Scottish metaphysical rationalist who maintained the essential distinction between matter and spirit, resisting the more advanced British epistemology of his century.

Having gone to Utrecht in the Netherlands as tutor to two young gentlemen in 1741, he went on an excursion to Spain in 1745 and there met the English political radical John Wilkes, for whose intellect he conceived a fervent admiration subsequently expressed in a number of letters.

Baxter published anonymously An Enquiry Into the Nature of the Human Soul (1733; 3rd ed., 1745; Appendix, 1750) and Matho, sive cosmotheoria puerilis (1738), a compendium of scientific knowledge. The Evidence of Reason in Proof of the Immortality of the Soul (1779) was edited from his papers by John Duncan.