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I don't have much background in philosophy, but I recently read an interesting paper about "emergence" (Anderson, 1972). In that paper, Anderson relates to the "reductionist" hypothesis.

When and by whom was this hypothesis first elucidated? Wikipedia and other sources did not state any origin, so I guess it must have been around for quite a while.

I would be specifically interested in who was first to apply the reductionist hypothesis to science.

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There is a view known as "reductionism" which is often attributed to the Vienna Circle. The strictest form of the view (which is the one most attributable to the Vienna Circle) is that non-reductive statements are in some sense meaningless.

From the paper you have linked though, I think you may be asking about a weaker form of reductionism:

The workings of our minds and bodies, and of all the inanimate or animate matter of which we have any detailed knowledge, are assumed to be controlled by the same set of fundamental laws

The idea that our minds and bodies work according to some physical (as opposed to supernatural) laws is often sourced to de La Mettrie, though of course as with any major idea it's hard to give one source.

The Wikipedia page on materialism lists thinkers going back as far as 600 BCE; the Cārvāka thinkers had ideas I think Anderson would find quite suitable, for example:

There is no heaven, no final liberation, nor any soul in another world... In this school there are four elements, earth, water, fire and air; and from these four elements alone is intelligence produced

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