We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side by-side product of partial orderings which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with ¬CH and Martin's axiom for countable p.o.-sets. An iterative version of the pseudo-product is used under an inaccessible cardinal to show the consistency of the club (...) principle for every stationary subset of limits of ω1 together with ¬CH and Martin's axiom for countable p.o.-sets. (shrink)

For a regular cardinal κ with κ<κ = κ and κ ≤ λ , we construct generically a subset S of {x ∈ Pκλ : x ∩ κ is a singular ordinal} such that S is stationary in a strong sense but the stationarity of S can be destroyed by a κ+-c. c. forcing ℙ* which does not add any new element of Pκλ . Actually ℙ* can be chosen so that ℙ* is κ-strategically closed. However we show that such (...) ℙ* itself cannot be κ-strategically closed or even <κ-strategically closed if κ is inaccessible. (shrink)

A partial ordering P is said to have the weak Freese-Nation property if there is a mapping tf : P → [P]0 such that, for any a, b ε P, if a b then there exists c ε tf∩tf such that a c b. In this note, we study the WFN and some of its generalizations. Some features of the class of Boolean algebras with the WFN seem to be quite sensitive to additional axioms of set theory: e.g. under CH, (...) every ccc complete Boolean algebra has this property while, under b 2, there exists no complete Boolean algebra with the WFN. (shrink)

The following results are proved: In a model obtained by adding ℵ 2 Cohen reals , there is always a c.c.c. complete Boolean algebra without the weak Freese-Nation property. Modulo the consistency strength of a supercompact cardinal , the existence of a c.c.c. complete Boolean algebra without the weak Freese-Nation property is consistent with GCH. If a weak form of □ μ and cof =μ + hold for each μ >cf= ω , then the weak Freese-Nation property of 〈 P (...) ,⊆〉 is equivalent to the weak Freese-Nation property of any of C or R for uncountable κ . Modulo the consistency of ↠ , it is consistent with GCH that C does not have the weak Freese-Nation property and hence the assertion in does not hold , and also that adding ℵ ω Cohen reals destroys the weak Freese-Nation property of 〈 P , ⊆ 〉 . These results solve all of the problems except Problem 1 in S. Fuchino, L. Soukup, Fundament. Math. 154 159–176, and some other problems posed by Geschke. (shrink)

An Enquiry into the Nature of Liberation: Bhaṭṭa Rāmakaṇṭha’s Paramokṣanirāsakārikāvṛtti, a Commentary on Sadyojyotiḥ’s Refutation of Twenty Conceptions of the Liberated State. Edited and translated by Alex Watson, Dominic Goodall, and S. L. P. Anjaneya Sarma. Collection Indologie, vol. 122. Pondicherry: Institut Français de Pondichéry, École française d’Extrême-Orient, 2013. Pp. 508. €38.

This paper discusses empty quotation (‘’ is an empty string) and lexical quotation (his praise was, quote, fulsome, unquote), it challenges the minimal theory of quotation (‘ “x” ’ quotes ‘x’) and it defends the identity theory of quotation. In the process it illuminates disciplinary differences between the science of language and the philosophy of language. First, most philosophers assume, without argument, that language includes writing, whereas linguists have reason to identify language with speech (plus sign language). Second, philosophers tend (...) to think of languages as abstract objects whereas linguists tend to think of them as natural objects. These foundational differences help to explain disagreements in grammaticality judgments and consequent disagreements in semantic theory. (shrink)

According to truth-conditional semantics, to explain the meaning of a statement is to specify the conditions necessary and sufficient for its truth. This book develops a more radical mentalist semantics by shifting the object of semantic inquiry. Classical semantics analyzes an abstract sentence or utterance such as "Grass is green"; in attitudinal semantics the object of inquiry is a propositional attitude such as "Speaker so-and-so thinks grass is green".

Quote marks, I claim, serve to select from the multiple ostensions that are produced whenever any expression is uttered; they act to constrain pragmatic ambiguity or indeterminacy. My argument proceeds by showing that the proffered account fares better than its rivals-the Name, Description, Demonstrative, and Identity Theories. Along the way I shall need to explain and emphasize that quoting is not simply the same thing as mentioning. Quoting, but not mentioning, relies on the use of conventional devices.

This article shows how, in recent works of cultural analysis, the concept of ‘assemblage’ has been been derived from key sources of theory and put to work to provide a structure-like surrogate to express certain prominent values of a modernist sensibility in the discourse of description and analysis. Assemblage is a sort of anti-structural concept that permits the researcher to speak of emergence, heterogeneity, the decentred and the ephemeral in nonetheless ordered social life. There are other related concepts, like collage, (...) which have been used to give these values substance in research, but currently assemblage is enjoying a popularity perhaps because of the continuing fascination of the work of Deleuze and Guattari. (shrink)

Moral philosophers widely believe that it is a part of the MEANING of 'ought' statements that they imply 'can' statements. To this thesis I offer three challenges, and then I conclude on a broader methodological note. (1) Epistemological Modal Argument: for all we know, determinism is true; determinism contradicts “ought implies can”; therefore we don’t know that 'ought' implies 'can'. (2) Metaphysical Modal Argument: determinism is conceptually possible; determinism contradicts “ought implies can”; therefore “ought implies can” is not an analytic (...) truth. (3) Semantic Argument: “You ought to X” is equivalent to “Do X!”; but “Do X!” does not entail that you can X, according to leading analyses of the imperative. (4) My two modal arguments are epistemologically significant, for they illustrate a general method for refuting a whole class of argument. (shrink)

This note concerns the model theoretic properties of logics extending the first-order logic with monadic second-order variables equipped with the stationarity quantifier. The eight variations of the strong downward Löwenheim–Skolem Theorem down to <ℵ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<\aleph _2$$\end{document} for this logic with the interpretation of second-order variables as countable subsets of the structures are classified into four principles. The strongest of these four is shown to be equivalent to the conjunction of CH and the (...) Diagonal Reflection Principle for internally clubness of S. Cox. We show that a further strengthening of this SDLS and its variations follow from the Game Reflection Principle of B. König and its generalizations. (shrink)