 The enormous impact of the adoption of quantifiers/bound variables on the world of logic and mathematics cannot be denied. However, that should not overshadow Peirce’s insight behind the new extended formalism. This section will explore how Peirce’s conviction about the novelty of the logic of relations led him to the introduction of quantifiers/variables. Hence, quantification theory, according to Peirce, is not a matter of a linear extension of formal vocabulary, but an expansion into territory that is qualitatively different from what Aristotelian logic covers. At the same time, we should not forget that Peirce extended the territory of logic in the spirit of Boole’s algebra of logic.