Thanks Ben
You say,
"If I speak of the "range" of "red" rather than of the range of "something red," "x{x is red}" or "Rx" etc., then it's quite possible that I will be taken to mean "red" as ranging over some portion of the spectrum, from, say, reddish-orange to reddish-purple, ..." (cut end)
Hmm. Interesting. A universe of qualities rather than a universe of things; without quantification. In the gamma graphs, Peirce suggests that it is easier to deal with qualities or aggregates of qualities as individuals. I will find the quote. I see vagueness arising unless "E' is introduced for individual qualities or aggregates of qualities.
Jim W
-----Original Message-----
From: Benjamin Udell <[EMAIL PROTECTED]>
To: Peirce Discussion Forum <peirce-l@lyris.ttu.edu>
Sent: Tue, 21 Mar 2006 10:15:46 -0500
Subject: [peirce-l] Re: naming definite individuals
-----Original Message-----
From: Benjamin Udell <[EMAIL PROTECTED]>
To: Peirce Discussion Forum <peirce-l@lyris.ttu.edu>
Sent: Tue, 21 Mar 2006 10:15:46 -0500
Subject: [peirce-l] Re: naming definite individuals
Jim, list,
Jim wrote:
> A general term has a "range" or "domain." A quantifier has a "scope." Peirce following DeMorgan called the domain a "universe of discourse." The variables x,y are general terms; as is the predicate letter J. (My post right before this raises a lot of questions about that predicate letter.) The schema ExAy(Jy<-->x=y) translates "there is something x such that for every y, y is J if and only if x is identical to y. I don't know what you mean by "purport." But I think that if either both domains are empty, or if the domain of x is non-empty and the universal quantifier has existential import, the statement is formally true.
I know that logical terminology. Generally one speaks of a _variable_, be it the variable x, a function f, etc., as having a range or domain. If I speak of the "range" of "red" rather than of the range of "something red," "x{x is red}" or "Rx" etc., then it's quite possible that I will be taken to mean "red" as ranging over some portion of the spectrum, from, say, reddish-orange to reddish-purple, as if the value or values of some variable predicate-style general were in question. I don't know where I picked up the use of the word "scope" in order to speak of "singular," "general," etc., maybe some old logic book, but it's a distinction that I need to make, and it also suggests that I'm not discussing range in the context of a mathematical theory. I usually say "scopes like the singular, the general, etc." so that my meaning is clear enough in contradistinction to that of quantifier scope.
The schema ExAy(Jy<-->x=y) is saying that there's some x of which "J" is uniquely true. That's how it fits into the context of my saying that, if it were the case that a general term were a term which purports to be general in the sense of being true of more than one object, then such a schema as ExAy(Jy<-->x=y) would be formally false.
"Purport" is a term encountered often enough in Quine. For instance, in _Methods of Logic_, 4th ed., p. 262
66~~~~
.... A singular term may or may not name an object. A singular term always _purports_ to name an object, but is powerless to guarantee that the alleged object will be forthcoming, witness 'Cerberus'. ....
~~~~99
and on p. 260
66~~~~
The division of terms into concrete and abstract is a distinction only in the kinds of objects referred to. The distinction between singular and general terms is more vital from a logical point of view. Thus far I have drawn it only in a vague way: a term is singular if it purports to name an object (one and only one), and otherwise general. Note the key word 'purports'; it separates the question off from such questions of fact as the existence of Socrates and Cerberus. Whether a word purports to name one and only one object is a question of language, and is not contingent on facts of existence.
In terms of logical structure, what it means to say that the singular term "purports to name one and only one object" is just this: _The singular term belongs in positions of the kind in which it would also be coherent to use variable 'x', 'y', etc._ (or in ordinary language, pronouns). ....
~~~~99
However, when we say that some term 'J' is true of exactly one thing x, we sometimes describe "J" as a singular term in the sense of a term which may just happen to be singular rather than purporting to be singular. My sense of it is that not everybody is familiar with the acceptation which Quine offers in his textbook definition of "singular" in formal logic.
Best, Ben
----- Original Message -----
From: [EMAIL PROTECTED]
Sent: Tuesday, March 21, 2006 2:31 AM
Subject: [peirce-l] Re: naming definite individuals
Ben
A general term has a "range" or "domain." A quantifier has a "scope." Peirce following DeMorgan called the domain a "universe of discourse." The variables x,y are general terms; as is the predicate letter J. (My post right before this raises a lot of questions about that predicate letter.) The schema ExAy(Jy<-->x=y) translates "there is something x such that for every y, y is J if and only if x is identical to y. I don't know what you mean by "purport." But I think that if either both domains are empty, or if the domain of x is non-empty and the universal quantifier has existential import, the statement is formally true.
Jim W
-----Original Message-----
From: Benjamin Udell <[EMAIL PROTECTED]>
To: Peirce Discussion Forum <peirce-l@lyris.ttu.edu>
Sent: Mon, 20 Mar 2006 22:46:51 -0500
Subject: [peirce-l] Re: naming definite individuals
Subject: [peirce-l] Re: naming definite individuals
Jim W., Frances, Jim P., Joe,
I'm having trouble keeping up with this thread, but I want to get to everything sooner or later.
Jim wrote,
>Ben
>You say,
>"I'm not able to find anything saying that the embodiment of a qualisign could be called a "replica" of the qualisign. I don't see why not, but I don't find anything saying that it would be okay." (end)
>You and I considered a sign that is not individual. If a sign is not individual, does it follow that its general? Consider a "free" logic where the variables are not bound. If a sign is not individual, then it is possible that it is neither individual nor general. I have changed modes. The replica of the qualisign must be possible.
>Jim W
I wish I knew. The Peircean scope system is particularly obscure to me in regard to quality. Quality is vague.
I haven't found a scope system in any philosophy that had more than a few "rubber bands & safety pins" for a terminology. It's my biggest pet peeve in philosophy. But anyway....
In contemporary deductive logic, a "general term" is, as far as I can tell, simply a term which does not purport as to scope. If it were general by purport or assumption, then a schema like "ExAy(Jy<-->x=y)" would be formally false. If (using "E!" as the unique-existence functor) E!x Hx, then "H" is singular, though not necessarily by purport. So then I guess it's no longer called "general," but I don't really know.
If we say that a sign truly corresponding to at least two things is general, and that a sign truly corresponding to only one thing is singular, then how does a free-variable logic let us escape the idea that any sign will be either singular or general? I'm not familiar with free-variable logic. Maybe you should take it from there, because what follows are my further boggings-down.
I would take qualities and qualisigns to be either general or such that they could be general. I.e., maybe there's only one thing that has a certain exact shade of blue, but there's no intrinisic reason for that, there could have been a second such-blue thing. Not every possible quality will be embodied even once, but then neither will every possible singular or every possible law. So quality doesn't seem vaguer to me than the other categories in that regard. A quality, certainly a sensory-style quality, belongs to some spectrum or gamut or multi-dimensional version of a spectrum in terms of which a mode of sensing or feeling _divides up the world_. So a given quality is (to my way of thinking) is neither singular nor fully universal, but in between -- a non-universal general, or, one could just as well say, a non-singular special. The inductive structure of alternatives among qualities, events (universes), etc., is the subject matter of fields like statistics. The deductive structure of such alternatives is the subject matter of fields like probability theory. Meanwhile "two," "seven" etc. are universal in the sense that any things can be among the two or the seven, their modifications & qualities are irrelevant. All that count are things' identities & distinctnesses, orderings, mappings, arrangements, etc. The deductive and often equivalentially deductive structure of such things is the subect matter of the pure maths. The abductive structure of such things (where you do have to take qualities & reactions, not to mention probabilities & the like, into account) is the subect matter of the special sciences. That's all to my fourish way of thinking, not Peirce's trichotomical way.
The existential particular doesn't nail down vagueness in the way that the hypothetical universal nails down generality. "ExHx" is vague as to which x is H, but in order to verify it I don't need to find the x which the assertor presumably found, instead I just need to find at least one x which is H, it certainly doesn't have to be the same one which the assertor presumably found. However, if one wants to understand the genesis of the semiosis, one may indeed want to find out which x the assertor found to be H. This is natural from a philosophical, inductive perspective and should not be regarded as merely a quaint wrinkle of Peirce's approach, a speed bump as it may initially seem to those of us (like me) who first learned deductive logic from the tradition ruled by Quine. "ExHx" is meaningfully vague in that respect.
Meanwhile the universal "Ax(Hx-->Jx)" is vague as to whether there are any H at all. It's vague as to whether there are any J. And so on. And when does the search for ever more H's and ever more non-J's end? The assertor does not supply you with a list of all x. (One doesn't automatically need to worry about ALL x in the case of "ExHx.") The assertor doesn't give you an ontics or an ontology. Of course one wants really to establish a law rather than maintain an ongoing mass-observational result. The (standard) objectual universal is a lot _vaguer_ than the substitutional universal which involves a definite list or at least some pretty definite ontical criteria.
And, meanwhile, the only way that I've found to capture, in terms of truth conditions, the idea of vagueness in the way that Peirce describes it, as in Peirce's phrase "a certain person whom I could name..." is by taking schematic terms as serving as _unknown constants_, "Ex x=j" "there is a certain person" and "ExJx" "there is something of a certain kind." Veiled references. She says "a _certain_ dog danced," and the fact that I find that some dog danced does not verify her assertion that that certain dog danced, whatever dog it was. I can't verify it unless I can show it to be formally true. This is not the "something," the Latin _aliquid_, but the "a certain thing," the Latin _quiddam_. Yet this, in the end, does _not_ really seem like the kind of vagueness that Peirce means. But I don't know why vagueness should be particularly connected with qualities as opposed to universals. "Blue" is vague as to which thing is blue. "There is something blue" is vague as to which thing is blue. "Everything is blue" is vague as to which things are everything. That's okay if right off the bat I see some things are not blue. "Everything is such that, if it is storm-blue, then it is food" is vague as to whether there's storm-blue and how much there is to look for. Vagueness simply doesn't seem like a scope to me.
Best, Ben
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