There are two senses of 'reduction' at play in this article; you can see it precisely at the point where Keith Hamnon says "complexity reveals that knowledge always reduces reality." I don't know whether the origin of this confusion is in Rika Preiser's The Problem of Complexity: Re-Thinking the Role of Critique or in Hamon's own interpretation. It doesn't matter: it's worth taking time to clearly distinguish between them. The 'reduction' of anti-reductionism consists of the idea that all knowledge can be derived or deduced from a set of statements of a certain type. The classical example is the idea in logical positivism that all knowledge is based on logical inference from observation statements. This is different from another sort of 'reduction' that is really a type of abstraction, that is, you create a model of something by selecting a few key properties and representing those. When we 'reduce' something to a painting, or a story, or a causal explanation, that's what we are doing. These two types of 'reduction' are very different processes, their semantics are different, and the inferences they support are different.
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