SOME LATER THOUGHTS ABOUT LOGIC!!
(AN ONGOING DIALOGUE WITH MYSELF-STARTED 7-12-2010)
IT IS TOO BAD THAT CASSIRER DID NOT POSSESS SOME OF THE
QUALITIES OF BERTRAND RUSSELL. RUSSELL’S WRITING WAS
COMPLETELY LUCID WHILE CASSIRER’S WAS “OBLIQUE” IN THE
EXTREME. BRILLIANT BUT OBLIQUE!
CASSIRER EVOLVED HIS NEW CONCEPT: THE MATHEMATICAL
CONCEPT OF FUNCTION, BUT NEVER DEVELOPED IT IN THE EXPLICIT WAY
THAT RUSSELL DID. CASSIRER NEVER SUPPLIED A LOGICAL CALCULUS
FOR HIS IDEA IN THE WAY THAT RUSSELL DID FOR SET THEORY.
CASSIRER ACCEPTED, WITH KANT, THAT THE FUNDAMENTAL
ORGANIZING PRECEPT WAS THE SERIES. AND YET I THINK THAT HIS REAL,
UNEXAMINED FUNDAMENTAL WAS ACTUALLY THE CONTINUUM –WHOSE
“SERIES”, AS WE CAN CLEARLY SEE FROM CANTOR’S WORK, WILL NEVER
GENERATE THE CONTINUUM!
CASSIRER NEVER DEVELOPED A CALCULUS EVEN FOR HIS
“MATHEMATICAL CONCEPT OF FUNCTION” IN ANY MEANINGFULL WAY. I
THINK HIS REAL FUNDAMENTAL WAS CONTINUOUS FUNCTIONS AND (THE)
CALCULUS. APPARENTLY COHEN, HIS TEACHER, HAD SUGGESTED
SOMETHING SIMILAR, BUT I AM UNABLE TO FIND A GOOD REFERENCE,
OTHER THAN A MERE MENTION OF THE FACT.
HOW, IN FACT, COULD CASSIRER’S “MATHEMATICAL CONCEPT(S) OF
FUNCTION”’S INTERACT. WHERE IS THE SUPPORTING CALCULUS? THE
INTERACTION OF MULTI-DIMENSIONAL SURFACES SEEMS TO HAVE A
RELEVANCY, BUT CASSIRER’S CONCEPT ALWAYS REMAINS BOUND IN
“SERIES” –EVEN WITHIN A GIVEN DIMENSION OF ANY SPECIFIC CONCEPT.
THIS IS NOT TO FAULT HIM –HIS WORK IS PROFOUNDLY BRILLIANT
AS I HAVE ACKNOWLEDGED –BUT TO SAY THAT IT IS UNFINISHED!
EXPANDING FROM THE SERIES TO THE CONTINUUM MAY SUPPLY
THE KEYWAY. BUT HOW???? I THINK HIS FUNDAMENTAL INSIGHT
EMBODIES CONTINUOUS FUNTIONS RATHER THAN “FUNCTION” IN ITS
MINIMALIST MEANING, (YEAH YEAH, I’VE HEARD OF THE KOCH
FUNCTION). I THINK CONTINUOUS FUNCTIONS ARE FUNDAMENTAL, AND
AN EXPANSION OF THE CALCULUS IS A PLAUSIBLE BEGINNING. BUT
AGAIN, HOW????
/////NOTE: 1-28-11
THINKING ABOUT THIS PROBLEM! IF LOGIC IS ACTUALLY “BIOLOGIC”, THEN WE GAIN ANOTHER PERSPECTIVE AND ANOTHER LINE OF
EMPIRICAL RESEARCH. I HAVE READ RECENTLY THAT SOMEONE HAS
ACTUALLY STARTED A COMPREHENSIVE PROJECT TO MAP THE TOTAL
NERVE CONNECTIVITY OF THE HUMAN BRAIN, (EXTREMELY DIFFICULT,
BUT NOT IMPOSSIBLE)! SUCH A MAP, ORIENTED IN PHYSICAL SPACE, AND
OVERLAID WITH NEUROCHEMICAL ACTIVITIES, COULD CONCEIVABLY
LEAD TO SUCH A FUNDAMENTAL “CALCULUS” FOR THE BIO-LOGIC! IT
WOULD CONSTITUTE PERHAPS A CRUDE MODEL, (CORRELATING W
WJ.FREEMAN’S), OF WHERE WE NEED TO GO! DOES THIS VIOLATE MY
FUNDAMENTAL PERSPECTIVE? ABSOLUTELY NOT, AS IT LIES WITHIN THE
PHYSICALIST (INTENTIONAL FORM) WHOSE RELATIVISM I HAVE
ALREADY DEALT WITH. THIS IS A PROBLEM REFLECTING “MEANING”SEMANTICS, NOT SYNTAX!
“CHAOS THEORY”, WITH ITS “WELLS OF ATTACTION”, FROM
FUNDAMENTAL GENERATORS, ETC. IS NOT OUT OF THE QUESTION HERE!
–“COMPLEXITY THEORY”?
SIDE THOUGHT: THERE ARE A REALLY GOOD COUPLE OF
SENTENCES I PUT INTO MY MARKETING PACKAGE: “MY ANSWER
INVOLVES A RADICAL REDEFINITION OF PHILOSOPHY ITSELF,
INCORPORATING AN EXTENSION OF ERNST CASSIRER’S THEORY OF
SYMBOLIC FORMS” WHICH SWABEY HAS DESCRIBED AS A GENUINE
EPISTEMOLOGICAL THEORY OF REALITY. IT IS THE ULTIMATE ‘THEORY OF
RELATIVITY’! IT IS THE “THEORY OF RELATIVITY” OF THE MIND! BUT
ACTUALLY IT IS MORE LIKE “GENERAL RELATIVITY” THAN LIKE ‘SPECIAL
RELATIVITY’” AS IT INCORPORATES A NOTION OF THE CURVATURE OF
“THE SPACE” ITSELF.
--> RIEMANIAN GEOMETRY?