Sheets, Diagrams, and Realism in Peirce by Frederik Stjernfelt

Author:Frederik Stjernfelt
Language: eng
Format: epub
Publisher: De Gruyter
Published: 2022-09-19T07:40:48.420000+00:00

Nota Notae

All of these check blocks are particular versions of a general scholastic principle discussed by Peirce, the so-called “Nota Notae” principle, referring to the claim that “Nota notae est nota rei ipsius”: the predicate of a predicate is a predicate of the thing itself.216 Originating in Aristotle's Categories, the principle was later taken up by Wolff, Kant, and Stuart Mill. The Latin version just given Peirce finds in Kant.217 Of course, here the notion “predicate” should be taken as referring to the meaning of the predicate, not the predicate word or expression itself. If it is taken to refer to the token or type of the predicate expression, the Nota Notae principle would be wrong (the fact that a predicate token is written with red ink does not imply that the object referred to is written with red ink; the fact that a predicate type stems from the 16th century does not imply that the object it refers to stems from that century, etc.). But if a certain color is very rare, it does follow that objects having that color are very rare. Or, Peirce's standard example, if humans are mortal, and Enoch is human, it follows that Enoch is mortal. Here, the Nota Notae gives rise to a syllogism: “mortal” is a second-order predicate of the first-order-predicate “human”, also holding for those which the first-order predicate holds for. The particular use of the principle in Peirce addressed here, however, highlight special cases where the first and second-order predicates of the Nota Notae are the same. Oftentimes, such cases will be meaningless (the red color of the red color, etc.): many predicates do not apply to themselves. Other predicates unproblematically apply to themselves (an utterance of an utterance, leading to any level of quotations of quotations; a sign of a sign, leading to any level of description of the sign's object). The issue of which predicates are thus self-applicable is not a formal one, decidable from formal criteria, but rather pertains to the regional ontology to which that predicate belongs. Here, Peirce's use of the Nota Notae focuses on a subset of those special cases where 1) the predicate is self-applicable and 2) its self-application does not at all change its meaning. While the utterance of an utterance is a special utterance, namely a quotation, the habit of a habit is simply that same habit. The former still conforms to the Nota Notae principle (because being quoted is also a property of the first utterance), but the latter belongs to that special subset of self-applicable predicates where f2(x) = f(x), so to speak. All of those are continuous in the special sense Peirce used when picking the term “continuous predicates”: applying the predicate to itself gives but the same predicate, just like joining one continuous line to another gives a continuum of the same power.

Thus, they form a rock bottom providing Peirce's seemingly byzantine logic and semiotics with a fundamental inventory of formal ontology: relations, continuous predicates, leading principles,

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