Tag: ancient philosophy

(by pyrrho for publishing jointly at MLW and DocuDharma)

Pythagoras: A Mathematical Universe

I will be using the print version of the Oxford “Dictionary of
Philosophy” to refresh myself for this series.

Links offered may or may not have been referenced to research this post. I
may or may not believe their assertions or have been exposed to them, but
they are given to ease your direct research further into Pythagoras. I try to
present them fairly and clearly. I am a skeptic myself, a relativist with
opinions on all these schools, and a tendency to eschew the doctrinaire side
of each of these schools, but as a skeptic, I’m equipped to give a philosophy
a fair shake. Myself, and tend to seek and emphasize the reusable tools each
school has to offer.

• Pythagoras at
  Wikipedia
• Stanford
  Encyclopedia of Philosophy on Pythagoras
• The Internet
  Encyclopedia of Philosophy: Pythagoras
• Pythagoras
  at History for Kids

Most of you will know Pythagoras from the Pythagorean Theorum, but
Pythagoras was not just a mathematician and geometrician. His mathematics was
not separate from his life and his ideas were not limited to mathematics. As
with all these ancient philosophies I am covering in this series, Pythagoras’
is also has a whole system concerned with how to live… a worldview. This
worldview is what I am looking at in this series, because these philosophies
serve as archetypes for worldviews, archetypes I seem to encounter daily, and
which you do to. Archetypes not fundamental, but nevertheless ancient and
soaked into us. The epicurean is looking for a pleasurable life, to find the
small pleasures and live simply Simply, perhaps, but still nearby these
pleasures. The stoic is more hardened, does not expect pleasure as reward and
even scoffs at it as such, being as indifferent to pleasure as they have
chosen to be to pain. The pythagoreans then are those that have their head in
abstractions. One imagines the sort that has had no time for epicurean
pleasures like meals, having been preoccupied with a logical proof. To these
sort, the sublime superiority of a mathematical pattern was and remains as
obvious as the rising sun.

Indeed, the followers of Pythagoras were prone to taking Pythagoras himself
as a god become human to teach mankind these sublime truths. I do not find it
surprising that such a man led to a philosophy including vegetarianism and a
semi-divine presumption. If that sound dismissive, I share the pythagorean’s
sensibilities, if more humbly so, with an eye to the errors it introduces
with its beauties. As for the nearly religious awe I can feel before a
mathematical truth, take pi, a ratio that relates, among other things, the
length of the side of a circle to the length of the sides of a square, such
that, if you were to take the width of a square, and the radius of the circle
having the same circumference as the “circumference” of the square, then the
relation between the two involves a number whose digits never end, which
cannot be finitely represented. To me that’s stunning, but that turning
square into a circle requires a transcendental number is not stunning but
fitting. It is sublime, divine, and while expected, only ironically. And that
the ratio is well named as a “transcendental” number is no doubt a product of
our shared if inexplicable love for the beauty of math and geometry.

Concomitant to this, however, is removal of the self from the material
world into the world of abstraction and the illusion that abstractions are
not even of this world. The pythagorean spirit, as archetype, might not even
concern itself with math or geometry, but some other family of abstractions.
But abstraction are made from material facts, from astronomy, from counting,
from imperfectly drawn lines in the sand, and from deducing concepts that can
explain the facts abstracted all at once. This has proved a practical and
rewarding endeavor, but it is a part of the loss of reason to consider an
abstraction so fine it’s not a part of this world. But now I have begun to
describe Plato… Pythagoras himself might in fact object, thinking the world
of mathematics imbued the world around us all the material reality it had for
us to perceive. If I may accept this archetype in such a light, it remains a
tactile abstractionism, we feel the mathematical world about us always. We
are not imperfect beings separated from this glory, but are abstract beauties
ourselves, actually made of it.

(by pyrrho for publishing jointly at MLW and DocuDharma)

Logic vs Natural Language

Ok, this is a strange thing. I put it in a video, because I want to. But I
know many of you are written word junkies, and believe, I mean that
literally, and in the kindest but also you-may-need-help way, so I will
explain my brief point.

The logical form of the “if-then”, such as “if A then B”, is The
Conditional, and it’s a fundamental part of and a basic building blocks of
formal logic, and for that matter, informal logic, and il-logic. But it is
defined in a way that is very different and strange when compared to the
natural language conditional.

A –> B is a way of saying “if A then B”.

A strange thing in logic is that “A –> B” is untrue, false, when A is
true, and B is false. So that leads to two strange things about the
conditional used in formal logic.

Firstly, it means that if both A and B are false, then then A –> B is
true… we wouldn’t think that in natural language. “If bananas are blue then
oceans are made of ginger ale” is true? Maybe, on the theory also supported
in logic that with nonsense you can prove any other nonsense.

Secondly, and what I address in the short video below, meant to either
relax or stimulate you, either way, is the fact that if B is true, then it
doesn’t matter if A is true or false. Contrary to that in natural language it
matters that A is related to B somehow, regardless of the truth value, as
they call it, of A and B.

The example from the video:

If I have viable orange seeds, then I can grow an orange tree.

A = I have viable orange seeds.

B : I can grow an orange tree.

In the historical mainstream of formal logic A–>B here is true because
“I can grow an orange tree” is true. In natural language, it’s also true,
but not for that reason, it’s true because both A and be both mention
oranges, and thus have a relationship, which happens to be true, because
orange trees come from orange seeds.

In logic, this is also true “if I have a puppy, then I can grow an orange
tree”. In natural language that is not true, unless there is some link
between the puppy and the orange tree.

I love logic, but it’s a tool, and I think this is a very serious issue in
terms of what the limitations are for logic as we understand it right now in
terms of applicability to the natural world. It is possibly this logic
holding us back from abstract gains in knowledge in fields other than
physics, due to small errors in ancient logical tools meant, really, to
codify our true thoughts on “if then”.