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When Archbishop Whately, for example, says, that the object of reasoning is “merely to expand and unfold the assertions wrapt up, as it were, and implied in those with which we set out, and to bring a person to perceive and acknowledge the full force of that which he has admitted,” he does not, I think, meet the real difficulty requiring to be explained, namely, how it happens that a science, like geometry, can be all “wrapt up” in a few definitions and axioms.
Examining this question by the aid of natural reason, I will proceed as follows: If any one wishes to persuade his fellows for or against anything which is not self-evident, he must deduce his contention from their admissions, and convince them either by experience or by ratiocination; either by appealing to facts of natural experience, or to self-evident intellectual axioms.
When he describes in the SECOND part his method of finding true terms, or rather the method of his school, when he describes this new method of finding 'ideas, ideas as they are in nature, powers, causes, the elements of history, or forms, as he more commonly calls them, when he describes this new method of deducing axioms, axioms that are ready for practice, he does, indeed, give us instances; but it so happens, that the instances are all of one kind there.
Unless these barbaric German tribes did come in and administrate, unless they really were very considerable in number, unless their character in truth was what this school postulated it to be vigorous, young, virtuous and all the rest of it unless there did indeed take place a struggle between this imaginary great German nation and the Mediterranean civilization, in which the former won and ruled as conquerors over subject peoples; unless these primary axioms have some historical truth in them, the theory which is deduced from them has no historical value whatsoever.
He begins at the beginning, and leads the learner, step by step, from the simplest propositions, called axioms, which rest upon metaphysical rather than mathematical proof, to high geometrical truths.
It consists in separating each department of knowledge into what are assumed to be its most simple elements, then of making so called self evident axioms with regard to these simple elements, and thereupon operating with the results obtained in this way. Thus a sociological question is to be "decided on simple axiomatic principles just as if it were a matter of elementary mathematics."
Their ethical books consist mainly of axioms principally derived from Arabic and Persian sources. Their religious works are borrowed from the Arabs. The Koran, of course, stands first, then comes a collection of prayers, and next a guide to the religious duties required from Mussulmen.
There is no science which does not begin by requiring you to believe the incredible." "Are you telling me the truth?" "I tell you the solemn truth that the doctrine of the Trinity is not so difficult to accept for a working proposition as any one of the axioms of physics.
Vast social reformations have originated in individual souls. Truths that now sway the world were first proclaimed by individual lips. Great thoughts that are now the axioms of humanity sprang from the center of individual hearts. Do not suffer others to shape your lives for you; but do all you can to shape them for yourselves.
Always handle any positively electrical body, whether it is charged with passion, or power, with some non-conductor between you and it, not with your naked hands. The above were some of the young gentleman's working axioms; and he proceeded to act in accordance with them. He began by paying his court more assiduously to his uncle.
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