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  1. Superficial differences between the special problems and techniques of the physical sciences and those of the biological sciences are sometimes cited as evidence for the autonomy of biology and for the claim that the methods of physics are therefore not adequate to biological inquiry.
  2. Superficial differences between the special problems and techniques of the physical science and those of the biological science are sometimes cited as evidence for the autonomy of biology and for the claim that the methods of physics are therefore not adequate to biological inquiry.

Which is the correct form of science, singular or plural?

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This is not a question of grammar; rather it is one of meaning. Your different examples have slightly different meanings. The first example makes clear that different sciences, for example, gynecology, paleontology, and genetics, share one characteristic, namely that they deal with entities that are or were alive, and that another set of disparate sciences share a different characteristic, namely that they deal with entities that neither are nor were alive. It is not implicitly claiming that there is no material difference between gynecology and paleontology.

The second example is subtly denying that there are any material differences between, for example, gynecology and paleontology: both are biology.

Which meaning you intend to convey determines whether to use the singular or the plural. As a matter of style, however, if you choose to stress the commonalities, it is probably better to use "biology" and "physics" rather than "the biological science" and "the physical science" because the latter two phrases do not sound idiomatic.

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In the U.S., either these would sound correct to me:

  1. Superficial differences between the special problems and techniques of the physical sciences and those of the biological sciences are sometimes cited as evidence for...

  2. Superficial differences between the special problems and techniques of physical science and those of biological science are sometimes cited as evidence for the autonomy of biology and for...

The first one of the above two sounds better to me.

In your original second example, you had "the physical science"... "the biological science". That doesn't sound right all to me... maybe in another country, but not in the U.S.

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