Online research in philosophy

Juxtaposing Cherríe Moraga's Loving in the War Years and Luce Irigaray's Speculum of the Other Woman, I explore the ways that sex and race intersect to complicate an Irigarayan account of the relations between mother and daughter. Irigaray's work is an effective tool for understanding the disruptive and potentially healing desire between mothers and daughters, but her insistence on sex as primary difference must be challenged in order to acknowledge the intersectionality of sex and race. Working from recent work on (...) the psychoanalysis of race, I argue that whiteness functions as a master signifier in its own right, and as a means of differentiation between the light-skinned Moraga and her brown-skinned mother. Irigaray's concept of blood deepens Moraga's account of her healing and subversive return to her mother. The juxtaposition of Moraga, Irigaray, and contemporary psychoanalysis of race can allow for a necessary revision of Irigaray's psychoanalysis that acknowledges the ways in which sexual difference is indexed by race and sheds new light on her account of the mother–daughter relation. (shrink)

Kruskal proved that finite trees are well-quasi-ordered by hom(e)omorphic embeddability. Friedman observed that this statement is not provable in predicative analysis. Friedman also proposed (see in [Simpson]) some stronger variants of the Kruskal theorem dealing with finite labeled trees under home(e)omorphic embeddability with a certain gap-condition, where labels are arbitrary finite ordinals from a fixed initial segment of ω. The corresponding limit statement, expressing that for all initial segments of ω these labeled trees are well-quasi-ordered, is provable in Π 1 (...) 1 -CA, but not in the analogous theory Π 1 1 -CA 0 with induction restricted to sets. Schutte and Simpson proved that the one-dimensional case of Friedman's limit statement dealing with finite labeled intervals is not provable in Peano arithmetic. However, Friedman's gap-condition fails for finite trees labeled with transfinite ordinals. In [Gordeev 1] I proposed another gap-condition and proved the resulting one-dimensional modified statements for all (countable) transfinite ordinal-labels. The corresponding universal modified one-dimensional statement UM 1 is provable in (in fact, is equivalent to) the familiar theory ATR 0 whose proof-theoretic ordinal is Γ 0 . In [Gordeev 1] I also announced that, in the general case of arbitrarily-branching finite trees labeled with transfinite ordinals, in the proof-theoretic sense the hierarchy of the limit modified statements $\mathbf{M}_{ (which are denoted by LM λ in the present note) is as strong as the hierarchy of the familiar theories of iterated inductive definitions (more precisely, see [Gordeev 1, Concluding Remark 3]). In this note I present a "positive" proof of the full universal modified statement UM, together with a short proof of the crucial "reverse" results which is based on Okada's interpretation of the well-established ordinal notations of Buchholz corresponding to the theories of iterated inductive definitions. Formally the results are summarized in $\S5$ below. (shrink)