Saturday, November 13, 2010

The Alternative to Naturalism

...is Philosophy, which revolves around debates between Naturalists and Theists. It is a few centuries since Philosophy was the alternative to Theism, but the mainstream of analytical philosophy remains Naturalism, which is essentially atheistic. Science, which Naturalists emphasise, is not atheistic, however, but agnostic. Indeed, the particular sciences are not just agnostic about God, but about most other things too, so that scientists make the most interesting connexions. But Naturalists, no less than Theists, aim not so much to join up the sciences, but to find holes in each others’ arguments.
......As a mathematician, I am quite interested in seeing how mathematics would differ from standard set theory were we created by a Perfect Being. Indeed, I suspect there is an argument from 2 + 2 = 4 to the existence of a Perfect Being who created us. Mainstream philosophy of mathematics takes ‘2 + 2 = 4’ to be what mainstream mathematics—whose foundation is axiomatic set theory—says it is, and aims to develop an atheistic epistemology of set theory. As they do so, their concepts become implausible (whence the possibility of such an argument).
......Ironically, it is because I am essentially a mathematician that my approach to philosophical problems would strike most analytical philosophers as insufficiently mathematical (formal). And incidentally, there is a famous story (quoted from blogcritics) that:
Czarina Catherine the Great of Russia was concerned about the deleterious effect the philosopher Diderot was having on the religious faith of the nobility who were listening to him hold forth on atheism in her court. She encouraged famous mathematician Leonard Euler to confront him, and he did, with the following challenge: “Sir, (a + bn)/z = x, hence God exists—reply!” Diderot, who, according to the story, was completely mystified by all things mathematical, fled the court and
Russia in deep humiliation. Diderot and Euler actually were in Russia at the same time, both at the invitation of the Czarina, but this is a joke at Diderot’s expense that neither Euler the man nor Euler the mathematician would have made. Even if it had been, Diderot—who was actually a fairly capable mathematician himself—would not have been stumped.

6 comments:

Xamuel said...

For a more serious and non-joke mathematical argument for "God", look up the simulation argument (my own article on it is here, though that hardly does justice to the actual paper, which is here (pdf)). Of course, in this case "God" has a very different sort of meaning.

enigMan said...

I've met the simulation argument before, in a talk at Glasgow by Nikk Effingham. That argument was that whereas we're very unlikely to be alone in the universe, e.g. to be the first space-faring species, we don't see aliens or evidence of their constructions. The conclusion was that we're living in a Matrix-style world. One problem with that argument is the assumption that we'd see aliens if they were there. Even if they were amongst us now, they could hide quite effectively by using vast computing power behind ubiquitous nanotechnology.

But another problem, which also affects your version, is that the notion of advanced aliens creating such a simulation is a notion that coheres with the world as we know it. According to the simulation argument, the world as we know it is just a simulation. So the problem, the question, is why would the apparent laws of physics within such a Matrix-style world be likely to resemble the real, underlying laws of physics in apposite ways? If the Matrix-style simulation was of a magical world, those within it might give an argument that they were likely to be under the spell of a very powerful magician.

Xamuel said...

I don't see why physics in the simulation should necessarily need to have any relation with physics a level above. (See also this comic: http://www.smbc-comics.com/index.php?db=comics&id=2055#comic )

There is the question of whether the laws of probability behave as we believe them to in the "real" world, but that doesn't defeat the simulation argument: if the laws of probability are as we know them, then the argument goes through; if they fail because we're in an inaccurate simulation, then that is one of the three disjuncts and we're done.

Looking forward to your series on theology btw. Keep the great posts coming :)

enigMan said...

You assume that (i) our descendents will be able to create AIs, (ii) with lives as ours seem to be, (iii) in great quantity, whence (iv) we are most likely to be in such a simulation. But (i) assumes that AI is physically possible, and your whole argument therefor relies on such a possibility being not too unlikely. And (ii) and (iii) rely on the real world having sufficient matter, energy and time to facilitate such progress. So, either the world is as it appears to be, but then we're not in a simulation, or anything like it. Or else we're in a simulation, or something like it. In the former case (ii) and (iii) appear to be OK, but I would question (i). In the latter case, (i) might be OK, but we've little reason to accept (ii) and (iii).

Suppose we accept that all 3 follow from how the world appears to be. That means that if the world is like that, then a random soul with experiences like ours would, in such a world, probably be in a simulation. But what of a random soul in such a world? It would probably not have experiences that were like the real world. Can we conclude that we probably don't? No, as you point out, for we do have such experiences. But what of a random soul with experiences like ours in any possible world? Well, again your argument seems safe, because in other worlds the real world is not going to be like this one, and so the soul would be in a simualtion, or something like it. The problem is that your argument was that we were likely to be simulations, so you need a vast number of possibilities compared to a smaller number.

Suppose we're likely to become extinct, very probably by advancing too far beyond our natural place in the world. Then out of all the possible souls, we might be most likely to be in the real world, before such a catastrophe. Despite your argument, a random soul would be most likely not to be a simulation. Whether or not that is the case depends on the details of how rapidly some possible futures produce vast numbers of simulations, compared with the proportion of possible futures in which that very progress proves too much for the human species. The fact that we got this far might be evidence for your conclusion, or it might indicate that we've been quite lucky, or it might say little given that we're still bouncing around the level of horsepower plus the possibility of nuclear or viral armagedon.

Furthermore, your (i) assumes that AI is physically possible, but we should really consider worlds in which our physics is such that it is, and other worlds too. You may consider the latter to be unlikely, given the evidence, but there are infinitely many of them. So we end up comparing infinite sets of possibilities; which are rather paradoxical. And surely we have, philosophically, to consider such worlds if we are already considering that the real world might be quite unlike the simualtion that we are in, for all that in that case we would indeed be in a simulation. After all, in such a world we might be unlikely to be a simulation...

enigMan said...

...to put the matter a bit more clearly, why would anyone take the simulation argument seriously? Presumably it is because they think that AI is physically possible. And presumably they think that because they are materialists. But if they are materialists then, prima facie, they don't think they're living in a simulation. So your argument amounts to a reductio of materialism. One lacuna in that reductio is that materialism may be compatible with the world being a simulation. But that does make quite a significant change to most people's view of materialism, to something more like most people's view of Idealism.

Another lacuna is that AI may not be physically possible. So your argument may be taken by many materialists to be a reductio of the possibility of AI that is indistinguishable from ourselves. To argue against that reductio (of your argument's first premise), you would have to argue that the world might be a simulation. But then other possibilities, such as dualism or Theism, may not seem to be ruled out by the evidence either. And as mentioned in my previous comment, introducing such possibilities ruins your argument. You don't then have a nice finite set of 'real-world' possibilities, for some random soul, but very complex and infinite sets.

enigMan said...

To put it another way, most simulations might be of magical worlds. If so then, if we were likely to be in a simulation, we would be likely to be in a magical world. So then the common assumption that this world is non-magical (which is especially common amongst those who accept strong AI) seems suspect. And if we then try to run the simulation argument with variable underlying physics, the possibilities become infinite and weird and we can no longer draw the conclusion that the controller of our simulation is worthy of the name "God" nor, indeed, that we are likely to be in a simulation.

It may seem that we are still likely to be in a simulation, since either the underlying physics is as it appears or not, and in the former case we run your simulation argument, and in the latter case we are in something like a simulation. But I think that there is still a subtle problem with that. E.g. the latter case includes worlds where strong AI is false (for those who think that strong AI is indicated by physics). E.g. it includes worlds where an evil magician has put us under a spell that lets us perceive the world as it is, but makes us very bad at physics. Etc.

One thing the simulation argument may be very good for is making materialists aware of the fact that science only gives us empirically adequate models of reality. Naturalists want us to believe those models, but scientists themselves tend to be more modest. After all, the history of science shows how theories can change in unpredictable ways. So physics doesn't say that we aren't living in a simulation, or that Idealism isn't true, or that miracles can't happen, etc. Similarly, it never said that atoms didn't have internal structures. Indeed, nor did it say what such internal structures would have to be like.