French neocritical idealist philosopher who rejected all necessary connection between universal laws and morality. Never an academic, Renouvier wrote prolifically and with great influence. He accepted Kant's critical philosophy as a starting point but drew vastly different conclusions. He held, for example, that phenomena are appearances of themselves only, not of things in themselves that lie beyond or beneath appearances. Since relationship pervades all categories of knowledge, each phenomenon is apprehended in relation to other phenomena.

Renouvier's background in mathematics (École Polytechnique 【“Polytechnic School”】, 1834–36) prompted his “law of numbers.” He saw each number as unique, distinctly itself, irreducible, but related to all other numbers. By applying this principle of uniqueness to human beings, he thereby precluded their absorption into a group consciousness or absolute mind. Having rejected the notion of infinite numbers, he moved on to a denial of all infinity, including infinity of space and time. He viewed God not as a substance or an absolute but as the moral order itself, capable of limitless perfection.

Renouvier identified human individuality with self-determination and free will, necessary postulates for morality and certitude in knowing. He made no distinction between knowledge and belief. Renouvier explained the consistency of human behaviour by pointing to the homogeneity of humankind.