Saturday, July 21, 2012

Two fatal flaws in Pandeist logic

Pandeism is a modern form of pantheism, and was mentioned briefly in my previous post.  Its advocates prefer the more modern term 'deism' rather than 'theism', in order to emphasize a connection with reason and logic, rather than the traditional theism of the Abrahamic kind.

My previous argument against pantheism,
We see that the Argument from Love has direct consequences concerning the systems of pantheism, nonduality and idealism. The necessity, if love is to function, of a deep division between divinity and us beloved beings is not allowed in pantheism. According to pantheism, we are all and entirely part of God, and that cannot be true if God is to love us unselfishly.
will not work with the pantheist, because they do not accept that God is Love in the first place, let alone Unselfish Love! Sad.

The logical heart of pandeism seems to be some 'theorems' which Robert G. Brown claims to have proved. His personal home page is here, and his university page is here. These theorems appear to prove that God must be identical with the universe. This has many alleged implications, such as that God cannot be a Creator, cannot Love the universe and its peoples, and theism (whereby God sustains the universe) must be false. 

The main theorem is quite simple. First we need to use Brown's definition of 'irreducible information':
We begin by mentally compressing the coordinate description - eliminating all redundant information. This leads us to an irreducible specification of the state of the Universe as a complete set of non-redundant coordinates (where a lot of the reduction will appear in the form of exact or approximate coordinate relationships, a.k.a. ``the laws of nature''). This information is self-encoded in the actual things that exist in the actual Universe.
Then we need to see his definition of 'omniscience':
God must possess a complete knowledge of the state of the Universe, right down to the last electron in the last space-time continuum, the last hidden dimension. 
with his definition of the Universe as 'everything that exists': our world and God.

Finally, then, his 'Pandeist Theorem' is:
If God exists, then God is identical to the Universe.
That is, the theorem is a statement of conditional pandeism. If God exists at all, God must be absolutely everything that exists.  It is therefore quite obvious that if God exists (has being), God must be either a part of the Universe or the whole UniverseGod by the property of omniscience must have precisely the irreducible information content of the entire Universe.

His Proof is given as:
Let us call the irreducible information content of the non-God part of the Universe IN, the irreducible information content of the God part of the Universe IG, and the irreducible information content of the entire Universe IU (where of course any of these quantities could be infinite).
It is obvious that:
I_U \equiv I_G + I_N

as the irreducible information content of the whole must match the total irreducible information content of the disjoint parts. Also,
I_N \not\equiv I_G
as the non-God and God parts are disjoint and cannot be mutually reducible. Clearly,
I_G \equiv I_U
as that's the meaning of omniscience. Therefore:
I_N \equiv \emptyset
The only way the irreducible information content of the non-God part of the irreducible information content of the entire Universe can be encoded in the irreducible information content of the God part is if the irreducible information content of the non-God part is null - no information at all.
No existing system has null information content (this is why we needed the principle that a physical systemis its own minimal encoding, that a system ``knows'' its own state in an incompressible way), so we conclude that if God exists at all, the non-God part of the Universe is (quite literally) no-thing, nothing. It does not exist.
Ian's Reply:

This is an unusual definition of the universe, since God is not usually assumed to be in the universe, but we can accept this as a temporary definition.

First Fatal Flaw in this Proof

1. Brown seems to take objects as composed of information. This is like a computer scientist, who takes  'bits' as the basic thing that exists. This is to treat 'form' as fundamentally existing. Plato would be happy.

However, natural scientists since Aristotle, Galileo and Newton know that substances are made out of something that is not purely formal, but have mass or energy.  This should be obvious to a physicist.

This has the consequence that two distinct existing things can have the same information. Two things, such as a finger and a fingerprint on glass, may share the same information, the same form and the same bits, but be ontologically distinct substances.

The 'irreducible information' of a finger and its fingerprint will be identical. Aspects of both are describable by the same form. Thus, when we aggregate two systems, it may well be that the aggregate has an irreducible information is less than the sum of their individual irreducible informations. The shared forms may be in each part, but do not need to be repeated in the whole's irreducible information.

This should be obvious. If we copy a 1 MB jpeg file on a computer, we have it stored in two places in the physical memory, but the irreducible information is not doubled. It is not 2 MB, but only 1 MB combined with a very short instruction about duplication. (This is how zip compression algorithms work!)

Let us apply this to the G + N = U aggregation that Brown uses in his proof above.

If God G is to be omniscient, then there must be information in God which is a copy of forms seen in the non-God world N. We may think of God's perception as having images of the world that convey the same information as the world does. That is what true perceptions are obviously about.

This implies, then, that the aggregate U has information much less than the total:

IU  <<  IG  + IN

because there is shared (common) information within G and N. Information is not additive between disjoint parts! Therefore his proof fails

Why did Brown make this mistake? Because he confused substance and form. In other words, he confused energy and information. He took the non-overlap of the God and non-God to be non-overlap of information, whereas it should be non-overlap of substance (energy, mass, or whatever). It is only this second non-overlap of substance which pertains to God and the world. It leads to egregious errors, we see, if we forget this fact.  God and humans may share forms: we may both know the forms of geometry, logic, mathematics generally, and many other formal things. Our disjointness does not stop us sharing information!

Second Fatal Flaw in this Proof

Brown says he accepts that any of  IGIN, and IU may be infinite. But he does not realize that adding a finite number to infinity leaves that infinity unchanged. This has been known for over 2000 years. Since God is traditionally taken to be infinite, then IG=infinity and IU=infinity. That is, we accept that  IG and  IU are equal in that sense, but Brown's (flawed) equality 
IU  I + IN
does not imply that IN = 0 when IU=IG=infinity! In this case, the proof fails again, even mathematically.

Brown's Second Proof

Brown as a Second Proof of this theorem, but it begins by assuming that "entropy is an extensive quantity - all of the information carrying capacity of the 'God channel' is being consumed by irreducibly specifying the God state and there is none left over for specifying the not-God state."

We saw above that information is not extensive or additive. This means that, for the purposes of Brown's argument, we can not assume that information is simply negative entropy. If information were extensive, then compression algorithms could never work, but they do. Information is not extensive, even in computers.

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