Synthesized answer
Hume argues that the infinite divisibility of space and time is impossible and contradictory [1, 5]. He posits that our ideas of space and time are not distinct entities but rather represent the manner or order in which objects exist [1]. Consequently, it is impossible to conceive of a vacuum or extension without matter, or a period of time without succession or change in any real existence [1].
Hume asserts that if something is capable of infinite division, it must consist of an infinite number of parts, and it's impossible to limit the number of parts without also limiting the division [4]. He contends that time, as it exists, must be composed of indivisible moments; otherwise, there would be an infinite number of co-existent moments, which he considers a contradiction [2]. The infinite divisibility of space implies the infinite divisibility of time, and if the latter is impossible, so is the former [2]. He suggests that the indivisible parts of space and time become inconceivable when not filled with something real and existent [1].
The passages do not fully elaborate on the specific logical steps or analogies Hume uses to demonstrate that the infinite divisibility of space…
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
r infinite divisibility is utterly impossible and contradictory. The other part of our system is a consequence of this. The parts, into which the ideas of space and time resolve themselves, become at last indivisible; and these indivisible parts, being nothing in themselves, are inconceivable when not filled with something real and existent. The ideas of space and time are therefore no separate or distinct ideas, but merely those of the manner or order, in which objects exist: Or in other words, it is impossible to conceive either a vacuum and extension without matter, or a time, when…
sterior or antecedent to another. It is certain then, that time, as it exists, must be composed of indivisible moments. For if in time we could never arrive at an end of division, and if each moment, as it succeeds another, were not perfectly single and indivisible, there would be an infinite number of co-existent moments, or parts of time; which I believe will be allowed to be an arrant contradiction. The infinite divisibility of space implies that of time, as is evident from the nature of motion. If the latter, therefore, be impossible, the former must be equally so. I doubt not but,…
visible parts or atoms, is extremely difficult, by reason of the vast number and multiplicity of these parts. SECT. II. OF THE INFINITE DIVISIBILITY OF SPACE AND TIME. Wherever ideas are adequate representations of objects, the relations, contradictions and agreements of the ideas are all applicable to the objects; and this we may in general observe to be the foundation of all human knowledge. But our ideas are adequate representations of the most minute parts of extension; and through whatever divisions and subdivisions we may suppose these parts to be arrived at, they can…
lges itself in those agreeable emotions, and will never be persuaded that its pleasure is entirely without foundation. From these dispositions in philosophers and their disciples arises that mutual complaisance betwixt them; while the former furnish such plenty of strange and unaccountable opinions, and the latter so readily believe them. Of this mutual complaisance I cannot give a more evident instance than in the doctrine of infinite divisibility, with the examination of which I shall begin this subject of the ideas of space and time. It is universally allowed, that the capacity of…
le. We have therefore no idea of space or extension, but when we regard it as an object either of our sight or feeling. The same reasoning will prove, that the indivisible moments of time must be filled with some real object or existence, whose succession forms the duration, and makes it be conceivable by the mind. SECT. IV. OBJECTIONS ANSWERED. Our system concerning space and time consists of two parts, which are intimately connected together. The first depends on this chain of reasoning. The capacity of the mind is not infinite; consequently no idea of extension or duration consists…