tmoody@sjuvax.UUCP (T. Moody) (10/28/85)
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In the _Critique_of_Pure_Reason_, Kant presented the distinction
between phenomenon and noumenon. "Phenomena" refers to what could be
loosely called "appearances." This includes, memories, mental images,
and other sorts of ideas, as well as sense-data. In short, phenomena
are whatever the mind can apprehend.
Scientific knowledge is about phenomena because it is about the
measurable appearances of things. Meter readings, cloud chamber
trails, and so forth, are all part of the way the world appears.
Dreams, too, are part of the way the world appears.
Most of us have a strong intuition that some appearances are
*veridical*, while others are not. For one thing, some of the
appearances are independent of the will in a way that others are not.
Thus, we tend to believe that some appearances correspond to the way
things really are, even though we cannot prove this.
"Noumenon" refers to the "thing-in-itself", apart from all
appearances. We cannot even say whether it is one or many, since
number is an artifact of the way the mind structures phenomena. In
fact, Kant said, we can't really say anything at all about noumenon,
other than that its existence appears to be a necessary condition of
the kind of experience we have of certain (will-independent)
phenomena. We cannot know what noumenon is *like*.
Kant's successors, such as Schopenhauer, found his hypostatization of
the noumenon unwarranted, and tended to deny it. This is why they are
called the German Idealists, since idealism is the philosophy that
states that mind-independent reality cannot be established. What is
ineffable -- the noumenon -- cannot be known to exist.
Cantor proved that not all infinite sets are the same size. In
particular, he proved that the real numbers are more numerous than the
natural numbers (positive integers).
A *name* of a number is a finite string of symbols, drawn from a
finite vocabulary of symbols. The digits "0" through "9", the radical
sign, "(", ")", "+","=", and so forth are what I'm talking about.
Thus "1/2 + 1/4 + 1/8 + ..." is a finite string, even though it
represents an infinite series.
There are only denumerably many names, because names are finite
combinations of a finite number of elements. All of the rational
numbers have names; some of the irrational numbers have names. "The
square root of two" is a name of the square root of two, for example.
But, since there are nondenumerably many reals numbers, it follows
that nondenumerably many of them do not have names. Call them the
"ineffable numbers." I can't, in principle, give you a specimen, but
it is proved that they exist. The ineffable numbers can only be
referred to collectively, not individually. They are not the roots of
any algebraic equations, since these equations would be names.
If this thinking is sound, then there is not any principled objection
to the noumenon, based on its ineffability. Consider, to make a true
statement about an individual, you must refer to it. So, you can
never make true statements about individual ineffable numbers. This
is just like what Kant said about noumenon, and what mystics say about
"ultimate reality."
Wittgenstein's famous "That of which we cannot speak, we must pass
over in silence" does not logically entail that reference limits what
there is.
Personally, I find this interesting.
Todd Moody | {allegra|astrovax|bpa|burdvax}!sjuvax!tmoody
Philosophy Department |
St. Joseph's U. | "I couldn't fail to
Philadelphia, PA 19131 | disagree with you less."