But these indemonstrable principles are appeals to intuition, synthetic judgments a priori.
Thus certain indemonstrable assumptions of mathematics would be only disguised definitions.
If one cause is demonstrable, another indemonstrable cause must be the intermediate; and the proof is in the first figure, and the conclusion affirmative and universal.
The truths immediate and indemonstrable (not known through a middle term) are the inductive truths, as Aristotle declares in many places, and most emphatically at the close of the Analytica Posteriora.
Thus, in speculative matters, the indemonstrable principles are not the habit itself whereby we hold those principles, but are the principles the habit of which we possess.
But wisdom draws conclusions from indemonstrable principles which are the object of the virtue of understanding, even as other sciences do.
But there are several firstindemonstrable principles.
Now the principle of the entire moral order is the last end, which stands in the same relation to matters of action, as the indemonstrable principle does to matters of speculation (Ethic.
The truth and knowledge of indemonstrable principles depends on the meaning of the terms: for as soon as we know what is a whole, and what is a part, we know at once that every whole is greater than its part.
Wherefore in speculative matters a demonstrative science is said to exercise judgment, in so far as it judges the truth of the results of research by tracing those results back to the first indemonstrable principles.
He is inclined, therefore, to regard as the function of metaphysics the complete statement of these ultimate, indemonstrable notions, and therefore the determination of the limits to knowledge by their means.
Such immediate or indemonstrable judgments, it is said, abound in our experience.
