Dear list:
I thought ‘ergo’ was simply identical with ‘hence’, which is what follows ‘the’ and ‘but’ in the argument CP 5.189. I believe *that* thought is simple and complex enough; for it contains terms, propositions and illation, as well. I see* even* the recognition that arguments may be drawn from persons. Best, Jerry R On Mon, Jun 12, 2017 at 2:00 PM, John F Sowa <s...@bestweb.net> wrote: > On 6/12/2017 11:21 AM, Jerry LR Chandler wrote: > >> Is computation power relevant to semiotics? If so, what are the forms of >> the propositions that transform illations to relations? >> > > As Peirce said, everything is relevant to semiotic. For starters, > read his 1887 article on "Logical machines": > http://history-computer.com/Library/Peirce.pdf > > That article is included as a pioneering work in Marvin Minsky's > bibliography of artificial intelligence. > > Ergo may refer to: >> * A Latin word meaning "therefore" as in Cogito ergo sum. >> * A Greek word έργο meaning "work", used as a prefix ergo- >> > > Peirce learned both Latin and Greek from his father. When he wrote > "ergo" in Latin letters, he meant ergo in Latin. > > There is no need for a transformation: illation *is* a relation > that relates propositions. Today, logicians distinguish two terms: > > 1. Implication is defined *formally* -- i.e., by the form (syntax) of > the propositions. Every rule of inference in Peirce's algebraic > notations of 1870 and 1885 and in the graph notations from 1896 on, > is specified *formally* -- i.e., by the syntactic form of the > propositions. > > 2. Entailment is defined *semantically* -- i.e., by the requirement > that proposition p entails proposition q if and only if q is true > of every case in which p is true. This criterion is independent > of the syntax of the propositions p and q. > > A syntactic rule of inference is *sound* if and only if it preserves > truth -- i.e., implication implies entailment. Every logician from > Aristotle to Peirce to the present has used that criterion to justify > their rules of inference. > > The converse of soundness is completeness: The rules of inference for > a logic are *complete* if and only if every entailment (p entails q) > can be demonstrated by a proof (p implies q). > > For first-order logic, Kurt Gödel (1930) showed that the usual rules > of inference are sound and complete. That is true for Peirce's FOL > rules for both his algebraic notations and his graph notations. > > But in 1931, Gödel proved his famous incompleteness theorem for > higher-order logic (more explicitly, the version in Whitehead & > Russell's _Principia Mathematica_). Gödel showed that there are > infinitely many HOL statements that are true, but not provable. > > Frankly, I feel a deep disconnect is lurking here somewhere. >> > > I hope that the above helps to show the connections. If you want more, > I recommend two kinds of studies: Peirce's sources from Aristotle to > the Scholastics, and Peirce's successors in the 20th and 21st centuries. > > I just noticed that I had replied to one of Gary F's earlier notes > by clicking "Reply" instead of "Reply list". That reply, copied > below, may also be helpful. > > John > ______________________________________________________________________ > > Gary, > > I certainly agree that the world needs more introductory tutorials > about many aspects of Peirce's theories. But different people with > different backgrounds need very different kinds of introductions. > > GF > >> While I can more or less appreciate the qualities of Peirce’s >> post-1906 presentation, I’m not looking for an optimal way of >> proving theorems, or for greater generality in that respect. >> I’m looking for a way of getting across the concepts of >> Firstness, Secondness and Thirdness. >> > > Peirce's logic and his 1-2-3 categories are both important, and there > are relationships between them. But any intro to any subject has to > be tailored to the background and interests of the students. > > Since very few people know anything about Peirce's EGs and very few > know his categories, trying to introduce both in the same lecture is > not likely to be successful. But I have been successful in teaching > EGs with the following slides: http://www.jfsowa.com/talks/egintro.pdf > > Over the years, I have taught beginners and advanced students -- but > at different speeds. The three most advanced groups were Dana Scott > and his logic seminar at CMU, Jon Barwise and his seminar at Indiana, > and John McCarthy and his seminar at Stanford. All three groups knew > logic very well, and I could relate predicate calculus to the material > in egintro.pdf in a one-hour lecture. > > For students with little knowledge of logic, I covered most of that > material in a 3-day short course (about 12 hours of lectures with > lots of questions and discussions). > > For a 5-day short course on "Patterns of Logic and Ontology", see the > outline and URLs below. The students all had a strong background > in computer science and with mixed levels of knowledge of logic and > artificial intelligence. > > The manager of the group (who paid for the course) wanted a tutorial > that covered a broad range of issues -- not just a course on Peirce. > The first lecture (patolog1.pdf) began with a historical intro that > went up to the early 19th c. I introduced Peirce in patolog2.pdf. > I added more as I went along, but it wasn't just a course on Peirce. > > John > ______________________________________________________________________ > > Patterns of Logic and Ontology > Five lectures: > > 1. Patterns of logic and ontology > http://www.jfsowa.com/talks/patolog1.pdf > > 2. Organizing and relating the patterns of logic > http://www.jfsowa.com/talks/patolog2.pdf > > 3. Methods of reasoning > http://www.jfsowa.com/talks/patolog3.pdf > > 4. Patterns of ontology > http://www.jfsowa.com/talks/patolog4.pdf > > 5. Semantics of natural languages > http://www.jfsowa.com/talks/patolog5.pdf > > These are slightly revised versions of the slides presented to the > Knowledge Systems Dept. at Mimos Berhad in Malaysia in March 2013. > > Morning sessions consisted of lectures based on these slides. > The afternoons were devoted to questions and discussions on > related issues concerning projects at Mimos Berhad. > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to > peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L > but to l...@list.iupui.edu 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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