Jim, list, Ben wrote: (Beginning with a quote from my earlier remarks)
>>>[Jim] 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". >>[Ben] 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." >[Jim] Well, here we differ. I maintain that it is extremely important to >keep in mind the conceptual distinction between Peircean firstness (quality or >form) and secondness (reaction or inertia). I further believe that all those >aspects of an object which we refer to as its qualities are a manifestation of >the object's form which in turn I believe is equivalent to the object's >organization in space and time. In turn I contend that an object's inertia >mass or resistance to movement is in effect a matter of its location in space >and time. The idea of a thing's relative spatiotemporal location's giving it its inertial and gravitational properties was proposed by Mach in physics but has not won general acceptance. >[Jim] I think this analogy works both figuratively and literally. But apart >from whether one accepts this physical analogy there remains a concpetual >distinction between form and location which I think you have conflated in your >example above. In your example of "pointing out" an objects form musically >or spatially what you have illustrated in not form per se but the location of >an object whose form you wish to highlight. One locates an object that has >form but form itself can not be pointed to as having a specific location >because form is a matter of organziation not merely location. .... This sounds like you're talking not about pointing out a form, pointing out its various parts, but about pointing out the _idea_ of form, or pointing out an idealized abstracted form in the sense of its not having a singular location. Now if somebody doesn't get that I'm pointing at the quality rather than the thing, then it may be a challenge to get the idea across, and other blue things may be helpful. If I want to point out the form as a separable idea, then icons are a good way to go too. But I may be concerned to point the form out but not as either an individual thing or as a qualitative appearance. Now, whether the setting is in a specific concrete place or in a vague "somewhere" or a general "anywhere," once you're there, the form consists in the relationality among the locations, to which you can point and, more importantly, which point to one another, and the form is the very balance holding among those mutual pointings-at. From among hundreds of stars you point out seven bright ones to somebody, and have thereby pointed out the constellation which they make, and they point at one another in such a way as to make it easier for the observer to pick them out. Insofar as the form consists in mutual pointings, it shouldn't be considered a quality like "blue." The main difference between a structure of force and movement, and an unbalanced force or movement, is just that -- balance & imbalance. Force and momentum are *distance* quantities (in a sense that mass, energy, and power are not), and are alliances of magnitude with *direction*, and, when various forces or motions are opposite to one another, and to the extent that they're collectively balanced, they make a structure, with aspects positional, kinetic, static, dyanamic. A structure is essentially an arrangement of forces or motions which are balanced, stably or unstably, such that any unbalanced portion of the force or motion is attributed to the force or motion of the observed system as a whole with respect to an observer at rest. Differently moving observers will therefore "divide" external motion (potential & actual) from internal motion (potential or actual) differently! So as different as they are by being internal and external, inside and outside, these things are the same thing in complementary modes, each is the other "inside out." The form may be abstracted unto diagramhood, where the parts are denoting each other. That's beyond concerns with quality of appearance or with location with respect to the observer. >[Jim] .... Form refers to the relative location of parts of whole not to the >overall location of the whole itself. Conversely location is not a matter of >form because location can have a unique center of gravity or focus which can >be pointed to or denoted. Note that Peirce treats indexicality in terms primarily, not of location or vicinity per se, but rather of reaction and resistance, which do seem more basic in the Peircean system. A form is a set of locations, pointing at each other. If you consider the inside apart from the outside, then you leave the larger concrete world out of it, which is really to leave yourself out of it, since all locatings in the larger world are by reference to yourself, and certainly not with regard to any ultimate frame of reference or ultimate shape of the concrete world, which are things that we know next to nothing about. So the mutual pointings of the parts of the form are still there, and they compel your attention, but you've left out their reference _to_ you in _your_ specific location in the world. This lets you impersonalize and abstract the form. It still has its center of focus, and the solar system has its center of gravity whether it's wheeling around the galaxy or adrift in one of the great voids. I think that with this discussion of centers of gravity you're really dealing with a separate issue, that of how one speaks of the precise location of an extended object, as well as deciding what really orbits what, which are issues exactly alike for an extended part as located relative to its a particular whole and for a system located in the larger concrete world. Anyway the form is still a structure of mutually opposed "indices," forces, motions potential & actual. Form is not a quality. A form may be abstracted for its appearance, but it may also be abstracted for the capacity of its parts to represent one another -- denote one another, map to one another. That's what a mathematical diagram is about. It doesn't need even to be visual. It could consist in a formula or array of algebraic symbols. > On the other hand, the essence of form can not be captured by mere denotation > and must instead be conveyed or refered to by connotation, implication or > illustration. One can of cource say an object with the form I wish to convey > is located there and thus denote a particular form in that sense. But > denoting is not connoting. Indexes denote, icons connote. The crux of > denoting is to locate an object (of whatever form) in space and time. The > crux of iconizing is to present the form of an object regardless of where it > might be located in space or time. It is generally agreed that in everyday > experience different objects may have the same form but can not have the same > location and that the same object can have different locations. But there is > less agreement as to whether or not an object can change its form and remain > essentially the same object. All of which is to argue that form and location > are conceptually distinct notions which can be used to cross reference one > another but ought not be conflated in ones thinking Illustration comes closest. Insofar as we're talking about visually apparent form, illustration is the way. But the essence of form is its parts indicating one another, moving into one another, etc., etc., like remappings of denotation, alterations -- (re)amassings, (re)sequencings, (re)sortings, (re)rankings, of subject(s). And in fact pure maths tend to be about remappings of objects, -- operations, functions, not to mention antiderivatives and equations like "x^2 + y^2 = 1". These mappings and remappings and transformations are not merely a way of getting at alterations of comprehension as in deductive math theories of logic, information, probability -- instead they are the focus of interest. Instead of apportioning a universe or total population among predicates, we're building up structures from subjects as generic units or as sheer continuous "stuff" (if I understand correctly what category theory has enabled). Instead of dividing up an ultimate quasi-solipsistic unity, we build up and down infinitely from units (or "stuffs") such that there's "always more." The crux of it is that there's more going on that comprehending and denoting. There are (a) transformations of denotation and (b) transformations of comprehension, which correspond roughly to (a) formal semantic concerns and (b) syntactical concerns, and more generally to (a) pure maths and (b) deductive maths of totalities, propositions, predicates. They abstract away from the idiosyncratic contents of the concrete world and of positive phenomena in general. They get very abstract but we find their seeds and young buds in ordinary language and experience. Now, in terms of signs, the unbalanced force acting brutely against resistance or unto reaction is taken as a primary case of the indexical. The structure is that which we take as the case of the mathematical diagram, which can count as, and "act on behalf of," its object(s) for experiential, decisional, etc. purposes. Yet these poles of correlations can reverse. Dynamic and mechanical forces & motions are considered the pre-eminently mathematical phenomenon in the concrete world. Experience, for its part, is not a "force" but an undergoing and bearing up under forces and it registers them. It's an accreted, evolved, and heavily dented and pockmarked structure, one heck of a record. Experience is associated with both trial and confirmation, both force and structure. These inversions of internal & external happen, as with rest mass and linear energy. The difference is that rest mass is invariant for variously moving observers, but not so the "internal" structure or its quantity. Variously moving observers will attribute different amounts and proportions of motion to the internal and external motions of a system, and the internal, "structural" share is not Lorenz-covariant or even vector-additive (unless you just vector-sum it to zero but that would be like calculating rest energy as if it were linear energy and of course getting zero, and anyway simply veils possible differences in the motion that's in there). The external motion is actually mathematics-friendlier & theory-friendlier than the motions potential & actual comprising the structure. I wish that I could say whether, when Merleau-Ponty was discussing reversibility, he would have included these kinds of inversions and inside-outs, but I don't know. Peirceans regard the mathematical diagram as an icon, yet the diagram may appear rather different than its object(s), which are general and may indeed, as generals, have no appearance of their own at all! How does one have an icon of something that has no appearance? I guess, the same way one has a "replica" of a symbol which has no appearance of its own. But this makes clear that, when Peirce calls something a "semblance," he does not necessarily mean anything sensory at all. Or does it? He speaks of quality as quality of feeling, and defines the icon in terms of its having the quality of the object. I think that there is a conflation of sensory semblance with any sort of equivalence and that it just leads to over-knitted confusion. A geometrical diagram, in its visual appearance, could be a qualisign, but if its object is a mathematical object, then its object has no real sensory appearance at all. So I would not call a geometrical diagram of a mathematical object an icon. Appearances, that is, appearances qua surfaces of hidden but explorable depths, are samples, tastes of things not summoned up by our construction of diagrams according to precepts and which call for ampliative induction. Such appearances are of more intrinsic interest to statistics and cenoscopy than to mathematics. But I would add the case of a singular object, in which the properties of a general which would be embodied by the object are what's in question -- e.g., a mathematical diagram could be reasonably considered, I think, to represent a concrete singular system in respect of its given mathematical properties when the system's possession of those properties is not in question; and a lawyer may act as proxy for his client as long as he does it representatively of his client's legal interests. There's a bit of fiction in such things, just as in all hypothetical things in general; the "would-be" orientation traditionally attributed to the icon comes pretty much from the classification of the mathematical diagram as an icon. As actual semblance, the natural icon does statistically suggest repetition of the appearance. Natural icons are about what appears to be, as opposed to what conditionally would have to be. In fact, part of the value of the diagram is to bridge enormous differences of appearance (which is why it helps statistics -- bringing surface resemblanes from different modalities to light) -- that's what math does, transforms while maintaining equivalences -- imagination is not about outward semblances but about transformations, metamorphoses. Sensory and intuitive faculties are about outward appearances and semblances. A diagram may be geometrical or may consist, for instance, in a formula or an array of algebraic symbols, whose behavior under transformations is observed. (See Peirce quotes CP Vol. 3, para.364, CP Vol. 2, par. 216, CP Vol. 3, par. 778, lower down at http://www.people.ex.ac.uk/PErnest/pome10/art4.htm ) It is constructed according to a general precept in order to show intelligible relations. In fact, insofar as the diagram is to represent generals which have no real appearance, and insofar as it is defined as being constructed according to a precept which enables and binds it to act legitimately and correctly "on behalf of" its object in response to change, and to do all this under observation, it already has its definition as something other than index, semblance, or symbol. It's defined by the legitimacy and recognition which it would deserve from an observer collaterally observing its object. >>[Ben] 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] Yes, this is true. but I don't think is contrary to what I'm saying >above. It wasn't meant to be contrary, but rather for a different emphasis. >[Jim] Thanks for your comments -- I look forward to more. Best wishes as >always, Yeah, but how MUCH more? I'm all tuckered out. I always do this to myself. Best wishes! Best, Ben --- Message from peirce-l forum to subscriber archive@mail-archive.com
