On 9/21/2018 3:05 PM, Helmut Raulien wrote:
so mathematics perhaps is the only example, for which Platon´s
idea of "idea" is correct. All phenomena can be explained with
mathematics. Though only afterwards, subsequently?
As Peirce said, diagrammatic reasoning is the foundation for
all necessary reasoning. It's the foundation for mathematics.
But people -- and probably higher animals -- have been using
it for millions of years. Look at the mathematical patterns
in Stonehenge, the pyramids, the Mayan, Inca, and Aztec ruins,
and the cave paintings and rock carvings around the world.
When ravens and monkeys solve some challenging problems, you
could call that applied mathematics. In some experiments,
they generalize a solution (diagram) for solving one kind
of problem to solve a different problem that has a similar
structure. But they're still doing applied math.
Pure math requires an abstract conceptualization, which seems
to be uniquely human. How far back that concept extends would
be a study for anthropology and comparative literature.
Plato wrote the clearest statement of it, but the idea is
probably much older. In fact, some of the mystical and poetic
writings in ancient civilizations seem to be attempts to state
the central issues. But those concepts are usually called
religious or philosophical -- e.g., logos, dharma, and dao.
there is "t" for a symbol [for time], but is there a mathematical
formula that explains the difference between going forward and
backwards in time? I know that there is "entropy", but it is all
axiomatic (laws of thermodynamics), and not based on pure
mathematics, or is it now??
When Peirce said that all the sciences depend on mathematics,
he was talking about a systematic classification that relates
the underlying theories of all the fields. But that is not
a historical study of how those sciences developed.
For example, look at the ravens and monkeys. They don't start
with a theory of pure math and apply it to their problems.
Instead, they start with specific problems. Sometimes they
can use analogies to apply an old solution to a new problem.
Analogies are also the basis for human thinking, as Peirce
observed. With language and other symbol systems, people
can abstract, generalize, and create more systematic theories.
People whose mathematical knowledge stops with arithmetic
wouldn't call that mathematics. Those who know geometry,
would recognize a broader range of applications. But Peirce
went all the way: All necessary reasoning is diagrammatic,
and mathematics is the study of necessary reasoning.
Pure math is the ultimate abstraction. But applied math was
discovered and used long before anyone mentioned pure math.
I remember vaguely something about a crystal theory, meaning
that some people have meant to have designed a sort of crystal
shaped thing meant to represent everything including time.
Never again heard of it,
I don't know, but it's possible that you may have come across
a diagram that I published about 20 years ago:
http://jfsowa.com/ontology/toplevel.htm
I still consider that diagram OK as an illustration. But I don't
emphasize it because there are many other issues that need to be
analyzed and discussed. For a more recent article about them,
see http://jfsowa.com/pubs/rolelog.pdf
John
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