He holds (i. 317) that it is merely from habit that we are unable to conceive the _last point_ of space or the _last instant_ of time. He holds (ii. 360) that it is strange that any one should rely upon the _à priori_ evidence that space or extension is infinite, or that nothing can be made of nothing. He holds (i. 304) that the first law of _motion_ is _rigorously true_, but that the axioms respecting the _lever_ are only _approximately_ true. He holds (ii. 110) that there may be sidereal firmaments in which events succeed each other at random, without obeying any laws of causation; although one might suppose that even if space and cause are both to have their limits, still they might terminate together: and then, even on this bold supposition, we should no _where_ have a world in which events were _casual_. He holds (ii. 111) that the axiom, that every event must have a cause, is established by means of an "induction by simple enumeration:" and in like manner, that the principles of number and of geometry are proved by this method of simple enumeration alone. He ascribes the proof (i. 162) of the axiom, "things which are equal to the same are equal to each other," to the fact that this proposition has been perpetually _found_ true and never false. He holds (i. 338) that "In all propositions concerning numbers, a condition is implied, without which none of them would be true; and that condition is an assumption which _may be false_. _The condition is that_ 1 = 1." 73. Mr. Mill further holds (i. 309), that it is a characteristic property of geometrical forms, that they are capable of being painted in the imagination with a distinctness equal to reality:--that our ideas of forms exactly resemble our sensations: which, it is implied, is not the case with regard to any other class of our ideas;--that we thus may have mental pictures of all possible combinations of lines and angles, which are as fit subjects of geometrical experimentation as the realities themselves. He says, that "we know that the imaginary lines exactly resemble real ones;" and that we obtain this knowledge respecting the characteristic property of the idea of space by experience; though it does not appear _how_ we can compare our _ideas_ with the _realities_, since we know the realities only _by_ our ideas; or why this property of their resemblance should be confined to _one class_ of ideas alone.