John Stuart Mill (1806–1873), in An Examination of Sir William Hamilton’s Philosophy (1865), vigorously attacked Hamilton’s notion that scientific principles are intuitively valid, rather than valid on account of their ability to provide causal explanations, as Mill thought.

Hamilton called “the conditioned” something that has been described or classified, and “the unconditioned” things that are without descriptions or classifications. His philosophy was an attempt to create a balance between the conditioned and the unconditioned. Hamilton wrote that “all that is conceivable in thought lies between two extremes, which, as contradictory of each other, can not both be true, but of which, as mutually contradictory, one must be true…. The law of the mind, that the conceivable is in every relation bounded by the inconceivable, I call the law of the conditioned.” Hamilton held the theological belief that the Infinite is “incognizable and inconceivable.”