James, all ...
Among the subtle shifts in scientific thinking that occurred during
the 19th Century, Boole gave us a functional interpretation of logic,
associating with every propositional expression — in the field we now
plow with boolean algebras, boolean functions, propositional calculus,
or Peirce's alpha graphs — a function from a universe of discourse X to
a domain of logical values, say B = {0, 1}, normally interpreted as the
values false and true, respectively. This may seem like a small change
so far as conceptual revolutions go but it made a big difference in the
future development, growth, and power of our logical systems.
Among other things, the functional interpretation of logic enables the
construction of a bridge from propositional logic, whose subject matter
now consists of functions of the form f : X → B, to probability theory,
that deals with probability distributions or probability densities of
the form p : X → [0, 1], whose values lie in the unit interval [0, 1]
of the real number line R. This allows us to view propositional logic
as a special case within the frame of a more general statistical theory.
This turns out to be a very useful perspective in real-world research
when it comes to moving back and forth between qualitative observations
and the data given by quantitative measurement. It is a bridge further,
connecting deductive and inductive reasoning, as Boole well envisioned.
Regards,
Jon
On 5/30/2017 3:39 PM, James Albrecht wrote:
This always struck me as being, at least, a parallel articulation of
quantum mechanics. Peirce knew that macro-scale knowledge was beset by
limits, and that these limitations became more problematic as precision
increased.
59. (2) By thus admitting pure spontaneity or life as a character of the
universe, acting always and everywhere though restrained within narrow
bounds by law, producing infinitesimal departures from law continually, and
great ones with infinite infrequency, I account for all the variety and
diversity of the universe, in the only sense in which the really *sui
generis* and new can be said to be accounted for.
Also, in the same work on chance, Peirce references Boltzmann, whose gas
laws helped lead Planck to the quantum nature of radiation.
On Sat, May 13, 2017 at 10:34 PM, Mike Bergman <m...@mkbergman.com> wrote:
I just encountered this assertion:
"In the present work we have indicated that a form of logic, relational
logic developed by C. S. Peirce, may serve as the foundation of both
quantum mechanics and string theory." [1]
Does the list have any comments, further references or criticisms on this
pretty bold statement?
Thanks, Mike
[1] A. Nicolaidis, 2008. "Categorical Foundation of Quantum Mechanics and
String Theory," arXiv:0812.1946, 10 Dec 2008. See
https://arxiv.org/pdf/0812.1946.pdf
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