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Positivism (as formulated by Mills & Comte) advocated an epistemology based solely around the 'scientific method'. No doubt due to the stunning successes it had already achieved by then.

Marx said that he took Hegel and turned him down: that is from spirit over matter to matter over spirit. Did he do this at the behest of Positivistic thought?

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Here is a student paper that argues:

Marx was not a positivist. Whilst on the surface Marx’s approach to the unity of science, empiricism, and causal laws appear to fulfil the positivist criterion, even a modest list of positivist tenets highlights the fundamental differences between positivism and Marx. For Marx, ideas are crucial, the unobservable can be of great importance, and causation must go beyond the mere succession of events to establish the underlying essence of things. Those that incorrectly label Marx to be a positivist fail to fully ‘appreciate the general philosophical position of Marx’ (Walker, 2001: 179).

It should be further emphasized though that Marx's anti-positivism (that is, his opposition to the unqualified and uncritical application of positivist methodology to understanding historical phenomenon) was fundamental to his method. McCarthy is correct that the embrace of positivism by many Marxists,

results from their lack of analysis of the epistemology which structures [Marx's] social critique and their general reliance on specific passages, many times pulled from context, to carry the weight of their positivistic readings of Capital.

So Marx was not a positivist, neither in theory nor in practice.

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The answer is no, when you examine his words, yes if you examine the deed:

wikipedia has:

Karl Marx died before the establishment of formal social science but nonetheless fiercely rejected Comtean sociological positivism (despite himself attempting to establish a historical materialist 'science of society')

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Positivism does not conceive knowledge as an activity: to positivists, the object of their study tells them what they need to know, thence they are stuck in contemplation of reality. As Marx pointedly remarks,

The chief defect of all hitherto existing materialism – that of Feuerbach included – is that the thing, reality, sensuousness, is conceived only in the form of the object or of contemplation, but not as sensuous human activity, practice, not subjectively.

This would be the case of positivism, either in its Comtian semi-religious approach or in its more common sense in the writings of Mill, Spencer, etc. Conversely, to Marx, knowledge is an active (thence "dialectical") process. One view is irreducible to the other, even if there are superficial similarities.

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