ABSTRACT
Notice, however, that even as soon as we come to Locke’s second example of ‘intuitive’ knowledge-that a circle is not a triangle-we no longer have an irreducible disagreement between simple, unanalysable ideas. A triangle may be defined as a plane figure bounded by three straight lines, and a circle as a plane figure bounded by a curved line which is everywhere equidistant from a central point-and given further axioms and definitions of Euclidean geometry it would indeed be possible to derive a formal contradiction from the statement ‘F is both a circle and a triangle.’ Even so, Locke would obviously maintain-again with considerable plausibility-that our ‘perception’ of the ‘disagreement’ between the ideas of a circle and a triangle is ‘immediate’, rather than being grounded in a demonstration from those axioms and definitions. The same applies to his third, arithmetical example that three equals one plus two: no proof of this from the axioms and definitions of arithmetic could make us any more assured of its truth than we are by simple reflection upon the meaning of the statement itself. (Indeed, we are less certain of those axioms and definitions than we are of such simple arithmetical truths as that three equals one plus two.) That some things are indeed known to us by ‘intuition’, as Locke suggests, certainly appears to be
at least a truth about our psychological condition-though whether it reflects anything special about the status of the objects of that knowledge seems altogether more debatable.
