Home > Uncategorized > So the followin…

So the followin…

December 19, 2013 Leave a comment Go to comments

So the following disjunctive conclusion is inevitable: Either mathematics is incompletable in this sense, that its evident axioms can never be comprised in a finite rule, that is to say, the human mind (even within the realm of pure mathematics) infinitely surpasses the powers of any finite machine, or else there exist absolutely unsolvable diophantine problems of the type specified . . . (Gödel 1995: 310)

Minds, Machines and Gödel, First published in Philosophy, XXXVI, 1961, pp.

The Lucas-Penrose Argument about Gödel’s Theorem, Internet Encyclopedia of Philosophy

To me it’s clear from the above quote that Gödel understands incompleteness as revealing that mathematics is not completable in the sense that it is not enough to contain the reality of human consciousness. I disagree with those who use incompleteness to suggest the opposite position, that incompleteness demonstrates the incompleteness of the powers of human approximation to contain the grandeur of computable truth. Certainly human understanding is limited, but that our understanding of the limitations of arithmetic mechanism is part of what falls outside of that limit.

Proving that we cannot prove ourselves consistent assumes, erroneously, that doubt is not also a form of belief which depends on an expectation of consistency. The mistake that is often made, in the Western mind’s eye, is that since belief in belief is the ultimate bad, then belief in disbelief must be the ultimate good. This bit of Manichean simplicity is exacerbated when the skeptic no longer sees their own skepticism as a form of belief, and takes it for granted that absolute doubt is possible, reasonable, and independent of unscientific bias.

Even the term ‘belief’ is a second order logic which presumes a first order doubt beneath any given feeling, thought, understanding, intuition, etc. We can see that we should question our own authority, but we forget that authority includes the very authority to question itself, and that such an inescapable authority can only be more primitive than either fact or fiction. Before fact can be wrestled from fiction, or fiction can be confabulated from fact, there must be a capacity to discern one from the other, and that capacity cannot be fiction. Descartes, in my view, didn’t go far enough in saying “Je pense donc je suis”, because it doesn’t specify whether I exist in thought, whether thought exists in me, or whether, as I suggest, thought and I are distinctions of sense which are within the primordial pansensitivity that underlies both uni- and -verse.

Instead of seeing the limits of our human perspective as evidence that all privacy is solipsistic and isolated, I suggest that our perspective is imperfect only to the extent that it is human. When we compare human perceptions to the low level common behaviors of measured objects, then there is a lot that we can learn from physics which we could not learn from human introspection alone.

The fallacy is to conflate our human ignorance with the superiority of measurement to sensation and to overlook that the ontology of measurement supervenes on some form of sensation. Once we compare (absolute experiential) apples to (absolute measurable) apples, we find that the latter cannot be more complete than the former. Physics and math are more complete than human experience, but as they are only experiences in which other experiences are reduced and measured to a generic abstraction, they are less complete than experience itself. No map of France actually leads to Paris, no matter how precise the directions are. A map of France can only contain a map of Paris, and a map of Paris can’t be Paris itself, because it is only a pattern built from generic measurements which do not know anything about Paris itself.

  1. No comments yet.
  1. No trackbacks yet.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Rationalising The Universe

one post at a time

Conscience and Consciousness

Academic Philosophy for a General Audience


Exploring the Origins and Nature of Awareness


BRAINSTORM- An Evolving and propitious Synergy Mode~!

Musings and Thoughts on the Universe, Personal Development and Current Topics

This is a blog where I explore spiritual and personal development themes and ideas. © JAMES MICHAEL J. LOVELL, MUSINGS AND THOUGHTS ON THE UNIVERSE, PERSONAL DEVELOPMENT AND CURRENT TOPICS, 2016-2020, ALL RIGHTS RESERVED.

Paul's Bench

Ruminations on philosophy, psychology, life

This is not Yet-Another-Paradox, This is just How-Things-Really-Are...

For all dangerous minds, your own, or ours, but not the tv shows'... ... ... ... ... ... ... How to hack human consciousness, How to defend against human-hackers, and anything in between... ... ... ... ... ...this may be regarded as a sort of dialogue for peace and plenty for a hungry planet, with no one left behind, ever... ... ... ... please note: It may behoove you more to try to prove to yourselves how we may really be a time-traveler, than to try to disprove it... ... ... ... ... ... ...Enjoy!


“Don’t try to be different. Just be Creative. To be creative is different enough.”


An idealistic blog where those who are searching/wandering/questioning can find an absolute qualia.


Zumwalt Poems Online

The Traditionalist

Revolt Against The Modern World

dhamma footsteps

postcards from the present moment




Observational Tranquillity.

Gray Matters

Traversing the blood-brain-barrier.

Writings By Ender

The Writer's Adventure


The greatest WordPress.com site in all the land!

%d bloggers like this: