Hume against the Infinite Divisibility of Space

Abstract

Hume argues for the finite divisibility of space by starting with proving against the infinite divisibility of space. First and foremost, according to Hume, the mind’s capacity is finite so that it is impossible to contain an infinite number of ideas. However, in terms of his concept of general ideas, Hume admits that the mind has the ability to call up an infinite number of ideas, if provoked. Next, through observations of the imagination and the impression, Hume demonstrates that there must be simple and minimal ideas which constitute the general ideas of space and time and are themselves indivisible. The fact that one might be able to perceive a smaller thing with the help of telescopes does not show that our mind is incapable of the smallest ideas, but that the mind could be mistaken to take what is not the smallest as the smallest. One question which is discussed most is whether Hume is legitimate to make the reference from impressions and ideas to things themselves. However, Hume is less concerned with the so-called nature of things and focuses on how things appear to human beings. On the other way, Hume builds his argument upon the existence of minima. For Hume, all ideas are imagistic and extended and if added up ad infinitum, they would result in infinitude. Therefore, no finite extension could be said to be constituted by infinite ideas. Since only what is resolved into units really exists, an infinite extension does not exist at all. This statement maps onto the discussion of the special composition question. Like what general ideas are to Hume, composition is nothing but the arrangement of basic elements for the mereological nihilists.