Jeff, List: I have been looking into this a bit more and came across another passage where Peirce discusses the difference between nominal and real definitions.
CSP: A *Definition *is either *Nominal *or *Real*. A nominal definition merely explains the meaning of a term which is adopted for convenience. I shall not make separate articles for such definitions nor state them formally. For they do not affect the course of development of the thought. A *Real Definition* analyzes a conception. As Aristotle well says (and his authority is well-nigh absolute upon a question of logical terminology), a definition asserts the existence of nothing. A definition would consist of two members, of which the first should declare that any object to which the *definitum*, or defined term, should be applicable would possess the characters involved in the definition; while the second should declare that to any object which should possess those characters the definitum would be applicable. And any proposition consisting of two members of this description and really contributing to the development of the thought would be a Real Definition. (NEM 4:285, c. 1901) The manuscript where this appears, "A Sketch of Dichotomic Mathematics" (R 4), is almost certainly a draft for what ultimately became "New Elements." Although the parallel text in the latter is much shorter, and the nominal/real distinction is missing, it is nevertheless quite similar. CSP: A *definition *is the logical analysis of a predicate in general terms. It has two branches, the one asserting that the definitum is applicable to whatever there may be to which the definition is applicable; the other (which ordinarily has several clauses), that the definition is applicable to whatever there may be to which the definitum is applicable. *A definition does not assert that anything exists.* (EP 2:302, c. 1901) In his post launching the "Ens necessarium" thread ( https://list.iupui.edu/sympa/arc/peirce-l/2024-08/msg00019.html), Gary F. mentioned that this "term in metaphysics and theology can be traced back to Francisco Suárez (if not further)." I subsequently observed that the Logic Notebook entry of 1908 Aug 28 presents Peirce's versions of Leibniz's principal of sufficient reason (PSR) and resulting *cosmological *argument ( https://list.iupui.edu/sympa/arc/peirce-l/2024-08/msg00050.html). Further investigation has led me to suspect strongly that it is primarily from Leibniz that Peirce got the idea of defining God as *Ens necessarium*. It turns out that Leibniz wrestled with the specific challenge of turning this nominal definition into a real definition by establishing that such a being is *possible*. In my post launching the "Peirce and Anselm" thread ( https://list.iupui.edu/sympa/arc/peirce-l/2024-08/msg00075.html), I offered this simple *ontological *argumentation for the reality of God. P3. If God is possibly real, then God is necessarily real. P2. God is possibly real. C2. Therefore, God is necessarily real. A1. If God is necessarily real, then God is actually real. C1. Therefore, God is actually real. There is no ambiguity since "possibly" is equivalent to "not necessarily not" and "necessarily" is equivalent to "not possibly not." P3 is stipulated in accordance with the nominal definition of God as *Ens necessarium*, A1 is the uncontroversial modal axiom T, and both C2 (from P3 and P2) and C1 (from C2 and A1) follow deductively by the classical inference rule of *modus ponens*. Hence, the argumentation is indisputably *valid*; so, if P2 is true, then the argumentation is also *sound*, such that C1 is likewise true. However, if P2 is false--if God is *not *possibly real, or even if God is possibly *not *real (P4)--then what follows deductively instead is that God is *not *actually real. In other words, as I have noted before, the persuasiveness of this argumentation hinges entirely on the perceived plausibility of P2 vs. P4. My understanding is that adding P2 (once demonstrated) to P3 would constitute a *real *definition of God as *Ens necessarium*. Like any definition, it still does not assert the *actual *reality of anything, only the *possible *reality of what it defines; but in this case, its actual reality then follows from the unique *nominal *definition of God as "that which would Really be in any possible state of things whatever" (R 339:[295r], 1908 Aug 28). Before exploring whether and how the truth of P2 *can*, in fact, be established, I will pause here to ask a question--is all this consistent with what you had in mind when you brought up nominal/verbal vs. real definitions? Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt >
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