Huperborea

Over at Pharyngula, a pseudointellectual with "just enough of learning to misquote," FrankT, attempted to criticize Gödel's Ontological Argument, a feat which is manifestly above his intellectual (I use the word loosely in reference to him) pay grade. I have copied the cognitively-impaired poser's comments and interspersed my responses below.

There are five axioms to it, and I will bold the ones that are bullshit:

1. A quality can be uniquely positive or negative.
(fails even a cursory Buddhist or Aristotelian analysis, but moving on)

This is a textbook example of pseudoargumentation. Moreover, it is positive or non-positive. Apparently, FrankT is unaware of the concept of zero.

2. If a quality is uniquely positive, then the qualities implied by having that quality are positive.
(I think this one slides, because it's basically definitional, not that it matters because I cannot name a single uniquely positive trait)

FrankT's inability to "name a single uniquely positive trait" is not my problem, nor is it Kurt Gödel's.

3. If two qualities are positive, both qualities together are positive.
(while I like "delicious" things and "intelligent" things, I would prefer that intelligent things not be delicious)

This is just as vapid a response as the tea "counterexample" offered by a guy at the Sierra Q&A. To quote Christopher Small:

In ordinary language, we might be inclined to say that one thing is greater than another if
the former has some positive attribute that the latter lacks. We might disagree with each
other as to the ranking of things or objects according to their value, but we must inevitably
make such judgements, whether we regard them as objective or not. In view of the
ambiguity of such concepts, it is important to understand what Gödel meant by a positive
attribute. In his own words he said that the operator Pos could be interpreted in a
moral-aesthetic sense, or in the sense of pure attribution. The concept of a predicate
being positive in a moral or aesthetic sense, provides no difficulty, at least initially.
Clearly, if Fx means that x is beautiful, we would be willing to accept that F is positive
in an aesthetic sense, even if we disagree in our judgements about beauty. If Fx means
that x is virtuous, we might grant the same, even if we have no idea what virtue is. But
what is meant by “pure attribution?” By “pure attribution,” Gödel states that we are to
understand that a predicate attributes some quality to an individual, and that the quality
contains no element of “privation.”

"Deliciousness" is not a positive property in either sense. Thus, FrankT's "counterexample" falls apart.

4. All properties are uniquely positive or negative and not both.
(this one is just actually laughable, so whatever)

Yet another textbook example of pseudoargumentation from intellectually-bankrupt FrankT. Moreover, as I noted above, it is positive or non-positive. Apparently, FrankT is unaware of the concept of zero.

5. Existence is a quality that is positive.
(existing would seem to have an overall degree of positiveness equal to the overall positiveness of the thing that either did or did not exist. Something baleful like a werewolf would be more negative if it existed than if it did not exist, while something awesome like the invisible pink unicorn would be more positive if it existed. And of course, something completely inconsequential like the celestial teapot would be just as meaningless if it existed as if it didn't)

Necessary existence is a positive, you damn moron. Gödel's Ontological Argument employs modal logic.

So basically it's really easy to refute, because all of the premises are wrong. Furthermore, there is a core problem with the logic, which is that just because an infinite series summation of positive traits would, given those premises, sum to the existence of an all powerful all whatever god-thing, doesn't mean that such an infinite series ever actually starts.

Achilles catches the tortoise, because Zeno's paradox is answered by Leibnitz and Newton and the infinite series of half distances does complete and total up to a whole. But Achilles does not catch every tortoise, he just catches the ones he chases. He has to start a series before he can finish it. And there is no reason to believe that anything ever started amassing an infinite series of all possible positive traits, even if there was such a thing.

Now, the Ontological Argument goes that basically by imagining the collection of all possible positive traits that you have in fact started that process - that your very own hubris is Achilles and that when you catch the tortoise it will be an omnipotent god. That is a level of solipsism and hubris that defies ready comprehension. But you can see why it might have appealed to St. Anselm, Leibnitz, and Kurt Gödel. Because they were all whack jobs who spent all their time thinking about infinity.

...

The fact that the Ontological argument is a total failure has little to do with the fact that it uses modalities. It's that both the premises and the logical chain after it are wrong. Perfectly valid attacks against it include attacking virtually any of the premises. But also the fact that infinite series summation just doesn't work that way. Convergent series reach conclusion and give real answers. But divergent ones don't. In the real universe there are no infinitely large rocks, infinitely large amounts of energy, infinitely large spaces, or infinitely powerful forces. Everything, even amongst the really stupidly large things, is finite.

So if someone has a series that includes infinite power or infinite anything else, then that series by definition never completes. So since it never finishes acquiring all the traits, there's no reason to believe it ever acquires "existence" either.

This is the most moronic part of an exceedingly moronic screed. So moronic, in fact, that it is not even wrong. (Yet, FrankT was still able to hoodwink a number of dupes over at Pharyngula, which speaks volumes.) First of all, Anselm, Leibniz, and Gödel were great thinkers, not "whack jobs," and it is offensive to see them labeled as such by FrankT, a noxious mediocrity. Moreover, an "infinite series summation" doesn't enter into it. Axiom 3 (as listed by FrankT, which follows the presentation on wikipedia) simply states that if p1, p2, ..., pn are positive then the collection, i.e.,
p1 AND p2...AND pn is positive. There is no infinite sum here.

Now, if we were talking about probability (we're not) and we looked at the probability of p1 AND p2 ... AND pn, i.e., the intersection (for the sake of argument treating the pk's as events, which they aren't), then we would have an infinite product of probabilities as n approached infinity provided the pk's were independent (again, treating the pk's as events, which is not the case). Even that stretch does not give an infinite sum, though. To arrive at an infinite sum, you would have to look at the probability of p1 OR p2...OR pn, i.e., the union of the pk's, which would be an infinite sum of probabilities as n approached infinity provided the pk's were mutually exclusive.

However, we are not dealing with probability and even if we were, the closest analog is an infinite product, not an infinite sum. (Incidentally, both the infinite product and the infinite sum I mentioned would fall in the interval [0, 1]). How this brain-dead pharyngulite came to associate Gödel's Ontological Argument with an "infinite series summation" is beyond me.

Incidentally, for those readers who do not know the difference between independent and mutually exclusive events, I recommend the following video I posted to youtube a couple of years ago.

And while Kurt Gödel ended his life of starvation because he was mortally afraid of being poisoned and would not eat unless his wife prechewed his food to assure him that it had not been poisoned, he was very good at thinking about infinity when he wasn't waiting for his wife to get out of the hospital so that he could eat again.

...

Which is why I was so surprised that our creationist friend stood up and said that his best argument for a god was Gödel's ontological proof. Because that one is a set of magic words written by a crazy man after he started wasting away into madness. That's like saying that your best argument for something is the last mad scratchings of Dr. Herbert West.

This is a low-blow but one I would associate with a mind of FrankT's caliber. Not only that, but it competes with his "infinite series" nonsense on the scale of utter stupidity. Kurt Gödel formulated his ontological argument long before he started suffering from paranoia and even if that were not the case, there is no reason to believe it would have adversely affected his mathematical work. The fact of the matter is that Gödel was far, far more intelligent and competent in his final days than FrankT could ever hope to be on his best day.

Labels: God, mathematics, philosophy, probability, theism, theology

As far as I know, there is no reason to believe the values of the physical constants are necessary, in which case, we have the following likelihood ratio:

P(physical constants and the universe in which we exist|God)/P(physical constants and the universe in which we exist|no God) =

P(physical constants|God)P(the universe in which we exist|physical constants and God)/
P(physical constants|no God)P(the universe in which we exist|physical constants and no God)

Now, P(the universe in which we exist|physical constants and God)/P(the universe in which we exist|physical constants and no God) is essentially one since it does not seem likely that our universe depends on whether the physical constants we observe arose by design or not. Therefore, the likelihood ratio takes the form:

P(physical constants|God)/
P(physical constants|no God)

which I argue is large since it is easy to conceive of God wishing to create a particular universe and choosing the appropriate values of the physical constants whereas a random selection would be very unlikely to achieve the correct values.

Incidentally, I "borrowed" this argument from David Bartholomew's article, "Probability, Statistics and Theology." (Journal of the Royal Statistical Society. Vol. 151, No. 1
1988, pp. 137-178)

Labels: God, physics, probability, statistics, theism, theology

A. Skorokhod is a big name in probability. The following is excerpted from one of his books:

1.1.1 Determinism and Chaos

In a deterministic world, randomness must be absent -- it is absolutely subject to laws that specify its state uniquely at each moment of time. This idea of the world (setting aside philosophical and theological considerations) existed among mathematicians and physicists in the 18th and 19th centuries (Newton, Laplace, etc.). However, such a world was all the same unpredictable because of its complex arrangement. In order to determine a future state, it is necessary to know its present state absolutely precisely and that is impossible. It is more promising to apply determinism to individual phenomena or aggregates of them. There is a determinate relationship between occurrences if one entails the other necessarily. The heating of water to 100°C under standard atmospheric pressure, let us say, implies that the water will boil. Thus, in a determinate situation, there is complete order in a system of phenomena or the objects to which these phenomena pertain. People have observed that kind of order in the motion of the planets (and also the Moon and Sun) and this order has made it possible to predict celestial occurrences like lunar and solar eclipses. Such order can be observed in the disposition of molecules in a crystal (it is easy to give other examples of complete order). The most precise idea of complete order is expressed by a collection of absolutely indistinguishable objects.

In contrast to a deterministic world would be a chaotic world in which no relationships are present. The ancient Greeks had some notion of such a chaotic world. According to their conception, the existing world arose out of a primary chaos. Again, if we confine ourselves just to some group of objects, then we may regard this system to be completely chaotic if the things are entirely distinct. We are excluding the possibility of comparing the objects and ascertaining relationships among them (including even causal relationships). Both of these cases are similar: the selection of one (or several objects) from the collection yields no information. In the first case, we know right away that all of the objects are identical and in the second, the heterogeneity of the objects makes it impossible to draw any conclusions about the remaining ones. Observe that this is not the only way in which these two contrasting situations resemble one another. As might be expected, according to Hegel's laws of logic, these totally contrasting situations describe the exact same situation. If the objects in a chaotic system are impossible to compare, then one cannot distinguish between them so that instead of complete disorder, we have complete order.

Labels: philosophy, probability