Gary F and Frederik, How about what I call the Hofstadter cubes (see the picture attached) as the decent indexical legisign standing for the concept of Complementarity ?
N. Bohr never gave any rigorous definition of the concept of
complementarity that he introduced to physics and philosophy in the early
decades of the 20th century. In 1995 [1, p. 524] I defined
complementarity in terms of three logical criteria:
(1) EXCLUSIVITY: A and B are mutually exclusive (.e., wave and particle)>
(2) ESSENTIALITY: A and B are essential to completely describe C (e.g.,
wave an particle properties of light).
(3) TRANSCENDENTALITY: C transcends the level where A and B have meanings
and yet serves as the source of A and B.
Evidently, the Hofstadter cubes embody all these three criteria, as
indicated the letters and other sybmols in the figure. The cubes
symbolizing C transcends the three orthogonal planes on which A and B
reside, since the cubes are hanging in a 3-dimensional space while A and B
reside on 2-dimensional palnes.
The figure also illustrates two kinds of complementarities C and C, the
former being 3-dimensional and the latter 2-dimensional. The difference
is that C are in the same planes as A and B so that they can be combined
mathematically, as exemplified by the de Broglie equation shown in the
bottom of the figure. In contrast, C is in a different space than A and B
and hence cannot be mathematically combined.
Many physicists and philosophers of science may believe that light (C) is
both wave and particle simultaneously because they appear together in a
mathematical equation, i.e., C. But, as the Hofstadter cubes clearly
demonstrate, C and C are not identical and hence light cannot be equated
with the combination of wave and particle, as Einstein, de Broglie, Bohm
and his followers believe. They in effect may be conflating C and C'.
For convenience, the two kinds of complementarities illustrated by the
Hofstadter cubes, may be called the 2-D complementarity and 3-D
complementarity. Most complementarity pairs written about in numerous
books and articles belong to the class of 2-D complementarity, and
discussions on 3-D complementary pairs seem rare.
With all the best.
Sung
___________________________________________________
Sungchul Ji, Ph.D.
Associate Professor of Pharmacology and Toxicology
Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University
Piscataway, N.J. 08855
732-445-4701
www.conformon.net
Reference:
[1] Ji, S. (1995). Complementarism: A Biology-Based Philosophical
Framework to Integrate Western Science and Eastern Tao, in
Psychotherapy East and West: Integration of Psychotherapies, Korean
Academy of Psychotherapists, 178-23 Sungbuk-dong, Songbuk-ku, Seoul
136-020, Korea, pp. 517-548. PDF available at
http://www.conformon.net under Publications > Proceedings and
Abstract.
> In Section 12 of Chapter 3, the discussion moves to the three types of
> Dicisigns listed in Peirce's "Nomenclature and Divisions of Triadic
> Relations", EP2:289-99.
>
>
>
> The main difficulty here, as Frederik points out, is that Peirce's
> examples
> of the Dicent Indexical Legisign given on EP2:297 "seem strangely wanting
> and peripheral" (NP, p. 95) - especially the "street-cry", a very vague
> designation. Here's the passage in question, where Peirce is enumerating
> varieties of Dicent Sinsign. After giving the usual weathercock as an
> example of the first variety, he says:
>
>
>
> "A second variety is a Replica of a Dicent Indexical Legisign. Thus any
> given street cry, since its tone and theme identifies the individual, is
> not
> a symbol, but an Indexical Legisign; and any individual instance of it is
> a
> Replica of it which is a Dicent Sinsign. A third variety is a Replica of a
> Proposition. A fourth variety is a Replica of an Argument. Beside the
> normal
> variety of the Dicent Indexical Legisign, of which a street cry is an
> example, there is a second variety, which is that sort of proposition
> which
> has the name of a well-known individual as its predicate; as if one is
> asked, "Whose statue is this?" the answer may be, "It is Farragut." The
> meaning of this answer is a Dicent Indexical Legisign."
>
>
>
> Notice that it's the meaning of this answer, and not the sentence
> expressing
> it, which is the Dicent Indexical Legisign. As for the "street cry", this
> makes sense to me if I apply it to the cry of a vendor in the street, such
> as the newsboy shouting "Extra! Extra!" (back when newspapers used to
> print
> "extra" editions), or the vendor in a stadium yelling "Peanuts! Popcorn!"
> or
> whatever. Here the object of the sign is clearly not the individual vendor
> but the individual item he's selling. The generic "cry" is a Legisign, but
> any instance of it is an index (involving an icon) of the item, and thus
> can
> be true or false, depending on whether it corresponds with the stylized
> description of it embedded in the "cry".
>
>
>
> Anyway, when we get down to such a fine-grained level of analysis, the
> bottom line is given by Peirce at the end of that same paragraph, thus:
>
> "It is a nice problem to say to what class a given sign belongs; since all
> the circumstances of the case have to be considered. But it is seldom
> requisite to be very accurate; for if one does not locate the sign
> precisely, one will easily come near enough to its character for any
> ordinary purpose of logic."
>
>
>
> So I'm content to leave it there. Though as always, questions on this
> section are welcome.
>
>
>
> gary f.
>
>
Sungchul Ji, Ph.D.
Associate Professor of Pharmacology and Toxicology
Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University
Piscataway, N.J. 08855
732-445-4701
www.conformon.net
Hofstadter_cubes.pdf
Description: Adobe PDF document
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