On 3/3/07, Mitchell Porter <[EMAIL PROTECTED]> wrote:
I also want to say something
about theories of plenitude, by which I mean theories according to which all possible Xs exist, or even that all possible Xs *necessarily* exist. Stathis, can you tell me *why* it is that all mathematical structures would 'exist necessarily'? I can see why it would be intellectually convenient *if* that were true, but can you actually explain the *mechanism* of 'necessary existence'? The theological use of the concept is illuminating. The universe exists, I don't know why. Maybe God made it; but then why does God exist? I can go into infinite regress; or I can suppose that some things exist for a reason other than that they were caused to exist by some agency external to them. For example, maybe they just had to exist, as a matter of logical necessity (although I can't right now exhibit the exact reason). Thus, I believe, the idea of a 'necessary existent' was born - it was perceived that *if there were such a novel mode of causation*, it would offer a third way between an infinite regress of gods, and a First Cause whose own existence was just an uncaused brute fact (and therefore presumably contingent). This genealogy of the concept does not in itself disprove the possibility that such a mode of causation actually exists, of course.
This raises the question of Anselm's ontological proof for the existence of God: that since God is the most perfect being imaginable, it would be contradictory if he did not exist, because then it would be possible to imagine a being just like God but with the additional attribute of existence, i.e. to imagine something more perfect than the most perfect being imaginable. This is a roundabout way of defining God as necessarily existing, and arguments from first cause therefore effectively reduce to the ontological argument if they are to avoid the infinite regress of gods, as you put it. But the problem with ontological type arguments is that they allow you to conjure up anything you like by simply defining it as existing. If there is a physical reality, things don't work like that. Statements of mathematics and logic, however, are necessarily true (or false). This is what I meant by saying that mathematical structures exist necessarily: not that "17 is prime" means you may meet a prime-looking number 17 walking down the street, but that 17 is necessarily prime, and not even God can change that. So *if* there is no separate physical reality, and what we always thought of as physical reality is just mathematical reality, it would solve the problem of why something rather than nothing exists, or why God exists, or why God made the world. I could probably write another essay critiquing your last statement that
'All it takes is one infinite computer to arise in this physical world and it will generate the mathematical Plenitude', except that I cannot guess what hidden premises lie behind it. 'All it takes' - is an infinite computer really such a small request?! Also, just because something is infinite doesn't mean that every finite possibility is in it somewhere - this is obvious even for real numbers.
There have been scenarios entertained for life's survival into the indefinite future which effectively are ways to fit infinite computational steps into whatever cosmological model is seen as likely (eg. Freeman Dyson, Frank Tipler), and that's restricting it to the type of universe that we observe. The program generating the Plenitude on such a computer need not be complex: a universal dovetailer will generate all possible computations and we might be living in the output of such a program right now. Then there is the question of what it means to implement a computation. If you look at it the right way, anything could be a computation. This has been given by John Searle as a reductio ad absurdum against computationalism, and explored by several other authors (eg. Hilary Putnam, David Chalmers, Greg Egan). The usual counterargument is that in order to map a computation onto an arbitrary physical process, the mapping function must contain the computation already, but this is only significant for an external observer. The inhabitants of a virtual environment will not suddenly cease being conscious if all the manuals showing how an external observer might interpret what is going on in the computation are lost; it matters only that there is some such possible interpretation. Moreover, it is possible to map many computations to the one physical process. In the limiting case, a single state, perhaps the null state, can be mapped onto all computations. Stathis Papaiaonnou ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=11983
