List: While delving into the secondary literature on the relationship between Peirce's thought and that of Leibniz, I came across a succinct explanation of how the latter distinguished between nominal and real definitions in a 2013 paper by Francesco Bellucci ( https://www.academia.edu/11573065/Peirce_Leibniz_and_the_threshold_of_pragmatism), which seems consistent with my understanding.
FB: Leibniz thinks that distinct cognitions correspond to nominal definitions, while adequate cognitions correspond to real definitions ... The former shows us *a* possible definition of the term, whereas the latter exhibits the *unique* definition of that term that alone prove[s] the possibility of the thing defined. (p. 337) In the version of the ontological argument formulated by Leibniz, "We define God as a Being from itself, or a Being from whose essence existence follows, or a necessary Being, from which this memorable proposition follows: if God is possible, he actually exists. Which is what we set out to demonstrate" (1678). Expressed in accordance with modern possible worlds semantics for modal logic and Peirce's metaphysical distinction between existence and reality, the *nominal* definition of God as *Ens necessarium* entails that if God is real in *any* possible world, then God is real in *every* possible world, including the *actual* world. However, Leibniz recognizes that turning this conditional proposition into a *real* definition requires establishing the truth of the antecedent, thereby confirming the truth of the consequent. GWL: This argument ... is not a Sophism, as some claim; and in my opinion it is only an incomplete argument, or something must still be supplied. But if nothing would be supplied, there is already a very considerable usefulness, incomplete as the argument is, in that it shows that the divine Nature has the privilege that It needs, for its Existence, only its possibility or essence. And furthermore, this argument yields at least presumptively the Existence of God. For every being ought to be judged possible until the contrary is proved, until it is shown that it is not possible at all. This is what is called *presumption*, which is incomparably more than a simple *supposition*, since most suppositions ought not to be admitted unless they are proved, but everything that has presumption for it ought to pass for true until it is refuted. Therefore the existence of God has presumption for it in virtue of this argument, since it needs nothing besides its possibility. And possibility is always presumed and ought to be held for true until the impossibility is proved. (1702) In the absence of a proof that the reality of a certain kind of being is impossible, Leibniz advocates *presuming* that it is possible, much like a person accused of a crime is legally presumed to be innocent until proven guilty. It is interesting to note that Peirce treats the term "presumption" as a synonym for "abduction" in his entry for "reasoning" in Baldwin's *Dictionary of Philosophy and Psychology* (CP 2.776-777, 1902), as well as in his brief logical definition of "presumption" itself for the same work ( https://archive.org/details/philopsych02balduoft/page/337). CSP: In logic: a more or less reasonable hypothesis, supported, it may be, by circumstances amounting all but to proof, or, it may be, all but baseless. Logical or philosophical presumption is non-deductive probable inference which involves a hypothesis. It might very advantageously replace hypothesis in the sense of something supposed to be true because of certain facts which it would account for. Moreover, Leibniz states plainly, in both early and late writings, that *all *his arguments for the reality of God ultimately rely on the principle of sufficient reason. "I claim that the existence of God cannot be demonstrated without this principle: nothing exists without a reason" (1677). "I dare say that without this great principle one cannot prove the existence of God, nor account for many other important truths" (1716). This is the basis for his *cosmological* argument--"there are contingent beings, which can only have their final or sufficient reason in the necessary being, a being that has the reason of its existence in itself" (1714)--as echoed by Peirce in his Logic Notebook. CSP: I show that logic requires us to postulate of any given phenomenon, that it is capable of rational explanation. Now, I say that the co-reality of the three universes 1st of Ideas, 2nd of Occurrences (existent things and actual events), 3rd of powers to bring two substances into relation to each other, (and I will call powers of this sort *Reasons*) must, accordingly, be supposed capable of rational explanation. ... Cosmology or the explanatory science of the Three Universes shows then plausibly at least how the Three Universes were produced, from an antecedent state. But their Phenomena are all the phenomena there are. The task of Cosmology is therefore to show how all phenomena were produced from a state of absolute absence of any; and logic requires that this problem [is] to be solved. But it must suppose something to be in that antecedent state, and this must be that which would Really be in any possible state of things whatever, that is, an *Ens Necessarium*. This Ens necessarium being, then, the Principle of all Phenomena, must be the author and creator of all that could ever be observed of Ideas, Occurrences, or *Logoi*. (R 339:[293r&295r], 1908 Aug 28) In my view, this amounts to a *real* definition of *Ens necessarium*, establishing that the possible reality of God (P2) is a *more reasonable* logical presumption (hypothesis) than its impossibility because it provides the "rational explanation" that "logic requires" for "the co-reality of the three universes." Regards, Jon On Sat, Sep 21, 2024 at 12:04 PM Jon Alan Schmidt <[email protected]> wrote: > 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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