Replies

me: We could probably find a number of things to agree on with reference to mathematics and physics. Even so, we may very well have a different paradigm there also - I am a mathematical Platonist, you may be a mathematical Aristotlean.

you: Not the best analogy, IMHO. Mathematics is an artificial construct. It is used to quantify, but it is not quantifiable.

Thank you for proving my point!

In the mathematical Aristotlean paradigm, the mathematician invents the mathematical structures.

In the mathematical Platonist paradigm, the mathematical structures exist and the mathematician comes along and discovers them. For example, pi exists, the mathematician discovered it.

The difference in paradigm affects not only one's view of the math but the physics and cosmology as well. And no doubt (at least in my case) extends to information theory and molecular biology.

For instance, all physical cosmologies (e.g. inflationary, multi-verse, multi-world, ekpyrotic, cyclic, imaginary time) presuppose space and time for physical causation. But in the absence of space, things cannot exist. And in the absence of time, events cannot occur.

Moreover, cosmic microwave background radiation measurements since the 1960's accrue to evidence there was a real beginning of space and time in this universe.

In effect, there was no infinite past to support the plentitude argument that anything that could happen, did. There can be no physical origin for space, time and therefore physical causation itself. All such physical cosmologies are "open."

Conversely, Max Tegmark's Level IV universe is "closed" precisely because it is radical Platonism. The mathematical structures really exist outside of space and time - and what the observer "in" space/time perceives is a manifestation of that reality.

A mathematical structure is an abstract, immutable entity existing outside of space and time. If history were a movie, the structure would correspond not to a single frame of it but to the entire videotape. Consider, for example, a world made up of pointlike particles moving around in three-dimensional space. In four-dimensional spacetime — the bird perspective — these particle trajectories resemble a tangle of spaghetti. If the frog sees a particle moving with constant velocity, the bird sees a straight strand of uncooked spaghetti. If the frog sees a pair of orbiting particles, the bird sees two spaghetti strands intertwined like a double helix. To the frog, the world is described by Newton’s laws of motion and gravitation. To the bird, it is described by the geometry of the pasta — a mathematical structure. The frog itself is merely a thick bundle of pasta, whose highly complex intertwining corresponds to a cluster of particles that store and process information. Our universe is far more complicated than this example, and scientists do not yet know to what, if any, mathematical structure it corresponds.

The Platonic paradigm raises the question of why the universe is the way it is. To an Aristotelian, this is a meaningless question: The universe just is. But a Platonist cannot help but wonder why it could not have been different. If the universe is inherently mathematical, then why was only one of the many mathematical structures singled out to describe a universe? A fundamental asymmetry appears to be built into the very heart of reality.

Tegmark: Parallel Universes

The difference is irreconcilable. The debate began with Plato and Aristotle, continued with Einstein and Gödel and continues today between Penrose and Hawking.

And there is a comparable irreconcilable difference between the natural man and the spiritual man:

[There is] therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit. For the law of the Spirit of life in Christ Jesus hath made me free from the law of sin and death. For what the law could not do, in that it was weak through the flesh, God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh: That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit.

For they that are after the flesh do mind the things of the flesh; but they that are after the Spirit the things of the Spirit. For to be carnally minded [is] death; but to be spiritually minded [is] life and peace. Because the carnal mind [is] enmity against God: for it is not subject to the law of God, neither indeed can be. So then they that are in the flesh cannot please God.

But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his. – Romans 8:1-9

For that reason, these debates can never end. Parties on opposing sides cannot make the other accept what they see, as Dog Gone suggested earlier on this thread.

In the Tegmark metaphor, the frog cannot see what the bird sees. To him, the bird's sense of reality is a delusion. To the bird, the frog's reality is a reduction, a construct. Nor can the bird accept the frog's sense of reality.

A Christian who is also a bird (mathematical Platonist) like I am – may also see the harmony between Scripture and Creation. Indeed, to me, the unreasonable effectiveness of mathematics is like God’s copyright notice on the Cosmos.

The heavens declare the glory of God; and the firmament sheweth his handywork. Day unto day uttereth speech, and night unto night sheweth knowledge. [There is] no speech nor language, [where] their voice is not heard. - Psalms 19:1-3

Logos is the root Greek word for Word which is a Name of God, a Name of Jesus Christ. It is also the root Greek word for logic:

In the beginning was the Word [Logos], and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made by him; and without him was not any thing made that was made. In him was life; and the life was the light of men. – John 1:1-4

To God be the glory!

The difference is irreconcilable.

Then what is to be gained from these debates, other than animosity?

...these debates can never end. Parties on opposing sides cannot make the other accept what they see, as Dog Gone suggested earlier on this thread.

I don't have an interest in "making" the other person "accept" what I see. I'd be completely satisfied if I could just get some indication that they actually "saw" it. Then if they want to dispute my statements regarding the "seen thing" on rational grounds, truly I'd welcome them to do that.

But that rarely, if ever happens around here. Mostly we engage in "spitting matches" — all heat and no light. Nobody learns a thing. Sigh....

Of course you know I'm a mathematical Platonist, just as you are. I wholly concur that mathematics exists in an independent, indeed one could almost say sovereign manner; and thus becomes susceptible to being "discovered."

Roger Penrose refers to the ontological status of mathematics as the Platonic world of mathematical forms, which are universal and thus completely "objective." To say that mathematics is "invented" by human beings is, to my mind, foolishness on the verge of hubris. For this is to make mathematics constructible on the basis of "subjectivity." How could such a thing attain the status of universality? FWIW.

Thank you dearest sister in Christ for your most excellent essay-post!

[ But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his. – Romans 8:1-9 ]

By this verse.. some have the SPirit of Christ(God) and some DO NOT.. WHich implys not all christians are christians.. or that being a christian is not a matter of what you say you are.. You might not be... Jesus said.... "You MUST be born again".. the first birth is not good enough..

About going to "church"... You can put puppies in a muffin tin and put them in an oven(church) but that don't make them muffins after processing..... Puppies are puppies and muffins are muffins..