However, a cautious reasoner will probably rather explain such cases deductively from the doctrine of evolution than endeavour to support the doctrine of evolution by them.
May we infer deductively that they have been attained because of the increase of speculative transactions?
On the other hand, they are constantly impressed by his power of reasoning both deductively and inductively, by the subtlety and fertility of invention with which he applies analogies, by the clearness and keenness of his observation, by the fulness of matter with which his mind is stored, and by the consecutive force, the precision and distinctness of his style, when employed in the processes of scientific exposition.
(d) Hence, first inductively and then deductively, the third law was originally discovered only as a law of collision or impact between bodies of ascertained weights and therefore masses, impressing on one another equal and opposite changes of momentum, and always reducing one another to a joint mass with a common velocity to begin with, apart from the subsequent effects of elasticity.
More generally, philosophic rationalism is opposed to empirical theories of knowledge, inasmuch as it regards all true knowledge as deriving deductively from fundamental elementary concepts.
So far as it is inductively true that all border-war is evil, it is deductively true that a given border-war is therefore evil.
This, however, would be insufficient to distinguish theosophy from those systems of philosophy which are sometimes called "speculative" and "absolute," and which also in many cases proceed deductively from the idea of God.
And if the controversy which this school has conducted with utilitarianism had turned principally on the determination of the matter of duty, there can be little doubt that it would have been forced into more serious and systematic effort to define precisely and completely the principles and method on which we are to reason deductively to particular rules of conduct.'
Hamilton always seems to be reasoning deductively from such principles.
The modern lunar theory began with Newton, and consists in determining the motion of the moon deductively from the theory of gravitation.