Simple finite axiomatizations are given for versions of the modal logics K and K4 with non-contingency (or contingency) as the sole modal primitive. This answers two questions of I. L. Humberstone.

Montague, Prior, von Wright and others drew attention to resemblances between modal operators and quantifiers. In this paper we show that classical quantifiers can, in fact, be regarded as S5-like operators in a purely propositional modal logic. This logic is axiomatized and some interesting fragments of it are investigated.

Between 300,000 and 250,000 years ago early humans in Africa and Eurasia began to use durable material substances and objects as media for signaling. Initially material signals were confined to ochre and other pigments, but over time objects such as beads were also added as technologies for sending messages. Changes in the types of materials used, their durability and costs, and the contexts of their disposal indicate a series of transitions in how early humans employed signaling media. Signaling theory from (...) biology suggests that shifts in technologies over the course of the Pleistocene reflect problems in coordinating action and resolving conflicts within increasingly large and internally differentiated societies. (shrink)

Lloyd Humberstone’s recently published Philosophical Applications of Modal Logic presents a number of new ideas in modal logic as well explication and critique of recent work of many others. We extend some of these ideas and answer some questions that are left open in the book.

Beads and other ‘body ornaments’ are very widespread components of the archaeological record of early modern humans (Homo sapiens). They appear first in the Middle Stone Age in Africa, and somewhat later in the Early Upper Paleolithic of Eurasia. The manufacture and use of ornaments is widely considered to be evidence for significant developments in human cognition. In our view, the appearance of these objects represents the interaction of evolved cognitive capacities with changing social and demographic conditions. Body ornamentation is (...) a medium or technology for communication, particularly of socially-relevant information. The widespread adoption of beads and other discrete objects as media for communication implies changes in the complexity and stability of social messages, as well as the scale of social networks. The relatively sudden appearance of beads in the Paleolithic archaeological record coincides with genetic and archaeological evidence for expansion of human populations. We argue that these changes reflect expanding scales of social interaction and more complex social landscapes resulting from unprecedentedly large and internally differentiated human populations. (shrink)

A notable early result of David Makinson establishes that every monotone modal logic can be extended to LI, LV, or LF, and every antitone logic can be extended to LN, LV, or LF, where LI, LN, LV, and LF are logics axiomatized, respectively, by the schemas □α↔α, □α↔¬α, □α↔⊤, and □α↔⊥. We investigate logics that are both monotone and antitone (hereafter amphitone). There are exactly three: LV, LF, and the minimum amphitone logic AM axiomatized by the schema □α→□β. These logics, (...) along with LI, LN, and a wider class of “extensional” logics, bear close affinities to classical propositional logic. Characterizing those affinities reveals differences among several accounts of equivalence between logics. Some results about amphitone logics do not carry over when logics are construed as consequence or generalized (“multiple-conclusion”) consequence relations on languages that may lack some or all of the nonmodal connectives. We close by discussing these divergences and conditions under which our results do carry over. (shrink)

Applications of game theory to moral philosophy are impededby foundational issues and troublesome examples. In the first part of this paper,questions are raised about the appropriate game-theoretical frameworks for applications to moralphilosophy and about the proper interpretations of the theoretical devices employed inthese frameworks. In the second part, five examples that should be of particular interest to thoseinterested in the connections between ethics and game theory are delineated and discussed. Thefirst example comprises games in which there is an outcome unanimously (...) preferred to the``solution'' of the game, appropriately defined. The second comprises games whose solution callsfor different players to employ different strategies. The third comprises games whosesolution calls for players to adopt mixed strategies. The fourth comprises games whose solutionrequires players to cycle among a variety of strategies. The fifth comprises games whose solutionrequires players to discriminate in morally inappropriate ways. (shrink)

The semantics of tense has received a great deal of attention in the contemporary linguistics, philosophy and logic literatures. This is probably due partly to a renewed appreciation for the fact that issues involving tense touch on certain issues of philosophical importance (viz., determinism, causality, and the nature of events, of time and of change). It may also be due partly to neglect. Tense was noticeably omitted from the theories of meaning advanced in previous generations. In the writings of both (...) Russell and Frege there is the suggestion that tense would be absent altogether from an ideal or scientifically adequate language. (Tense was not the only blemish of natural language to be removed, of course, but tense is a more serious omission than, say, pronouns because it is present in every sentence of the language.) Finally, in recent years there has been a greater recognition of the important role that all of the so-called “indexical” expressions must play in an explanation of mental states and human behavior. Tense is no exception. Knowing that our friend died is cause for mourning, knowing that he dies is just another confirmation of a familiar syllogism. (shrink)

The system obtained by adding full propositional quantification to S5 is known to be decidable, while that obtained by doing so for T is known to be recursively intertranslatable with full second-order logic. Recently it was shown that the system with two S5 operators and full propositional quantification is also recursively intertranslatable with second-order logic. This note establishes that the map assigning [1][2]p to \squarep provides a validity and satisfaction preserving translation between the T system and the double S5 system, (...) thus providing an easier proof of the recent result. (shrink)

The prisoner 's dilemma game has acquired large literatures in several disciplines. It is surprising, therefore, that a good definition of the game is hard to find. Typically an author relates a story about captured criminals or military rivals, provides a particular payoff matrix and asserts that the PD is characterized, or illustrated, by that matrix. In the few cases in which characterizing conditions are given, the conditions, and the motivations for them, do not always agree with each other or (...) with the paradigm examples elsewhere. In this paper we describe several varieties of PD's. In particular, we suggest there are two distinctions among PD's with philosophical significance, the pure/impure and the utilitarian/nonutilitarian distinctions. In the first section, we explain and characterize the two distinctions. In the second, we discuss an issue of moral philosophy that illustrates the significance of the former. (shrink)

Evolutionary Transitions in Individuality have been responsible for the major transitions in levels of selection and individuality in natural history, such as the origins of prokaryotic and eukaryotic cells, multicellular organisms, and eusocial insects. The integrated hierarchical organization of life thereby emerged as groups of individuals repeatedly evolved into new and more complex kinds of individuals. The Social Protocell Hypothesis proposes that the integrated hierarchical organization of human culture can also be understood as the outcome of an ETI—one that produced (...) a “cultural organism” from a substrate of socially learned traditions that were contained in growing and dividing social communities. The SPH predicts that a threshold degree of evolutionary individuality would have been achieved by 2.0–2.5 Mya, followed by an increasing degree of evolutionary individuality as the ETI unfolded. We here assess the SPH by applying a battery of criteria—developed to assess evolutionary individuality in biological units—to cultural units across the evolutionary history of Homo. We find an increasing agreement with these criteria, which buttresses the claim that an ETI occurred in the cultural realm. (shrink)

The aim of this study is to determine to what extent the tense markers of tense logic represent what is represented by the tense forms of natural language. To achieve this, it will be necessary to report the findings of linguistics on what the tense forms of natural languages do represent. The justification for this study lies in a fundamental difference between natural and logical languages. Where natural languages develop to meet the needs of their speakers, logical language is used (...) for testing the validity of argument of a certain kind. Tense logic has been used to examine philosophical issues, and in linguistics to examine how tenses describe many different possible structures of time. (shrink)

Le dilemme du prisonnier occupe une place centrale dans la théorie morale de Gauthier, mais cette place est en évolution. Dans «Morality and Advantage», ce dilemme fournit un modèle montrant comment la moralité peut avoir des propriétés apparemment contradictoires. Dans Morals by Agreement, il pose un problème particulier pour l’opinion selon laquelle un comportement moral est individuellement rationnel. Suite à ces publications, certains experts en théorie des jeux ont contesté l’idée voulant que le dilemme du prisonnier soit un cadre approprié (...) pour réfléchir sur la théorie morale. La première partie de cet article examine les rôles du dilemme du prisonnier dans l’œuvre de Gauthier. La deuxième partie présente un projet, incluant des composantes descriptives et normatives, qui développe les idées de «Morality and Advantage» tout en le préservant de la critique des théoriciens des jeux. (shrink)