Class, Relation, and Number

2018 ◽  
pp. 105-138
Keyword(s):  
Class Relation

What Could It Mean to Say, “Capitalism Causes Sexism and Racism?”

2018 ◽  
Vol 46 (2) ◽  
pp. 229-246
Author(s):  
Vanessa Wills ◽  
Keyword(s):  
Human Life ◽  
Social World ◽  
Economic Life ◽  
Economic Factors ◽  
Human Species ◽  
Class Relation ◽  
Economic Class ◽  
Definite Form ◽  
Identity Based ◽  
Correct Understanding

Marxism is a materialist theory that centers economic life in its analysis of the human social world. This materialist orientation manifests in explanations that take economic class to play a fundamental causal role in determining the emergence, character, and development of race-and sex-based oppression—indeed, of all forms of identity-based oppression within class societies. To say that labor is mediated by class in a class-based society is to say that, in such societies, the class-based division of that activity which produces and reproduces the human species is the definite form in which labor appears, and that the human life which is the product of that self-making activity bears its stamp. Marxism’s emphasis on economic factors as central in the constitution and development of human life has been seized upon as evidence of its alleged “class reductionism”—its supposed tendency to think of all aspects of human life as direct and simple expressions of a class relation. No such thing follows; quite the opposite, a correct understanding of the relationships among capitalism, racism, and sexism only further highlights how central the struggle against each is to the struggles against any of the others.

Toward useful type-free theories. I

1984 ◽  
Vol 49 (1) ◽  
pp. 75-111 ◽  
Author(s):  
Solomon Feferman
Keyword(s):  
Ordinal Number ◽  
Point Of View ◽  
The Other ◽  
Class Relation ◽  
Ordinal Numbers ◽  
Logical Point ◽  
The One

There is a distinction between semantical paradoxes on the one hand and logical or mathematical paradoxes on the other, going back to Ramsey [1925]. Those falling under the first heading have to do with such notions as truth, assertion (or proposition), definition, etc., while those falling under the second have to do with membership, class, relation, function (and derivative notions such as cardinal and ordinal number), etc. There are a number of compelling reasons for maintaining this separation but, as we shall see, there are also many close parallels from the logical point of view.The initial solutions to the paradoxes on each side—namely Russell's theory of types for mathematics and Tarski's hierarchy of language levels for semantics— were early recognized to be excessively restrictive. The first really workable solution to the mathematical paradoxes was provided by Zermelo's theory of sets, subsequently improved by Fraenkel. The informal argument that the paradoxes are blocked in ZF is that its axioms are true in the cumulative hierarchy of sets where (i) unlike the theory of types, a set may have members of various (ordinal) levels, but (ii) as in the theory of types, the level of a set is greater than that of each of its members. Thus in ZF there is no set of all sets, nor any Russell set {x∣x∉x} (which would be universal since ∀x(x∉x) holds in ZF). Nor is there a set of all ordinal numbers (and so the Burali-Forti paradox is blocked).

Horizontal Relations: A Note on Brenner's Heresy

1999 ◽  
Vol 4 (1) ◽  
pp. 171-180 ◽  
Author(s):  
Ellen Meiksins Wood
Keyword(s):  
Explanatory Power ◽  
Marxist Theory ◽  
Class Relation ◽  
Fundamental Assumption ◽  
Laws Of Motion ◽  
The Way

AbstractOne fundamental assumption seems to underlie – explicitly or implicitly – every critique of Brenner I have seen: that there can be no such thing as a Marxist theory of competition, the ‘horizontal’ relation among many capitals, that does not presuppose the ‘vertical’ class relation between capital and living labour. To start (if not also to end) with the relation between capital and living labour is the only way to establish one's Marxist credentials (establishing those credentials does, by the way, seem to be the critical, even the sole, issue for those who engage Brenner's argument on that plane, without considering the empirical or explanatory power of his argument). In support of that assumption, more than one critic has invoked Marx's comment that competition does not produce or explain capitalist laws of motion but merely executes them, as their visible manifestation in the external movements of individual capitals. Predictably, too, some critics have gleefully turned against Brenner the charge he has famously levelled against other Marxists: that his focus on competition and the market makes him a ‘neo-Smithian’.

scholarly journals Chern Classes of Splayed Intersections

2015 ◽  
Vol 67 (6) ◽  
pp. 1201-1218 ◽  
Author(s):  
Paolo Aluffi ◽  
Eleonore Faber
Keyword(s):  
Chern Class ◽  
Main Tool ◽  
Ample Divisor ◽  
Chern Classes ◽  
Transversal Intersection ◽  
Class Relation ◽  
Singular Varieties ◽  
Nonsingular Variety

AbstractWe generalize the Chern class relation for the transversal intersection of two nonsingular varieties to a relation for possibly singular varieties, under a splayedness assumption. We show that the relation for the Chern–Schwartz–MacPherson classes holds for two splayed hypersurfaces in a nonsingular variety, and under a strong splayedness assumption for more general subschemes. Moreover, the relation is shown to hold for the Chern–Fulton classes of any two splayed subschemes. The main tool is a formula for Segre classes of splayed subschemes. We also discuss the Chern class relation under the assumption that one of the varieties is a general very ample divisor.

David Harvey’s theory of uneven geographical development: A Marxist critique

2017 ◽  
Vol 41 (3) ◽  
pp. 511-536 ◽  
Author(s):  
Raju J Das
Keyword(s):  
Spatial Relations ◽  
State Theory ◽  
Vantage Point ◽  
The State ◽  
Production Of Space ◽  
Class Relation ◽  
Internal Relation ◽  
Spatial Dispersal ◽  
Shed Light

The Marxist geographer, David Harvey, has written extensively and influentially about the production of space under capitalism and, in particular, uneven geographical development. This article is a Marxist critique of Harvey’s theory of uneven geographical development. It presents his theory around six interconnected theses: spatial concentration thesis, spatial dispersal thesis, surplus absorption or spatial fix thesis, uneven geographical development-as-ideology thesis, the uneven geographical development and the state connection thesis, and uneven geographical development–associated political thesis. His theory has shed light on certain aspects of the internal relation between capitalist accumulation and uneven geographical development, giving due emphasis to uneven geographical development’s contradictory character. It is, however, problematic on multiple grounds. It under-stresses the class relation, including the value-relation, between capital and labour, and correlatively fetishizes the power of spatial relations. While Harvey connects uneven geographical development to capitalist crisis, his theory of crisis is deeply inadequate. His theory also fails to systematically integrate the insights of state theory into it, and to the extent that the state is present, its essential class character remains under-emphasized. Finally, Harvey draws some conclusions about anti-capitalist political practice from his theory of uneven geographical development which are problematic from a Marxist vantage point. In particular, his view of the concept of the proletariat in Marxism and his scepticism towards the role of the proletariat in the fight against capital are contestable.

Subset-Class Relation, Common Pitches, and Common Interval Structure Guiding Estimations of Similarity

2007 ◽  
Vol 25 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Tuire Kuusi
Keyword(s):  
The Other ◽  
Voice Leading ◽  
Class Relation ◽  
The Common ◽  
Common Interval ◽  
Highly Uniform

THE PRESENT STUDY EXAMINED THE importance of subsetclass relation for closeness estimations. Two experiments used set-class pairs consisting of a pentad class and a tetrad class represented by block chords, and approximately half of the pairs accomplished the subset-class relation. In the first experiment the number of common pitches was systematically varied. In the second experiment the intervals between the lowest pitch and the other pitches were either similar in both chords (except for the interval missing from the tetrachord) or dissimilar, but the chords shared no common pitches. The degree of set-class consonance was also varied. The results of the experiments indicated that the number of common pitches and the common interval structure were important factors guiding closeness estimations. The subset-class relation was important since it enabled a maximum number of common pitches, maximally similar intervals, or highly uniform voice-leading between chords.

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