List, Catherine: On Mar 3, 2015, at 1:41 PM, Catherine Legg wrote:
> The logical tradition that Peirce was responding to with his piece "Logical > Extension and Comprehension" was basically a 'term logic', according to which > this rough formula held: > > Breadth x Depth = k (where k is some constant) > > > QUESTIONS: In what sense, and to what degree might this 'information' be > measured? (If not in some absolute sense, then perhaps relatively, between > propositions?) Doesn't the very notion of measuring this value conflict with > Peirce's contrite fallibilism, which holds that what a given term will come > to mean to us is not something that can be decided in advance of scientific > inquiry? In other words, scientific terms can hold a great deal of implicit > information as well as the explicit information that scientists are working > with at a given time. > Once again, I offer simple answers from the formal view of logic expressed in chemistry and the perplex number system: Information about a chemical can be expressed in terms of the molecular formula, one of the fundamental principles of chemistry, historically introduced by Lavoisier and Dalton about the turn of the 19 Century, some 60 years before this text was conceived. The molecular formula is the breadth of the material content. It is referenced in the table of elements (TOE) and the perplex numerals (aka the atomic numbers). It specifies what is present and the RELATIVE ratio of the components as a partition of a molecular number as a representation of the thing itself. It is an explicit measure of the logical content of the instance at hand, as determined by physical analysis. The breadth of information in any chemical structure is subject to measurement The molecular formula of individual DNA, RNA and protein molecules are known from physical measurements. Are these sufficient example of breadth of information and its correspondence with qualia? The depth of the information of any member of the TOE or perplex numeral is the implicit in it forms of presentations to the senses. The SAME perplex numeral can be a member of uncountably many different molecular numbers. The SAME chemical symbol can related to several different valence states. The reactivity of each chemical element differs with the context of the immediate surroundings. The changes of attributes of any chemical compound is related to basic physical measures. Many chemical forms same be perceived as solids, liquids or gases - exactly the same matter from the physical components but radically difference human experiences. And, by the way, with different physical attributes. The concept of information as > Breadth x Depth = k (where k is some constant) simply means that for a given the same perplex number (as breadth), the same depth of sorts or kinds of experiences will be experienced as attributes. If the context of the measurements of the depth changes, the depth measurements will change. In simpler terms, if the experiments are reproducible, consistency is to be expected between the the breadth and depth of observation. Thus, the value of each constant is different for each perplex number. In even simpler terms, the unity of nature demands consistency. (This is sharply different from the uniformity of nature.) CSP's use of the notion of multiplication in this context is rather lax, but the ground of meaning for the two semantic terms, breadth and depth, seems rather simple enough. Of course, this interpretation of breadth and depth in terms of perplex number theory is remote from the meaning of the term (Shannon) "Information" in computer sciences (and set theory!). With regard to the distinction between term logic and proposition logic, you note that the meaning of a term must have a definition, that is, a sentence. But, keep in mind the crisp distinction between a philosopher's "predicate" and the copulative forces of a copula. Cheers jerry
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