 However, these explicit ways to handle existential statements are limited to unary predicates or Aristotelian syllogisms, and cannot go beyond them. Instead, we would like to examine Peirce’s multiplication and exponential expressions between relations and properties more carefully. Let’s recall \(\binary{l}\unary{w}\) means “a lover of some woman” while \(\binary{l}^{\unary{w}}\) “a lover of every woman”. Here Peirce’s proposal for individual terms gets in the picture so that existential and universal quantifiers may become more explicitly represented. Peirce suggests individuals be denoted by capitals (DNLR [CP 3.96]). For example, for unary predicate \(\unary{w}\), if \(\unary{w} &gt; 0\), then \(\unary{w} = \unary{W}' \cunion \unary{W}'' \cunion \unary{W}''' \cunion \cdots\), where each of \(\unary{W}'\), \(\unary{W}''\), \(\unary{W}'''\),…denotes an individual woman. Hence,