Sunday, January 27, 2008 | Reason : In the News | print version

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Math Religion Trouble

by The Star

Thanks to notdeluded for the link.

http://www.thestar.com/article/297564

THE GOD EQUATION
Math + religion = Trouble

Actually, since Pythagoras the relationship between men of numbers and the Deity has been more along the lines of love-hate, but it's a rich vein

Ron Csillag
Special to the Star

Which math-phobic among us has not beseeched God for help with another colon-clenching algebra or calculus exam? Had we heeded the words of the German mathematician Leopold Kronecker, perhaps we would have realized we've been talking to the wrong person: "God made the integers; all else is the work of man."

Pythagoras, who gave us his eponymous theorem on right-angled triangles, headed a cult of number worshippers who believed God was a mathematician. "All is number," they would intone.

The 17th-century Jewish philosopher Baruch Spinoza echoed the Platonic idea that mathematical law and the harmony of nature are aspects of the divine. Spinoza, too, posited that God's activities in the universe were simply a description of mathematical and physical laws. For that and other heretical views, he was excommunicated by Amsterdam's Jewish community.

German mathematician Georg Cantor's work on infinity and numbers beyond infinity (the mystical "transfinite") was denounced by theologians who saw it as a challenge to God's infiniteness. Cantor's obsession with mathematical infinity and God's transcendence eventually landed him in an insane asylum.

For the Hindu math genius Ramanujan, an uneducated clerk from Madras who wowed early 20th-century Cambridge, an equation "had no meaning unless it expresses a thought of God." Though an agnostic, the prolific Hungarian mathematician Paul Erdos imagined a heavenly book in which God has inscribed the most elegant and yet unknown mathematical proofs.

And famously, Albert Einstein said God "does not play dice" with the universe.

What is it with God and mathematics? Even as science and religion have quarrelled for centuries and are only recently exploring ways to kiss and make up, mathematicians have been saying for millennia that no truer expression of the divine can be found than in an ethereally beautiful equation, formula or proof.

Witness, for example, such transcendent numbers as phi (not to be confused with pi), often called the Divine Proportion or the Golden Ratio. At 1.618, it describes the spirals of seashells, pine cones and symmetries found throughout nature. Other mysterious constants like alpha (one-137th) and gamma (0.5772...) pop up in enough odd places to suggest to some that they are an expression of the underlying beauty of mathematics, and to others that someone or something planned it that way.

But does that translate into actual belief?

The New York Times reported recently that mathematicians believe in God at a rate 2 1/2 times that of biologists, quoting a survey of the National Academy of Sciences. Admittedly, that's not saying much: Only 14.6 per cent of mathematicians embraced the God hypothesis, versus 5.5 per cent of biologists (versus some 80 per cent of Canadians who believe in a supreme being).

Count John Allen Paulos among the non-believers. A mathematician who teaches at Temple University in Philadelphia and who has popularized his subject in bestselling books such as Innumeracy and A Mathematician Reads the Newspaper, Paulos's latest offering is a slim but explosive volume whose title is self-explanatory: Irreligion: A Mathematician Explains Why the Arguments for God Just Don't Add Up (Hill & Wang).

This newest addition to the neo-atheist field crowded by the likes of Richard Dawkins, Christopher Hitchens, Sam Harris and others emboldened by the recent transformation of non-belief from a 97-pound weakling into a he-man, Paulos thankfully employs little math, preferring to see things, as he tells us, in the stark light of "logic and probability."

Deploying "a lightly heretical touch," he dissects a playlist of "golden oldies" that includes the first-cause argument (sometimes tweaked as the cosmological argument, which hinges on the Big Bang), the argument for intelligent design, the ontological argument (crudely, that if we can conceive of God, then God exists), the argument from the anthropic principle (that the universe is "fine-tuned" to allow us to exist), the moral universality argument, and others.

The famous Pascal's wager — that it's in our self-interest to believe in God because we lose nothing in case He does exist — is upended as logically flawed, based on what statisticians call Type I and Type II errors.

Lord knows Paulos isn't the first mathematician to proclaim his lack of religious faith. Cambridge's famous wunderkind G.H. Hardy loudly and proudly adjudged God to be his enemy. To Erdos, God, if He existed, was "the supreme fascist."

Even as Paulos works to refute the classical arguments for God's existence, he does something too few of his mindset do: Chide non-believers for unsportsmanlike conduct.

"It's repellent for atheists or agnostics," he admonishes, "to personally and aggressively question others' faith or pejoratively label it as benighted flapdoodle or something worse. Those who do are rightfully seen as arrogant and overbearing."

That doesn't prevent him from doffing the gloves. The ontological argument is "logical abracadabra.'' The design, or teleological argument, is a "creationist Ponzi scheme'' that "quickly leads to metaphysical bankruptcy.''

Much of theology is "a kind of verbal magic show.'' A claim that a holy book is inerrant because the book itself says so is another logical black hole.

However, math, specifically something called Ramsey theory, which studies the conditions under which order must appear, can account for the illusion of divine order arising from chaos.

Paulos provides a nice counterpoint to theoretical physicist Stephen Unwin's 2003 book The Probability of God, which calculated the likelihood of God's existence at 67 per cent, and to Oxford philosopher Richard Swinburne's use of a probability formula known as Bayes' theorem to put the odds of Christ's resurrection at 97 per cent.

Those and other efforts remind one of the story, perhaps apocryphal, of Catherine the Great's request of the German mathematical giant Leonhard Euler to confront atheist French philosopher Denis Diderot with evidence of God. The visiting Euler agreed, and at the meeting, strode forward to proclaim to the innumerate Frenchman: "Sir, (a+bn)/n = x, hence God exists. Reply!"

Diderot was said to be so dumbfounded, he immediately returned to Paris.

To Paulos, the tale is a great example of "how easily nonsense proffered in an earnest and profound manner can browbeat someone into acquiescence."

His arguments notwithstanding, Paulos concedes that there's "no way to conclusively disprove the existence of God."

The reason, he notes, is a consequence of basic logic, but not one "from which theists can take much heart."

As for the problem of good and evil, he defers to fellow atheist, the Nobel Prize-winning physicist Steven Weinberg: "With or without religion, good people will do good, and evil people will do evil. But for good people to do evil, that takes religion."

Or as Paulos might say, no mathematician has ever deliberately flown planes into buildings.

Ron Csillag is a freelance writer from Thornhill.

Posted: Sunday, January 27, 2008 | Permalink

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1. Comment #116742 by ChrisMcL on January 27, 2008 at 10:16 am

Awesome!

I was holding off from buying Paulos' book. But now after reading this review, I have to get it this week.

Other Comments by ChrisMcL

2. Comment #116760 by SilentMike on January 27, 2008 at 10:50 am

Another book.

The more the merrier I say. We'll drown them; surround them with reason from all sides, till they have to breath some of it in.

Other Comments by SilentMike

3. Comment #116783 by Friend Giskard on January 27, 2008 at 11:47 am

"It's repellent for atheists or agnostics," he admonishes, "to personally and aggressively question others' faith or pejoratively label it as benighted flapdoodle or something worse. Those who do are rightfully seen as arrogant and overbearing."

Twit.

Religion needs to be held up for public ridicule as often as possible, especially before the eyes of the young. While we have no actual vaccine against religion, we can still weaken its power to take hold of young people's minds by fostering an atmosphere in which the point of view that holds religion to be utterly ridiculous and contemptible is highly visible to all members of society. If the media were to give frequent exposure to the point of view that laughs at religion, and openly reviles the pushers of religion, they would be doing for the public no less a service than the doctors who immunise us against certain diseases.

As long as there remains any part of the world in which political power is wielded, or basic human rights are denied, in the name of religion, the mockery and belittling of religious beliefs should be regarded as an absolute moral good.

Other Comments by Friend Giskard

4. Comment #116793 by Geoff on January 27, 2008 at 12:42 pm

Firstly, it's "maths" not "math".

Good article, though, I shall be buying that book.

I'm currently re-reading a book called "nature's numbers" by Ian Stewart; I can recommend it.

Other Comments by Geoff

5. Comment #116796 by Janus on January 27, 2008 at 12:53 pm

Well said, Giskard. It's amazing how many otherwise rational people buy into the dogma that ridiculing ridiculous beliefs is intolerant or arrogant.

As you've implied, refraining from ridiculing religious beliefs in the name of politeness can only give the mistaken impression that these beliefs are perfectly normal and rational.

Other Comments by Janus

6. Comment #116800 by Nails on January 27, 2008 at 1:17 pm

Witness, for example, such transcendent numbers as phi (not to be confused with pi), often called the Divine Proportion or the Golden Ratio. At 1.618, it describes the spirals of seashells, pine cones and symmetries found throughout nature.

Pardon my ignorance, but I thought it was e .....
Nice article though.
I'll add the book to my ever growing list of 'to buy'.

Other Comments by Nails

7. Comment #116802 by strengthofmind on January 27, 2008 at 1:27 pm

As in the article, the Golden Ratio 1.618 is phi, not e.

Other Comments by strengthofmind

8. Comment #116804 by heathen2 on January 27, 2008 at 1:33 pm

I haven't read his book, but doesn't Paulos attack belief when he calls it "a kind of verbal magic show.'' ?

Seems like he is doing what he finds repellant in others. I'm okay with his attack on beliefs, in fact I'm all for it.

Other Comments by heathen2

9. Comment #116814 by stereoroid on January 27, 2008 at 2:12 pm

Which math-phobic among us has not beseeched God for help with another colon-clenching algebra or calculus exam?

Erm... me?

Other Comments by stereoroid

10. Comment #116818 by Geoff on January 27, 2008 at 2:20 pm

e is the base of natural logarithms (The "e" is generally thought to refer to Euler, although it's sometimes confusingly called "Napier's constant")

2.718, approximately.

Not often I get a chance to bring my specialist subject into a predominantly biology forum!

Other Comments by Geoff

11. Comment #116853 by mmurray on January 27, 2008 at 3:56 pm

It's math in the US, Canada and maths in UK, Australia etc.

Michael

Other Comments by mmurray

12. Comment #116868 by BathTub on January 27, 2008 at 5:00 pm

I read Innumeracy a few years ago, quite a fun book.

Other Comments by BathTub

13. Comment #116883 by Blake C. Stacey on January 27, 2008 at 5:36 pm

Oh, for crying out loud: why can't we get a review which quotes a relevant passage in full, or at least gives a complete paraphrase? I've got Irreligion right here, and I'm gonna copy a chunk of page 79. Right after the "rightfully seen as arrogant and overbearing" remark, Paulos writes the following:

It's been my experience, at least in this country, that it is more likely to be the religious who personally and aggressively question atheists' and agnostics' lack of faith or pejoratively label it as secular autism or worse. The latter question and labeling seem especially arrogant as there is no compelling argument for the existence of God.

I find it hard to disagree. The verbal assaults upon the Uppity Atheists perpetrated by "moderate" religionists and those among the godless who just want everybody to stay quiet have come to resemble a madness of the center. It's a new in-group mentality, built upon one of the oldest criteria: the people who are In are the ones who are willing to say, "Let's not rock the boat."

The only place I could find where Paulos takes a "neo-atheist" to task in a specific way is on page 110:

This phenomenon of an assumed religious inheritance and its many consequences is not necessarily "wicked" or an "abuse," as Richard Dawkins has suggested, but it does indicate that religious beliefs generally arise not out of a rational endeavor but rather out of cultural traditions and psychological tropes.

Pretty mild stuff. And even by the end of that paragraph, he's approving of Dawkins:

To refer to Catholic children, Protestant children, or Islamic children is to assume that the children automatically inherit their parents' worldview. Although often true, this assumption isn't a necessary fact of life, and, as Dawkins has wisely noted, it might be salubrious if referring to children in this way came to sound as wrong-headed as referring to them as Marxist children or capitalist children.

[emphasis added]

By the way, strong evidence exists to the effect that the story of Euler and Diderot is indeed apocryphal. The short version is that Diderot was himself a mathematician and Euler had better manners; a slightly longer retelling can be found at the following URL,

http://www.sunclipse.org/?p=433

if you'll excuse my blatant self-promotion.

Other Comments by Blake C. Stacey

14. Comment #116884 by AtheistAspy on January 27, 2008 at 5:37 pm

Who said that there is a curious effectiveness in mathematics?

Any thoughts as to why mathematical reasoning corresponds so well to the physical world?

The physicist Max Tegmark offers a possible explanation here:
http://www.americanchronicle.com/articles/24386

Other Comments by AtheistAspy

15. Comment #116901 by heathen2 on January 27, 2008 at 6:28 pm

Blake,

Thanks for including the rest of the Paulos quote. It does change the meaning somewhat. I agree that the full quote would have been the right thing to print in the review, but that would not have suited the reviewer so well it seems.

Other Comments by heathen2

16. Comment #116908 by Blake C. Stacey on January 27, 2008 at 7:02 pm

Who said that there is a curious effectiveness in mathematics?

Eugene Wigner called the effectivenss of mathematics "unreasonable". Many other people don't see it that way.

Any thoughts as to why mathematical reasoning corresponds so well to the physical world?

Well, first of all, a lot of mathematics was invented following the example of the physical world. So, what's the big surprise? You could probably cook up an "anthropic" argument, following Dawkins' lead (pp. 135 and following in The God Delusion), and say that any Universe which did not show the kind of regularity which we can capture in mathematics is not a Universe friendly to life, let alone intelligence. . . .

For some contemplations on this subject, including remarks by Paulos, see here:

http://scienceblogs.com/evolutionblog/2007/09/is_math_a_gift_from_god.php

Other Comments by Blake C. Stacey

17. Comment #116911 by Double Bass Atheist on January 27, 2008 at 7:12 pm

The New York Times reported recently that mathematicians believe in God at a rate 2 1/2 times that of biologists, quoting a survey of the National Academy of Sciences. Admittedly, that's not saying much: Only 14.6 per cent of mathematicians embraced the God hypothesis, versus 5.5 per cent of biologists (versus some 80 per cent of Canadians who believe in a supreme being).

Canadians? Canadians??? What the heck do Canadians have to do with a mathematicians vs biologists comparison?
Is the author just trying to be funny?!
Am I misreading something?

Other Comments by Double Bass Atheist

18. Comment #116912 by Steve Zara on January 27, 2008 at 7:15 pm

and say that any Universe which did not show the kind of regularity which we can capture in mathematics is not a Universe friendly to life, let alone intelligence. . . .

I don't find that blog entry convincing, as, in reality, the universe is not that regular mathematically. Chaos rules, and any but the simplest of physical systems have to be dealt with by approximations.

Other Comments by Steve Zara

19. Comment #116940 by Cartomancer on January 27, 2008 at 8:47 pm

Medieval Historian Hobby Horse Alert, skip it if you like...

He went straight from Pythagoras to Spinoza! Bah! This sort of thing REALLY rubs me up the wrong way. You have no idea how irksome these little illustrative histories in collected anecdote form are to me. They're almost always the same - choose the most famous classical proponent of a genre because they're the only one anyone is likely to have heard of, congratulate him on making a jolly good start to it all, then skip straight over the rest of antiquity and the entire middle ages to land slap bang in the early modern period where enightened renaissance humanists pick up the torch. Then carry on with a selection of the famous names from the last five centuries until we reach the present day.

I'll leave it to Goldy and Al-rawandi to point out how eurocentric this view generally is, but even if it is only a history of western civilization we are suggesting (which can be just about justified in narrative terms) there really is no excuse to simply excise anything that happened for the two millennia between the fourth century BC and the sixteenth century AD.

Taking this mathematics and religion example, we've got more than enough material to go on. How about the Neoplatonic schools with their weird emanationist ideas about the purity of number? What about the Venerable Bede's musings on the nature of time and number? What about Gerbert of Aurillac, the medieval mathematician who later became Pope Sylvester I but gained a reputation for dabbling in dangerous saracen magic because of his studies? What about Thierry of Chartres who tried to explain the Trinity with the analogy of the formula 1x1=1 (with the father and the son being the two 1s and the holy spirit, properly filioque compatible, being the act multiplication). What about Adelard of Bath's translation of Euclid? What about deacon Robert of Chester's translation of the Algebra and Almucabola of the Muslim Al-Khwarizmi (and, if he is the same as Robert of Ketton, of the Koran as well)? What about Robert Grosseteste's commentary on the third book of Aristotle's Physics where he theorises about the possibility of multiple infinities in the mind of God a good 700 years before Cantor? What about Roger Bacon's praise of mathematics as the root of all science and knowledge, both human and divine?

This is yet another flagrant example of the unspoken anti-medieval concensus that modern society still has not broken away from. It gives the mendacious impression that nothing happened during the Middle Ages as far as the transmission of ideas goes, and reinforces the stereotype that they were backward and sterile, when in fact the successes of the Quattrocento Renaissance and beyond were build on solid foundations and cultural experiments laid down in the medieval centuries. People do not add the five- or six- sentence potted histories to the beginning of their articles because they are legitimately trying to outline the broad sweep of historical change - that would be a valid endeavour - no, they do it primarily to lend an air of sampled erudition to their writing. It's a rhetorical trick, simple as that. It's saying "look at me, I can command a dizzying array of facts from across the span of human history about this subject, I must know what I'm talking about". And yet the layman takes it as a carefully researched list of highlights and perpetuates the myth.

Ooooh it makes me so angry!

Other Comments by Cartomancer

20. Comment #116942 by dragonfirematrix on January 27, 2008 at 8:57 pm

Just one comment on the quoted text below from the article:

"As for the problem of good and evil, he defers to fellow atheist, the Nobel Prize-winning physicist Steven Weinberg: "With or without religion, good people will do good, and evil people will do evil. But for good people to do evil, that takes religion.""

MY COMMENT ON THE ABOVE: It certainly does appear that religion today (as throughout history) is doing (as religion wants to do) plenty of evil.

Other Comments by dragonfirematrix

21. Comment #116971 by AtheistAspy on January 27, 2008 at 11:41 pm

"You could probably cook up an "anthropic" argument, following Dawkins' lead (pp. 135 and following in The God Delusion), and say that any Universe which did not show the kind of regularity which we can capture in mathematics is not a Universe friendly to life, let alone intelligence. . . ."

That's basically what Max Tegmark argues. He hypothesizes what he calls a Type IV multiverse, in which different universes correspond to "mathematical structures." He also states that most physicists are Platonists. I first read about it in Scientific American and am not sure about the credibility of neo-Platonism.

(BTW, how do you box quotes?)

Other Comments by AtheistAspy

22. Comment #116990 by rod-the-farmer on January 28, 2008 at 1:37 am

Only 14.6 per cent of mathematicians embraced the God hypothesis, versus 5.5 per cent of biologists (versus some 80 per cent of Canadians who believe in a supreme being).

I suspect this is because the article appeared in the Toronto Star, one of the major Canadian newspapers. More details from the 2001 census are available at
http://www12.statcan.ca/english/census01/Products/Analytic/companion/rel/canada.cfm.

including this comment

In addition, far more Canadians reported in the 2001 Census that they had no religion. This group accounted for 16% of the population in 2001, compared with 12% a decade earlier.

The next census where religion is tracked is not due until 2012, and based on MY personal experience, the 16% number is going to increase again, substantially.

AtheistSpy You can box in a quote using the blockquote command, surrounded by <> characters to start it, and the same again to end it, with the command word preceded by a / character.

Cartomancer Whooaaa, easy there big fella. Since the "review" was from a daily newspaper, I suspect the writer did not have enough space to do more than a cursory glance at relevant literature. Not every reporter is a fan of Cadfael.

Other Comments by rod-the-farmer

23. Comment #117009 by Duff on January 28, 2008 at 3:29 am

I, personally, will be as kind in my denunciations of the religious types as I would be of the ninny who suggests a troll lurks under yon bridge.

Cartomancer,
I seem to recall no less a thinker than Bertrand Russell saying that after a certain philosopher, I forget which, who lived a little after the time of Christ, no great thinker appeared again for a thousand years, until the Rennaissance. Mostly due to the influence of the church. Sorry to be so general, but I don't have the time at the moment to look up the details.

Other Comments by Duff

24. Comment #117026 by jeepyjay on January 28, 2008 at 5:30 am

For many mathematicians, particularly those addicted, like Cantor, to speculations in the "paradise" (as Hilbert called it) of transfinite numbers, Mathematics is itself a Religion. It leads them to waste their life on such absurdities as the Banach-Tarski paradox:

http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

This is just fantasy mathematics. In my view a high proportion of currently published papers in mathematics, dealing with things like Hilbert Spaces, are as pointless as medieval theologians discussing how many angels could dance on the head of a pin.

Other Comments by jeepyjay

25. Comment #117029 by mikeshin on January 28, 2008 at 5:53 am

1/243 = 0.004115226337448559...

therefore god exists

Other Comments by mikeshin

26. Comment #117031 by MPhil on January 28, 2008 at 5:57 am

jeepjay,

I strongly disagree here. Mathematics, like logic and set theory are a conceptual construct. We have "found" in logic (which is also the basis of mathematics) an immensely powerful tool. Through the axioms of mathematics, which can be called "structural science", we have constructed a system of which we haven't even discovered some of its consequences. This kind of mathematics is simply "exploring the boundaries of conceptual space".
As with predicate logic - mathematics is an incredibly powerful tool with so many applications that we can never hope to find all of them. It is a tool too powerful for a single mind to understand - but it reflects the fact that humans have the power to conceive of self-contained, highly structured conceptual systems that can be used to model the world around us.

Think of string theory with its hidden dimensions. Geometry and topology within such multi-dimensional curved space was probably also seen as pure mathematical speculation without any application or connection with reality. Don't dismiss logical exploration of concepts simply because there are no applications. Even if there are none to come, this is still information about our conceptual space.

The Banach-Tarski paradox is surely contradicting common sense... but that's why it is so interesting to explore, because it is a logical consequence of the axioms of set theory, topology and general mathematics, all of which we accept.

I agree that there were and are mathematicians who overstep the boundaries and think what they're doing has deep or "mysterious" metaphysical consequences. Well - it does have consequences for our view of the conceptual capabilities of the mind and logical (hence "metaphysical" in a broad sense) possibilities of existence.

Other Comments by MPhil

27. Comment #117118 by Cartomancer on January 28, 2008 at 9:40 am

Duff, Comment #24,

That's precisely the sort of thing I am on about. Russell, great thinker though he undoubtedly was, grew up steeped in Victorian anti-medieval attitudes. Serious study of medieval intellectual history didn't really begin in the English-speaking world until the early twentieth century (Germany was only slightly quicker off the mark). Ignorance of medieval history is a self-perpetuating meme: if people think nothing worthwhile happened for a thousand years then they won't go and find out what actually did happen. The meme is spread at the most basic level by journalists of this sort, though they are perhaps not culpable since they carry the meme themselves. Atheists in particular are too keen to write everything off as coming under the aegises of the church and thus irrelevant, when medieval thought is just as much a foundation for modern philosophy as classical and renaissance thought, indeed, were it not for what happened during the medieval centuries there would be no classical thought for Renaissance thinkers to work with.

Other Comments by Cartomancer

28. Comment #117218 by bawruss on January 28, 2008 at 12:23 pm

jeepyjay said:

This is just fantasy mathematics. In my view a high proportion of currently published papers in mathematics, dealing with things like Hilbert Spaces, are as pointless as medieval theologians discussing how many angels could dance on the head of a pin.

Not sure what current papers on Hilbert Spaces focus on, but the concept seems quite practically relevant (from Wikipedia):

Hilbert spaces arise naturally and frequently in mathematics, physics, and engineering, typically as infinite-dimensional function spaces. They are indispensable tools in the theories of partial differential equations, quantum mechanics, and signal processing. The recognition of a common algebraic structure within these diverse fields generated a greater conceptual understanding, and the success of Hilbert space methods ushered in a very fruitful era for functional analysis.

Other Comments by bawruss

29. Comment #117297 by Cartomancer on January 28, 2008 at 2:25 pm

Gaaah! Angels on the head of a pin! Again with the Enlightenment misrepresentations of Medieval thought! (slides into silent but fuming apoplectic rage)...

Other Comments by Cartomancer

30. Comment #117313 by MPhil on January 28, 2008 at 2:38 pm

Cartomancer,

I study philosophy, and I must honestly that from the end of classicism with the philosophies of Plato and Aristotle (and their altogether worthless Roman "refurbishments") until Descartes and Spioza - there have been almost no worthwhile contribution to serious philosophy that I know of (With some exceptions, the most major one being Ockam). Why? Because it's all been "theosophy" basically - exploring the doctrines and attempting to rationalize them. Some nice Ideas were there, as in Ockam... but nothing of the magnitude of the greats of classicism or renaissance (and after).

Other Comments by MPhil

31. Comment #117340 by jeepyjay on January 28, 2008 at 3:19 pm

Cartomancer: Gaaah! Angels on the head of a pin! Again with the Enlightenment misrepresentations of Medieval thought! (slides into silent but fuming apoplectic rage)...

Sorry to upset you Cartomancer. But there is something to be said for the caricature:

http://www.straightdope.com/classics/a4_132.html

Mediaeval philosophers were in a bit of a theological bind, but to cheer you up there were some great mathematicians.

Other Comments by jeepyjay

32. Comment #117356 by NakedCelt on January 28, 2008 at 4:02 pm

3. Comment #116783 by Friend Giskard:

"It's repellent for atheists or agnostics," he admonishes, "to personally and aggressively question others' faith or pejoratively label it as benighted flapdoodle or something worse. Those who do are rightfully seen as arrogant and overbearing."

Twit.

Religion needs to be held up for public ridicule as often as possible, especially before the eyes of the young. While we have no actual vaccine against religion, we can still weaken its power to take hold of young people's minds by fostering an atmosphere in which the point of view that holds religion to be utterly ridiculous and contemptible is highly visible to all members of society. If the media were to give frequent exposure to the point of view that laughs at religion, and openly reviles the pushers of religion, they would be doing for the public no less a service than the doctors who immunise us against certain diseases.

As long as there remains any part of the world in which political power is wielded, or basic human rights are denied, in the name of religion, the mockery and belittling of religious beliefs should be regarded as an absolute moral good.

Ha ha ha ha ha ha ha. How can anybody be such a fucking moron? You're full of shit, Giskard, and you know it. I mean, how can anybody take such an obviously intellectually bankrupt position seriously? You must have the brains of a footballer...

Have I convinced you yet?

What, no?

Think about that.

Other Comments by NakedCelt

33. Comment #117358 by Steve Zara on January 28, 2008 at 4:10 pm

Ha ha ha ha ha ha ha. How can anybody be such a fucking moron? You're full of shit, Giskard, and you know it. I mean, how can anybody take such an obviously intellectually bankrupt position seriously? You must have the brains of a footballer...

Have I convinced you yet?

I think you are confusing laughing at beliefs and ranting at people.

Other Comments by Steve Zara

34. Comment #117368 by Cartomancer on January 28, 2008 at 4:38 pm

Well, the specific comment about the angels on the head of a pin was meant as a joke - it is an enlightenment caricature of medieval scholasticism in itself and given the circumstances seemed appropriate to comment on. Nevertheless, my substantial point is valid - it IS a caricature, but most laymen think it did actually happen that way, and miss the underlying story.

The thing about medieval philosophy, indeed any kind of historical philosophy, is that it should be taken on its own merits, rather than viewed from the standpoint of modern critics and modern values. It's all very well to laugh at people like Aquinas and John Duns Scotus because they embroiled themselves in mind-numbingly complicated arguments about the precise way their aristotelian metaphysics applied to the data of religious theory, but this is taking their age entirely out of context and ignoring the contribution it made to later thought. Purely inductive logical reasoning in the Aristotelian mould was eventually and rightly abandoned toward the end of the Middle Ages, but this is because it proved insufficient for the tasks to which it was put rather than because society changed markedly. The picture painted by renaissance humanists of a sudden, brilliant shift from logic-chopping medieval misery to shining renaissance rationalism is grossly exaggerated. In reality the scholastic project evolved and changed in response to the increasing difficulty of explaining reality from purely inductive arguments. It is also a gross misnomer to assume that scholastic thought was either monolithic or reductible solely to inductive aristotelianism. It was neither of these things, but caricatured few-sentence histories of the period tend to obscure the subtleties, of which there were many.

It is the equivalent of saying that there was no political philosophy written between Hobbes and the late twentieth century simply because the theories of fascism and marxism have been demonstrated to be unworkable and misleading. We only know just how misleading they are because they have been tried out and found wanting - should we really be blaming the medievals for giving their all to trying out what looked like a good idea only to abandon it because it was wrong? We would not have an Ockham without a Scotus for him to criticise. We would not have a Dante without the ideas of Aquinas and Simon of Tournai for him to transform. We would not have a Kepler without the optical work of Alhacen, Roger Bacon, Witelo and John Pecham - not to mention the translation of Euclid and Ptolemy into Latin which occurred in the mid twelfth century. To use an evolutionary metaphor, it would be like claiming that there was no change in the sophistication of the eye between the development of light-sensitive cells and the formation of the lens simply because what happened later was far more sophisticated and impressive. The groundwork needs to be done before a significant departure can be made, and to assume otherwise is grossly unhistorical - Just because it is a part of the story that might be overlooked by those with certain personal critera for the definition of progress does not mean it is not an integral part of the story at all.

I would, of course, expect a modern philosopher to criticise the medieval contribution to his own discipline because it has been superceded. As an historian I would criticise Herodotus, Thucydides, Froissart and Roger of Hoveden on their methodology, but as a historiographer I know that their thought is a product of their circumstances. As an historian of philosophy you should do the same - the world's most intelligent people actually struggled with these problems for generations, that is all the value they need to tell us something about the society and its priorities.

The explosion in the quantity and variety of post-medieval thought that we notice can be put down to a large extent to the invention of printing and the strong, established position of the early modern University as a centre of learning - both which arose from medieval roots. Printing was a crane which enabled knowledge to flourish and travel far more widely, enabled peer review and comparison of findings on a wider scale. It also allowed individual scholars to read far more widely than before. With it intellectual progress quickened - it did not begin again ab initio.

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35. Comment #117372 by MPhil on January 28, 2008 at 4:57 pm

Cartomancer,

you're principally right. But I don't belittle those thinkers. They were brilliant people attempting to applying rational thinking to irrational doctrine in the hope of getting at some "deep truths". That's what I belittle. Surely there was an "evolution" of thought - and no Ockam/Ockham/Occam's thinking wouldn't exist in that way without Duns Scotus.

And yes, of course a philosophers criticizes abandoned areas of his own discipline.

The point I was trying to make was that in contrast to Plato's and Aristotle's intellectual achievements the one's of scholasticism are quite frankly largely embarrassing - just for that reason that they were applying Aristotle's thinking to irrational dogma. As I said - I am counting Ockam's philosophy as probably the one great intellectual achievement there.

Yes, you are right - from a historical perspective. No question. But I am criticising the ideas, not the genealogy or the thinkers. I am thinking as critically about the ideas Aristotle and Plato as I do about Quine and Mackie... and Duns Scotus, Aquinas, Canterbury and Eckhart (okay, that last one is mysticism)... and I have to say, the latter four's thinking doesn't stand up nearly as well as the others'.

____________________________________
Please excuse the orthographic mistakes - it's late and I'm not entirely sober :)

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36. Comment #117376 by Cartomancer on January 28, 2008 at 5:26 pm

I guess this is simply the difference between what a philosopher does and what an historian of philosophy, or indeed any kind of historian does. Alas, from my perspective, it is all too often the former whose discipline reaches the public eye, rather than the latter.

Of course people need their narratives, even their five line potted history narratives of this sort, to make sense of the past. It just irks me that the narratives they alight upon are so shot through with anti-medieval bias and the facts are barely known outside the realm of the specialist. What the man in the street gets is "oh, so everybody was stupid, the evil church ruthlessly suppressed dissenting opinion and nothing even remotely interesting happened". I guess I should just write this too off as a product of historical circumstance and the lingering influence of post-renaissance self definition in european culture...

It's times like this that really make me wish I could drink alcohol!

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37. Comment #117377 by Cartomancer on January 28, 2008 at 5:36 pm

I might also like to point out that the medievals really had no way of knowing just how irrational and unfounded their trust in scripture and revelation really was. To them the God Hypothesis was pretty much the only explanation for the existence of the world around them, and whatever they thought of the ontological argument or the first causes arguments, the argument from design remained a fairly compelling one to pretty much everybody until well into the eighteenth century. If you believe that there is a god who has all power over the universe, and that he has revealed himself in the bible (which, given the state of biblical textual scholarship, not to mention ignorance of other world religions, was also much easier to do back then), then you really have no choice but to take revelation as scientific data and fit it into your scientific worldview.

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38. Comment #117378 by sent2null on January 28, 2008 at 5:40 pm

Jeepjay,

With that statement regarding Hilbert Spaces you really spoke beyond your ken. There is much practical hard science that has developed from exploring them.

Would you have said the same thing in the early 18th century when the idea of imaginary numbers was being fleshed out? Imaginary numbers are pivotal to the foundations of electrical and electronic analysis upon which the modern technological world is built! And that is just an easy example.

I however don't see Mathematics as something we constructed, though many patterns and structures have been created utilizing the basic truths of mathematical theory it is a bit arrogant of us to think that we are the first to have discovered these patterns. I give good odds, that a billion years ago civilizations across 10,000 galaxies long dead came across the same patterns we've stumbled into and "invented" the same structures, to me math is the truth of what can be (and not just in the physical sense)...it is the analysis of all possibility. This is far far more grand than what I consider a dismissal by calling it "a tool", it is not a tool it is everything... and our current success with exploring it are akin to a baby's first words vocalized before a long life of more complex speech to come.

Mathematics is, we just happen to have discovered its usefulness and given names to the tiny fraction of relationships that it contains that we have been unblinded enough to see(thanks to their being used by systems in the physical world that we find important to understand). I think the idea that math is some how tied to our mode of conception is pure rubbish, it could be true that our mental processes constrain the type of structures we have success in finding in Mathematics but that says nothing of all that it contains..which in my view are every structure conceivable by us or not.

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39. Comment #117379 by Polydactyl on January 28, 2008 at 5:46 pm

Cartomancer, when you have finished the thesis, you have a book, or books to write. With your knowledge, fluency, and skill with words you could aim at something like a professorship in the public understanding of the Middle Ages.
We can't tackle religion in the present without the past.

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40. Comment #117381 by Cartomancer on January 28, 2008 at 5:49 pm

Aww... thanks. I shall remember that tomorrow while my supervisor excoriates me for having done nothing of practical value toward said thesis in the last two months...

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41. Comment #117440 by MPhil on January 28, 2008 at 8:06 pm

Cartomancer,

I agree with pretty much all of what you say. Just some small things bother me:
-The church really did do disgusting things, and oppression is just one of them
-Considering the literacy levels and living conditions, I don't think most people were really concerned with the arguments. The thinkers were, ie the people who had enough economic and social security to have time, energy and liberty to deliberate about those things... guess that makes about point something percent of the population, or maybe even a one digit percentage.
-I definitely do agree, as I already said, about the "product" of the time thing. But that just goes to show... had there been as much liberty of thought and speech etc as there was in Greece of Aristotle's time (add a sufficiently liberal mindset... unlike the one that lead to the death of Socrates) the philosophy would have been a lot more interesting. But that's just idle speculation.

-The reason why I am judging the ideas from the standard of critical thinking rather then as a historical product is because they are forwarded to be "eternally true" and objective, they are meant to be judged that way. It's important to know the historical circumstances in which they arose, but that is not relevant in judging how true or viable they are.

I for one would feel pretty insulted if my philosophical ideas were discussed merely as a product of their time and shown the courtesy of not judging to harshly because I couldn't have known any better.... let me, my actions and my holding those positions be judged that way - but not the positions themselves.

I just hope you don't lump me in with those people who are ignorant of the historical circumstances and judge the people and their holding these opinion without taking these things into account.

Anyway, yes - public understanding of medieval thinking, that would be nice. Of course I'd want to have the same for classical Greece, Rome, Renaissance, Baroque, Pre-classicism, Classicism, Romanticism etc etc... I just happen to think historical knowledge is interesting and important. (Okay, I admit I have yet to find a major field of study that I don't find interesting :)

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42. Comment #117444 by Cartomancer on January 28, 2008 at 8:32 pm

Well, sure, I never said the Middle Ages were perfect! I sure as hell wouldn't want to live there...

It's an interesting counterfactual speculation as to what a different Middle Ages might be like in a parallel universe, but, as I have said before, counterfactual history generally gets us nowhere since we can't run history again with different starting premises. My job would be a damn sight easier if we could! I'd definitely be interested in swapping Socrates, Plato and Aristotle for Aquinas, Scotus and Ockham then seeing what they come up with in each others' oevre. Then we could swap round with Spinoza, Kant and Leibniz, then a play-off against Dawkins, AC Grayling and Bertrand Russel, then...

I'm not entirely keen on saying that the Middle Ages were illiberal when compared with classical antiquity - the example of Socrates does stand out rather, and the intellectual elites of both societies are similarly tiny and privileged - though I certainly admit that they were shockingly illiberal compared to what most of us have now. The caveat does of course apply that both "Middle Ages" and "Classical Antiquity" are exceedingly broad terms and admit of a huge degree of internal variety, both temporal and geographical.

I am also something of a standard bearer for the idea that the unifying, societal focus of medieval european thought, centred as it was around a church with an ethic of discovering one absolute truth, prevented such fragmentation of the intellectual elite into the rival schools that we see during late antiquity. That's something of a different argument however, and probably deserves a lot more time and dedication than it can be given here.

As far as casting ideas in their historical context versus rational examination of them from the position of present understanding, I think we're basically just approaching it from different sides. Religious people claim something is relevant for all time, and while you would disprove it from a modern standpoint, I prefer to point out that it has a very specific underpinning in a particular period of history, the basic premises of whose thought even they themselves do not accept anymore. As an historian perhaps I am more resigned to the fact that my thoughts are largely a product of the society I find myself in. Ah, c'est la vie...

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43. Comment #117446 by MPhil on January 28, 2008 at 8:56 pm

Sent2null,

I'm not sure you are entirely aware of the ontological implications of what you're saying. That is, you just implicitly denied materialism... of course you may be aware of that and actually hold the position that metaphysical universals exist as entities - but as for me, that position seems untenable.

Let me address each point on its own: I think it entirely possible that other civilizations (should there have been such things) have come up with something functionally equivalent to our mathematics. In fact, if those hypothetical civilizations deserve that name, I'd pretty much say they would have had to. But this does not mean that mathematics is not a conceptual construct!

While quantity is a natural category (IMO), numbers (or graphs etc...whatever) themselves are not entities. If they were, they would have to be metaphysical entities of a highly queer nature, as they would have to be linked to natural entities and the relations among them - as is evident when you consider that applicabilty of mathematics. This would be denying materialism, where a materialistic account of mathematics can be given (if at all, the most nonnatural entities you have to assume are sets, as was shown by Quine).

You seem to be making a category mistake. Mathematics is a conceptual construct, the things it is able to model aren't. Think of the axioms...they are unproven, assumed statements in a formal language (that being pretty much the definition of "Axiom").
I will continue on this, but I think this is the time to make another point: Logic is more basic than mathematics. Mathematics is impossible without logic, but logic is possible without mathematics. So when we come to more basic points about reality and its models, I will use "logic" where you used "mathematics"

So, the axioms are formal, unproven statements assumed to be true. If they are not a conceptual construct, what are they? They are not physical objects or relations between objects, so they would have to be metaphysical entities. They describe supposedly (and probably) necessary relations - they are descriptions of the way things are or have to be. BTW, this is another very basic reason why I think you "really" mean "logic". Logical axioms are assumed to be either "the necessary limitations on how we can think" or "the necessary limitations on the way things can be". A final, justified decision between these two is impossible, as the former will be true if the latter is true, but the latter must not be true if the former is. Therefore, accepting that we cannot (analytically true) know (think) something illogical, the decision between these two is impossible. The former is true from all we know, the latter is all we have justification to assume, because we couldn't coherently think otherwise, but that might just be a limitation of our reasoning faculty.

So, since Axioms are propositions, they themselves are conceptual, not physical or a relation between physical entities. With them out of the way, lets turn to theorems. Theorems are arrived at by drawing inferences from a set of axioms. All mathematical sentences (meaning provable propositions) are arrived at by drawing logical inferences from the set of all axioms or a subset thereof. Thus, they - as propositions - are still conceptual.

There is nothing within mathematics that is not conceptual - by virtue of mathematics being a set of propositions (axioms, theorems and simple statements). However, the things mathematics is principally able to model are not. This is not the set of intended or actual applications, but what the construct in it self is able to model of reality, whether or not we ever find out. That is why I said that mathematics (and more so: logic (including set theory), as mathematics is an extension thereof) is such an extremely powerful tool, more powerful probably than we can imagine.

With my position explained that far, I think you might see why in this case "tool" is definitely not derogatory or demeaning in any way. There is simply nothing in the human mind more powerful than logic (I don't mean motivationally, just in case anyone was tempted to mention emotions), and its most powerful expansion, mathematics.

I also think (correct me if I'm wrong) that you might be thinking that without mathematics itself being something "more" than conceptual, we couldn't account for the success we had in applying it. I for one think this is utter rubbish. I think it is pretty much natural that a species evolving in an environment (universe) where the entities behave in a certain way will find a way to model that way things behave conceptually, given enough time. Also, an account of "truth" of a statement can be given within such a naturalistic account (note: what is meant is the truth of a proposition, not 'knowing that a proposition is true'): truth can be described as a systematic and largely uniformity between the structure of the neuronal activation-pattern and the (structure of the) state-of-affairs described by the proposition. It is also natural to assume that a species evolving in a world where things behave according to certain patterns would have a means representation of the structure of these patterns, whether conscious or not.

I really do think you confuse the way things behave and the systematicity of relations among things with our way to model these ways-of-behaving, these relations and their systematicity. Yes, there is such a thing as the systematicity, but it is not an entitiy, nothing which can be properly said to exist alongsinde the entities whose relations it governs... but mathematics is not that, it is the way we model this. Thus, and thus only can we say that

Mathematics is

... and the view I was deconstructing and contradicting here is irreconcilable with materialism, as it requires genuinely metaphysical entities.

If you're interested... read up on the problem of universals and the philosophy of mathematics and logic.

Hope you don't mind this post being so long.
-Mike

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44. Comment #117450 by MPhil on January 28, 2008 at 9:16 pm

Cartomancer,

Concerning the final sentence of your last post: "as a historian", I bet you are---and I'd say you'd have to be.

But don't conclude from that that there are no objective, or at least principally-universally-intersubjectively accessible standards of thinking.
That would be a non-sequitur (and a debilitating one akin to the postmodern aporia, leading to a position from which no judgements whatsoever can be made, unable to even be justified while accepting its basic premises)

Basically, what I'm saying is - a non-judgemental attitude is essential to historical studies, because you want to approach the ideal of finding out, acknowledging and making public anunbiased account (factual) about times and events past. Still, you need a certain set of axioms which you simply accept to be able to do anything.

An argument can always be judged at least from a point of formal logic, that being the structure of arguments - and ever since Aristotle gave us the precursors of formal logic do we have to tools to do so in a uniform, objective way arriving at incontrovertible conclusions.
("If [A->B] and [A], then [B]" for example)

I also acknowledge that my thoughts are largely the product of the society I find myself in - but still, I do think that there are some very very basic truths we know about humankind and the universe which are not relative to society, as they have been acknowledged either directly or indirectly in every argument, every forwarded position everywhere.... that being principally: logic.
Even the mystics and those denying the importance or universality of logic concerning thought made use of just that by virtue of forwarding arguments. Logic is the principal structure of language ("grammaticity"), even before it was employed consciously.

A complete relativism is just not even pragmatically tenable.

So, to sum it all up: I think we need to discriminate between a position and holding-that-position in judgement, and I think this can be done in an objective way, employing logic for judging the conclusiveness of arguments.

Of course, entire positions and statements about the world are always dependent on more than logic (which is principally methodological)... they also require assumed facts... and these are never objectively, verifiably true. If that was your point, I apologize for the rant :)

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45. Comment #117472 by NakedCelt on January 28, 2008 at 10:59 pm

Comment #117358 by Steve Zara:

Ha ha ha ha ha ha ha. How can anybody be such a fucking moron? You're full of shit, Giskard, and you know it. I mean, how can anybody take such an obviously intellectually bankrupt position seriously? You must have the brains of a footballer...

Have I convinced you yet?

I think you are confusing laughing at beliefs and ranting at people.

Oh, please. Like that's a meaningful distinction. You think beliefs exist separately from people? You think people can have their thoughts ridiculed and not feel insulted themselves? What a farcically stupid idea.

...Is that any better?

It's not, is it?

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46. Comment #117479 by Janus on January 28, 2008 at 11:26 pm

Ridiculous beliefs need to be ridiculed sometimes, though. Never doing so creates the impression that they aren't ridiculous.

If you come across someone who believes that Elvis Presley is still alive, you don't nod politely, and carefully, non-offensively begin to point that the Elvis believer might have made one or two logical errors, do you? You just laugh, or stare incredulously, or shake your head in amazement, or ask if the guy is quite sane.

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47. Comment #117500 by miaka on January 29, 2008 at 1:34 am

As for the comment: no mathematician has deliberately flown planes into buildings....

Ouch. Let's not forget Ted Kaczynski, the unabomber, was a mathematician.

Practicing mathematics does not make people immune to crazy or irrational behavior.

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48. Comment #117505 by miaka on January 29, 2008 at 1:46 am

Oh, and as for that comment by jeepyjay that writing papers about Hilbert spaces is akin to talking about how many angels can dance on the head of a pin. Maybe, *maybe* you could say that about certain obscure areas of math that hardly anyone works on except for a few professors at universities no one has heard of. Maybe.

But Hilbert spaces? Could you have picked a worse example than that? That's like one of THE most useful and ubiquitous mathematical constructs ever. I'm hard-pressed to name an important area of science that isn't, in some way, connected to a mathematical result that relies on Hilbert spaces. All of quantum mechanics is essentially talking about Hilbert spaces. Fourier transforms--another Hilbert space topic. The list goes on and on. Do just a little bit of research before you make these preposterous pronouncements.

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49. Comment #117606 by Cartomancer on January 29, 2008 at 8:17 am

MPhil,

I'm not entirely sure where your account of the objective, axiomatic underpinnings of reality contradicts anything I have said. Though I will admit that perhaps I wasn't entirely clear. Of course I believe that there actually are rules of logic and would never think to extend the concept of relativism from cultural studies into epistemology - that way, surely, madness lies.

All I was getting at is the fact that, with our imperfect knowledge of past societies, we must necessarily fill the gaps to the best of our ability - both in terms of facts and of posited causal processes. These processes are several stages of complexity up from basic logical axioms and must be reached through empirical rather than purely deductive reasoning. It's bad enough that our objective evidence is open to so many different interpretations and readings, but our cultural understandings of the processes which give rise to complex historical phenomena are also temporary, somewhat skewed, and subject to revision with the arrival of fresh evidence. It certainly behoves us not to bring in further obstacles to understanding by deliberately approaching the whole phenomenon with arbitrary criteria of "progress" or suchlike and awarding points based on what we ourselves find amenable. Perhaps this problem is a lot less prominent in modern philosophy, but it is not absent altogether and certainly was not absent from philosophy throughout its history.

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50. Comment #117775 by NakedCelt on January 29, 2008 at 3:16 pm

Comment #117479 by Janus:

Ridiculous beliefs need to be ridiculed sometimes, though. Never doing so creates the impression that they aren't ridiculous.

If you come across someone who believes that Elvis Presley is still alive, you don't nod politely, and carefully, non-offensively begin to point that the Elvis believer might have made one or two logical errors, do you? You just laugh, or stare incredulously, or shake your head in amazement, or ask if the guy is quite sane.

I'm afraid it would make no difference, though. No matter how ludicrous an idea seems to you, it doesn't seem ridiculous to the person who believes it. Making it clear that you think it's stupid will only convince them that you're a scoffer and a moron.

Let's not forget that some scientific ideas are, at least intuitively, equally bizarre: abiogenesis, designerless design, Zahavian self-handicapping, relativistic time dilation, quantum indeterminacy, and dark energy spring to mind. You have to look really closely at the evidence and the maths to realize that hey, these actually do make sense. Creationists get a lot of mileage out of scoffing at the first two in particular. Ridicule is not reason.

As for how you do convince someone their belief is wrong... I'm afraid the only way to be sure is to start from their own assumptions and work forwards gradually. While, at every point, making sure they don't think of you as an opponent � because, regardless of our belief systems, humans are still primates and the primary purpose of language, from our genes' point of view, is alliance formation.

I've given this example in another comment already, but recently I was chatting to a guy who believes in Lemuria and stuff like that, and he brought up the subject of pole shifts. Rather than scoff at him, and rather than browbeat him with physics (which I would have had to look up in a textbook anyway), I said "But the shaft from the central chamber of the Great Pyramid points directly towards the present celestial North Pole." Which I'd seen on a TV documentary sometime, and which he accepted immediately as evidence that there hadn't been a pole shift since the Great Pyramid was built. Because I was on his wavelength, you see.

St Paul might have been a credulous true believer and a sexist bastard, but he knew the art of persuasion: "To the strong I became as one strong, that I might win the strong. To the weak I became as one weak, that I might win the weak. I have become all things to all men, that I might by any means win some."

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