# Must explanatory mathematical systems of the world lead to infinite regress?

Call the world as it presents itself to us world-1

The regularity & order in the world demands explanation - hence we have a mathematically consistent description of the world. Call this world-2.

But surely the same situation again applies here: that the regularity & order is manifestly displayed in world-2 demands an explanation. Suppose that this is another mathematically consistent explanation for this. Call this world-3.

and so on.

We appear to have an infinite regress. Does this mean that any mathematical description of the world can never be complete in itself?

A rough example of this is the description of our own universe in the standard model. Then the explanation of fine-tuning demands explanation - some treatments consider then the perspective of a larger multiverse.

• What would a mathematically consistent explanation of a mathematically consistent explanation be? Also, in what sense are the mathematically consistent models of world-1 explanations? It seems that they represent rather than explain. If you're interested in a similar argument against metaphysical realism, check out Putnam's "Model Theoretic Argument". It is summarized in section 4.5 of the linked article. – Dennis May 29 '13 at 16:15
• @Dennis: ok, I can see why you say & agree that they represent. But its also true that are in some sense an explanation in say the way occams razor 'chooses' the simlest explanation; or would you say the simplest representation here? – Mozibur Ullah May 29 '13 at 17:52
• Wouldn't the most complete, simplest explanation of world-1 be world-1 itself; or a copy of world-1? A mathematical model explaining world 1 would have to encompass world 1 itself then draw its conclusions from that (otherwise where would conclusion be drawn from?), thus making it a more complex explanation of world 1 than world 1 is itself. So if world 2 is the simplest, least complex, and complete explanation of world 1, world 2 is then just world 1 or a copy of world 1. By the same principle world 3 is world 2, so on. – KDecker May 29 '13 at 18:37
• @Dennis: Its also possible to find a simpler explanation that is also more complex. For example some features of the ring of integers are more readily explained when one considers all rings (of a suitable kind). Together they form a geometric object. An apposite example would be the circle - said to be by the greeks the most perfect shape - but they also came up with hyperbolae, and parabolas (imperfect shapes) - which can be fitted together into one geometric shape. Now by analogy think of the circle as the representation of our world. – Mozibur Ullah May 29 '13 at 19:48
• I might add this could be taken to any, I guess, system or reality. Maybe only certain systems can do this; describe themselves fully. For instance Rule 110 of cellular automata is shown to be Turing complete. So you could create rule 110, within rule 110, the entirety of the system within itself. – KDecker May 29 '13 at 21:46