...equal to the half of thirty, expresses a relation between these numbers. Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is any where existent in the universe. Though there never were a circle or triangle in nature, the truths...

...equal to the half of thirty, expresses a relation between these numbers. Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is any where existent in the universe. Though there nerer were a circle or triangle in nature, the truths...

...equal to the half of thirty, expresses a relation between these numbers. Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is any where existent in the universe. Though there never were a circle or triangle in nature, the truths...

...every affirmation which is either intuitively or demonstratively certain. — Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is any where existent in the universe. Sect. IV. p. 27. The only objects of the abstract sciences or of...

...equal to ihe half of thirl//, expresses a relation between these numbers. Propositions of this kind are discoverable by the mere operation of thought,...dependence on what is anywhere existent in the universe. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for...

...characterises these truths of the second class thus : — ' Propositions of this kind are * See Note at end. discoverable by the mere operation of thought, without...dependence on what is anywhere existent in the universe: though there never were a true circle or triangle in nature, the truths demonstrated by Euclid would...

...which I see one end, has got another end. Shall I call this a matter of fact or a relation of ideas? On trial it refuses to come under either. If it is...what is anywhere existent in the universe." But if BO, this proposition that a rope of which I see one end has got another end, cannot be a relation of...

...equal to the half of thirty, expresses a relation between these numbers. Propositions of this kind are discoverable by the mere operation of thought,...dependence on what is anywhere existent in the universe. Though there nover were a circle or triangle in nature, the truths demonstrated by Euclid would for...

...those of which geometry, algebra, and arithmetic treat, and which are either intuitively certain, or ' discoverable by the mere operation of thought, without...dependence on what is anywhere existent in the universe,' as, for example, the truths demonstrated by Euclid, which would be equally incontestable even ' though...

...differ from all other kinds of belief. What is meant by the assertion that " propositions of this kind are discoverable by the mere operation of thought...dependence on what is anywhere existent in the universe " ? Suppose that there were no such things as impressions of sight and touch anywhere in the universe,...