We define a propositionally quantified intuitionistic logic Hπ + by a natural extension of Kripke's semantics for propositional intutionistic logic. We then show that Hπ+ is recursively isomorphic to full second order classical logic. Hπ+ is the intuitionistic analogue of the modal systems S5π +, S4π +, S4.2π +, K4π +, Tπ +, Kπ + and Bπ +, studied by Fine.

We define a propositionally quantified intuitionistic logic $\mathbf{H}\pi +$ by a natural extension of Kripke's semantics for propositional intutionistic logic. We then show that $\mathbf{H}\pi+$ is recursively isomorphic to full second order classical logic. $\mathbf{H}\pi+$ is the intuitionistic analogue of the modal systems $\mathbf{S}5\pi +, \mathbf{S}4\pi +, \mathbf{S}4.2\pi +, \mathbf{K}4\pi +, \mathbf{T}\pi +, \mathbf{K}\pi +$ and $\mathbf{B}\pi +$, studied by Fine.

Where humans can manipulate and integrate the information they receive in subtle and ever-changing ways from context to context, computers need structured and context-free background information of a sort which ontologies can help to provide. A domain ontology captures the stable, highly general and commonly accepted core knowledge for an application domain. The domain at issue here is that of the life sciences, in particular molecular biology and bioinformatics. Contemporary life science research includes components drawn from physics, chemistry, mathematics, medicine (...) and many other areas, and all of these dimensions, as well as fundamental philosophical issues, must be taken into account in the construction of a domain ontology. Here we describe the basic features of domain ontologies in the life sciences and show how they can be used. (shrink)

The integration of standardized biomedical terminologies into a single, unified knowledge representation system has formed a key area of applied informatics research in recent years. The Unified Medical Language System (UMLS) is the most advanced and most prominent effort in this direction, bringing together within its Metathesaurus a large number of distinct source-terminologies. The UMLS Semantic Network, which is designed to support the integration of these source-terminologies, has proved to be a highly successful combination of formal coherence and broad scope. (...) We argue here, however, that its organization manifests certain structural problems, and we describe revisions which we believe are needed if the network is to be maximally successful in realizing its goals of supporting terminology integration. (shrink)

Fine and Kripke extended S5, S4, S4.2 and such to produce propositionally quantified systems , , : given a Kripke frame, the quantifiers range over all the sets of possible worlds. is decidable and, as Fine and Kripke showed, many of the other systems are recursively isomorphic to second-order logic. In the present paper I consider the propositionally quantified system that arises from the topological semantics for S4, rather than from the Kripke semantics. The topological system, which I dub , (...) is strictly weaker than its Kripkean counterpart. I prove here that second-order arithmetic can be recursively embedded in . In the course of the investigation, I also sketch a proof of Fine's and Kripke's results that the Kripkean system is recursively isomorphic to second-order logic. (shrink)

Gyula begins with a contrast between contemporary scare-quotes essentialism and Aristotelian full-blooded essentialism. The former is a semantic thesis couched in the vocabulary of possible-worlds semantics, holding that some terms are rigid designators, while the latter is a metaphysical thesis, couched in a more ancient vocabulary, holding that things have essences. Gyula argues that the more traditional metaphysical framework deserves reconsideration, both because it can help us with problems arising from the contemporary approach, and because it possesses greater expressive power (...) than the contemporary approach. He presents a fragmentary formal semantics for the traditional approach, and argues that this semantics enables us to see how the problems of contemporary essentialism can be avoided while at the same time other properly metaphysical issues, which are unapproachable from within the contemporary model due to its expressive weakness, become available for investigation. The semantics that he presents seems intended to establish the intelligibility of the traditional vocabulary, and so of the thesis of Aristotelian essentialism which is couched in it. Gyula then argues that this thesis is in fact true, using the vocabulary which the semantics has rendered legitimate. (shrink)

R. K. Meyer once gave precise form to the question of whether relevant implication can be defined in any modal system, and his answer was `no'. In the present paper, we extend S4, first with propositional quantifiers, to the system S4π+; and then with definite propositional descriptions, to the system S4π+ lp . We show that relevant implication can in some sense be defined in the modal system S4π+ lp , although it cannot be defined in S4π+.

R. K. Meyer once gave precise form to the question of whether relevant implication can be defined in any modal system, and his answer was `no'. In the present paper, we extend $\mathbf{S4}$, first with propositional quantifiers, to the system $\mathbf{S4\pi}+$; and then with definite propositional descriptions, to the system $\mathbf{S4\pi}+^{lp}$. We show that relevant implication can in some sense be defined in the modal system $\mathbf{S4\pi}+^{lp}$, although it cannot be defined in $\mathbf{S4\pi}+$.

Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, □ is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and □ can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system (...) be a topological space X together with a continuous function f. f can be thought of in temporal terms, moving the points of the topological space from one moment to the next. Dynamic topological logics are the logics of dynamic topological systems, just as S4 is the logic of topological spaces. Dynamic topological logics are defined for a trimodal language with an S4-ish topological modality □ , and two temporal modalities, ○ and * , both interpreted using the continuous function f. In particular, ○ expresses f’s action on X from one moment to the next, and * expresses the asymptotic behaviour of f. (shrink)

Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, □ is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and □ can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system (...) be a topological space X together with a continuous function f. f can be thought of in temporal terms, moving the points of the topological space from one moment to the next. Dynamic topological logics are the logics of dynamic topological systems, just as S4 is the logic of topological spaces. Dynamic topological logics are defined for a trimodal language with an S4-ish topological modality □, and two temporal modalities, ○ and *, both interpreted using the continuous function f. In particular, ○ expresses f’s action on X from one moment to the next, and * expresses the asymptotic behaviour of f. (shrink)

In ‘Fair Infinite Lotteries’ (FIL), Wenmackers and Horsten use non-standard analysis to construct a family of nicely-behaved hyperrational-valued probability measures on sets of natural numbers. Each probability measure in FIL is determined by a free ultrafilter on the natural numbers: distinct free ultrafilters determine distinct probability measures. The authors reply to a worry about a consequent ‘arbitrariness’ by remarking, “A different choice of free ultrafilter produces a different ... probability function with the same standard part but infinitesimal differences.” They illustrate (...) this remark with the example of the sets of odd and even numbers. Depending on the ultrafilter, either each of these sets has probability 1/2, or the set of odd numbers has a probability infinitesimally higher than 1/2 and the set of even numbers infinitesimally lower. The point of the current paper is simply that the amount of indeterminacy is much greater than acknowledged in FIL: there are sets of natural numbers whose probability is far more indeterminate than that of the set of odd or the set of even numbers. (shrink)

The topological semantics for modal logic interprets a standard modal propositional language in topological spaces rather than Kripke frames: the most general logic of topological spaces becomes S4. But other modal logics can be given a topological semantics by restricting attention to subclasses of topological spaces: in particular, S5 is logic of the class of almost discrete topological spaces, and also of trivial topological spaces. Dynamic Topological Logic interprets a modal language enriched with two unary temporal connectives, next and henceforth. (...) DTL interprets the extended language in dynamic topological systems: a DTS is a topological space together with a continuous function used to interpret the temporal connectives. In this paper, we axiomatize four conservative extensions of S5, and show them to be the logic of continuous functions on almost discrete spaces, of homeomorphisms on almost discrete spaces, of continuous functions on trivial spaces and of homeomorphisms on trivial spaces. (shrink)

In The Revision Theory of Truth (MIT Press), Gupta and Belnap (1993) claim as an advantage of their approach to truth "its consequence that truth behaves like an ordinary classical concept under certain conditions—conditions that can roughly be characterized as those in which there is no vicious reference in the language." To clarify this remark, they define Thomason models, nonpathological models in which truth behaves like a classical concept, and investigate conditions under which a model is Thomason: they argue that (...) a model is Thomason when there is no vicious reference in it. We extend their investigation, considering notions of nonpathologicality and senses of "no vicious reference" generated both by revision theories of truth and by fixedpoint theories of truth. We show that some of the fixed-point theories have an advantage analogous to that which Gupta and Belnap claim for their approach, and that at least one revision theory does not. This calls into question the claim that the revision theories have a distinctive advantage in this regard. (shrink)

In light of a well-documented deficit in theory of mind found in high-functioning individuals with autism and Asperger Syndrome, this article explores HFA and AS children’s social-cognitive understanding of other people as reflected in their linguistic performance when answering mundane, everyday questions posed by their family members during dinnertime interaction. Ethnographic observations and video recordings of spontaneous interaction at home reveal that, contrary to findings in cognitive psychological research, the majority of the time the children were able to detect their (...) interlocutors’ communicative intentions and produce relevant responses that were marked by their conversational partners as acceptable. This article proposes that this success is due in part to parents who, through different strategies, facilitate their HFA and AS children’s access to socio-cultural perspective-taking and their interlocutors’ intentions, and better their children’s communicative skills. (shrink)

Thomas Ricketts has developed a powerful interpretation of Frege on judgment, truth and logic. Recently, Ricketts has modified his reading, holding that judgment is an act of knowledge-acquisition; this rules out incorrect judgment. I argue that Ricketts goes too far here. I criticize the textual basis for Ricketts's new view, and show that the interpretive problems which led him to this change can be met without such extreme measures. Thus, I defend Ricketts' earlier view against his own later modification. Along (...) the way I discuss Kant and Brentano on judgment, and I explore Fregean argument concerning the objectivity of truth. (shrink)

Stephen Maitzen argues that divine command metaethics must be mistaken because it is committed to the implausible assumption that the sentence ‘God is good’ is a tautology. In this article, I show that a charitable interpretation of R. M. Adams’ version of divine command metaethics is not committed to accept this assumption. I conclude that Maitzen’s objection merely manages to refute a strawman version of divine command metaethics.

Youth sports have been recognized as an arena for men to meet increased cultural expectations of being involved in their children’s lives. Indeed, in contrast to other child care practices, many men are eager to take part in their children’s organized sports. Drawing on an ethnographic study of middle-class families in the United States, this study examines how men juggle two contrasting cultural models of masculinity when fathering through sports—a performance-oriented orthodox masculinity that historically has been associated with sports and (...) a caring, inclusive masculinity that promotes the nurturing of one’s children. Through a detailed analysis of how fathers’ sports involvement unfolds on the ground, we show how men, in order to portray themselves as “good” fathers, attempt to strike a balance between pushing their children to excel and supporting them regardless of their performance. We propose that although men may value inclusive masculinity when fathering through youth sports, at the same time they exercise orthodox masculinity in other domestic domains. (shrink)

Ted A. Warfield has recently employed modal logic to argue that compatibilism in the free-will/determinism debate entails the rejection of intuitively valid inferences. I show that Warfield's argument fails. A parallel argument leads to the false conclusion that the mere possibility of determinism, together with the necessary existence of any contingent propositions, entails the rejection of intuitively valid inferences. The error in both arguments involves a crucial equivocation, which can be revealed by replacing modal operators with explicit quantifiers over possible (...) worlds. I conclude that the modal-logical apparatus used by Warfield obscures rather than clarifies, and distracts from the real philosophical issues involved in the metaphysical debate. These issues cannot be settled by logic alone. (shrink)

Let ${{\mathcal L}^{\square\circ}}$ be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality □ and a temporal modality ◦, understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language ${{\mathcal L}^{\square\circ}}$ by interpreting ${{\mathcal L}^{\square\circ}}$ in dynamic topological systems, i.e., ordered pairs 〈X, f〉, where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have shown (...) that S4C is sound and complete for this semantics. S4C is also complete for continuous functions on Cantor space (Mints and Zhang, Kremer), and on the real plane (Fernández Duque); but incomplete for continuous functions on the real line (Kremer and Mints, Slavnov). Here we show that S4C is complete for continuous functions on the rational numbers. (shrink)

History of philosophy is embedded into the theory of history. Two different philosophies, but we still have similar basic connections between different parts of each philosophy and a closer similarity of these two relativist thinkers. Gadamer, as a disciple of Heidegger, worked out the philosophical hermeneutics (Truth and Method, 1960) established by Heidegger in the early 20s. He embedded his approach of the history of philosophy in his hermeneutics, particularly in his description of history grasped as a chain of historically (...) effected events. Rorty, as a neopragmatist thinker, classified first the philosophers as systematic and edifying in his Philosophy and the Mirror of Nature (1979), but later, in his Contingency, Irony and Solidarity (1989), he already speeks about history of philosophy as the history of metaphors. Despite their differences, it may be proved, on the one hand, that some part of their philosophies is primus inter pares; on the other hand, they both are relativists in some sense, and claim that we can have only narratives about the history of philosophy. (shrink)