Diminishing Returns

Reduction is a familiar problem in contemporary analytic philosophy, which often concerns itself with the reducibility or irreducibility of mind, thought, consciousness, among other things, to matter, and specifically the material processes of the brain. The philosophical heritage of the concept is in fact quite old, and extends beyond the problems of 'mind', finding its origin in the most fundamental metaphysical concern. We know that at least since Aristotle, the ultimate form of ontological question, "What is?", is subjected to a formula in which Being is already thematized in terms of being-in. We can only approach the question, "What is?", in terms of what is in-itself, or otherwise, what is in-another. The concern is then that of reduction, of reducing everything that is to what it is in, to what holds, contains, or admits it. This concern persists at least until Spinoza, Kant, and Hegel.

The term reduction derives from the Latin dcere, to bring or lead, modified by the prefix re-, thereby, to lead back, bring back, return. Returning has the double sense of returning to a place one has been, and returning something to its proper owner or place. Reduction, then, has the sense of leading beings back, bringing them back, returning them to their proper place, source, origin. It gives the sense in which the reducible has gone astray, is out of place, dislocated, and definitively cut off from its ground or propriety. Yet we must also say that in returning the being to its proper place, we must reveal its being-in, in-another, and hence return it to what it is in, lead it back to where it is. This amounts to showing a being as displaced in its very place.

We should not be so quick to assume that the reducibility of beings in-another is inverted in the irreducibility of being in-itself, as if this being cannot be lead back but is eternally in place, its proper place, that is, itself as identical with its place. There is nothing evident about this, and it is just as easy to say that being in-itself is reducible, as the function of being-in has been shown to be the returning of being to where it is, of revealing the dislocation of being in that it is otherwise than its place. Being in-itself is reducible, just as beings in-another are reducible to that other. This means that Being in-itself is reducible to itself, in that it can be returned to itself, or that it returns itself. Here we can only note the problems of ipseity that are beginning to propigate and restlessly cry out. I will begin to address these problems in a following post on historicity.

We can at least say that, insofar as the being returns to itself, finds itself in-itself, that it is not itself, it is itself what is in-itself but not-itself. Having returned to itself, it is therefore not necessary for itself, but can be lead back to itself, finding itself as having been without - outside of itself and itself without the being that is in-itself. The Being in-itself is at once in-and-not-itself: it is not in-another, but it is what is other in-itself.

Deduction proceeds from the universal concept to the particular case, showing the case to be contained analytically in the concept, the propriety of the particular with respect to the universal. It brings out the particular from the universal. de-dcere: to lead out, lead away from, bring down or carry down, to carry out. As with Moses, who carries the universal Law, the Decalogue, down to the people. Induction proceeds from the particular case, showing the concept to be justifiable and intelligible on behalf of the relations between cases, and hence, the propriety of the universal with respect to the particular. It leads to the universal from the particular. in-dcere: to lead toward, lead into, bring to or bring about.

Reduction proceeds, we can say, from the particular to the particular, as the returning the particular to its place qua particular, yet without reference to the specificity of the universal concept. This is the logic of the example that Aristotle demonstrates in the Analytica Prioria, as Agamben reads it. Yet Aristotle only hints at such a logic, in a brief exposition that last only a few lines. Elsewhere in his work, such a logic is assimilated to traditional deduction, in which the particular properly belongs to the universal. To quote Agamben, "Yet Aristotle’s treatment of the paradigm is in a way inadequate, though he had these beautiful ideas of the paradigm as going from the particular to the particular, he does not seem to develop this point and like Kant still sticks to the idea that the individuals concerned in the example belong to the same genus." If we refuse to subordinate this logic to the former two logics, as is typical in the philosophical tradition, and instead give it priority, it will mean drastic consequences for ontology, as well as politics, as the recurrent theme of 'leading' should forshadow.