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• Introduction
• A Note On the Text
• Acknowledgments
• A Compend of Logic
• Dissertation On the Origin of Philosophy and Its Principal Founders and Exponents 1
• Prolegomena the Definitions and Divisions of Logic
• Part I: On Apprehension
• Part II: On the Noetic Judgment and the Proposition
• Part III: On Discourse
• Appendix On Topics, Fallacies, and Method
• A Synopsis of Metaphysics Comprehending Ontology and Pneumatology Second Enlarged Edition
• Part I: On Being and the Common Attributes of Things
• Chapter 1: On Being ( De Ente )
• Chapter 2: On the Axioms of Metaphysics
• Chapter 3: On the Properties of Being
• Chapter 4: On the Principal Divisions of Being
• Chapter 5: On the Categories and the General Properties of Being
• Part II: On the Human Mind
• Chapter 1: On the Powers of the Mind, and First On the Understanding
• Chapter 2: On the Will
• Chapter 3: Whether Spirit Is a Different Thing From Body
• Chapter 4: On the Union of the Mind With the Body, and On a Separate State 1
• Part III: On God
• Chapter 1: In Which It Is Shown That There Is a God
• Chapter 2: On the Natural Virtues of God
• Chapter 3: On the Divine Virtues Concerned With Understanding
• Chapter 4: On the Will of God
• Chapter 5: On the Operations of God
• On the Natural Sociability of Mankind
• Inaugural Oration

CHAPTER 2

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.

[They are not viewed in God5

However much there may be a common agreement of all men about the truth of these axioms, as well as about all demonstrated truths, among those who understand demonstrations, it must not be imagined that all men view this unique truth in some common nature, as if it were a kind of mode inherent to it. For the fact is that when several men have ideas that are very similar to each other but not the same, they will also see similar connections and relationships between them. The only permissible conclusion is that all men have been equipped with a similar power of reason.]6

Axioms of little use

They are equally in error who think axioms so important that they believe them to be necessary or very useful in every act of knowing.7 For singular and less general propositions become known first even without the help of axioms, though by their help truths previously ascertained are more easily explained to others.

[All axioms are known of themselves once the mind directs itself to see them. Their credit does not come from induction; no credit resting on that ground would be very strong, but their credit we see is very strong.]8

4.

Two axioms which are quite useful

Among metaphysical axioms that are especially useful are two which are completely true when we are speaking of objects, not of ideas: every being exists, and a real quality or property or action is to be attributed only to a being. With their help we avoid a perennial confusion of metaphysics, when things which are proper to ideas or words are ascribed to things external to the mind. We would often avoid the temptation to make this mistake, if in metaphysics we gave ourselves the instruction that “every adjectival term needs its substantive,” even though this is not the case in Latin grammar.

From these axioms this corollary follows: “All abstract, affirmative propositions are hypothetical when they concern things, not ideas,” where the existence of the object is understood as an antecedent condition without which they are not true.

[Other axioms are sometimes collected here in vain. “It is impossible for the same thing to be and not to be; everything is or is not; the whole is greater than its parts; things which agree with a third thing agree with each other.” And many others like them, of which some have no use; others are not relevant for common life. But afterward9 some axioms will be proposed which are not useless.]10

[1 ]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.”

[2 ]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.”

[3 ]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.”

[4 ]The three paragraphs enclosed in brackets were added in 1744.

[5 ]Malebranche, The Search After Truth, bk. 3, pt. 2, chap. 6, p. 234: “our view is that we see God when we see eternal truths.”

[6 ]This paragraph was added in 1744.

[7 ]Le Clerc made extensive use of axioms in his ontology: for example, concerning existence (chap. 6); concerning wholes and parts (chap. 7); concerning causes (chap. 10). In the preface, p. 3, he proposed that he would show “how all our ideas lead to undoubted axioms.”

[8 ]This paragraph was added in 1744.

[9 ]This note was added in 1749: “See Chapter 4, Section 5 [p. 91]: on causes. Wolff, in his Ontology, has recently given an account of axioms and their usefulness, with a diligence that will appear unclear to some.” Hutcheson had ordered the “Logica,” “Psychologia,” and “Cosmologia” of Christian Wolff during his term as quaestor for the library of the University of Glasgow, 1732 to 1734. The “Ontologia” or “Philosophia Prima sive Ontologia” was ordered for Glasgow University Library in 1736, GUA 26624.

[10 ]This paragraph was added in the third edition.