On 9/22/2018 10:59 AM, marty.rob...@neuf.fr wrote:
/It is evident that a possible can determine nothing but a Possible,
it is equally so that a Necessitant can be determined by nothing but
a Necessitant./
Thank you for that reminder (EP 2.481). In an earlier note on
another topic, I discussed Peirce's three universes: possibilities,
actualities, and necessities. That note would have been clearer if
I had remembered to cite EP 2.481, but I forgot.
Although it's slightly off-topic for this note, I'll present a
revised explanation of an issue that is central to Peirce's thought:
1. Pure mathematics is the theory of all possibilities. Every
possibility is a pattern that can be represented by a diagram.
2. Since a necessitant can only be determined by a necessitant,
Every mathematical theorem must begin with a statement that is
necessarily true.
3. In Peirce's existential graphs, truth is represented by a
blank Sheet of Assertion. Every theorem of pure mathematics
begins with the same two steps: (1) By the rule of double
negation, draw a nest of two ovals around a blank area on SA.
(2) by the rule of inserting anything into a negative area,
insert the hypothesis (a possibility represented by a diagram)
into the outer oval (the if-area).
4. By the EG rules of inference, iterate the hypothesis or parts
of it, as needed, into the inner oval (the then-area). Continue
with other EG rules until the inner oval contains the conclusion.
This shows that every necessitant is a theorem of pure mathematics
that has been derived from another necessitant (a blank SA). But
the content of that necessitant includes hypothetical diagrams.
Therefore, pure mathematics is the theory of all possibilities
and necessities. All other sciences (including common sense)
apply diagrams of pure mathematics (pure possibilities) to the
observed patterns (actualities) in their subject matter.
For many practical applications, no pure mathematician had ever
thought about the kinds of diagrams that occur in that subject.
Therefore, scientists and engineers in every field are often
required to do the work of mathematicians in discovering novel
kinds of patterns.
Albert Einstein, for example, had an excellent visual imagination,
which enabled him to invent his famous Gedanken experiments. But
some say that his first wife Mileva was a better mathematician,
and she helped him with the details of the theories. Minkowski
later reinterpreted Einstein's diagrams as abstract 4-D patterns,
which Einstein applied for the general theory of relativity.
In summary, observed patterns of actualities are often the
inspiration. Then imagination elaborates the actual patterns
into a series of abstract possibilities. Pure mathematics
proves theorems about them, and applied mathematics uses those
theorems to explain the actualities and make plans for the future.
For anyone who would like a quick review of Peirce's rules and
proofs in existential graphs, see slides 31 to 41 of
http://jfsowa.com/talks/egintro.pdf
John
-----------------------------
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 .
