[Third of a Series]:
The F.E.D. "Meta-Leibnizian Proposition" --
Dear Reader,
In 1666, while Isaac Newton was progressing rapidly toward his discovery/invention of the differential [and integral] calculus, Gottfried Wilhelm Leibniz, the later co-discoverer of that calculus, was progressing too, but on a different project, a project to derive a different "calculus": the project of discovering/inventing the [Latin name] <<Characteristica Universalis>> -- the universal language for the <<Mathesis Universalis>>, the "Universal Subject-Matter", "Universal Knowledge", or "Universal Science", which Descartes, Leibniz, and others had long been seeking to discover.
By <<Characteristica Universalis>> Leibniz meant a "universal character-language", i.e., a "universally-applicable algebra" -- a mathematical -- ideographical -- language that would use "characters" -- e.g., "letters" of the alphabet, as does ordinary algebra -- to represent its quarry -- its unknowns -- as well as, perhaps, it knowns, a "quarry" which would not be limited to "quantities", as with ordinary algebra, but that would include qualitative unknowns -- sought-after but not-yet-discovered philosophical and scientific concepts, or categories, whose discovery would thereby be facilitated, via [qualo-quantitative] calculation.
This <<Characteristica Universalis>> would thus be a language for discovery of new results, as well as being a language for presentation of those results.
Below are some quotes from the wikipedia article on Leibniz's <<Characteristica Universalis>> quest that may serve to further familiarize readers previously unfamiliar with this saga.
For more about this saga, see --
http://en.wikipedia.org/wiki/Mathesis_universalis
http://en.wikipedia.org/wiki/Characteristica_universalis
Selected familiarizing quotes [some italic and underline emphasis added by M.D.] --
"A universal language of science
Leibniz said that his goal was an alphabet of human thought, a universal symbolic language (characteristic) for science, mathematics and metaphysics.
According to Couturat, "In May 1676, he once again identified the universal language with the characteristic and dreamed of a language that would also be a calculus—a sort of algebra of thought." (1901, chp 3.).
This characteristic was a universalisation of the various "real characteristics".
Couturat wrote that Leibniz gave Egyptian and Chinese hieroglyphics and chemical signs as examples of real characteristics writing:
This shows that the real characteristic was for him an ideography, that is, a system of signs that directly represent things (or, rather, ideas) and not words, in such a way that each nation could read them and translate them into its own language."
The F.E.D. "Meta-Leibnizian Proposition" --
Dear Reader,
In 1666, while Isaac Newton was progressing rapidly toward his discovery/invention of the differential [and integral] calculus, Gottfried Wilhelm Leibniz, the later co-discoverer of that calculus, was progressing too, but on a different project, a project to derive a different "calculus": the project of discovering/inventing the [Latin name] <<Characteristica Universalis>> -- the universal language for the <<Mathesis Universalis>>, the "Universal Subject-Matter", "Universal Knowledge", or "Universal Science", which Descartes, Leibniz, and others had long been seeking to discover.
By <<Characteristica Universalis>> Leibniz meant a "universal character-language", i.e., a "universally-applicable algebra" -- a mathematical -- ideographical -- language that would use "characters" -- e.g., "letters" of the alphabet, as does ordinary algebra -- to represent its quarry -- its unknowns -- as well as, perhaps, it knowns, a "quarry" which would not be limited to "quantities", as with ordinary algebra, but that would include qualitative unknowns -- sought-after but not-yet-discovered philosophical and scientific concepts, or categories, whose discovery would thereby be facilitated, via [qualo-quantitative] calculation.
This <<Characteristica Universalis>> would thus be a language for discovery of new results, as well as being a language for presentation of those results.
Below are some quotes from the wikipedia article on Leibniz's <<Characteristica Universalis>> quest that may serve to further familiarize readers previously unfamiliar with this saga.
For more about this saga, see --
http://en.wikipedia.org/wiki/Mathesis_universalis
http://en.wikipedia.org/wiki/Characteristica_universalis
Selected familiarizing quotes [some italic and underline emphasis added by M.D.] --
"A universal language of science
Leibniz said that his goal was an alphabet of human thought, a universal symbolic language (characteristic) for science, mathematics and metaphysics.
According to Couturat, "In May 1676, he once again identified the universal language with the characteristic and dreamed of a language that would also be a calculus—a sort of algebra of thought." (1901, chp 3.).
This characteristic was a universalisation of the various "real characteristics".
Couturat wrote that Leibniz gave Egyptian and Chinese hieroglyphics and chemical signs as examples of real characteristics writing:
This shows that the real characteristic was for him an ideography, that is, a system of signs that directly represent things (or, rather, ideas) and not words, in such a way that each nation could read them and translate them into its own language."
"Others, such as Jaenecke, for example, have observed that Leibniz also had other intentions for the characteristica universalis, and these aspects appear to be a source of the aforementioned vagueness and inconsistency in modern interpretations. According to Jaenecke,
"the Leibniz project is not a matter of logic but rather one of knowledge representation, a field largely unexploited in today's logic-oriented epistemology and philosophy of science.
It is precisely this one-sided orientation of these disciplines, which is responsible for the distorted picture of Leibniz's work found in the literature."
As Couturat wrote, Leibniz criticized the linguistic systems of George Dalgarno and John Wilkins for this reason since they focused on --
...practical uses rather than scientific utility, that is, for being chiefly artificial languages intended for international communication and not philosophical languages that would express the logical relations of concepts.
He favors, and opposes to them, the true "real characteristic," which would express the composition of concepts by the combination of signs representing their simple elements, such that the correspondence between composite ideas and their symbols would be natural and no longer conventional."
"In the domain of science, Leibniz aimed for his characteristica . . . depicting any system at any scale, and understood by all regardless of native language. Leibniz wrote:
"And although learned men have long since thought of some kind of language or universal characteristic by which all concepts and things can be put into beautiful order, and with whose help different nations might communicate their thoughts and each read in his own language what another has written in his, yet no one has attempted a language or characteristic which includes at once both the arts of discovery and judgement, that is, one whose signs and characters serve the same purpose that arithmetical signs serve for numbers, and algebraic signs for quantities taken abstractly.
Yet it does seem that since God has bestowed these two sciences on mankind, he has sought to notify us that a far greater secret lies hidden in our understanding, of which these are but the shadows.""
"Leibniz talked about his dream of a universal scientific language at the very dawn of his career, as follows:
He favors, and opposes to them, the true "real characteristic," which would express the composition of concepts by the combination of signs representing their simple elements, such that the correspondence between composite ideas and their symbols would be natural and no longer conventional."
"In the domain of science, Leibniz aimed for his characteristica . . . depicting any system at any scale, and understood by all regardless of native language. Leibniz wrote:
"And although learned men have long since thought of some kind of language or universal characteristic by which all concepts and things can be put into beautiful order, and with whose help different nations might communicate their thoughts and each read in his own language what another has written in his, yet no one has attempted a language or characteristic which includes at once both the arts of discovery and judgement, that is, one whose signs and characters serve the same purpose that arithmetical signs serve for numbers, and algebraic signs for quantities taken abstractly.
Yet it does seem that since God has bestowed these two sciences on mankind, he has sought to notify us that a far greater secret lies hidden in our understanding, of which these are but the shadows.""
"Leibniz talked about his dream of a universal scientific language at the very dawn of his career, as follows:
"We have spoken of the art of complication of the sciences, i.e., of inventive logic... But when the tables of categories of our art of complication have been formed, something greater will emerge. For let the first terms, of the combination of which all others consist, be designated by signs; these signs will be a kind of alphabet. It will be convenient for the signs to be as natural as possible . . .. If these are correctly and ingeniously established, this universal writing will be as easy as it is common, and will be capable of being read without any dictionary; at the same time, a fundamental knowledge of all things will be obtained. The whole of such a writing will be made of . . ., as it were, . . . of a kind of pictures — just as the ancient Egyptians did, and the Chinese do today. Their pictures, however, are not reduced to a fixed alphabet... with the result that a tremendous strain on the memory is necessary, which is the contrary of what we propose.""
"Rescher, reviewing Cohen's 1954 article, wrote that:
"Rescher, reviewing Cohen's 1954 article, wrote that:
Leibniz's program of a universal science (scientia universalis) for coordinating all human knowledge into a systematic whole comprises two parts: (1) a universal notation (characteristica universalis) by use of which any item of information whatever can be recorded in a natural and systematic way, and (2) a means of manipulating the knowledge thus recorded in a computational fashion, so as to reveal its logical interrelations and consequences (the calculus ratiocinator)."
The F.E.D. proposition with regard to Leibniz's quest can be summed up as follows --
A <<Characteristica Universalis>>, to fulfill Leibniz's definition and vision thereof, must be a dialectical <<Characteristica Universalis>>.
F.E.D. holds further that their NQ dialectical ideography already achieves a rudimentary version of such a dialectical <<Characteristica Universalis>> --
http://www.dialectics.info/dialectics/Briefs.html
http://www.dialectics.info/dialectics/Briefs_files/_Brief1-29JUL2008_OCR.pdf
http://www.dialectics.info/dialectics/Briefs_files/_Brief2-29JUL2008_OCR.pdf
http://www.dialectics.info/dialectics/Briefs_files/F.E.D.-Brief2-part3-07DEC2008_OCR.pdf
They also hold that certain successor systems of dialectical arithmetic/algebra that arise later in the
The F.E.D. proposition with regard to Leibniz's quest can be summed up as follows --
A <<Characteristica Universalis>>, to fulfill Leibniz's definition and vision thereof, must be a dialectical <<Characteristica Universalis>>.
F.E.D. holds further that their NQ dialectical ideography already achieves a rudimentary version of such a dialectical <<Characteristica Universalis>> --
http://www.dialectics.info/dialectics/Briefs.html
http://www.dialectics.info/dialectics/Briefs_files/_Brief1-29JUL2008_OCR.pdf
http://www.dialectics.info/dialectics/Briefs_files/_Brief2-29JUL2008_OCR.pdf
http://www.dialectics.info/dialectics/Briefs_files/F.E.D.-Brief2-part3-07DEC2008_OCR.pdf
They also hold that certain successor systems of dialectical arithmetic/algebra that arise later in the
meta-systematic dialectical axioms-systems-progression described by the Dyadic Seldon Function NQ dialectical meta-model of the dialectic of these dialectical-mathematical axiomatic systems [wherein N_ denotes the Peano first-order-logic-only axiomatic system of the "Natural Numbers", N] --
)-|-(s = (N_)^(2^s)
-- provide progressively richer realizations of such a Trans-Leibnizian, dialectical <<Characteristica Universalis>>, on the basis of a Trans-Leibnizian, empirically-justified "monadology", which they term the "meta-monadology" of the "meta-genealogy" of the cosmos.
The F.E.D. immanent critique of the ideology of Leibnizianism can be grasped heuristically, using the Q dialectical ideography, and using the step s = 1 Triadic Seldon Function, as follows --
)-|-(s.......= .......
(Leibnizianism)^(3^s);
)-|-(s = 0...= ...
(Leibnizianism)^(3^0) ...=...
(Leibnizianism)^(1) ...=...
Leibnizianism;
)-|-(s = 1...=...
(Leibnizianism)^(3^1)...=...
(Leibnizianism)^3...=...
)-|-(s = (N_)^(2^s)
-- provide progressively richer realizations of such a Trans-Leibnizian, dialectical <<Characteristica Universalis>>, on the basis of a Trans-Leibnizian, empirically-justified "monadology", which they term the "meta-monadology" of the "meta-genealogy" of the cosmos.
The F.E.D. immanent critique of the ideology of Leibnizianism can be grasped heuristically, using the Q dialectical ideography, and using the step s = 1 Triadic Seldon Function, as follows --
)-|-(s.......= .......
(Leibnizianism)^(3^s);
)-|-(s = 0...= ...
(Leibnizianism)^(3^0) ...=...
(Leibnizianism)^(1) ...=...
Leibnizianism;
)-|-(s = 1...=...
(Leibnizianism)^(3^1)...=...
(Leibnizianism)^3...=...
((Leibnizianism).x.(Leibnizianism))..x..
(Leibnizianism)...=...
(Leibnizianism)..x..
((Leibnizianism).x.(Leibnizianism))...=..
Leibnizianism..+..
Contra-Leibnizianism..+..
Trans-Leibnizianism...=...
L..+..C..+..q/CL...=...
L..+..C..+..T...
[---)...
q/1..+..q/2..+..q/(2+1)...
-- in which the "ideo-ontological category" L, or Leibnizianism, functions as specific
L..+..C..+..q/CL...=...
L..+..C..+..T...
[---)...
q/1..+..q/2..+..q/(2+1)...
-- in which the "ideo-ontological category" L, or Leibnizianism, functions as specific
"ideo-<<arche'>>", or "first thesis", and in which the "ideo-ontological category" C, or
Contra-Leibnizianism, functions as its "contra-thesis", i.e., as the <<aufheben>> immanent-critique / immanent-negation / self-negation of L, or Leibnizianism, and in which the "ideo-ontological category" q/CL, or T, standing for
Trans-Leibnizianism, functions as "uni-thesis", i.e., as the reconciliation of, or "complex unity" of, Leibnizianism and
Contra-Leibnizianism, or of C, and L.Contra-Leibnizianism, functions as its "contra-thesis", i.e., as the <<aufheben>> immanent-critique / immanent-negation / self-negation of L, or Leibnizianism, and in which the "ideo-ontological category" q/CL, or T, standing for
Trans-Leibnizianism, functions as "uni-thesis", i.e., as the reconciliation of, or "complex unity" of, Leibnizianism and
Regards,
Miguel
No comments:
Post a Comment