My sense is that there’s some equivocation (perhaps even by Peirce) over the term existence.
It seems to me that Peirce’s use of “real” is really about predication. Part of the confusion is things like mathematical objects. To follow Quine you can quantify over them but as soon as you start using terms like “exist” I think it’s easy to get confused unless one is clear about ones ontology. Sometimes Peirce uses exists as “appears in existence” while at other times loosely as spatio-temporal object. A good quote on this is the following: For what is it for a thing to be Real ? [---] to say that a thing is Real is merely to say that such predicates as are true of it, or some of them, are true of it regardless of whatever any actual person or persons might think concerning that truth. Unconditionality in that single respect constitutes what we call Reality. Consequently, any habit, or lasting state that consists in the fact that the subject of it would , under certain conditions, behave in a certain way, is Real , provided this be true whether actual persons think so or not; and it must be admitted to be a Real Habit , even if those conditions never actually do get fulfilled. ['A Sketch of Logical Critics', EP 2.457-458, 1911 http://www.helsinki.fi/science/commens/terms/real.html <http://www.helsinki.fi/science/commens/terms/real.html> Looking at my archive I found the following from Ben (who’s been silent of late) that seems helpful. It gets at reality but also raises the question of existence as the really the question of singulars. I should note, in case you haven't encountered this issue before, the distinction that Peirce sometimes made between the singular and the individual. He was not consistent in his terminology through the years. In "Questions on Reality", MS 148 Winter-Spring 1868 http://www.iupui.edu/~peirce/writings/v2/w2/w2_18/v2_18.htm <http://www.iupui.edu/%7Epeirce/writings/v2/w2/w2_18/v2_18.htm> , Peirce defines two kinds of individual: the singular individual or the singular as he called it for short, and the general individual , or the individual as he called it for short. The singular individual (also called the singular ) exists only at one place and one date and occupies no space and no time. In other words, it is a point-instant, or maybe one should say an existent confined to a point-instant. The general individual (also called the individual ) exists only at one place at a time and occupies space and time. In that terminology, it is the singular and the general that are sharply opposed; and the individual can be either. I generally think of the "general individual" as being you or me or a river or a cloud, but as Gene Halton pointed out to me in August 2011 http://permalink.gmane.org/gmane.science.philosophy.peirce/7228 <http://permalink.gmane.org/gmane.science.philosophy.peirce/7228> A word may be in several places at once, six six , because its essence is spiritual; and I believe that a man is no whit inferior to the word in this respect. [Peirce. CP 7.591, W 1:498, Lecture XI at the Lowell Institute in 1866] Back to your post. I agree that this involves the nominalism/realism question. Peirce defines the real not only as that which is what it is independently of particular minds' opinions, but also furthermore as that which would be found by anybody's sufficient investigation. If one accepts Peirce's definition of the word "real," then it's hard for me to see what would be left for nominalism to argue about. But the word "real" seems to carry for many people a lot of freight that it did not carry for Peirce. They want "real" to mean "actual" (in the latter word's English-language sense) and not let their variables wander between planes, or something like that. It reminds me of the yearning for a single, monolithic universe of discourse such that Russell actually worried that the natural numbers run too high for the number of particles in the actual universe. Peirce did not regard the real as only the fully determinate (which taken in the strongest sense amounts to fully, absolutely determinate microstates, which he regarded as unreal) or only the causally agential or only the directly observable, and so on. Peirce seemed to see in the singular or individual even a certain falseness or lack or insufficiency of reality (certainly he saw ignorance and error in being an individual person apart from others, in "Some Consequences of Four Incapacities"; and in "Questions on Reality" linked above, he says "In short, those things which we call singulars exist, but the character of singularity which we attribute to them is self-contradictory " - but I don't know how or whether his views on the point-instant singular individual changed in later years). As regards the 'mental' character of generals, Peirce even affirmed it (I think), but held that they are not merely mental. He takes the mentality aspect further in his objective idealism in his physical metaphysics; but he regarded ontology/general metaphysics (locus of the question of the reality of generals) as more basic.
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