Ben, List: I changed the subject line to match the topics that your post addresses.
BU: I think Peirce seldom if ever wrote about the result of "infinite" inquiry. He said that inquiry pushed far enough or for long enough will reach the truth - sooner or later - but still inevitably. We are using different terms but seem to be saying essentially the same thing. The pragmaticistic definition of truth as what an infinite community *would *affirm after infinite investigation is derived from Peirce's well-known statement, "The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth, and the object represented in this opinion is the real" (CP 5.407, EP 1:139, 1878). In my own words, truth is the final interpretant of every sign whose dynamical object is a reality. Accordingly, what I am discussing is a real but potential or ideal infinity, not an actual infinity; again, a regulative principle and an intellectual hope--what Peirce sometimes calls a "would-be." He says so himself in the subsequent paragraph. CSP: Our perversity and that of others may indefinitely postpone the settlement of opinion; it might even conceivably cause an arbitrary proposition to be universally accepted as long as the human race should last. Yet even that would not change the nature of the belief, which alone could be the result of investigation carried sufficiently far; and if, after the extinction of our race, another should arise with faculties and disposition for investigation, that true opinion must be the one which they *would ultimately* come to. "Truth crushed to earth shall rise again," and the opinion which *would finally* result from investigation does not depend on how anybody may actually think. (CP 5.408, EP 1:139, 1878; bold added) Moreover, in his very next published article, he refers to "an *unlimited *community" and "a hope, or calm and cheerful wish, that the community may last *beyond any assignable date*," thus facilitating "the *unlimited *continuance of intellectual activity" (CP 2.654-5, EP 1:150, 1878; bold added). His further definitions of truth after the turn of the century reflect his even stronger embrace of scholastic realism, as well as his development of semeiotic. "Truth is that concordance of an abstract statement with the *ideal limit* towards which *endless investigation would tend* to bring scientific belief" (CP 5.565, 1902; bold added). "Now thought is of the nature of a sign. In that case, then, if we can find out the right method of thinking and can follow it out,--the right method of transforming signs,--then truth can be nothing more nor less than the last result to which the following out of this method *would ultimately* carry us" (CP 5.553, EP 2:380, 1906; bold added). BU: As I recall, Peirce had doubts about the reality of things in mathematics, but he thought that some of those things imposed themselves on the mind with a forcefulness very like that of the real. These might be the remarks that you have in mind. CSP: The pure mathematician deals exclusively with hypotheses. Whether or not there is any corresponding real thing, he does not care. His hypotheses are creatures of his own imagination; but he discovers in them relations which surprise him sometimes. A metaphysician may hold that this very forcing upon the mathematician's acceptance of propositions for which he was not prepared, proves, or even constitutes, a mode of being independent of the mathematician's thought, and so a *reality*. But whether there is any reality or not, the truth of the pure mathematical proposition is constituted by the impossibility of ever finding a case in which it fails. (CP 5.567, 1902) The realities that pure mathematicians study are not actualities (2ns) with which they react, but logical possibilities (1ns) that they imagine, along with necessary consequences (3ns) that they draw from them--some of which can be far from obvious when they initially formulate their hypotheses, and are thus surprising whenever they are discovered. Peirce's distinction between corollarial and theorematic (or theoric) reasoning comes into play here, even though both are deductive (e.g., see CP 7.204-5, EP 2:96, 1901; NEM 4:1-12, 1901; CP 4.612-6, 1908; NEM 3:602, 1908). As a result, "Mathematics is purely hypothetical: it produces nothing but conditional propositions. Logic, on the contrary, is categorical in its assertions" (CP 4.240, 1902). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Tue, Dec 2, 2025 at 1:33 PM Benjamin Udell <[email protected]> wrote: > Jon, list, > > I dip in for a moment, then vanish. I wanted to reply to posts by Edwina, > Robert, and Ulysses but got busy as I do these days. I hope I'll get to > those. > > Jon, you wrote, > > What an infinite community *would* affirm after infinite investigation is > precisely how Peirce explicates the meaning of *truth* in practical > terms--those beliefs whose corresponding habits of conduct *would* never be > confounded by any *possible* future experience. > > I think Peirce seldom if ever wrote about the result of "infinite" > inquiry. He said that inquiry pushed far enough or for long enough will > reach the truth - sooner or later - but still inevitably. The inquiry that > continues indefinitely, by an indefinite community of inquirers, will > attain, sooner or later, definite increase of knowledge. Each increase in > actual knowledge occurs, as I understand it, at a finite remove from the > inquiry's beginning, while you sound like you're discussing an actual > infinity - e.g., an infinity of years or an infinity of one year's achieved > subdivisions (sounds like it would get infinitely hot) - after which the > truth is reached. I remember over 10 or 15 years ago discussing on > peirce-l with Clark Gobel the idea of an inquiry into the full meaning of > one's wife, not just one's wife as a sign of this or that or the weather > today, but as one's wife per se, as representing everything that one's wife > may represent. I thought that such an inquiry was so open-ended that maybe > it _would_ require an eternity of inquiry, like the final entelechy of the > universe (or whatever Peirce called it) maybe because a real example of > "full meaning" is somehow too 2nd-order semiosic, to be dealt with > finitely. Well, Clark seemed not to like that idea, while I was thinking > vaguely (indeed as I'm no expert) of Turing oracles and the like. > > I ought to note that, as to the reality of undiscovered legisigns, Peirce > himself seemed reluctant to assert the reality of things in pure > mathematics - discovered or undiscovered. I've long much leaned in favor of > it - maths as discovered, not invented. The mathematician Kronecker split > the difference, saying that God created the integers, all the rest is the > work of man. As I recall, Peirce had doubts about the reality of things in > mathematics, but he thought that some of those things imposed themselves on > the mind with a forcefulness very like that of the real. Unfortunately I > lost the email drafts where I kept the quotes. Maybe one will need to > allow of "grades" of realness. I have no idea how to do that in a > non-handwaving way. > > Best, Ben >
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