Hi George,
I agree that there is a great deal of interest within modern Christianity in seeking better approaches to core dogma, I was continuing from Peter's earlier comment vis a vis the historical roots.

WRT Euclid, I tend to Feynman's view, which was that Euclidean insistence on fundamental axioms caused a mindset within mathematicians and to some extent logicians more generally that made it difficult to advance to more general cases. As you know, it was ultimately the poorly framed 5th axiom that proved the undoing of that way of thinking and lead to a proper geometry of the sphere.

That criticism can't be made about Newton. His way of thinking was an early model for the scientific method. He was a paragon of unconventionality and a great example of always questioning accepted wisdom, including his own.

Philosophy is an interesting case, because it has flourished alongside and because of a great deal of cross-fertilisation with the natural sciences and mathematics. Aquinas was an excellent scholar and very much interested in reasoned speculation. He introduced a new level of rigour into his speculations about the nature of reality, but lacked the tools to be properly comprehensive and undoubtedly both knew and lamented that.

Aquinas is one of the great exemplars of the way in which theology has lead toward science and modern philosophy.

Craig,
Speaking in the context of what is believed by fundamentalists, you've said above. "... only some forms of speculation are allowed and speculative results are regarded as unassailable dogma ... "

I don't mind your turn of phrase, yet I hardly think this description belongs to 'fundamentalists' alone. I think you're more so describing what's common to all humanity. All our methods, beliefs, philosophies, 'isms' and creeds have their speculations, their boundaries, their 'quarantined' areas, and their unassailable dogma. It's only the human condition you are describing, common to us all.

And I think you've staked your own faith claim, though speculative, with as much conviction as any common parishioner I've seen in church:
"I'm hopeful that empirical science, combined with new approaches to metaphysics that flexibly encompass qualitative models as well as mathematics ... " is what you think might be the recipe to bring us on track? Do you really believe in your heart we'll find the unified theory for everything?

Add a little reason, speculation, self conviction, salt, simmer and stir. We can all propose a recipe. For we all have that measure of faith that's there to be appropriated.

Hi Craig,

I do not understand what Feynman meant (I have not heard of this before) but in general I am sceptical about historical “ifs”. We can say what would happen with a compound if we add or remove an ingredient, but how can we know how essential is this or that “historical ingredient”, whether geometry (or philosophy) would have developed the way Feynman prefers, without Euclid or other “ingredient”? Or does he really think that Euclid’s contemporaries would have understood what Feynman would have instead wanted him to state? Have all the premodern thinkers who accepted the “truth” that the square of a number cannot be negative set mathematics back?

With hindsight we might prefer Newton’s or Aquinas’ contribution to our understanding of the world to that of Euclid who, after all, lived centuries before both, so he was much more removed than the two from how we try to understand the world today.

I am not sure what you mean by “geometry of the sphere”, since as a surface embedded in the three-dimensional Euclidean space it was well treated (e.g. by Gauss) within what we now call Euclidean geometry.

Hi Dan,
I don't dispute that faith is important and if you've followed some of Peter's other recent threads you'll see a fairly extensive defence of religion from me. Positivism is itself a kind of faith and that too is important.

I think you're also right that the tendency to quarantine aspects of knowledge is common in academia and other hierarchical organisational structures but it's by no means always been the case. The Enlightenment was notably characterised by a highly cross-disciplinary approach, as was the Greek Golden Age. It is also increasingly the case in our modern age of information that cross-disciplinary collaboration is seen as a norm, while easy access to information means that the lines between fields are increasingly blurred.

Yes, I really do believe we will eventually find out enough about the world to have a "theory of everything", including a genuine understanding of humans as a group species. What's more, I think that when we do, it will become obvious that what has been called "divine" is an emergent property of the interactions between the things that make up the self-organising "system of the world". This is what Maturana called "autopoiesis".

Are you familiar with Luhmann's work? http://en.wikipedia.org/wiki/Niklas_Luhmann

He was one of the first to try to bring some of the ideas of dynamical complexity into sociology and in my view is undervalued by a profession that has been obsessed with oversimplification and constructionalism. Even such relatively simplistic approaches to complexity as structuration have failed to find much traction, but this is changing, once again due to cross-disciplinarity.

Hi George,
re: Feynman, I'll let him explain it himself. This is some video of one of his lectures. I think I may have referenced this before. He discusses the difference between a Euclidean axiomatical dogmatic approach and the more modern (although he points out that it actually predates Euclid) approach of making useful assumptions and working in whatever direction is necessary to arrive at the desired result. As you will note, Feynman's objection is not to the postulates that Euclid used, but to the assumption that they defined the only possible path to a proper understanding.

https://www.youtube.com/watch?v=YaUlqXRPMmY

Gauss had to abandon the fifth axiom (or more correctly, modify it to fit with what was obviously the case on the sphere) to make his geometry work, which was what I was getting at. Riemann and others then generalised it further. There really was no reason it couldn't have happened a great deal sooner though, because there was a great deal of knowledge about the geometrical properties of spheres for centuries before Gauss's work. It was only the perceived inviolate nature of Euclid's axioms that limited acceptance of non-Euclidean models.

I'll include a link to Wikipedia for those who may not have a mathematical bent.

http://en.wikipedia.org/wiki/Non-Euclidean_geometry

Dear George,

I have little to add because you summed the situation very well:

<<I think theology has “significantly failed” only as far as it has seen its belief system, and what can be deduced from it, amenable to empirical (scientific) verifications. The same as - I believe - science will fail when it tries to answer questions that in many cultures belonged to the realm of religion for millennia.

The difference is that (Christian) theology was acting as ersatz-science for centuries...>>

Which was wrong - the clergy were supposed to teach their flock the way to God, not about the ways of the world.

While the ultimate Reality, or God, is indescribable, sometimes it is necessary to encourage the people with inspirational stories that help them to find the strength and courage to proceed on the difficult path, to work against their human/animal nature, to improve their character and develop an attitude of devotion.

Take the Sabbath: it is of spiritual advantage to set aside regular times for rest and reflection. When simple-minded people asked "why?", it was helpful to tell them the creation-story, how even God rested on the seventh day.

However, somewhere, somehow, the purpose was nearly forgotten and the story acquired a life of its own, grew out of proportion and even spilled into the realm of science, conflicting with geology, astronomy, biology, etc.

This cannot be described as religion, but as an accident.