The article analyzes the relationship between the principle of infinitism, which asserts the manifold infinity (inexhaustibility) of the universe, and the principle of simplicity, which proclaims that the universe is in some sense simple or, at least, amenable to a fairly simple description and explanation. The article shows that the ontological interpretation of the principle of simplicity, that is, the assumption that reality (the universe) is simple in one sense or another, is diametrically opposed to the principle of infinitism. It is also shown that the epistemological interpretation of the principle of simplicity consists in the assumption that a scientifically (philosophically) cognizable fragment of the universe, despite its infinite complexity, can be more or less adequately described and explained using relatively simple theoretical models. Finally, it is demonstrated that the principle of simplicity in its epistemological interpretation is ubiquitous in special scientific and philosophical cognition and is the basis of an effective cognitive strategy. Such a strategy is implemented primarily through the procedures of reduction and abstraction, the essence of which is to transform a cognizable, infinitely complex fragment of the universe into a relatively simple subject of special scientific or philosophical cognition.