Piggybacking a bit on an earlier post, this from Francis Hutcheson’s A Synopsis of Metaphysics (2nd ed., 1744) on the “axioms of metaphysics”:
1. What an axiom is
Metaphysical axioms are defined as the most general propositions, self-evident and unchangeable. Not every proposition which is self-evident is unchangeable; nor is every unchangeable proposition self-evident.
In what sense they are innate
The ancients spoke of these axioms as innate in the sense that it is natural for men to understand them, since we have such a power of reason in us as will lead almost all men to a knowledge of them.1 Some recent writers,2 however, speak of axioms as innate only if they have been known and recognized from the moment that the mind was born. In this sense these axioms are not innate; their most general terms arise in the mind at a very late stage, only after it has made many comparisons of individual ideas and abstractions from qualities, distinguishing one from another. And the fact that all men readily agree to these axioms does not prove that they have been known from the start or impressed on the mind from the start. For all will assent to any proposition, including a singular proposition, which concerns any sensible object presented to it, when there is an obvious connection or opposition between subject and predicate; yet these authors say that singular and sensible ideas are not innate.
2. [No principle is the first of all
There is no absolutely first principle of human cognition. For there are very many axioms, as well as a large number of less general propositions, which are known of themselves; and in every demonstration or series of syllogisms, each extreme term has to be found once in some proposition which is self-evident; otherwise it will not be licit to draw a conclusion.
Some men have wasted a great deal of effort in elaborating a criterion of truth, since there is no criterion to be found other than the faculty of reason itself or the power of understanding which is native to the mind.
Self-evident assertions, as well as proven truths, are said to be eternal and immutable, because whenever any mind turns to consider them, it will see the connection or contradiction between subjects and predicates which is asserted in the proposition. We do not need to seek any other cause of this connection than that which formed the ideas themselves, since in certain ideas other ideas are necessarily implied by their own nature, so that they cannot be fully and distinctly thought without them. Hence the truth of such propositions cannot be altered even by the power of God, since the subject cannot be conceived or thought without immediately including the predicate.]3,4
3. Axioms indubitable
It is not credible that anyone can seriously doubt these axioms. If anyone doubted about everything, he would certainly be always at a stand. Nor would the assertion I think (although it is the first of all absolute propositions) help to elicit any other proposition in anyone who had doubts about axioms, not even to prove the very fact that he himself exists. Much less will this absolute proposition establish abstract conclusions. For abstract conclusions arise from abstract propositions alone, and absolute conclusions from absolute propositions.
- Aristotle, Metaphysics, 997 a7, 1005 b33. The notion that axioms should be considered innate derives not from Aristotle but from Neoplatonist commentators on his work, remarked above, introduction, pp. xxvi-xxvii and “Dissertation on the Origin of Philosophy,” pp. 7-8. De Vries, Determinationes Ontologicae, chap. 2, sec. 3, p. 102: “Axioms are commonly called innate truths because they so shine out with their own light that … the mind of every man rushes into agreement with them of its own accord.”
- Locke, Essay, bk. 1, chap. 2, sec. 4, p. 49. Jean Le Clerc, Pneumatologia seu de Spiritibus, chap. 5, sec. 22, p. 102: “Metaphysical axioms are said to be eternal truths, … [and] innumerable men, either idiots or barbarians, declaim that these are innate ideas, as if they were but to no avail.”
- De Vries, Determinationes Ontologicae, chap. 2, sec. 4, p. 102: “Hence they are called both immediate propositions and common notions; in fact they are also eternal and immutable truths, seeing that not even by divine power can they by any other means be other than they are.”
- The three paragraphs enclosed in brackets were added in 1744.