Jon, Jeff, All, JAS: After all, *"when we have carried analysis so far as to leave only a continuous predicate, we have carried it to its ultimate elements"* (SS 72, 1908 Dec 14). Accordingly, my analysis of an EG is that *the names and lines are subjects, respectively denoting abstract general concepts and concrete indefinite individuals*, while *the syntax of their attachments signifies the pure/continuous predicate*.[emphasis added: GR]
GR: I obviously agree. Best. Gary R "Time is not a renewable resource." gnox *Gary Richmond* *Philosophy and Critical Thinking* *Communication Studies* *LaGuardia College of the City University of New York* <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail> Virus-free. www.avg.com <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail> <#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2> On Wed, Aug 5, 2020 at 8:56 PM Jon Alan Schmidt <[email protected]> wrote: > Jeff, All: > > JD: As far as I can see, the scroll is a special kind of iconic sign > because it expresses the continuity in the relationship between antecedent > and consequent of the conditional, and this mirrors the continuity in the > relationship between premisses and conclusions in an argument. > > > I agree; in fact, it expresses and mirrors not just the *continuity* of > that relationship, but also its *asymmetry*. All semeiosis is > inferential process, a continuous hyperbolic sequence that always and only > has one direction--from premiss to conclusion, from antecedent to > consequent, from object to interpretant. > > I am in general agreement with your other comments, as well. In > particular, my interests here are primarily philosophical--as the subject > line reflects--which is why I keep insisting on the derivative nature of > negation while recognizing that treating it as a primitive does not > necessarily affect the *appearance *of the resulting EGs. As I just > noted in my other post, it does make an important difference in the > *interpretation > *of those EGs, which is why I believe that we should follow Peirce's > advice to add a small darkened circle to a shaded area when it is intended > to represent negation rather than the antecedent of a consequence. > > Another potential difference in interpretation is where we choose to draw > the line between the subjects and predicate of a proposition. I take > Peirce seriously when he states that "the proper way in logic is to take as > the subject whatever there is of which sufficient knowledge cannot be > conveyed in the proposition itself, but collateral experience on the part > of its interpreter is requisite ... leaving the *pure *predicate a mere > form of connection" (NEM 3:885, 1908 Dec 5). After all, "when we have > carried analysis so far as to leave only a continuous predicate, we have > carried it to its ultimate elements" (SS 72, 1908 Dec 14). Accordingly, my > analysis of an EG is that the names and lines are subjects, respectively > denoting abstract general concepts and concrete indefinite individuals, > while the syntax of their attachments signifies the pure/continuous > predicate. > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Structural Engineer, Synechist Philosopher, Lutheran Christian > www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt > > On Tue, Aug 4, 2020 at 10:17 PM Jeffrey Brian Downard < > [email protected]> wrote: > >> Jon Schmidt, John Sowa, List, >> >> It might be helpful to make a clearer distinction between what is >> advantageous for the purposes of developing the EGs as a formal system of >> mathematical logic and what is advantageous for the purposes of developing >> theories of philosophical logic. >> >> For the sake of illustrating the importance of the distinction, let me >> take up the following assertion >> >> Jon Schmidt: "Hence I continue to maintain that the cut for negation >> must be *derived *from the scroll for consequence with a blackened inner >> close, rather than treated as a primitive, even when shading is employed >> instead." >> >> For the purposes of developing systems of mathematical logic, the >> logician can adopt various starting points in setting up the logical >> grammar for a given system. In symbolic systems, the rules determine what >> does and does not count as a well-formed-formula. The same holds in the >> case of the EGs. The grammatical rules determine what counts as a >> well-formed-graph. >> >> Given all the work he has done on the symbolic systems of logic, Peirce >> sees that there are a number of different ways of setting up the >> grammatical rules that will, when taken together with the rules of >> inference and transformation, yield consistent results. For the sake of the >> EGs considered as a formal system, the scroll and two nested circles are >> logically equivalent. What is more, it makes no difference for the beta >> graphs whether the scroll (used to represent the conditional) or a shaded >> area >> within a boundary (used to represent negation) is taken as "primitive" in >> one sense or another. >> >> Having said that, I do think there is a special philosophical >> significance that Peirce attaches to the scroll as a representation of the >> conditional. I do not think that it is mere artifact of his early >> explorations of the graphs. As Peirce points out, the graphs can be used to >> express any sort of proposition. As such, they can be put to use in >> philosophical inquiry for the sake of analyzing the logical relationships >> between any set of premisses and conclusions. >> >> For the sake of giving a deeper philosophical analysis of the different >> classes of arguments we need to apply the EGs to the problem of analyzing >> synthetic forms of inference. In doing so, it will be helpful to have a >> variety of different icons that can be used to study the grounds of the >> validity of inductive and abductive inference. (MS 296, 499) >> >> As far as I can see, the scroll is a special kind of iconic sign because >> it expresses the continuity in the relationship between antecedent and >> consequent of the conditional, and this mirrors the continuity in the >> relationship between premisses and conclusions in an argument. In the case >> of inductive and abductive inferences, the conditionals may take a variety >> of forms: epistemic, alethetic, deontic, etc. In each of these cases, the >> topological character of the relations may vary. >> >> Based on my own inquiries using the graphs to analyze these forms of >> inference, thinking about the relationship between the scroll and the >> shaded area representing negation has been a fruitful endeavor. It is >> possible that it has been fruitful given the fact that I am still at an >> early point in my application of the graphs to these problems of critical >> logic. >> >> Yours, >> >> Jeff >> Jeffrey Downard >> Associate Professor >> Department of Philosophy >> Northern Arizona University >> (o) 928 523-8354 >> >>> <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail> Virus-free. www.avg.com <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail> <#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>
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