. 2015a. Aristotle's semiotic triangles and pyramids. Bulletin of Symbolic Logic. 21 (2015) 198. ► JOHN CORCORAN, Aristotle's semiotic triangles and pyramids. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: corcoran@buffalo.edu Imagine an equilateral triangle "pointing upward"-its horizontal base under its apex angle. A semiotic triangle has the following three "vertexes": (apex) an expression, (lower-left) one of the expression's conceptual meanings or senses, and (lower-right) the referent or denotation determined by the sense [1, pp. 88ff]. One example: the eight-letter string 'coleslaw' (apex), the concept "coleslaw" (lower-left), and the salad coleslaw (lower-right) [1, p. 84f]. Using Church's terminology [2, pp. 6, 41]-modifying Frege's-the word 'coleslaw' expresses the concept "coleslaw", the word 'coleslaw' denotes or names the salad coleslaw, and the concept "coleslaw" determines the salad coleslaw-recalling Frege's principle that sense determines denotation. Church [2, p. 6] wrote: We shall say that a name denotes or names its denotation and expresses its sense. [...] Of the sense we say that it determines its denotation, or is a concept of the denotation. Aristotle seems cognizant of distinctions going beyond those in semiotic triangles. The expression Aristotle's semiotic pyramids seem warranted by Aristotle's Categories, 1a1: When [two] things have a name (onoma) in common and the concept (logos) of being (ousia) which corresponds to the name in each case is different, they are called same-named (homonuma). Thus, for example, both a man and a picture [of an animal] are called animals. These have only a name in common. In each case the name's concept of being [an animal] is different; for if one says what being an animal is for each of them, one will give two distinct concepts. Semiotic triangles and pyramids in Aristotle's logic are compared to those in Church's [2]. [1] JOHN CORCORAN, Sentence, proposition, judgment, statement, and fact, Many Sides of Logic, College Publications, 2009. [2] ALONZO CHURCH, Introduction to Mathematical Logic, Princeton, 1956.