Jim, Gary, list, >[Jim] Ben Udell wrote:
>>[Ben] But first, on a general note, let me say that among the issues driving >>my current display of confusion & error, is the question: if comprehension >>is for quality & predicate, while denotation is for objects >>(resistances/reactions), then what dimension is for representational and >>logical relations themselves? Words like "not," "probably," "if," etc. do not >>designate either qualities or objects, nor do they represent objects as >>having this or that quality. What, then, do they connote? What do they denote? >[Jim] Here's my take on the questions you raise above. I would say that >symbols convey information and that they represent or stand for the meaning of >objects. Objects (which may be tangible or abstract) have both qualities >(forms) and locations (centers of gravity). The meaning of an object (its >consequence for other objects) depends upon both the object's qualities and >location. The center of gravity is not always the center of compelling interest. A tall boat with big sails, you may point at its mid-height in order to point it out. Its center of gravity may be lower. And there are physical forces besides gravitation. > One can indicate the location of an object (or at least to its center of > gravity). An object which perfoms this function is called an index. One can > not readily point to the quality or form an object because form is not a > matter of the object's location but of how the object is organized in space > and time. To the contrary, I think that one can and does point out a form, run one's finger around it, and point out qualities, shine lights on them, and so forth. One can point things out in music while the music is playing. Spatial form is especially subject to being traced out. And the presentation of an icon requires pointing out the icon itself. "It was greenish-blue -- like this thing here." What the iconic presentation of appearances makes possible is the representation of things that are too remote or otherwise inconvenient to be pointing at, and the representing of things with more generality. >[Jim] However one can illustrate the form or quality of an object by providing >a copy of another object that has similar properties. An object that performs >this function is called an icon. To adequately represent or stand for an >object's meaning we must refer to both its connotation and location. >Moreover, I think it is a mistake to restrict the notion of objects to >concrete tangible entities -- An object is anything that can be represented. > Abstract objects such as relations also have forms and locations that can be >connoted and denoted as discussed below. It's the sign that has connotation (in the sense of comprehension or intension). An object having connotation is an object being discussed as a sign while being called an object. >[Jim] It is my view (and I think Peirce's) that words or symbols such as >"not", "probably", "if" etc refer to and stand for abstract objects >(relations) that have that do indeed have specifiable forms and locations. >"Not", for example can, perhaps, be loosely defined as the abstract quality >of lacking membership in a particualar class. Many, perhaps all, objects can >participate in the abstact relational quality of "not" being a member of some >class. If that's true, then the denotation of "not" is universal and its comprehension is accordingly thin -- nil. Its location is everywhere and its qualities nil. And I think that that might be the right way to look at it. Yet it's a strong, definite word. And if, on the other hand, we made it follow the pattern of the word "probably," then as "improbable chair" means a chair such that the odds are or were against its even existing, so "nottish chair" would mean a nonexistent chair. Now the denotation is zero and the comprehension is that of any contradictory predicate. However, this involves turning adverbs into adjectives rather than treating them as elliptical, and I think that your way makes more sense. "Not" almost means "different (than)." One important difference between them is that "different" is pretty much always used in some respect in which both sides of the difference are positively embodied, while "not" is used in connection even with impossible objects, e.g., "That is not a square triangle." Everything is in that boat, nothing is a square triangle, but that doesn't make everything "different," let alone weird. And "different" applied without qualification usually refers to a contextually understood quality or modification which is denied in regard to the "different" object. >[Jim] And these sorts of abstract relations can be illustrated and pointed to. > What makes "not" and all other abstractions difficult to conceive and >illustrate is that abstractions are not forms or qualities of concrete objects >themselves but are forms of the way in which concrete objects relate to one >another. Logical relationships are abstact properties of the time/space >continuum in which all concrete objects swim. To illustrate them we need to >point to actions (and their consequences) over time and involving more than >one concrete object. That's why math is not for all of us -- me for example. > A symbol that does not perform the iconic and denotative function is like a >gesture without movement -- sound and fury signifying nothing. Again, >myself a good example. Despite what Gary says, I think that this sort of thing was a problem with Awbrey's thinking -- the retreat into abstraction. What mode of representation is 1st-order "not" -- not some higher-order abstract connotation or denotation, of which we can devise manifold versions -- can deal with it in terms of intension, or in terms of extension and classes or model theory and multiple universes. Maybe the quantum Many Worlds Interpretation is true. It is, indeed, saying that all alternatives -- whose structures are the subject matters of deductive mathematical theories of logic, information, and probability -- are in fact embodied across quantum branchings. As with quantum mechanics, one can think about these things like "not" and "probably" and never get over their weirdness and _Twilight Zone_ qualities (though quantum mechanics seems to be a heck of a lot weirder). It seems to me that with "not" we have not so much comprehension or denotation, as a _straightforward generalized manner of alteration (and not mere modification) of comprehension_, and an accordant alteration of denotation. "Not" makes "not blue" out of "blue." The comprehension is flipped, likewise the denotation is shifted from one portion of the universe to the rest of the universe excluding that portion. You're saying that we do not directly witness or represent representational relations, but have to do mockups in terms of comprehension and denotation. We certainly have to give concrete examples, but after a while one grasps words like "if" and "not." I think that we directly and unabstractly represent representational and logical relations with words like "not." Adverbs (though not adverbs of manner) and conjunctions are their most appropriate grammatical form. You have the word "not" denoting everything and therefore comprehending (="connoting" in your sense) nothing; then you shift and have it having qualities and location in abstract, higher-order senses. We can spin some pretty find garb out of qualities and locations for representational relations, which make them more tractable, let us discuss them as objects. But we already see them plain in simple 1st-order words like "not" which, in fact, remain indispensable in all higher-order structures. We still end up talking about "belonging" and "_not_ belonging" to a class, etc. And there's never any getting away from that need for words like "not." So what is this "not," as such, in its first-order sense, which is indeed indispensable at all higher orders or levels? We're not going to build reaction and quality out of "purely" representational relations, but we won't do the opposite either. Now, Peirce actually says that there is a third category, that of representational relations. And it seems to be represented not by a dimension of information like comprehension and denotation, but rather by transformations of information. Symbols like "not" determine the interpretant to perform those transformations. Then it appears that information is conveyed sometimes more efficiently by those transformations than by always "spelling things out," which can't always be done. Something's not blue? I can't even say "it's red or orange or yellow or green or -- purple!" because "or" is another logical-relation word. All I could do is say what color the thing _is_, which will make clear that it isn't blue. I may not know what color it is. The logical-relation words allow tons of useful vagueness. So, those transformations do amount to another element or aspect, if not a dimension (as in the formula "comprehension x denotation = information), of information. We just don't have a name for it. When we isolate it, its bearer, its sign, may look like a mere gesture, but that doesn't mean that it is in fact empty. That it must ultimately be connected to icons & indices doesn't mean that there is no representational mode for it other than comprehension and denotation. In fact icons & indices won't get far without some help from symbols, and it likewise appears that there is a mode of representation which works through transformations of information and which is neither comprehension nor denotation. >[Jim] But most of all -- Thanks for all the interesting observations and >references. Much food for thought in what you've provided. >[Gary] I would tend to agree with this analysis, Jim. I'm trying to remember >if you tried to make it when Jon Awbrey was arguing for "pure symbols" a while >back. This would seem to address that issue rather neatly. Thanks for the food for thought from both of you! Best, Ben --- Message from peirce-l forum to subscriber archive@mail-archive.com
