What is an axiom?

1. In De Corpore, Hobbes writes: ‘A primary proposition is one in which the predicate is a name which explains the subject by means of a number of names.’ The example immediately given is the primary proposition: ‘A human is a rational, animated body’, which progressively reveals multiple determinations or aspects of the single given subject, in this case a human. This, Hobbes tells us, is what it is to be a definition, and the sense of such claims constitute truths that are indemonstrable in principle. He goes on: ‘There are some who add certain other propositions, which they call “primary” or “principles”, namely axioms or common notions. However, they are not really principles, because they can be proved (even if their self-evidence means that they do not need to be proved).’ (Hobbes, De Corpore, §3.9) And yet it is not clear how an axiom or common notion would be proven, since they are neither propositions nor definitions. Continue reading “What is an axiom?”

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Place and Expression

This is a response I gave to a paper entitled ‘Leibniz on Place’ by Jen Nguyen at DePaul’s philosophy graduate conference yesterday, 2.11.2017.

Nguyen’s paper raises a fascinating series of issues in the context of Leibniz’s metaphysics, which to my mind come down to this central question: where is a place? In some ways, as she notes, Leibniz’s view on place is commonsensical enough: a place will turn out to be a point of view on the world; this is its intrinsic determination, as opposed to the purely extrinsic or formal definition, according to which a place is a set of coordinates in abstract three-dimensional space. And if this squares with common sense, it’s due to a strange sort of phenomenological intuition, rather like how, to borrow from Wilfrid Sellars’ terminology, we sense an incompleteness in the ‘scientific image’ of the world and supplement it with the ‘manifest image’. We want to say: no, this place, this room, is not defined by the amount of space, the quantitative distance between the walls, the placement of the windows, the positions of these tables and chairs; rather it is a matter of the way we perceive it, what it opens up for us, how we are determined within it, a question of perspective and orientation, affect and delimitation: it is how we express it. Continue reading “Place and Expression”