List: On Nov 13, 2015, at 8:55 PM, Franklin Ransom wrote:
> [FR] I don't really understand how one can make the claim that the concept of > discrete units is the unstated pre-supposition underlying CSP's graph theory. I suggest you consult an undergraduate text on Graph Theory. It is an abstract mathematical form of the logic of relations that underlies algebra. Each graph node is distinct and carries mathematical information. > But really, what does this all have to do with the relation between > distinctness and information anymore? Frankly, your responses infer that you miss the essential points of the distinctness of discrete mathematics from the continuum, the welding together of a seamless whole such that any mark mars it. In other words, the nature of algebra. I suspect that you will find it necessary to develop new levels of abstraction to make sense out of my posts. I wrote a paper on Algebraic Biology (in Axiomathes) several years ago which may be helpful to you, but I doubt it. If you wish to learn more about these issues, I recommend works on mereology and the philosophy of mathematics, such as: The Applicability of Mathematics in Science (Sorin Bangu) or Mereology and Location (Shieva Kleinschmidt). As well as Category theory. You are, of course, perfectly free to believe whatever you wish. I do not have either the time or interest to attempt to change your belief system. If you are extremely motivated, it may be an interesting journey. At his finest, CSP reaches extra-ordinary levels of abstract that takes years to sort out. At least, that is my experience. As one mathematician noted, "There is no Royal Road to Geometry", you got to figure it out for yourself. Cheers Jerry > Jerry, list, > > Responses interleaved. > > On Fri, Nov 13, 2015 at 4:29 PM, Jerry LR Chandler <[email protected]> > wrote: > Frank, Ben, List: > > > On Nov 11, 2015, at 4:52 PM, Franklin Ransom wrote: > >> This is all to say that I'm not entirely sure what Jerry want to get at >> with talking about "units of measure", and if by that he means something >> other than the information conveyed by signs; and in particular, terms. > > As is often the case, communication between different disciplines often go > awry. In this case, my comments reveal a deep split in the concept of units > (and union of units). I am referring to systems of logical thought and the > symbols that were used by CSP to bridge pragmatism to mathematics. (These > symbols are artifacts of thought.) > > > [FR] What deep split? And which systems of logical thought and symbols used > by CSP to bridge pragmatism to mathematics? > > For the philosophical context of the units, I recommend: > Aristotelian-Thomistic Philosophy of Measure and the International System of > Units (SI): Correlation of International System of Units With the Philosophy > of Aristotle and St. Thomas > by Peter A. Redpath (Author) > > The concept of units of measure is of one of the fundamental concepts of the > natural sciences and related applied mathematical subjects, such as economics. > This topic is of particular concern to CSP philosophy as he spent several > years working on measuring gravitational units and their integration into > physical unit systems in the 1870 - 1880s. The concept of discrete units is > the unstated pre-supposition underlying CSP Graph theory. > > > [FR] I don't really understand how one can make the claim that the concept of > discrete units is the unstated pre-supposition underlying CSP's graph theory. > My understanding is that Peirce is motivated in part by the development of > topology (which has much more to do with continuity), in which metrical > concerns drop out of sight. The graphs take no concern for measurement. I > take it, of course, that by discrete units you mean discrete units of > measurement. As for discrete individuals, of course these are accounted for > in the existential graphs, and there is no reason to claim that the concept > of discrete individuals is an "unstated pre-supposition" of the graphs. > > A unit is a measure of one thing relative to other things. While units have > proper names, systems of units relate these proper names in well-defined ways > such that the calculations are consistent, complete (hopefully) and generate > an exact decision. Very, very often, CSP writes in terms of "units" rather > than in terms of mathematical variables or modern set theory. > > > [FR] I'm not sure where CSP writes in terms of "units." Since the claim is > that they appear "[v]ery, very often," would it be possible to offer textual > support for this claim? > > The basic physical system of units are all related to one another. (Think > metric system) They are: mass, distance, time, temperature, brightness of > light, electricity and mole. Physical calculations are all based on these > units or further definitions of relations among these units. > see: http://physics.nist.gov/cuu/Units/units.html > > The basic logical chemical units are the the individual chemical elements. > All chemical calculations are based on these units. The related chemical > units include molecules, molecular weight, molecular formula, molecular > structure and molecular number. (I introduced the logical term "molecular > number" for the logical operators linking (connecting) atomic numbers, > valence (electricity) and graph theory (mathematics)) > > The basic biological units are individual species and Linnaeus's hierarchy. > > > [FR] I am somewhat confused by whether a unit is some individual or > particular, or something general, a type or kind. Clearly an individual > species will be something general. Are units (of measurement) always types? > And I'm really lost as to how Linnaeus's hierarchy is supposed to be a 'unit > of measurement'. > > In set theory, each element is a unit of a set (except for the empty set ) and > a union of units is a set or class. > That is, a union unites the elements. (Think Venn diagrams.). > The class resulting from the union is a unity. > > Thus, the assertion: > "The union of the units unites the unity" > is a statement about forms of symbolic addition. > > In particular, this assertion applies to arithmetic addition as well as > addition of atoms to beget (emergent) molecules. > > > [FR] The concept of union has a technical meaning in set theory, which is > such that the union of a collection of multiple sets is a set that includes > all of the distinct members of each of the sets of the collection. I don't > think this concept of union fits with the Venn diagram thought. Now, setting > aside the terminological confusion, the assertion "The union of the units > unites the unity," if, as is said, is a statement about forms of symbolic > addition (which I take to include both arithmetic and logical addition, as > well as, it seems, emergent wholes), then I see a couple of problems here, > since set theory has been brought in to support the statement. In set theory, > individuals don't typically get counted over more than once. So if there are > two sets, and the two sets share some members in common, it turns out that > when the sets are united, the result is not an arithmetic addition, but a > logical addition. It is also clear that the addition of atoms in a set do not > result in emergent molecules, because sets don't treat of the idea of > emergence; and in particular, emergent properties. That is, a set does not > have properties that accrue to it due to there being certain members of the > set. One would probably require symbolic or mathematical logic to help along > with understanding how the members are related to each other, and from there > we might possibly start talking about properties due to the atoms being > related to each other in specific ways. In any case, set theory is not enough > to do the work required. > > But these few words are remote from the origin of this thread. > The question of the grammatical relation between "distinction" and > "information" was the motive force that caught my eye. > > In this regard, the name of the unit confers the objective information > content of the unit. > In simple terms, the name of an atom conveys the unit of addition for that > atom. The union of atoms, each with an atomic number, confers the molecular > number by addition of the parts of the whole (mereology). > > Note the profound distinction between the verbs in these two sentences! In > this sense, within the logic of chemistry, "conveys" infers a predicate > relation in contrast to "confers" which infers a copulative relation among > the atoms. > > > [FR] First of all, the issue was not between distinction and information, but > between distinctness and information. Secondly, I'm still not sure what you > mean by "grammatical." Further, given what I have said above about how > problematic the set-theoretical account of the 'union of the units uniting > the unity' is, everything said after "[i]n simple terms" won't make sense. > Actually, what you say is even more confusing, because you then mention > mereology for the union of atoms, but union was defined with respect to set > theory, which in itself contradicts any mereological treatment. Finally, I > don't know why the name of the unit confers the objective information content > of the unit. In CSP's theory of information, it will be the term's > participation in synthetic propositions which confers it information, and not > simply its name. > > But really, what does this all have to do with the relation between > distinctness and information anymore? > > -- Franklin > > -------------------------------------------- > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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