In this blog post I shall be addressing the question "What exists?". This is a thorny issue and before going further I must warn the reader that my thoughts on this matter are in a state of flux (hence I may soon change my mind on these matters). Never the less I shall present the state of my thinking on this.

1) There is some way of representing universes as mathematical entities (specifically infinite sequences in finitary languages (for mathematicians I am assuming AC)). My basis for this is simple: I regard mathematics as the study of all possible universes.

If mathematics does not allow the representing of universes (or at least their modelling for the questions in hand) then I regard mathematics to be incorrect or deficient in some way.

2) Two universes should be regarded as the same if their representations can be calculated from each other (in an objectively computational way). If universe A is represented 01010201... and universe B is represented 0011001100220011... then there is a simple way to calculate one from the other & vice versa and so universes A and B should be considered identical. This is a decidedly strong principle and should not be accepted without some deep thought. It has some interesting consequences in ethics and aesthetics (perhaps another post topic).

This would imply that all finite universes are essentially the same (a very strong claim!). I don't have any issue with this personally but you would if you believed that infinite universes were impossible (and perhaps for other reasons too). It does not imply that all infinite universes are the same though.

3) There are two notions of existence. Firstly what entities exist somewhere out there. Secondly what entities exist that could in principle effect you.

3a) Consider all possible universes. The question should be: "Which of these possible universes exist?". Now if some possible universes exist and some do not we can ask "Why do some exist and others not?". Either there is some logical difference between the contents of these possible universe or there is not. If there is no logical difference then the fact of the existence of those universes is entirely arbitrary (A bad position I'd hope you agree). If there is a logical difference we are asked to accept that the presence of some feature of possible universes makes them exist (say the property of having cats alive at some point in their history). Again any such internal feature conferring existence if highly dubious. It seems evident to me that under these conditions that in fact all possible universes should be taken to exist or all possible universes must be taken not to exist. From these two possibilities I'd plump for the former!

3b) The second notion of existence can be defined roughly as follows: Everything that has effected you or might at some future time effect you must be taken to exist. Everything else does not exist.

Now for the punch line: The second notion of existence is generally the most useful. After all the tiger thats walking down the street outside your front door in a parallel universe is of no immediate concern to you. However, when engaged in discussions concerning the probability of our universe the first definition is key. Hence my answer to the question of why our universe has the apparent fine tuning it has is "All possible universes exist so there is nothing to explain."

4) Seeing a universe from a perspective is like projecting that universe down in some way. Imagine the universe as a wire model and your perspective as the shadow it casts on the table top. Different ways of representing a universe are different universal perspectives.

A word of caution: This does not imply moral relativism. The moral decisions you make must still be made from your perspective (although not necessarily with just any moral theory).

I may put up another post soon arguing why I think this attitude to the concept of existence implies that qualia don't exist and that the strong AI thesis is probably correct.

My goodness, Magister Dawson; you tackle the hardest metaphysical issues. You are a brave individual!

Your point '1.' - I was discussing with Michael about this, and Michael (I told him misunderstandingly) thought you meant as describing normal entities in the way that Mechanics or Statistics does; so, to mathematically represent the belief function in probability epistemology, or the idealisation of laws of nature in mechanics. I told him this was probably NOT what you mean. Michael's interpretation of your point is a seperate issue; you are making the EVEN BOLDER (and more unique) claim that UNIVERSES can be mathematically represented. We think you need to say more about this, as it seems promising. It's a more interesting point than the actual topic of this post.

Another curiosity I have: How far do you think this criterion of existence in relation to possible universes appeals to our intuition?

Many non-philosophers (inc. 'continental philosophers') and non-logicians wonder what is the point of mentioning these weird entities of 'possible worlds'.

I don't actually hold this wonder, but I wonder how you would justify to those who are unfamiliar with this whole 'possible universe' talk why it is important to think about these things.

Lets not isolate ourselves from the very people we try to emendate and improve by alienating them with what they see as very weird talk!

Always a pleasure to read you, Dawson.

Destre

Posted by: Destre | 16 December 2007 at 01:36

I will write more about mathematically representing universes in another post. But briefly more detail on (1): All the information about a universe at all locations within that universe can be collected together (in universes with a notion of time all times and places). A means of coding must be chosen to represent that information mathematically. Once a coding is chosen the information can be represented by a mathematical object (I'd say a set is the right mathematical object for this task).

The coding is unimportant because (2) guarentees that whatever coding you choose the representations you get will correspond to the same universe.

I would tend to justify talk about possible universes by saying that in many problem solving instances you need to think outside the problem to actually solve it. When one solves a problem in geometry it almost always involves constructing new lines, circles that were not in the original puzzle. In solving big problems in our universe (or about it) it would be foolish to think that we would not even need to imagine how things might have been.

One other example in challenging the subjugation of women it was necessary to imagine another possible world (one where women were free to vote and to decide their own life choices).

Posted by: Barnaby Dawson | 17 December 2007 at 14:25