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

In response to bogus claims from the audience that Gödel's Ontological Argument is circular, I articulated the most basic form a premise would take in modal logic (related to the topic at hand), i.e., if God exists, then he exists necessarily. The audience, in unison, shouting back "IF God exists..." to which I replied, "YES IF, that's the form mathematical arguments take. In mathematics we define an object and then seek to prove it exists." I was trying to show them that a premise of the form "If P then necessarily P" is legitimate and not "circular." The following is excerpted from this article:

"If God exists, then it is necessary that he exists."

In this example, "necessary" has narrow scope, that is, its scope is restricted to the proposition's consequent, rather than the whole proposition. The proposition claims that if God does in fact exist, then His existence is a necessary one. This is a special claim about God which is not true of other things; for instance, it is thankfully not the case that if Osama bin Laden exists then he necessarily exists. If the scope of the modality were broad, then the proposition would say that it is necessarily the case that if God exists then He exists. While this is true, it is true of everything including Osama bin Laden.

In these two examples it is clear what the scope of the modality is, but in other sentences it is not clear whether the modality has a broad or narrow scope. The modal scope fallacy occurs when this amphiboly is exploited.

The audience was hopeless, however, and accused me of being an obtuse creationist. I refer the interested reader to my previous comments on Dawkins' fan club, wherein I combat similar inanity. Also, I refer the interested reader here for what a mathematician (i.e., "Tarski") who publishes research and does not accept Gödel's Ontological Argument wrote in response to an pretentious atheist who was similarly clueless in asserting that the argument is transparently circular.

"Tarski" in brief:

There is a difference between saying that Gödel just simplemindedly begged the question and recognizing that not only do we usually take truths in axiomatic system to be based on the assumed truth of the axioms, it is also the case that the ontology of the entities derived in existential proofs must lean on the ontology of the axioms in some way also; but this seems tricky to me.

This type of thing does not interfere with the work of (most) mathematicians and scientists.

To be continued...

Labels: Christianity, God, science, theism

The question I posed to PZ was:

"In your own words, your contributions to science are piddling. [Those are your words, not mine. I just happen to agree with them.] To that I would add that your arguments against God are just as risible as those of Dawkins and the other occupants of the new atheist clown car. Given that, why should anyone who is not already one of your chamchas pay attention to you as opposed to others who are far more accomplished and rational?"

(I added the bracketed part upon hearing a feral growl from the audience.)

PZ responded by trying to dismiss me as a creationist. Now, I don't mind being labeled a creationist, provided it is understood that I accept that the age of the earth is measured in billions of years and that I am not solicitous about the historicity of anyone before Abraham. However, my question/challenge to PZ had nothing to do with creationism, except in the broadest sense of someone who thinks God created life (somehow). I interjected that my question had nothing to do with creationism and PZ replied that his talk was about creationism. (Except the last slide was about atheism, not creationism, and that was the slide to which I was responding.) PZ then claimed I used a creationist tactic by quote-mining him in that I did not include his caveat about most (all?) individual scientific contributions being piddling. (I'll let the reader judge whether I quote-mined PZ.)

PZ then asked me which arguments for God I accepted/endorsed. I mentioned Gödel's Ontological Argument and then he adroitly turned the tables on me by asking me to defend it. Now, I was prepared to address some of PZ and others' anemic/fallacious arguments against/misrepresentations of theistic arguments but I was not prepared to defend Gödel's Ontological Argument. To adequately defend it I would needed worked out notes and access to a white board at center stage. It was essentially impossible for me to argue for it unprepared and from a seat in the audience, and I started to say as much, but I was egged on by PZ and essentially told to "put up or shut up" by a rude, corpulent chin-beard dressed in black (whose volubility was inversely proportional to his knowledge.)

Now, I'm anxious even when teaching my own class. (Although, it typically subsides as the class progresses.) However, despite my anxiety, I tried to articulate that God has every positive property necessarily and that necessary existence is a positive property.

However, at this point the audience started complaining. Zeno (a mathematics instructor at a CC in Northern CA) objected that it wasn't really a proof. I thought he was claiming that no such argument from Gödel existed, so I objected. (He later clarified that he disputed that it was a real proof, not that it existed.) Zeno and the audience made much of the fact that I described myself as a statistician, but I have a bachelors in mathematics, and even though I studied statistics in grad school, I've had graduate level mathematics courses and my advanced degree is from a mathematics department.

PZ, like his friend Dawkins, dismissed Gödel's Ontological Argument as a word game, a philosophy instructor at Sierra said "You've packed 'existence' into the very definition of God, and so your argument is circular" and some dude up front said something about thinking a certain tea was positive but that his friend did not, thereby claiming to establish the subjectivity of positivity and "refuting" the argument. This was followed up by someone in the back (sitting next to Heidi) saying "moral relativism for the win!" (The same guy also asserted that Gödel's Ontological Argument was "bullocks.")

To be continued...

Labels: Christianity, God, science, theism

My preliminary thoughts:

I did not expect to end up spending the night with PZ Myers. I also did not expect to be asked to defend Kurt Gödel's Ontological Argument, which I was unprepared to do. (Although, even if I were prepared, I do not think I could have done it justice as a critical respondent among an, umm, unsympathetic audience.) I give credit to PZ for unexpectedly turning the tables and essentially catching me flat-footed; it won't happen again.

Anyway, I met some nice people and I am glad I went to BJ's with the group afterward (PZ graciously invited me) because I met Mr. D, with whom I really enjoyed reminiscing about a high school where he taught and I was a student.

I will write more later.

Labels: Christianity, God, theism

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

Happy Πασχα!

Labels: Christianity, God, Jesus

The following is the creed Arius offered to Constantine at his request (you need to have installed Greek fonts to see the original Greek):

Πιστεύομεν εἰς ἕνα Θεόν,
We believe in one God,

πατέρα παντοκράτορα·
the Father Almighty;

Καὶ εἰς κύριον Ἰησοῦν Χριστόν, τὸν υἱὸν αὐτοῦ,
And in the Lord Jesus Christ, his Son,

τὸν ἐξ αὐτοῦ πρὸ πάντων τῶν αἰώνων γεγεννημένον,
who was begotten of him before all ages,

θεὸν λόγον,
the Divine Logos,

δἰ οὗ τὰ πάντα ἐγένετο, τά τε ἐν τοῖς οὐρανοῖς καὶ τὰ ἐπὶ τῆς γῆς,
through whom all things were made, both those in the heavens and those on the earth;

τὸν κατελθόντα καὶ σαρκωθέντα,
who came down and was made flesh;

καὶ παθόντα,
and suffered;

καὶ ἀναστάντα,
and rose again;

καὶ ἀνελθόντα εἰς τοὺς οὐρανούς,
and ascended to the heavens;

καὶ πάλιν ἐρχόμενον κρῖναι ζῶντας καὶ νεκρούς.
and shall come again to judge the quick and the dead.

Καὶ εἰς τὸ ἅγιον πνεῦμα.
And in the Holy Ghost;

καὶ εἰς σαρκὸς ἀνάστασίν,
and in the resurrection of the flesh;

καὶ εἰς ζωὴν τοῦ μέλλοντος αἰῶνος,
and in the life of the world to come;

καὶ εἰς βασιλείαν οὐρανῶν,
and in a kingdom of heaven;

καὶ εἰς μίαν καθολικὴν ἐκκλησίαν τοῦ θεοῦ, τὴν ἀπὸ περάτων ἕως περάτων.
and in one Catholic Church of God which extends to the ends of the earth.

(Excerpted from Philip Schaff's Creeds of Christendom, vol. 2)

Labels: Arius, Christianity, God, Jesus, theology

As I see it, God (the Father) is incorporeal and the Holy Spirit is an aspect of God (the Father), not a separate person.

Psalm 51:11

Do not cast me away from your presence, and do not take your holy spirit from me.

John 4:24

24‘...God is spirit, and those who worship him must worship in spirit and truth.’


Luke 24:39

39 “...Handle Me and see, for a spirit does not have flesh and bones as you see I have.”

Labels: Christianity, God, Holy Spirit, theology

I think this video by Living Hope Ministries is well done and I definitely recommend it.

Labels: Bible, Christianity, frauds, God, Jesus, Joseph Smith, Mormonism

I do not care for Al Sharpton, and I do not think it is fair to say Mormons do not believe in God. However, it is entirely fair to say that they espouse a false conception of God. The correct conception of God entails the following:

• God has no material parts.
• God is not distinct from his essential attributes.
• God's essential attributes are not distinct from one another.
• God is not distinct from His existence.

(The list is not exhaustive.)

The Mormon conception of God fails on these points.

Labels: Christianity, God, Mormonism, philosophy, politics, theology

Comfort and Cameron mean well but they fared poorly, as I expected. However, the Rational [sic] Responders were also inept. They advanced several false claims, such as conservation of mass-energy being the 3rd law of thermodynamics (it is related to the 1st law) and that it implies matter is eternal; quite to the contrary, it is likely that at the big bang the gravitational field and its fluctuations introduced more energy into the system (ex nihilo).

I would have mopped the floor with the Rational [sic] Responders, of course. :)

(via Peezee)

Labels: Christianity, God, theism, vapid atheists

Early Christians rightly judged Cicero a righteous pagan. The following excerpt is from his De natura deorum (translation by Francis Brooks):

V.

Now Cleanthes, who belongs to our own school, said that [idea] of [God] had been formed in men’s minds owing to four causes...As the fourth and most important cause of all he names the uniformity of motion, the revolutions of the heavens, the grouping of the sun, and moon, and all the stars, their serviceableness, beauty, and order, the mere appearance of which things would be a sufficient indication that they were not the result of chance. Just as a man going into a house, or gymnasium, or market-place, would find it impossible, when he saw the plan, and scale, and arrangement of everything, to suppose that these things came into being uncaused, but would understand that there was some one who superintended and was obeyed, so in the case of such vast movements and alternations, in the orderly succession of phenomena so numerous and so mighty, in which the measureless and infinite extent of past time has never deceived expectation, it is much more inevitable that he should conclude that such great operations of nature are directed by some intelligence.
VI.

Chrysippus, again, speaks in a way which, though his own mind is a very keen one, he seems to have learnt direct from nature, rather than to have discovered himself. “For if,” he says, “there is something in nature which the mind, the reason, the strength, and the power of man would be unable to produce, surely that which does produce it is higher than man; now the heavenly bodies, and all those phenomena which observe an everlasting order, cannot be created by man; consequently that by which they are created is higher than man. And what could you say this was rather than God? For if there [is] no [God], there can be nothing higher in nature than man, since he alone possesses reason, and nothing can surpass reason in excellence. But that there should be a man who thinks that in the whole universe there is nothing higher than himself shows senseless arrogance. There is, then, something higher, and therefore there is assuredly a God.” Is it the fact that if you saw a large and beautiful house, you could not be persuaded, even if you did not see the master, that it had been built for the sake of mice and weasels, and would you not present the appearance of downright imbecility if you supposed that all this adornment of the world, all this diversity and beauty of the heavenly bodies, all this might and amplitude of sea and land, were a dwelling-place belonging to you and not to the immortal [God]?...And yet, on the ground even of man’s intelligence, we ought to consider that there exists some mind of the universe, one that is keener than his and divine. “For whence,” as Socrates says in Xenophon, “did man get hold of the mind he has?”...
VII.

And the element which surpasses all these, I mean reason, and if we care to express it by a variety of terms, intelligence, design, reflection, foresight, where did we find, whence did we secure it? Shall the universe possess all other qualities, and not this one which is of most importance? Yet surely in all creation there is nothing nobler than the universe, nothing more excellent and more beautiful. There not only is not, but there cannot even be imagined anything nobler, and if reason and wisdom are the noblest of qualities, it is inevitable that they should exist in that which we acknowledge to be supremely noble. Again, who can help assenting to what I say when he considers the harmonious, concordant, and unbroken connection which there is in things? Would the earth be able to have one and the same time for flowering, and then again one and the same time in which it lies rough? Or could the approach and departure of the sun be known, at the time of the summer and winter solstice, by so many objects spontaneously changing? Or the tides of the sea, and of narrow straits, be affected by the rising or setting of the moon? Or the dissimilar movements of the planets be maintained by the one revolution of the whole sky? It would be certainly impossible for these things to come to pass in this way, with such mutual harmony amongst all parts of the universe, if they were not held together by one divine and all-pervading spirit...

Labels: Cicero, God, philosophy, theology

I think the following verses are among the most well known of John Milton's great poem:

What in me is dark
Illumin, what is low raise and support;
That to the highth of this great Argument
I may assert Eternal Providence,
And justifie the wayes of God to men.

Paradise Lost

Labels: Christianity, God, poetry, theology

Moses Maimonides is among the greatest of Jewish thinkers.

(M. FRIEDLÄNDER translation)

Book III, Chapter LI

My son, so long as you are engaged in studying the Mathematical Sciences and Logic, you belong to those who go round about the palace in search of the gate. Thus our Sages figuratively use the phrase: “Ben-zoma is still outside.” When you understand Physics, you have entered the hall; and when, after completing the study of Natural Philosophy, you master Metaphysics, you have entered the innermost court, and are with the king in the same palace. You have attained the degree of the wise men, who include men of different grades of perfection. There are some who direct all their mind toward the attainment of perfection in Metaphysics, devote themselves entirely to God, exclude from their thought every other thing, and employ all their intellectual faculties in the study of the Universe, in order to derive therefrom a proof for the existence of God, and to learn in every possible way how God rules all things; they form the class of those who have entered the palace, namely, the class of prophets.

Labels: God, mathematics, philosophy, theology

(Edward Pusey translation)

Book V, Chapter II

On the Vanity of Those Who Wished to Escape the Omnipotent God.

They discourse many things truly concerning the creature; but Truth, Artificer of the creature, they seek not piously, and therefore find Him not; or if they find Him, knowing Him to be God, they glorify Him not as God, neither are thankful, but become vain in their imaginations, and profess themselves to be wise...

Labels: Christianity, God, theology

Amanda Marcotte offers a false dichotomy:

...how a supposedly good god allows so much evil on his watch is only a rude question because it’s basically a philosophical dead end. Either god is capricious and allows evil for the hell of it or he doesn’t exist.

Either Amanda is willfully ignorant or she has exceeded her intellectual capacity.

Labels: Amanda Marcotte, God

Reasonable Faith with William Lane Craig

(via Right Reason)

Labels: Christianity, God, philosophy

(no text)

Labels: Christianity, God, Jesus

True Law is right reason in agreement with nature; it is of universal application, unchanging and everlasting; it summons to duty by its commands, and averts from wrongdoing by its prohibitions. And there will not be different laws at Rome and at Athens, or different laws now and in the future, but one law, both eternal and unchangeable, will be valid for all nations and all times, and there will be one master and ruler of all, God, for of this law he is the founder, judge, and lawgiver.

(De republica 3.33, as cited by Richard Horsley.)

Labels: Cicero, God, morality, natural law

I admire Kurt Gödel's Ontological Proof of God. (Just as I admire Gödel himself.) Dr. Christopher Small has a good discussion of Gödel's proof here.

Labels: God, mathematics