We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.

We investigate the theory IΔ 0 + Ω 1 and strengthen [Bu86. Theorem 8.6] to the following: if NP ≠ co-NP. then Σ-completeness for witness comparison formulas is not provable in bounded arithmetic. i.e. $I\delta_0 + \Omega_1 + \nvdash \forall b \forall c (\exists a(\operatorname{Prf}(a.c) \wedge \forall = \leq a \neg \operatorname{Prf} (z.b))\\ \rightarrow \operatorname{Prov} (\ulcorner \exists a(\operatorname{Prf}(a. \bar{c}) \wedge \forall z \leq a \neg \operatorname{Prf}(z.\bar{b})) \urcorner)).$ Next we study a "small reflection principle" in bounded arithmetic. We prove that for (...) all sentences φ $I\Delta_0 + \Omega_1 \vdash \forall x \operatorname{Prov}(\ulcorner \forall y \leq \bar{x} (\operatorname{Prf} (y. \overline{\ulcorner \varphi \urcorner}) \rightarrow \varphi)\urcorner).$ The proof hinges on the use of definable cuts and partial satisfaction predicates akin to those introduced by Pudlak in [Pu86]. Finally, we give some applications of the small reflection principle, showing that the principle can sometimes be invoked in order to circumvent the use of provable Σ-completeness for witness comparison formulas. (shrink)

We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.

As hubs of global exchange, port cities are host to inconvenient and contested pasts. Many of these pasts have yet to be fully recognized. In the wake of demonstrations against racial injustices this summer, the PortCityFutures team discussed how our own research practices relate to systemic inequalities within port cities. It was concluded that we need to better understand how these contested and complex pasts, legacies of diversity and segregation, and colonial pasts impact port cities today.

This paper tries to clarify, strengthen and respond to two prominent objections to the development and use of human enhancement technologies. Both objections express concerns about the link between enhancement and the drive for hyperagency. The first derives from the work of Sandel and Hauskeller—and is concerned with the negative impact of hyperagency on social solidarity. In responding to their objection, I argue that although social solidarity is valuable, there is a danger in overestimating its value and in neglecting some (...) obvious ways in which the enhancement project can be planned so as to avoid its degradation. The second objection, though common to several writers, has been most directly asserted by Saskia Nagel, and is concerned with the impact of hyperagency on the burden and distribution of responsibility. Though this is an intriguing objection, I argue that not enough has been done to explain why this is morally problematic. I try to correct for this flaw before offering a variety of strategies for dealing with the problems raised. (shrink)

In the beginning of the 1970s, Michel Foucault dismisses the terminology of ‘exclusion’ for his projected analytics of modern power. This rejection has had major repercussions on the theory of neoliberal subject-formation. Many researchers disproportionately stress how neoliberal dispositifs produce entrepreneurial subjects, albeit in different ways, while minimizing how these dispositifs sometimes emphatically refuse to produce neoliberal subjects. Relying on Saskia Sassen’s work on financialization, I argue that neoliberal dispositifs not only apply entrepreneurial norms, but also suspend their application (...) for groups that threaten to harm the population’s profitability. Neoliberal dispositifs not only produce entrepreneurial subjects, but also surplus populations that are expelled from the overall population to maintain its productivity. Here, the concept of ‘exclusion’ is appropriate if understood in Agamben’s sense of an inclusive exclusion. The surplus population is part of neoliberal dispositifs, but only as the element to be abandoned. (shrink)

We show that any coherent complete partial order is obtainable as the fixed-point poset of the strong Kleene jump of a suitably chosen first-order ground model. This is a strengthening of Visser’s result that any finite ccpo is obtainable in this way. The same is true for the van Fraassen supervaluation jump, but not for the weak Kleene jump.

For a classical theory T, ℋ(T) denotes the intuitionistic theory of T-normal (i.e. locally T) Kripke structures. S. Buss has asked for a characterization of the theories in the range of ℋ and raised the particular question of whether HA is an ℋ-theory. We show that Ti∈ range(ℋ) iff Ti = ℋ(T). As a corollary, no fragment of HA extending iΠ1 belongs to the range of ℋ. A. Visser has already proved that HA is not in the range of (...) H by different methods. We provide more examples of theories not in the range of ℋ. We show PA-normality of once-branching Kripke models of HA + MP, where it is not known whether the same holds if MP is dropped. (shrink)

Kripke frames (and models) provide a suitable semantics for sub-classical logics; for example, intuitionistic logic (of Brouwer and Heyting) axiomatizes the reflexive and transitive Kripke frames (with persistent satisfaction relations), and the basic logic (of Visser) axiomatizes transitive Kripke frames (with persistent satisfaction relations). Here, we investigate whether Kripke frames/models could provide a semantics for fuzzy logics. For each axiom of the basic fuzzy logic, necessary and sufficient conditions are sought for Kripke frames/models which satisfy them. It turns out (...) that the only fuzzy logics (logics containing the basic fuzzy logic) which are sound and complete with respect to a class of Kripke frames/models are the extensions of the Gödel logic (or the super-intuitionistic logic of Dummett); indeed this logic is sound and strongly complete with respect to reflexive, transitive and connected (linear) Kripke frames (with persistent satisfaction relations). This provides a semantic characterization for the Gödel logic among (propositional) fuzzy logics. (shrink)

This collection for a course in Social Thought and the Critique of Power includes selections from Sandra Bartkey, Wendy Brown, Judith Butler, Luc Boltanski, Eve Chiapello, Juergin Habermas, Margaret Kohn, Saskia Sassen, Margit Mayer, David Ciavatta, Michael Hardt, Antonio Negri, and Jeremy Waldron. Selections include material on the city, neoliberalism, computer-mediated life, precarity, cosmopolitanism, and gender. This packet may still be available as a print-on-demand title at the Ryerson University Bookstore.

This study examines playgrounds as lenses on urban transitions to explain the link between urban transformations and changes in the discourse of play and childhood. Specifically, it compares Soviet public playgrounds and post-Soviet privatized playscapes in the city of Yekaterinburg, Russia, through primary observation and secondary data analysis. Using the framework of social reproduction developed by Cindy Katz and Saskia Sassen to explain how the local forces affect cities, my analysis shows that the shift in the discourse of play (...) and childhood in the post-Soviet period is hinged on global influences combined with local transformations, from the abandonment of Soviet ideals of communal play spaces to the embracement of today’s consumerist play places. Whereas the old Soviet playgrounds have uncertain purposes, in contemporary Yekaterinburg private playgrounds offer a narrative of play in terms of leisure, love, and convenience for parents. Children turn into consumers of private play, leaving most of the Soviet playgrounds as idle spaces in the city. This article argues that Yekaterinburg’s shift toward participating in the globalized economy combined with its transition from the Soviet ideals maintains social relations and reproduces social inequalities in childhood, as this condition favors consumerist narratives of play. I conclude that the playgrounds in Yekaterinburg are bystanders of new global ecologies whereby social, political, and economic transformations become an impetus to reproduce new ways of seeing the social importance and meaning of play and playgrounds. (shrink)