Sunday, March 19, 2006

Philosophy in need of help

I was debating with Richard at Philosophy et cetera And yet again we are pondering a hypothetical.

If this is what happens in philosophy classes nowadays I think they seriously need an injection of scientists into their debates!

1) Everyone starts off in the blissful sphere. But each day, one more person gets permanently transferred across to the agony sphere, where they reside for the rest of eternity.

2) Everyone starts off in the agony sphere. But each day, one more person gets permanently transferred across to the blissful sphere, where they reside for the rest of eternity.

Which scenario is better? The answer, paradoxically, appears to be "both". At any moment in time, there will be infinitely many people in the original sphere, and only a finite number who have been transferred across. So option 1 is better.

However, each particular person will spend only a finite amount of time in the first sphere, whereas they will spend an eternity in their post-transfer home. So option 2 is better.


To avoid question-begging, we must adopt ...[an] objective perspective on the question. For example, imagine you're a benevolent God, faced with the choice of creating one or other of these worlds.

What Richard does is proposes a hypothetical combines this with some assumptions about how maths works and in doing so creates some clear contradictions – the then ponders why there is a contradiction.

1) He specifically denies an (omnipotent) god the power (and only this power) to resolve infinities or see the conclusion of one. For example this god is able to see a time when any single individual has moved sphere but not see a time when most individuals will have moved over to the new sphere. Despite the fact that being outside of time, infinite time would mean nothing to him.
If you are going to do this how can you propose the perspective?

2) which brings us to the second error. Richard assumes (without really explaining why) in this scenario you would know person 1 at time 0 who has to wait for one day and be able to work from here to find person two and day two etc. This sounds logical at first until you think about it
A) you were looking at an example of this what are the odds you would be at the very beginning of time?
There are two perspectives god and individual.
i) If you are god (as Richard suggests) the question is meaningless because you see ALL of the scenario instantly because you are outside time (matter/time are related).

ii) If you are an individual and it is random your odds would be 0 (limx(x0)) the only thing you would be likely to see is an uncountable set of people in both spheres and uncountable periods before or since transfer.
The individual that you would have data on would have a “time to wait” (or n as Richard puts it) which was too big for you to count (bigger than any conceivable real number [go on – I dare you to conceive of a bigger one]) so too would his neighbors – all of them. There would be issues with subjecting any of these numbers to maths except in as far as they are very large.

3) Richard seems to perform some functions on infinity while denying the legitimacy of others.

For example Richard defines a special infinity by saying an infinite number of people all have a finite number of days in each sphere. Essentially performing a reverse “sum of the numbers less than” function on infinity and producing a finite number while talking about infinity being a “direction” and immune to things like multiplication. Why this function would be exempt is strange (or is it just another entirely arbitrary constraint?), but then why does he not then resolve other functions involving infinities? (ones more useful to the solution). Furthermore if these methods of comparison change the problem (as opposed to being cosmetic) one has to wonder what else is missing. Regardless - it breaks down simple assumptions such as the number of people being related to the numbers people are allocated.

Meanwhile he also continues to talk about things like "for all n" in an infinite set. This implies knowledge of what happens all across the infinite range the same infinite range that he seems to refuse to allow to be combined in the usual (1,1,1,1,1…)/(2,2,2,2,2…) = (½,1/2,1/2) ( I.e. lim (y)/lim (x)) or any other mathmatical methodology.

4) While Richard in part treats infinities as unsolvable this isn’t how we deal with infinities in the physical sciences, which is related to the context in which he is applying it. Physicists often face examples of infinity, what they do is utilize strategies such as “renormalization”. Generally they will start to talk about the result that the formulae tends towards as the number/s approach infinity (as in the above point) or look at the real results and extrapolate. These methods are used to solve al sorts of problems and physics would be crippled without it. There are also branches of maths which can deal more directly with infinite set maths, such as hyperreal maths.

5) In a practical sense physics would still take a dim view of Richard’s approach. Richard suggests that there is a start and an infinite end of the timeline / population. Now, Time or space could theoretically be infinite BUT it is also reversible – start and end are not fundamentally different (except for entropy). Therefore if there is first person seeing a future of sphere hopping it is also valid to see a last person looking back on a history of it. They can’t get to each other by traveling along the infinity (like a “person” inside and outside of a black hole) but that doesn’t mean they don’t equally “exist”.

6) Regardless - infinity is an ill defined number. This means you cant think of it just like a number. In that sense any infinity might as well be the same – but you can’t say it IS the same.


Philosophically I am also interested in how this effects Richard’s beliefs. For example if you believe that such a case exists what are the moral rules for individuals? If one is trying to maximize utility one soon realizes that it is unsolvable no matter what you do in fact if infinity plus one = infinity (the stricter definition that Richard uses of insolvability) then there is no moral obligation to do anything.
This would be the case if
1) there is infinite time
2) there exist an infinitely greater being
3) there is infinite space
4) there are infinite alternate universes
5) there is a way of achieving infinite utility and some one does achieve it
And a host of other infinite related things
I expect most people would be inclined to believe in one of those. However people dont usually see it as jsutifying throwing ones hands in the air as a philopophy of life (that would be justified by other things!).


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