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Re: Clarification--faith

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  • Will Brown
    ... work ... Speaking of the Pythagorean Theorem, I stumbled across a proof I think is unique. I was messing around with the Gudermannian function in an
    Message 1 of 8 , Oct 21, 2002
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      --- In gnosticism2@y..., "Gerry" <gerryhsp@y...> wrote:
      > --- In gnosticism2@y..., Coraxo <coraxo@e...> wrote:
      > > If I may interject:
      > >
      > > The aspect of Faith is not limited to religion and mysticism.
      > >
      > > In fact a great deal of faith is placed upon the scientific model
      > in which
      > > we live; . . . .
      > >
      > > So in the end we put a great deal of faith in the experimental
      work
      > of
      > > others rather than constantly proving to ourselves that the square

      > of the
      > > hypoteneuse is equal to the sum of the squares of the sides of a
      > right
      > > triangle.
      > >
      > > Forgive my intrusion
      > >
      > > Corax
      >
      >
      >
      > Not an intrusion, Corax. This is your haven, too. In fact, if we
      > mention enough Pythagorean models, we may find that Aleibiades is
      > still lurking out thereĀ—havent't heard from her in a while.
      >
      > Gerry

      Speaking of the Pythagorean Theorem, I stumbled across a proof I think
      is unique. I was messing around with the Gudermannian function in an
      attempt to put it into a geometrical form, which I did, and out it
      popped. For what it is worth, here is a description of it.

      Begin with a right triangle, legs A & B with hypotenuse C. From that,
      construct a rectangle with width A and one length [B + C] and the
      other length [C + B]. That will create two triangles, one with legs A
      & [C +B] and the other with legs A & [C - B]. Prove (I'll let you do
      that) that the two triangles similar. From that, A/[C - B] = [C -
      B]/A, and that's it.
    • aleibiades
      Oh, I m lurking around. G2 has just gotten entirely too prolific for me to keep up with. :) So, Coraxo . . . I agree with you about putting faith in the
      Message 2 of 8 , Oct 21, 2002
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        Oh, I'm lurking around. G2 has just gotten entirely too prolific for
        me to keep up with. :)

        So, Coraxo . . . I agree with you about putting faith in the
        experimental work of others, sort of. Mathematicians, scientists,
        and engineers are usually asked to prove everything before they are
        able to use it. Once you have proven something, though, it's free
        game to use as part of any other proof or practice. Now, in reality,
        most "proofs" amount to copying someone else's work without any real
        understanding. This is the closest allegory I can think of to the
        difference between "gnosis" and "praxis".

        What I have always thought was interesting, in our discussions
        about "faith" in here, is that most people seem to be blindly for it,
        or against it. To go back to the math allegory, even though a^2 +
        b^2 does equal c^2, and can be mathematically proven, first you have
        to agree on the definitions of a triangle and of a right angle. That
        involves, of course, assuming that there are such things as "sides"
        and "lengths" and that they matter.

        At some point, if you are going to get anywhere in math (and I
        believe in understanding the rest of the universe, as well) you've
        got to make some assumptions and hope you don't run into a
        contradiction too far down the road. Now, the question is whether
        you try to pare those assumptions down to the bare minimum, and then
        carefully test each new construction from those assumptions; or
        whether you just keep blithely making assumptions, and wait to see
        how badly they trip you up. So, I guess what I am saying is, at the
        bottom level there is always some sort of "leap of faith". The
        question for me has always been whether you build solidly on that,
        with increased understanding (gnosis); or whether you build what you
        need to as you need to, with the goal of it "working" to get you
        through (praxis).

        So, when I read through the Nag Hammadi, I see all these
        constructions. The Tripartite Tractate is a great example--it starts
        with a set of givens about the father, builds from that to the son
        and the Church, then to the Aeonic emanations, and so on. Okay, so
        the arguments aren't mathematically testable, but there is a logical
        progression from the one thing to the next thing, and the belief
        system is experimentally testable, so to speak. :)

        Back to lurking,
        Alei

        --- In gnosticism2@y..., "Gerry" <gerryhsp@y...> wrote:
        > --- In gnosticism2@y..., Coraxo <coraxo@e...> wrote:
        > > If I may interject:
        > >
        > > The aspect of Faith is not limited to religion and mysticism.
        > >
        > > In fact a great deal of faith is placed upon the scientific model
        > in which
        > > we live; . . . .
        > >
        > > So in the end we put a great deal of faith in the experimental
        work
        > of
        > > others rather than constantly proving to ourselves that the
        square
        > of the
        > > hypoteneuse is equal to the sum of the squares of the sides of a
        > right
        > > triangle.
        > >
        > > Forgive my intrusion
        > >
        > > Corax
        >
        >
        >
        > Not an intrusion, Corax. This is your haven, too. In fact, if we
        > mention enough Pythagorean models, we may find that Aleibiades is
        > still lurking out thereĀ—havent't heard from her in a while.
        >
        > Gerry
      • coraxo
        ... The epistemological issue with empirical science is that rigorous proof does not exist. The method is inductive and creates hypotheses or models which have
        Message 3 of 8 , Oct 22, 2002
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          aleibiades wrote:


          Oh, I'm lurking around.  G2 has just gotten entirely too prolific for
          me to keep up with.  :)

          So, Coraxo . . .  I agree with you about putting faith in the
          experimental work of others, sort of.  Mathematicians, scientists,
          and engineers are usually asked to prove everything before they are
          able to use it. 
          The epistemological issue with empirical science is that rigorous proof does not exist. The method is inductive and creates hypotheses or models which have explanatory and predictive power, and are parsimonious. Nevertheless, most scientific observation is statistically validated and the models do not account for every possible variable. Thus, the factor of "chance" is allowed for by setting the degree of randomness acceptable in the model.

          The lay person however, does not usually understand this and accepts on "faith" that what he or she is told is "proven". This is one of the biggest failings of our culture is the inability to process this information as hypothetical rather than factual.

          Case in point the recent see-saw over breast self examination, previously people faithfully believed that self-examination increased the probability of early detection and lower mortality from BC. Now, with more rigorous study and probably variable selection, BSE has not been shown to decrease mortality and increase early cancer detection. Hormone replecement therapy has also been shown to increase coronary vascular disease at a rate which is unacceptably higher that the benefit of decreasing hip fractures from osteoporosis.

          Yet, in our society people accept these medical statements on FAITH! Billions of dollars of wealth are pumped into belief systems that are later shown to be inaccurate or untrue.

          The inductive process is different from the deductive process of Euclidean geometry and other mathematics. Like you stated, one starts with first principles and works outwards to models of planes and polygons based on the primary sets of assumptions - assumtions which are accepted a priori, but are not themselves provable.

          But scientific positivism does not "prove" anything, at least in the sense of what I consider "proof". Anything which is evidence based is bound to contain error.
          <Similar to what you state below>

          At some point, if you are going to get anywhere in math (and I
          believe in understanding the rest of the universe, as well) you've
          got to make some assumptions and hope you don't run into a
          contradiction too far down the road.  Now, the question is whether
          you try to pare those assumptions down to the bare minimum, and then
          carefully test each new construction from those assumptions; or
          whether you just keep blithely making assumptions, and wait to see
          how badly they trip you up.  So, I guess what I am saying is, at the
          bottom level there is always some sort of "leap of faith".  The
          question for me has always been whether you build solidly on that,
          with increased understanding (gnosis); or whether you build what you
          need to as you need to, with the goal of it "working" to get you
          through (praxis).
          I agree with your assessment below, the NHL texts start with a first principle and work outwards from that point. In order to account for "error", something which the stoics and platonists did not accept in their perfect Demiurge and his creation, one of the Aeons falls out of balance with the rest of the Aeonic hierarchy. The rest of the story is about restoring balance.


          So, when I read through the Nag Hammadi, I see all these
          constructions.  The Tripartite Tractate is a great example--it starts
          with a set of givens about the father, builds from that to the son
          and the Church, then to the Aeonic emanations, and so on.  Okay, so
          the arguments aren't mathematically testable, but there is a logical
          progression from the one thing to the next thing, and the belief
          system is experimentally testable, so to speak.  :)

          Back to lurking,
          Alei
          The belief system may or may not be experimentally testable (predictive), but in terms of explanatory power I think the Valentinian, Sethian and Barbeloite models have great strength. In addition to which each model also has some degree of internal consistency. These in themselves are cause for serious consideration.

          Now about the idea of the internal world, I think it is self evident that the internal world is more "real" than the external. The external world is something we surmise from internal phenomena - sense data. Because the projection of this sense data is external to what we believe to the our locus of control, we assume these events are in fact outside of ourselves. The fact that they are representational of what is being observed does not enter consideration in most cases. Thus it would seem reasonable to assume that without the virtue of consciousness shining onto these external objects, they are dark and formless. Since it is the consciousness which imputes form and light and meaning to these objects, it then stands to reason that in this sphere of awareness exist other powers and principles which are anterior to self awareness and  which project meaning and form onto the field of awareness, and not necessarily upon the field of perception (we do not necessarily see, hear, tase, touch the Aeons, but perceive them through their movements in consciousness).

          It is these noetic principles which are the topic of the NHL and how they affect internal personal behavior and awareness, and how they act out in the "outside" world.

          That's my 2 cents for now, thank you for your comments "A".

          Corax


          --- In gnosticism2@y..., "Gerry" <gerryhsp@y...> wrote:
          > --- In gnosticism2@y..., Coraxo <coraxo@e...> wrote:
          > > If I may interject:
          > >
          > > The aspect of Faith is not limited to religion and mysticism.
          > >
          > > In fact a great deal of faith is placed upon the scientific model
          > in which
          > > we live; . . . .
          > >
          > > So in the end we put a great deal of faith in the experimental
          work
          > of
          > > others rather than constantly proving to ourselves that the
          square 
          > of the
          > > hypoteneuse is equal to the sum of the squares of the sides of a
          > right
          > > triangle.
          > >
          > > Forgive my intrusion
          > >
          > > Corax
          >
          >
          >
          > Not an intrusion, Corax.  This is your haven, too.  In fact, if we
          > mention enough Pythagorean models, we may find that Aleibiades is
          > still lurking out there—havent't heard from her in a while.
          >
          > Gerry



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