[peirce-l] Re: The roots of speech-act theory in the New List

[Benjamin Udell]

Jim,   >[Jim Willgoose] (I responded to your later message first.) I agree with a lot here. The idea that there are objective possibilities that are true, regardless of our knowledge, has been arguably the central issue in discussions of philosophical realism for 2500 years. The idea of objective indeterminacy is a part of that. Consider that a proposition which reflects an objectively indeterminate state of affairs is not bivalent. (I assume that a God would know that it is not bivalent. S/he would be omniscient.)   In the concrete world, the most obvious case of objective indeterminacy is that of quantum mechanics. For point A there will be some point B regarding which the info doesn't exist at point A as regards the determination of point B. Yet that info will exist eventually. Or, if in accordance with the "superdeterminism" interpretation of quantum mechanics, there is superluminal determinism, then the relevant info can't be available to subluminal entities at point A. I can't say whether it is fair to deny that such info _actually_ exists at all until at least point B. This gets into a more general question about _actuality_, which Peirce defined as reactiveness. Putting aside superluminal determination, there is to note that it takes light 10,000 years to cross the visible Milky Way. Does the Milky Way _actually_ exist as an _actual_ coherent whole with respect to a duration briefer than 10,000 years? Should one double the duration in order to allow for two-way interaction? Well, expressed in light-units, the width of the Milky Way and the time which light takes to cross its width are the same. (The only other kinematics time-version of length of which I'm aware is L/v, the amount of time that an object takes to pass its length through a given point at rest, a quantity which is obviously highly variable like velocity and which approaches infinity as velocity approaches zero). This question, with which I've played (nothing more) occasionally for decades, is of particular interest in regard to whether the current claim, that our Big Bang universe is spatially infinite, amounts to a claim that it is _actually_ infinite in spatial extent. Maybe it doesn't amount to such a claim. Decades ago a physics student, a roommate of mine, told me "existence travels at the speed of light." Still more generally, the inevitable imprecision and errors of measurements guarantees some imprecision and errors in our knowledge. Since therefore even the final interpretant would involve leaving room for such error, and since the real depends on the final interpretant, therefore the real itself must be subject, in some sense, to imprecision and "errors" or nonconformity to laws -- at least laws that we can formulate. Peirce wrote in "The Architecture of Theories" (CP6.7-34), "...within another century our grandchildren will surely know whether the three angles of a triangle [in actual space] are greater or less than 180 degrees,-- that they are _exactly_ that amount is what nobody ever can be justified in concluding."  Also B. Roy Frieden http://en.wikipedia.org/wiki/B._Roy_Frieden is of interest in regard to inevitable error's and imprecision's consequences for "reality itself." John Collier has said at peirce-l that an information channel can't convey infinite information. Infinite information is what would be needed for infinite precision, I think, unless there were some sort of "perfect analog" measuring device and some mental "perfect analog" way to cognize the results, some sort of continuum which potentially could actualize any of its potential points. (I'm averse to actual infinities but, if I remember correctly, Peirce is not averse to actual infinities.) But the moment that info must be translated or encoded or decoded into an incommensurate form (e.g. continuous into discrete), then imprecision must become involved. Now, this is the part where I have special trouble developing a clear idea. In the foregoing sense, it _seems_ that we are not alone in necessary imprecision -- the world's parts seem subject to necessary imprecision, and chance is mathematically founded in the world. However, the world doesn't "know" that it is sometimes trying to "translate" between incommensurate forms, rather we are trying to use one form incommensurate with another in order to learn about the other. That sounds less vague than it should in order to reflect what I'm trying to think about. Anyway, still more generally, there is the question of insoluble mathematical problems, including many that have been proven insoluble. Peirce somewhere says that even these would prove amenable to inductive and abductive approaches. Well, there is a blur of issues here. Penrose talks hypothetically of "oracles" which can solve problems which require infinities of computation, a higher degree of oracle for each higher aleph, or something like that. How would we verify that something were such a higher oracle? As a practical matter, it seems that the world is riddled with chance and uncertainty at every level. I remember years ago an issue of _Scientific American_ announcing that uncertainty had been proven to exist in mathematics.   >[Jim] Just some terminological notes. "1st order" logic usually means the universe of discourse and the domain of the variables are individuals. "2nd order" logic usually means the discourse is about collections, properties, or relations.  I am not sure what you mean by "standard."   By "standard 1st-order logic" I mean what is commonly found in contemporary logic textbooks, of which I take Quine's _Methods of Logic_ as a prime example. I'm not saying that I agree with Quine about everything, I'm just saying that his 1st-order logic has been taken as a standard.   As I understand it or misunderstand it, the difference between 1st-order & 2nd-order was originally opened up as a way of distinguishing between the axiomatically complete system and the axiomatically incomplete system.  However, this soon evolved into the distinction between (axiomatically complete) logic not applied to its own expressions and a (axiomatically incomplete) logic about the _expressions_ used in the axiomatically complete logic. These expressions are abstract objects but are still linguistic. Then in math one gets into abstract nonlinguistic objects, collections, properties, etc., in general.   >[Jim] A lot hinges on that. You say,   >>[Ben] "The idea that a true proposition (zero-place predicate) about concrete things is true of all concrete things everywhere and everywhen seems -- somehow -- at odds with the idea that the relevant information is not everywhere and everywhen, if indeed chance is real (for my part, I think it's real)" (end)   >[Jim] I am not sure I understand this. We can replace a variable with an individual.  If an individual satisfies a predicate, it is called "zero-place." Some logics allow "substitution of identity." Any individual can be substituted for another that satifies the predicate with certain restrictions.  I think of formal logic as a set of rules that, in part, allow us to represent things. If we don't like the representation, we can change the rules. A large part of logic is not monolithic. The "flat in or out" universe is a problem of identity. We seem to need this to manage many affairs no matter how rough the identity is. I am not sure why the big bang universe is a problem for 1st order logic.   "Ax(Rx v ~Rx)" and "Ex(Rx v ~Rx) are, by contemporary standards, zero-place terms -- sentences -- and are true (aside from non-bivalence issues), the first in all universes, the second in all non-empty universes. It contains no individual constant. The schema "Ex(Rx v ~Rx)" formally implies the schema "Ay(Ax[Rx v~Rx])y". Generally, where "p" is a sentence schema, "p <--> Ax px" is valid, true under all substitutions in all universes. "p <--> (Ex px)" is valid for most purposes, true under all substitutions in all non-empty universes. But it's the propositions about individuals which seem a bit peculiar when predicated of things a long, long time ago, very far away. Many find it somewhat counterintuitive. What sort of predication is it really, when one predicates the proposition "Socrates thinks deeply" of the planetary nebula out of which our solar system was formed? Or predicates the proposition "Socrates thinks deeply" of some distant and ancient pulsar? It feels like saying that it was already determined, way back then and there, that Socrates was going to think deeply. Some say that space and time really are that blocklike. But such a thing is not proven by a logical formalism which merely assumes it (or is construed as assuming it). Others say that it doesn't matter, and that it's just a formal thing anyway and doesn't imply such a massive determinism, and that logic is logic. Now, to say that in fact future-anchored propositions are not already true "in" the past in such a way as to permit the future-anchored proposition's predication of past subjects, is to say that the future proposition's subjects and the past subjects are not in quite the same universe of discourse. But this seems to call for something like fuzzification of the relationship of belonging to a universe of discourse or for some sort of temporal logic which might amount to something similar. Some temporal logics have been devised, though I'm not acquainted with their particulars.   As for flat-out identity/otherness, it's not so clear to me that the laws of identity, non-contradiction, etc., rule out relationships of partial identity, degrees of identity, etc. In fact, a sign, according to Peirce, is in a kind of partial identity with its object -- except in the limit case, the sign is _other_ than its object, yet is _almost_ its object, enough in order to convey information though not acquaintance of its object. The sign is a kind of "ghost" of the object, a ghost _pursuing_ solidity, its path illumined by the interpretant, and its solidification, settlement, entelechy, achieved and "en-habited" in the verification.   Best, Ben Udell http://tetrast.blogspot.com/   -----Original Message----- From: [EMAIL PROTECTED] To: peirce-l@lyris.ttu.edu Sent: Mon, 11 Sep 2006 12:53 PM Subject: [peirce-l] Re: The roots of speech-act theory in the New List Jim,   I should add, upon re-reading your comments, that the idea of possibility that I've been discussing has pretty much been in terms of ignorance, but it seems to me that the terms don't need to be essentially in terms of ignorance. If one is talking about a future event, then the reason for one's ignorance of the outcome may be the uncertainty and vagueness of current things themselves as determinants of the future -- the uncertainty is not just "in one's head," nor even just "necessarily in one's head, by the nature of intelligence." I think that Peirce agrees that not all uncertainty is merely epistemic, since he holds that chance is real.   For my own part, I consider standard 1st-order logic as a low-resolution, "low-pixelage" picture of the real for this reason among others. The idea that a true proposition (zero-place predicate) about concrete things is true of all concrete things everywhere and everywhen seems -- somehow -- at odds with the idea that the relevant information is not everywhere and everywhen, if indeed chance is real (for my part, I think it's real). That is to say that our concrete Big-Bang universe differs in some logically deep way from a 1st-order logical universe of discourse -- well, who could be shocked! shocked! by that, but what I mean is, that the idea of a flat-out in-or-out membership in a universe of discourse seems a crude beginning for understanding what sort of universe of "discourse" and information it is that we actually live in. It's not that I've forgotten that, in a 1st-order logical universe, there can be true contingent propositions which don't imply each oth   Best, Ben Udell http://tetrast.blogspot.com --- Message from peirce-l forum to subscriber archive@mail-archive.com