This paper criticizes non-constructive uses of set theory in formal economics. The main focus is on results on preference aggregation and Arrow’s theorem for infinite electorates, but the present analysis would apply as well, e.g., to analogous results in intergenerational social choice. To separate justified and unjustified uses of infinite populations in social choice, I suggest a principle which may be called the Hildenbrand criterion and argue that results based on unrestricted axiom of choice do not meet this criterion. The (...) technically novel part of this paper is a proposal to use a set-theoretic principle known as the axiom of determinacy ), not as a replacement for Choice, but simply to eliminate applications of set theory violating the Hildenbrand criterion. A particularly appealing aspect of \ from the point of view of the research area in question is its game-theoretic character. (shrink)

We prove that all finitely axiomatizable tense logics with temporal operators for ‘always in the future’ and ‘always in the past’ and determined by linear fows time are coNP-complete. It follows, for example, that all tense logics containing a density axiom of the form ■n+1F p → nF p, for some n ≥ 0, are coNP-complete. Additionally, we prove coNP-completeness of all ∩-irreducible tense logics. As these classes of tense logics contain many Kripke incomplete bimodal logics, we obtain many natural (...) examples of Kripke incomplete normal bimodal logics which are nevertheless coNP-complete. (shrink)

In this paper, we are going to analyze the phenomenon of modal incompleteness from an algebraic point of view. The usual method of showing that a given logic L is incomplete is to show that for some L and some cannot be separated from by a suitably wide class of complete algebras — usually Kripke algebras. We are going to show that classical examples of incomplete logics, e.g., Fine logic, are not complete with respect to any class of complete BAOs. (...) Even above Grz it is possible to find a continuum of such logics, which immediately implies the existence of a continuum of neighbourhood-incomplete Grz logics. Similar results can be proved for Löb logics. In addition, completely incomplete logics above Grz may be found uniformly as a result of failures of some admissible rule of a special kind. (shrink)

In this article, we tell a story about incompleteness in modal logic. The story weaves together an article of van Benthem, “Syntactic aspects of modal incompleteness theorems,” and a longstanding open question: whether every normal modal logic can be characterized by a class of completely additive modal algebras, or as we call them, ${\cal V}$-baos. Using a first-order reformulation of the property of complete additivity, we prove that the modal logic that starred in van Benthem’s article resolves the open question (...) in the negative. In addition, for the case of bimodal logic, we show that there is a naturally occurring logic that is incomplete with respect to ${\cal V}$-baos, namely the provability logic $GLB$. We also show that even logics that are unsound with respect to such algebras do not have to be more complex than the classical propositional calculus. On the other hand, we observe that it is undecidable whether a syntactically defined logic is ${\cal V}$-complete. After these results, we generalize the Blok Dichotomy to degrees of ${\cal V}$-incompleteness. In the end, we return to van Benthem’s theme of syntactic aspects of modal incompleteness. (shrink)

In this paper, we introduce an extension of the modal language with what we call the global quantificational modality [∀p]. In essence, this modality combines the propositional quantifier ∀p with the global modality A: [∀p] plays the same role as the compound modality ∀pA. Unlike the propositional quantifier by itself, the global quantificational modality can be straightforwardly interpreted in any Boolean Algebra Expansion (BAE). We present a logic GQM for this language and prove that it is complete with respect to (...) the intended algebraic semantics. This logic enables a conceptual shift, as what have traditionally been called different “modal logics” now become [∀p]-universal theories over the base logic GQM: instead of defining a new logic with an axiom schema such as □φ→□□φ, one reasons in GQM about what follows from the globally quantified formula [∀p](□p→□□p). (shrink)

This paper provides several examples of how modal logic can be used in studying the XML document navigation language XPath. More specifically, we derive complete axiomatizations, computational complexity and expressive power results for XPath fragments from known results for corresponding logics. A secondary aim of the paper is to introduce XPath in a way that makes it accessible to an audience of modal logicians.

As with any historical study, including that of knowledge and ideas, the progress of the semiology of the theater is subject to periodicity. The aim of any division into periods is to obtain a global view, even at the price of simplifications, but it can also bring out the hidden aspects of the phenomena under study.The semiology or semiotics of the theater, that is, the application of the idea of sign to the art of the spectacle, has a long past, (...) in which several stages may be distinguished, and first of all those that I would call the presemiology and the protosemiology of the theater. (shrink)

Argues that the key distinction between human and nonhuman social cognition consists in our complex, diverse and flexible capacities to shape each other's minds in ways that make them easier to interpret.

Argues that the key distinction between human and nonhuman social cognition consists in our complex, diverse and flexible capacities to shape each other's minds in ways that make them easier to interpret.

Discusses philosophical ethics in the canonical Gospels, both in its normative (formal and material) dimension, and in a descriptive dimension (as science about morality). It argues that the ethics present in the Gospels has a universal and non-denominational character, although it is not reduced to it. The author argues that in the Gospels Jesus mad acceptance and the implementation of ethical goods, values and material norms dependent on the level of ethical awareness of his recipients. --Book cover.

Hilary Putnam (1926–2016) was prone to change his mind on variety of philosophical issues and almost constantly to modify his views. The last period of the development of his philosophy is known as the phase of commonsense or natural realism, eloquently presented in his 1994 Dewey Lectures. This paper is focused on three facets of his position and tries to identify three difficulties it encounters. Firstly, Putnam claims that in the contemporary realism debate we have, on the one hand, proponents (...) of extravagant metaphysical realism, and, on the other hand, advocates of various versions of irresponsible antirealism. Unfortunately, the delineation of the debate is too coarse-grained, since there are many forms of metaphysical realism, and lumping together various antirealisms is confusing and unhelpful. Secondly, Putnam’s naïve direct realism in the philosophy of perception seems incompatible with his transactional account of perception. Thirdly, for some time Putnam was under a spell of Wittgensteinian quietism that distorted the true character of his philosophical ideas. (shrink)

The article presents two concepts of indexicality. The first, more standard and narrow, identifies indexicality with systematic (meaning controlled) context-sensitivity. The second, broader (derived from the work of Jerzy Pelc), conceives indexicality in terms of the potential variability of the general semiotic characteristics expressions (with respect to the context of use). The text introduces the concept of a pragmatic matrix that serves for a schematic representation of contextual variation. I also recapitulate briefly the views of Jerzy Pelc on the meaning (...) (manner of use) and use of expressions, and briefly indicate its relationship approaches with contemporary debates around contextualism and status of non-sentential speech acts. Finally, the relationship between the broader notion of indexicality and the directival theory of meaning is analyzed. (shrink)