (shrink)

Fibring is defined as a mechanism for combining logics with a first-order base, at both the semantic and deductive levels. A completeness theorem is established for a wide class of such logics, using a variation of the Henkin method that takes advantage of the presence of equality and inequality in the logic. As a corollary, completeness is shown to be preserved when fibring logics in that class. A modal first-order logic is obtained as a fibring where neither the Barcan formula (...) nor its converse hold. (shrink)

The aim of this paper is to present a new perspective under which branching-time semantics can be viewed. The set of histories (maximal linearly ordered sets) in a tree structure can be endowed in a natural way with a topological structure. Properties of trees and of bundled trees can be expressed in topological terms. In particular, we can consider the new notion of topological validity for Ockhamist temporal formulae. It will be proved that this notion of validity is equivalent to (...) validity with respect to bundled trees. (shrink)

The transition semantics presented in Rumberg (J Log Lang Inf 25(1):77–108, 2016a) constitutes a fine-grained framework for modeling the interrelation of modality and time in branching time structures. In that framework, sentences of the transition language L_t are evaluated on transition structures at pairs consisting of a moment and a set of transitions. In this paper, we provide a class of first-order definable Kripke structures that preserves L_t-validity w.r.t. transition structures. As a consequence, for a certain fragment of L_t, validity (...) w.r.t. transition structures turns out to be axiomatizable. The result is then extended to the entire language L_t by means of a quite natural ‘Henkin move’, i.e. by relaxing the notion of validity to bundled structures. (shrink)

Gennaro Chtjerchia, Dynamics of meaning: anaphora, presupposition, and the the of grammar. Chicago and London: The University of Chicago Press, 1995.xv+ 270 pp, £59.95, £31.95 G. Pr...

The articles in the symposium “Teaching Early Modern Philosophy: New Approaches” provide theoretical reflections and practical advice on new ways of teaching undergraduate survey courses in early modern philosophy. This introduction lays out the rationale for the symposium and summarizes the articles that compose it.

Cultural evolution studies are characterized by the notion that culture evolves accordingly to broadly Darwinian principles. Yet how far the analogy between cultural and genetic evolution should be pushed is open to debate. Here, we examine a recent disagreement that concerns the extent to which cultural transmission should be considered a preservative mechanism allowing selection among different variants, or a transformative process in which individuals recreate variants each time they are transmitted. The latter is associated with the notion of “cultural (...) attraction”. This issue has generated much misunderstanding and confusion. We first clarify the respective positions, noting that there is in fact no substantive incompatibility between cultural attraction and standard cultural evolution approaches, beyond a difference in focus. Whether cultural transmission should be considered a preservative or reconstructive process is ultimately an empirical question, and we examine how both preservative and reconstructive cultural transmission has been studied in recent experimental research in cultural evolution. Finally, we discuss how the relative importance of preservative and reconstructive processes may depend on the granularity of analysis and the domain being studied. (shrink)

This chapter discusses the relation between Christian Wolff's philosophy and the methodological views of early modern experimental philosophers. The chapter argues for three claims. First, Wolff's system relies on experience at every step and his views on experiments, observations, hypotheses, and the a priori are in line with those of experimental philosophers. Second, the study of Wolff's views demonstrates the influence of experimental philosophy in early eighteenth-century Germany. Third, references to Wolff's empiricism and rationalism are best identified or replaced with (...) references to his endorsement of the tenets of experimental philosophers and of a mathematical demonstrative method. (shrink)

People’s awareness of tactile stimuli has been investigated in far less detail than their awareness of stimuli in other sensory modalities. In an attempt to fill this gap, we provide an overview of studies that are pertinent to the topic of tactile consciousness. We discuss the results of research that has investigated phenomena such as “change blindness”, phantom limb sensations, and numerosity judgments in tactile perception, together with the results obtained from the study of patients affected by deficits that can (...) adversely affect tactile perception such as neglect, extinction, and numbsense. The similarities as well as some of the important differences that have emerged when visual and tactile conscious information processing have been compared using similar experimental procedures are highlighted. We suggest that conscious information processing in the tactile modality cannot be separated completely from the more general processing of spatial information in the brain. Finally, the importance of considering tactile consciousness within the larger framework of multisensory information processing is also discussed. (shrink)

We study the computability-theoretic complexity and proof-theoretic strength of the following statements: (1) "If X is a well-ordering, then so is ε X ", and (2) "If X is a well-ordering, then so is φ(α, X)", where α is a fixed computable ordinal and φ represents the two-placed Veblen function. For the former statement, we show that ω iterations of the Turing jump are necessary in the proof and that the statement is equivalent to ${\mathrm{A}\mathrm{C}\mathrm{A}}_{0}^{+}$ over RCA₀. To prove the (...) latter statement we need to use ω α iterations of the Turing jump, and we show that the statement is equivalent to ${\mathrm{\Pi }}_{{\mathrm{\omega }}^{\mathrm{\alpha }}}^{0}{-\mathrm{C}\mathrm{A}}_{0}$ . Our proofs are purely computability-theoretic. We also give a new proof of a result of Friedman: the statement "if x is a well-ordering, then so is φ(x, 0)" is equivalent to ATR₀ over RCA₀. (shrink)

This major publication is a history of the semantic tradition in philosophy from the early nineteenth century through its incarnation in the work of the Vienna Circle, the group of logical positivists that emerged in the years 1925-1935 in Vienna who were characterised by a strong commitment to empiricism, a high regard for science, and a conviction that modern logic is the primary tool of analytic philosophy. In the first part of the book, Alberto Coffa traces the roots of (...) logical positivism in a semantic tradition that arose in opposition to Kant's theory that a priori knowledge is based on pure intuition and the constitutive powers of the mind. In Part II, Coffa chronicles the development of this tradition by members and associates of the Vienna Circle. Much of Coffa's analysis draws on the unpublished notes and correspondence of many philosophers. The book, however, is not merely a history of the semantic tradition from Kant 'to the Vienna Station'. Coffa also critically reassesses the role of semantic notions in understanding the ground of a priori knowledge and its relation to empirical knowledge and questions the turn the tradition has taken since Vienna. (shrink)

Abortion is largely accepted even for reasons that do not have anything to do with the fetus' health. By showing that (1) both fetuses and newborns do not have the same moral status as actual persons, (2) the fact that both are potential persons is morally irrelevant and (3) adoption is not always in the best interest of actual people, the authors argue that what we call ‘after-birth abortion’ (killing a newborn) should be permissible in all the cases where abortion (...) is, including cases where the newborn is not disabled. (shrink)

This open access book discusses individual, collective, and institutional responsibilities with regard to vaccination from the perspective of philosophy and public health ethics. It addresses the issue of what it means for a collective to be morally responsible for the realisation of herd immunity and what the implications of collective responsibility are for individual and institutional responsibilities. The first chapter introduces some key concepts in the vaccination debate, such as ‘herd immunity’, ‘public goods’, and ‘vaccine refusal’; and explains why failure (...) to vaccinate raises certain ethical issues. The second chapter analyses, from a philosophical perspective, the relationship between individual, collective, and institutional responsibilities with regard to the realisation of herd immunity. The third chapter is about the principle of least restrictive alternative in public health ethics and its implications for vaccination policies. Finally, the fourth chapter presents an ethical argument for unqualified compulsory vaccination, i.e. for compulsory vaccination that does not allow for any conscientious objection. The book will appeal to philosophers interested in public health ethics and the general public interested in the philosophical underpinning of different arguments about our moral obligations with regard to vaccination. (shrink)

A brief theoretical review of the current state of the art of embodiment research in clinical psychology has been expounded in order to highlight the key role that embodied conceptualization has on the understanding and explanation of several mental disorders, such as eating disorders, schizophrenia and depression. Evidence has suggested that mental disorders may be explained as disturbances of embodiment, from the disembodiment to the hyperembodiment. In order to understand how some clinical conditions are affected by cultural models, we propose (...) and define a new framework called Exbodiment, complementary to the Embodiment approach to cognition. Mental disorder is strictly related to the subject-culture interaction that may be explained as a two way process in which embodiment and exbodiment are complementary points of view. In this perspective, embodiment may be seen as the “top-down” process, while exbodiment the “bottom-up” one. The introduction of exbodiment conceptualization highlights how subject is both receiver and interpreter of social influence. Subject is the target of a cultural pressure and, at the same time, enacts its own embodied culture in world. Exbodiment conceptualization may help clinicians to better understand and explain the role of culture in the onset and maintenance of mental disorders. (shrink)

In recent works, Chomsky has once more endorsed a computational view of rulefollowing, whereby to follow a rule is to operate certain computations on a subject’s mental representations. As is well known, this picture does not conform to what we may call the grammatical conception of rule-following outlined by Wittgenstein, whereby an elucidation of the concept of rule-following is aimed at by isolating grammatical statements regarding the phrase ‘to follow a rule’. As a result, Chomskyan and Wittgensteinian treatments of topics (...) immediately connected with rule-following, namely linguistic competence and understanding, are utterly different from one another. There are two possible stances that computationalists like Chomsky may adopt with regard to the discrepancy between the two aforementioned modes of dealing with rule-following, namely a conciliatory and a non-conciliatory attitude. According to the former attitude, grammatical remarks on and computationallyoriented theories of rule-following investigate one and the same topic although admittedly at different levels, namely a conceptual and an empirical one. According to the latter attitude, grammatical remarks are just a preliminary step in the investigation of rule-following which scientific advancement, presently represented by computationally-oriented theories on this matter, is well entitled to put aside. In what follows, however, I will try to show that both stances are problematic. The conciliatory attitude simply does not work, for it hardly copes with the fact that the concept of rule-following does not supervene, even weakly, on the property of rule-following, namely the property instantiated in the mental/cerebral phenomena that computationally-oriented theories of rule-following study. To take the contrary attitude, on the other hand, is to end up with another disappointing result, namely that the computational treatment of rule-following ultimately deals with something different from that which we wished to gain knowledge of when we began our inquiry into rule-following.. (shrink)

Cultural evolution researchers use transmission chain experiments to investigate which content is more likely to survive when transmitted from one individual to another. These experiments resemble oral storytelling, wherein individuals need to understand, memorize, and reproduce the content. However, prominent contemporary forms of cultural transmission—think an online sharing—only involve the willingness to transmit the content. Here I present two fully preregistered online experiments that explicitly investigated the differences between these two modalities of transmission. The first experiment (_N_ = 1,080 participants) (...) examined whether negative content, information eliciting disgust, and threat-related information were better transmitted than their neutral counterpart in a traditional transmission chain setup. The second experiment (_N_ = 1,200 participants) used the same material, but participants were asked whether or not they would share the content in two conditions: in a large anonymous social network or with their friends, in their favorite social network. Negative content was both better transmitted in transmission chain experiments and shared more than its neutral counterpart. Threat-related information was successful in transmission chain experiments but not when sharing, and finally, information eliciting disgust was not advantaged in either. Overall, the results present a composite picture, suggesting that the interactions between the specific content and the medium of transmission are important and, possibly, that content biases are stronger when memorization and reproduction are involved in the transmission—as in oral transmission—than when they are not—as in online sharing. Negative content seems to be reliably favored in both modalities of transmission. (shrink)

In ancient China, art has never been a substitute for the category of ‘truth’ in the sense of Western aestheticism, but a mimic for goodness and beauty. The image in traditional Chinese aesthetics never transcended the idea to the level of Western abstraction, and that is because the artistic expression bore a social synthesis, rather than metaphysical, between human beings, reality, and the world. However, the Ming Dynasty introduces a Dionysian discourse that challenges the Apollonian tradition.

In just the last decade, many conference proceedings have been published on Plato’s Timaeus and its influence on the history of philosophy. The present vo­lume, which is the result of a symposium held at Seoul National University in September 2011, testifies to the enduring and widespread interest the Platonic dia­logue is able to elicit. The nine studies here collected by Euree Song center on the figure of the demiurge as maker of the world and they all deal with authors who, (...) while having di... (shrink)