Sir William Hamilton's Philosophy of the Conditioned [pp. 472-510]

Sir William Hamilton's
is from the endless "addibility" of number: an infinite quantity
can have only a negative idea. "The great and inextricable
difficulties which perpetually involve all discourses concerning
infinity, whether of space, duration, or divisibility, have been
the certain marks of a defect in our ideas of infinity, and the
disproportion the nature thereof has to the comprehension of
our narrow faculties;" and he instances at great length the
same puzzles which Hamilton brings forward. God is incomprehensibly infinite. (Essay ii., xvi., xvii.) We have no clear
idea of substance. Power and cause are known both by
sensation and reflection. (ii., xxiii.) The existence of things is
to be known only by experience. (iv., iii., 31.)
Hume held similar views in general to these of Locke, but
started the opinion that some of the supposed relations of
objects are only relations of ideas. Definitely holding that our
ideas are states of mind, he says, "there is a kind of preestablished harmony between the course of nature and the
succession of our ideas; and though the power and forces by
which the former is governed be wholly unknown to us; yet
our thoughts and conceptions have still, we find, gone on in the
same train with the other works of nature." (Essays, 2, 64.)
The relation of cause and effect especially engaged his attention,
as that on which all reasonings concerning matters of fact are
founded, that by which alone we can go beyond the evidence of
our memory and senses. He examines in detail the information from the outward senses, and that from the operation of
our own minds, and, Hamilton says, has decided the opinion of
philosophers that the idea of power or necessary connection is
not derived from either of these sources. Whence is it then?
Hume says that when we have several times had ideas in succession where there is a change in the object, the one idea
draws the other after it by an instinct or "mechanical tendency," so that when we see the first, we feel that the other is
coming, and this instinctive subjective connection of the ideas
is the original from which we conceive the causal connection
between the objects which the ideas represent. All inferences from effect to cause, or cause to effect, must proceed from
experience of connection between their ideas. As we never
have had experience of the making of worlds, for example, we
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