Gary, list, I pasted below my post Gary's post from [PEIRCE-L] Re: [biosemiotics:5398] Re: What kind of sign is a "gene"? to show to what I'm responding, separating out this discussion from a discussion of Ch. 5 of Kees's book that we were having that is no longer relevant to Kees's book and from the discussion of Peirce's theory of information in respect to the question "What kind of sign is a 'gene'?", which question is not of particular interest to myself.
Gary, you mention that: "In the logic of relations (as opposed to the more traditional syllogistic logic), the *predicate* of a proposition provides any depth it has, by *signifying* (iconically or symbolically) the recognizable *form* which is shared by object and sign, and conveyed to the interpretant by the act of recognition or the event of interpretation. The *subject* of the proposition *denotes* (indexically) its object, and thus the indexical relation provides the proposition with its breadth." In the earlier work found in the Harvard lectures of 1865, and later the paper "Upon Logical Comprehension and Extension", we don't find the logic of relations. At least, not that I know of? Would you please offer me some references to Peirce's discussion of the logic of relations with respect to the theory of information? It's not that I doubt you; certainly it sounds right. I'm just embarrassed to admit that I don't have as much familiarity with Peirce's work on the logic of relations, so I would love to find out where I could read him discussing these topics together, if you happen to have any ready-to-mind references. Also, you said "by *signifying* (iconically or symbolically) the recognizable *form* which is shared by object and sign". Might you be able to elaborate a little on why you said iconically *or* symbolically? Is there a difference in the way that a proposition is interpreted, whether the predicate informs the proposition iconically or symbolically? Or if you believe this makes a difference in the depth of the proposition? -- Franklin Lists, Continuing my earlier post to the biosemiotics list, here's a very condensed summary of the semiotic ideas I consider most relevant to the question in the subject line. The kind of sign that is complete enough to convey *information* is traditionally called a *proposition*. A verbal proposition is a symbol, and pieces of it (such as words) are traditionally also called "symbols." But it conveys information by combining an *indexical* sign with an *iconic* one, and it's the *combination* of those two functions, rather than the symbolic function, that enables the sign to convey information about its object to its interpretant. Peirce defines information as the logical product of two quantities traditionally called "breadth" and "depth". [[ ... logicians have recognized since Abélard's day and earlier that there is one thing which any sign, external or internal, stands for, and another thing which it signifies; its denoted breadth, its "connoted" depth. They have further generally held, in regard to the most important signs, that the depth, or signification, is intrinsic, the breadth extrinsic (CP 8.119). ]] Breadth is *extrinsic* because it refers to the object, which is necessarily *other* than the sign and related to it *indexically*. Depth is *intrinsic* because it refers to the (more or less specific) *form* of the sign itself, which is related *iconically* to the object and to the interpretant determined (and thus *informed*) by the sign. In the logic of relations (as opposed to the more traditional syllogistic logic), the*predicate* of a proposition provides any depth it has, by *signifying* (iconically or symbolically) the recognizable *form* which is shared by object and sign, and conveyed to the interpretant by the act of recognition or the event of interpretation. The *subject* of the proposition *denotes* (indexically) its object, and thus the indexical relation provides the proposition with its breadth. *Information* increases when the breadth is increased, when we learn that a known form actually applies to an *object* that we didn't already know it applied to. Information also increases when depth is increased, when the *form* applied to a known object is specified or determined more fully than it was before. A sign must have *some* breath *and* depth in order to represent a *fact*. [[ What we call a "fact" is something having the structure of a proposition, but supposed to be an element of the very universe itself. The purpose of every sign is to express "fact," and *by being joined with other signs*, to approach as nearly as possible to determining an interpretant which would be the *perfect Truth*, the absolute Truth, and as such (at least, we may use this language) would be the very Universe (EP2:304; italics Peirce's, bold mine). ]] Now here's where MS 7 comes in -- http://www.cspeirce.com/menu/library/bycsp/ms7/ms7gf.htm -- because it helps to remind us that both a sign and its object can have any degree of complexity, right up to the complexity of the Universe itself. This complexity can be regarded either analytically or synthetically, in the case of an informative proposition, *or any sign sufficiently complete to convey information*. If the sign we're talking about is the genome, it should be obvious that both the sign and its object are very complex indeed. I'll finish this (for now) by quoting some of the most relevant statements about this from MS 7, and invite you to apply these*to the genome and its object*. I think this is likely to increase the depth of our concepts of both *sign* and *object*, and elucidate the relations between them. Secondly, a sign may be complex; and the parts of a sign, though they are signs, may not possess all the essential characters of a more complete sign. Thirdly, a sign sufficiently complete must be capable of determining an *interpretant* sign, and must be capable of ultimately producing real results. For a proposition of metaphysics which could never contribute to the determination of conduct would be meaningless jargon. On the other hand, the cards which, slipped into a Jacquard loom, cause appropriate figures to be woven, may very properly be called signs although there is no conscious interpretation of them. If not, it can only be because they are not interpreted by signs. ... Fourthly, a sign sufficiently complete must in some sense correspond to a real object. ... like all other signs sufficiently complete, there is a single definite object to which it must refer; namely, to the 'Truth,' or the Absolute, or the entire Universe of real being. *Sixthly*, a sign may refer, in addition, and specially, to any number of parts of that universe. *Seventhly*, every interpretant of a sign need not refer to all the real objects to which the sign itself refers, but must, at least, refer to the Truth.*Eighthly*, an interpretant may refer to an object of its sign in an *indefinite* manner. ... Tenthly, a sign sufficiently complete must signify some quality; and it is no more important to recognize that the real object to which a sign refers is not a mere sign than to recognize that the quality it signifies is not a mere sign. [gf note: This "quality" is what I referred to earlier as the "form" (in *information*).] Since this semiotic analysis was made by Peirce in relation to "the foundations of mathematics," we might expect some problems in applying it to the genome, to its object, and to its interpretation by the internal dynamics of the organism. But I think it's general enough to apply to them too, and I'd be happy to address any of the problems that readers would like to pose. gary f.
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