Re: Contradiction in Rucker?

Roderick A. Carder-Russell (
Tue, 15 Jul 1997 08:30:45 -0400 (EDT)

On Tue, 15 Jul 1997, Mitchell Porter wrote:

> I suspect he's saying that we can directly perceive omega,
> as directly as we can perceive sounds or colors - although
> not through any of the five senses, but through some other
> faculty of mind (e.g. "intellect" or "intuition"); and that
> he will count as empirical evidence, not only sense-data,
> but also "intuition-data", derived from that extra faculty.

The following is from a private message that I sent to Eric Watt
Forste yesterday. It is applicable here, for it gives yet another
interpretation of Rucker's intended message. Upon rereading, I don't
believe that he intended anything nearly as interesting as we have been
considering. I believe that he is simply stating that the concept of
Omega is given a priori, then further understood, along with lower
infinities, empirically. I also give a brief refutation of the Kantian
view of this, in the following text:

I did...return to the text to ponder the surrounding paragraphs
and I have come up with this: In the sentence immediately following the
paragraph that I extracted the original object of debate from, Rucker says
this, "We have a primitive concept of infinity". He then goes on to
mention how it is inspired, not giving a solid reason, but rather
referring to the "same deep substrate of mind that conditions religious
thought", this can be pre or post rational, but it really doesn't matter
in this case, because he goes on to further clarify our conception of
infinities. "By means of set-theoretic analysis of Absolute Infinity [our
omega], we attain knowledge of many lower infinities-the transfinite
ordinals and cardinals".
My revised view of his text tells me that the initial concept of
infinity, as Absolute Infinity, is given a priori, whereas we arrive at
further understanding empirically. This isn't the Kantian synthetic a
priori, for in this case it is given first, then further understood. In
the case of a synthetic a priori, I believe that one arrives at or
discovers an innate concept empirically, only then recognizing it as an a
priori and eternal truth. Hence, we are given new knowledge (synthetic)
from an eternal truth. This of course could just be my own twist on Kant.
A fun subject nonetheless, and great fuel for hours of intensely enjoyable

> I'm not sure about this. A priori knowledge is supposed to
> be had without appeal to perception. Rucker might agree that
> the existence of omega is not an analytic truth, but he
> might say that we only know about omega because we "perceive"
> it (again, where "perceive" would have to include the alleged
> faculty by which one is directly aware of mathematical
> entities).

Much agreed! One must note, however, that your definition of
"perceive" is essential to this statement.

Roderick A. Carder-Russell
Student-Computer Science, Philosophy
Specializing in Man-Machine Symbiosis
Suspension Member-Alcor Foundation
Information Systems Consultant-Technology Syllogistics