This paper considers two cognate notions: task and goal. Samokhvalov and Ershov, in their “Contemporary Philosophy of Mathematics,” argued that existing problems in the foundations of mathematics follow from insufficient precision of the task notion. A mathematical task is set only if we have a criterion of verifying its proof. Similar considerations arise for the notions of purpose/goal. We cannot attain the goal without having a criterion of its attainment; otherwise we can assume that the goal is already attained. The theory of functional systems (TFS) developed by Anokhin and many other distinguished scientists of his school is one of the few known physiological theories in which the notions of goal/purpose, result, anticipation and goal-directed behavior are the principal ones. Hence, TFS is a theory in which purposefulness is regarded as a principle of physiological activity. We present TFS as a theory of anticipatory functional systems characterized by purposeful activity.