The Dictionary of Human Geography

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at times extensively on mathematical examples

to explicate his theory of value, as well as on

quantitative information about poverty and

capital–labour relations in nineteenth-century

Britain. Marx has been criticized by main-

stream economists for mathematical in-

competence, particularly for errors in his

‘transformation problem’, which sought some-

what unsuccessfully to show that prices

of production (long-run market prices) are

determined by labour values. Sraffa (1960)

demonstrated, however, that neo-classical

macroeconomics had the same mathematical

limitations, being only logically correct if

production technologies are identical in every

sector of the economy. Morishima showed

that Marx’s theory of exploitation can be

deduced mathematically from his theory of

capitalism: capitalists can only make positive

monetary profits if labour is exploited in

labour value terms. This triggered scholarship

in analytical Marxism.

In economics and sociology, analytical

Marxism stressed developing deductive theor-

ies consistent with Marx’s theorization of cap-

italism. Much of this work, pioneered by John

Roemer, John Elster, George Cohen and Erik

Olin Wright, is grounded inrational choice

theory– the belief that macro-features of

society are the consequence of the self-inter-

ested actions of informed, rational economic

actors. Taking the same starting point asneo-

classical economics, remarkably they show

that under Marxian assumptions a very differ-

ent view of capitalism emerges. Exploitation

occurs, the opposed economic interests of

workers and capitalists generateclassstruggle

over the economic surplus, capitalism is un-

stable, and individuals choose to join exploit-

ing and exploited classes because of initial

wealth and endowment differences. These

scholars have rejected Marx’s labour theory

of value. Empirically, however, observed

long-term market prices are indeed closely

correlated with labour values, suggesting that

such rejection is premature. These rational

choice Marxists are criticized for their ground-

ing in rational choice behaviour, and insist-

ence on deductive reasoning, which are seen

as inconsistent with Marx’s dialectical logic

(see dialectic: see also Roemer, 1982,

1986b; Carver and Thomas, 1995).

Geographers have applied mathematical

reasoning to a Marxian analysis of the capital-

istspace-economy, without grounding this

in individual rational choice. Like Harvey’s

dialectical analysis, Sheppard and Barnes

(1990) demonstrate that the incorporation of

spacecomplicates some of Marx’s theoretical

propositions. Space further destabilizes the

capitalist dynamics ofuneven development,

increases the likelihood that the interests

of individual capitalists are in conflict with

class interests and catalyses conflict between

places that can undermine class dynamics.

Equilibrium analysis is thus of little value,

as equilibria are most unlikely and always

unstable. Unlike Harvey, it is deduced that

space undermines labour value as the founda-

tion of Marxian analysis. Empirically, Webber

and Rigby (1996) show thatfordismwas not

the golden age of postwar capitalism,contra

regulation theory. Recent advances incom-

plexity theory suggest that mathematical

analysis of complex systems such as capitalism

approximates many aspects of dialectical

reasoning, suggesting that Marx’s own resort

to mathematics was not in tension with his

philosophical approach. es

Suggested reading

Roemer (1986); Sheppard and Barnes (1990).

anarchism Apoliticalphilosophythat is

anti-authoritarian, seeking the elimination of

thestateand its replacement by a decentral-

ized social and political self-governing social

order. Anarchist social order is not the absence

of government, but a form of self-government

that does not demand obedience. It is a mix-

ture of libertarian, utopian andsocialistideas

that counterspowerand hierarchy through

voluntary, and usually local, decentralized

communities. Cook (1990) identified five

different forms of anarchism – individualism,

collectivism, anarchistcommunism, anarcho-

syndicalism and pacifism. Anarcho-feminism

andsituationismare also relevant varieties

of anarchism that have been utilized by

geographers. Geographers Peter Kropotkin

and Elise ́e Reclus were among the early pro-

ponents of anarchistcommunism. Both were

active members of the academic geography

community in the late 1800s and early 1900s

(Kearns, 2004), though their political leanings

were ignored as ‘baggage’ by the geography

establishment, which was focused upon im-

perial and national projects (MacLaughlin,

1986). Kropotkin’s belief that ‘the duty of

socially-concerned scientists lay in articulating

the interests of subordinate social classes and

combating poverty, underdevelopment and

social justice’ (quoted in MacLaughlin, 1986,

p. 25) lay at the heart of theradical geography

that emerged in the late 1970s. However,

the initial identification of anarchism as a

Gregory / The Dictionary of Human Geography 9781405132879_4_A Final Proof page 27 31.3.2009 9:44pm

ANARCHISM