Elements of the philosophy of the human mind. By Dugald Stewart. Rev. and abridged, with critical and explanatory notes, for the use of colleges and schools. By Francis Bowen ...

REASONING AND DEDUCTIVE EVIDENCE. 423
iNor ought it to be forgotten, that it is in pure mathemnatics
alone, that definitions can be attempted with propriety at the
outset of our investigations. In most other instances, some previous discussion is necessary to show, that tfhe definitions which
we lay down correspond with facts; and, in many cases, the
as such in some of the ancient theories of cosmogony; these chemists,
about a century ago, discovered that it was compounded of two gases.
The chemist will tell you that it is not impossible, that it is even probable,
that every one of the sixty substances now counted as elementary, will
ultimately be decomposed. Of course, the vast number of compounded
olljects of which natural history takes cognizance, are still more imperfectly known in their qualities and relations, than those substances vwhich as
yet are reckoned elementary. This limited acquaintance with the subjects
of investigation must lead only to qualified, and, in the logical meaning
of the term, uncertain, conclusions respecting them.
Pure logic and pure mathematics are not so much sciences, as methods
of scientific inquiry, or orgyna, of investigation and proof. They are
modes of reasoning, irrespective of the subjects or facts about which we
reason, and therefore applicable to all subjects. In the syllogism, for
instance, the conclusion follows with absolute certainty from tile premises,
the truth of the premises being presupposed; whether this truth rests
upon sensible evidence, or intuition, or a previous demonstration, is of no'consequence. The principles of the syllogism, then, are pure abstractions; and the letters of the alphabet, or purely arbitrary marlks, taken
as signs of any ideas or facts whatsoever, are the most convenient notation for expressing them. If the premises are matters of fact, or contingent trlth, the conclusion will also be a matter of fact, or contingent
truth; only the relation between the premises and conclusion is a metaphysical trut.h, and as such is made known by intuition.
The case is perfectly similar with mathematics, in which we employ a
notation of the same sort. In its pure form, this science proceeds from
abstraction to abstraction, the truth developed by it havingl no foundation
in frtct, and never being exemplified in the external world. If an event
in the physical world, or a proposition founded on experience, be taken
as a dcttutz, or point of departure for the inquiry, however long the chain
of mathematical reasoning may be which proceeds from it, the result at
which we arrive, is a truth of the same order with the one which formed
the basis of the investigation. It has lost nothing, and it has gained
nothing, in point of logical certainty, through the process to which it has
been subjected. Lowell Lectures on Mlletaphysical and Ethical Science.
Lecture I.I