 Intuitionistic logic is an offshoot of L.E.J. Brouwer’s intuitionistic mathematics. A widespread misconception has it that intuitionistic logic is the logic underlying Brouwer’s intuitionism; instead, the intuitionism underlies the logic, which is construed as an application of intuitionistic mathematics to language. Intuitionistic mathematics consists in the act of effecting mental constructions of a certain kind. These are themselves not linguistic in nature, but when acts of construction and their results are described in a language, the descriptions may come to exhibit linguistic patterns. Intuitionistic logic is the mathematical study of these patterns, and in particular of those that characterize valid inferences. An inference rule is valid if, whenever the statements in the premises describe truths of intuitionistic mathematics, a construction can be found that makes true the statement that is obtained by applying the rule. What the principles of logic need to preserve is therefore not, as in classical logic, mind-independent truth, but mental constructibility. Various principles of classical logic, most notably the Principle of the Excluded Middle, then become insufficiently grounded, and certain classical theorems even contradictory. The theorems in intuitionistic logic that formally contradict classical theorems depend on elements of intuitionistic mathematics that are incompatible with classical mathematics; this illustrates how in intuitionism logic is based on mathematics and not the other way around.