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For other uses, see Irreducibility (disambiguation).

The principle of Irreducibility, in philosophy, has the sense that a complete account of an entity will not be possible at lower levels of explanation and which has novel properties beyond prediction and explanation. Another way to state this is that Occam's razor requires the elimination of only those entities that are unnecessary, not as many entities as could conceivably be eliminated. Lev Vygotsky provides the following illustration of the idea, in his Thought and Language:

"Two essentially different modes of analysis are possible in the study of psychological structures. It seems to us that one of them is responsible for all the failures that have beset former investigators of the old problem, which we are about to tackle in our turn, and that the other is the only correct way to approach it.
The first method analyzes complex psychological wholes into "elements". It may be compared to the chemical analysis of water into hydrogen and oxygen, neither of which possesses the properties of the whole and each of which possesses properties not present in the whole. The student applying this method in looking for an explanation of some property of water — why it extinguishes fire, for example — will find to his surprise that hydrogen burns and oxygen sustains fire ....
In our opinion the right course to follow is to use the other type of analysis, which may be called "analysis into units". By "unit", we mean a product of analysis which, unlike elements, retains all the basic properties of the whole, and which cannot be further divided without losing them. Not the chemical composition of water, but its molecules and their behaviour, are the key to the understanding of the properties of water ..."

In other words: to conserve the properties under investigation, it is necessary to remain within a certain level of complexity. Irreducibility is most often deployed in defence of the reality of human subjectivity and/or free will, against those who treat such things as folk psychology, such as Paul and Patricia Churchland.

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