Re: Contradiction. Was: Probability

From: Brent Meeker <>
Date: Sat, 08 Nov 2008 14:11:47 -0800

A. Wolf wrote:
>> I'm well aware of relativity. But I don't see how you can invoke it when
>> discussing all possible, i.e. non-contradictory, universes. Neither do I see
>> that list of states universes would be a teeny subset of all mathematically
>> consistent universes. On the contrary, it would be very large. It would
>> certainly be much larger than that teeny subset obeying general relativity or
>> Newtonian physics or the standard model of QFT in Minkowski spacetime.
> You said: "So universes that consisted just of lists of
> (state_i)(state_i+1)... would exist, where a state might or might not
> have an implicate time value."
> I was trying to express that the universe in which we reside isn't
> separable into a set of lists of states. It's more mathematically
> complex than that.
> Some mathematical models are self-contradictory, and some are not.
> This is true regardless as to how you formulate a foundation of
> mathematics, and it forms the basis for understanding and proving
> mathematical truths. I believe that a mathematical structure complex
> enough to capture the entire set of events that define a universe must
> be non-self-contradictory to be a truthful model for that universe.
> There are mathematical structures which are self-contradictory because
> they are predicated upon axioms which ultimately contradict
> themselves; these structures are not well-defined and cannot be a
> basis for existence. Such a basis would make existence itself
> ambiguous, because all things would have to exist and not-exist at the
> same time, and not in the quantum way--with no discernable structure
> or foundation at all.
> I'm not certain what you're trying to argue, but it seems like you
> think that anything you can imagine must have a well-founded
> mathematical basis...?

So long as it is not self-contradictory I can make it an axiom of a mathematical
basis. It may not be very interesting mathematics to postulate:

Axiom 1: There is a purple cow momentarily appearing to Anna and then vanishing.

but by the standard that everything not self-contradictory is mathematics it's
just as good as Peano's.

>You can imagine all you like, but it won't
> bring into being a universe where Godel's incompleteness theorems
> don't hold, for example. The fundamental things that we know about
> mathematics itself transcend any particular realization of the
> universe.
> Anna

I'm arguing that "all mathematically consistent structures" is itself an ill
defined concept. A mathematical structure consists of a set of axioms and rules
of inference. So I supported my point my giving an example in which the set of
axioms is an infinite set of propositions of the form "state i obtains at time
i" where "state i" can be any set of self-consistent declarative sentences
whatsoever. I leave the set of rules of inference empty - so there can be no
contradiction inferred between states. Then according to the theory that all
mathematically consistent structures are instantiated (everything exists) this
set exists and defines a "universe" just as well as general relativity or
quantum field theory (perhaps better since we can't be sure those theories are


You received this message because you are subscribed to the Google Groups "Everything List" group.
To post to this group, send email to
To unsubscribe from this group, send email to
For more options, visit this group at
Received on Sat Nov 08 2008 - 17:11:58 PST

This archive was generated by hypermail 2.3.0 : Fri Feb 16 2018 - 13:20:15 PST