Month: March 2013

Weak necessity and negated deontics: a view from Russian

Igor Yanovich

29 Mar 2013, 2pm-3:30pm, Manchester 227

The proper analysis of “weak” vs. “strong” necessity deontics (should and ought vs. must and have to) and the scopal interaction of different deontics with negation are two topics much discussed in the recent literature. In this talk, I will present data from Russian that shed new light on both, underscoring the importance of using cross-linguistic data when considering universal semantic issues. The thread uniting the two topics will be the importance of advice modality.

Russian features a rich deontic system, with more than half a dozen of necessity deontics. I will show that this rich system does not contain a single categorical contrast between weak and strong necessity, as in English. Instead, different tests commonly used for English as well as other languages (cf. von Fintel and Iatridou 2008) as all targeting the same distinction turn out to divide the Russian deontic space into different groupings. Thus the category of weak necessity is no more than an illusion created by the interplay of several independent properties which do not have much to do with the strength of modal force.

One of such properties is the ability of a given modal to be used as (for lack of a better term) an advice modal. “Advice modality” seems to be a special type of modality, comparable to such categories as teleological or metaphysical modality. It seems to be characterized by three properties: 1) it chooses one of the possible alternative courses of actions, thus solving a certain decision problem; 2) it needs to be endorsed by the speaker in matrix contexts, and by the attitude bearer under attitudes; 3) it always scopes over clausemate negation. All English modals that can be used as advice modals have other readings as well, but Russian features modal stoit that conveniently can only be used in advice. Furthermore, for most Russian necessity deontics, relative scope with negation is not fixed, unlike in English, Greek, Dutch, German, Spanish (cf. Iatridou and Zeijlstra 2013). This creates a convenient testing ground. I will describe that modal’s behavior compared to other modals of Russian and English, and discuss how the three properties of advice modality may be related to each other.

The classical continuum without points

Stewart Shapiro

14 Mar 2013, 4pm-5:30pm, Manchester 227

We develop a point-free construction of the classical one-dimensional continuum, with an interval structure based on mereology and either a weak set theory or logic of plural quantification. In some respects this realizes ideas going back to Aristotle, although, unlike Aristotle, we make free use of contemporary actual infinity. Also, in contrast to intuitionistic analysis, Bishop’s constructive analysis, and smooth infinitesimal analysis, we follow classical analysis in allowing partitioning of our “gunky line” into mutually exclusive and exhaustive disjoint parts, thereby demonstrating the independence of “indecomposability” from a non-punctiform conception. It is surprising that such simple axioms as ours already imply the Archimedean property and the interval analogue of Dedekind completeness (least-upper-bound principle), and that they determine an isomorphism with the Dedekind-Cantor structure of R as a complete, separable, ordered field. We also present some simple topological models of our system, establishing consistency relative to classical analysis. Finally, after describing how to nominalize our theory, we close with comparisons with earlier efforts related to our own.