Forgive Us our Sins, Mr. Darwin
Mike Riggs | September 15, 2008, 2:25pm
The Anglican Church is fashioning a public apology to one of history's most shat-upon scientists, Charles Darwin:
The Church of England owes Charles Darwin an apology for misunderstanding his theory of evolution and making errors over its reaction to it, a senior clergyman said today....
"People, and institutions, make mistakes and Christian people and churches are no exception. When a big new idea emerges which changes the way people look at the world, it's easy to feel that every old idea, every certainty, is under attack and then to do battle against the new insights.
"The church made that mistake with Galileo's astronomy, and has since realised its error. Some church people did it again in the 1860s with Charles Darwin's theory of natural selection. So it is important to think again about Darwin's impact on religious thinking, then and now – and the bicentenary of Darwin's birth in 1809 is a good time to do so.
"It is hard to avoid the thought that the reaction against Darwin was largely based on what we would now call the 'yuk factor' - an emotional not an intellectual response - when he proposed a lineage from apes to humans."
While somewhat late to the party, the Anglicans are at least better at admitting their foibles than the One True Church, which is currently building a statue to commemorate Galileo:
"It's an effort to make him a symbol, an attempt to make Galileo one of the emblems of the church," says Mr. Galluzzi, whose museum houses two of Galileo's telescopes. "It's the church which needs rehabilitation on this case, not Galileo. He was right."On the other side of the barricades, meanwhile, some Roman Catholics think the church has already done more than enough to make up with Galileo.
Atila Sinke Guimarães, a conservative Catholic writer, dismisses the church's mistreatment of Galileo as a "black legend."
The scientist, he says, got what he deserved. "The Inquisition was very moderate with him. He wasn't tortured."
As the western branches of the Anglican Communion have liberalized over the last several decades, their membership numbers have plummeted. In Africa, on the other hand, where Anglican ministers espouse a fire and brimstone theology akin to American Evengelicalism with a hint of Orthodox Roman Catholocism, membership is on the rise.
It would seem that the more a Christian denomination Anglicanism encourages intellectual freedom—or doubt, as the believers call it—the less able it is to sustain or grow its membership. Why can't Anglicans be more like some Jews and some Buddhists, occasional intellectual stars in a contemporary religious dark age? Because Christianity Anglicanism thrives only if its adherents believe that dogmatic obedience is a non-negotiable requisite for salvation. Waiving that requirement amounts to relinquishing a monopoly on salvation.
Someone Who Doesn't Want to Lose His Job | September 16, 2008, 12:06am | #
LMNOP:
All that Godel is showing is that the list of possible objects creatable by the axiomatic system is not enumerable, and that there is no way to conclusively test whether any given construct is decidable within the set of axioms.
Not exactly. It isn't the objects creatable within the system that Hilbert and Russell and so on (later to include Godel) were concerned with, but the axioms
required to create the system itself. Their goal was to come up with a simple, enumerable list of axioms (not results) that would generate mathematics. This is what Godel showed was impossible. Any finite, humanly constructable list of axioms and symbols cannot generate all of mathematics (and in fact we aren't helped if we allow the list to be infinite but still enumerable). Any such list leaves undecidable "holes". If one wishes to have some finite list of causes (axioms) for our effect (mathematics), Godel's work shows us that this is impossible.
The problem of generalizing Godel's two theorems to the physical world is that by logical exclusion, if a phenomenal object exists, by that very virtue there is demanded hierarchical causes which derive from those that generate reality generally.
Also, it's important to note that I am not attempting to generalize Godel's theorem to the actual
physical world. I am merely granting you a counterexample, within the
mathematical world, to your claim that every effect or end result (in this case mathematics) must have no more than finitely many hierarchical causes (in this case axioms). Axioms would certainly, I think, be viewed as hierarchical causes of mathematics, and Godel's theorem shows that we don't get the whole of mathematics with only finitely many axioms. If non-physical counterexamples are not satisfactory to you, then this one certainly wouldn't be, thought it
at least shows that in some
non-physical realms there are effects with no finite list of causes - houses with no finite number of support beams.
Godel's theorems would only be a serious challenge to the account of finite efficient causes if mathematical objects are real objects (Mathematical Platonism). I think there are some very good reasons to believe that mathematical objects are not real in the Platonic sense.
Since however you aren't interested in a counterexample from the mathematical world, I have to grant that enumerating an infinite list of causes for some physical phenomenon won't really be possible. However, I'm still not quite sure I understand why you claim it is so obvious that any effect (even in the physical realm) only admits at most finitely many hierarchical causes.
I'm not saying that this is necessarily untrue, just that it is non-obvious. If I can find counterexamples in realms such as mathematics, I am not sure what precludes the possibility of counterexamples in the physical world.
Anyway, I have to grade. I will try to remember to check this tomorrow in case the thread isn't dead and you answer.
Elemenope | September 16, 2008, 1:01am | #
Forgive me for babbling, it's very late. :)
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It's not that I am uninterested in the mathematical counter-example, it is merely that I think that constructed grammars are off-point when dealing with physical reality.
But even if they weren't, I don't think the result of Godel's theorems actually has the implication as regards to the problem at hand that you think it does. Re-frame in this way: for any given mathematical object, there exists some set of axioms which define its behavior. It may be true that the entire set of mathematical objects cannot be defined by any enumerable set of axioms, but severally, each mathematical object is well-defined by some set of axioms. The impossibility theorems show only that there exists for any given enumerable set of axioms some object not decidable by them.
In this frame, consider the set of all sets of enumerable axioms (which, I know, is not a well-formed set; indulge me). For any given mathematical object, we can be certain that its axiomatic hierarchical description lands somewhere in the domain of that set of sets. We simply can't enumerate the members of the superset as such, only severally as each discrete set of axioms. Thus we can never construct a set of axioms that will explicate the grammar of all mathematics, but that does not exclude the observation that all mathematical objects have a hierarchical causal termination somewhere in the domain of the superset.
That is, to borrow from the
Godel Escher Bach every well-formed string generated by a grammar falls into four categories; theorems, negations of theorems, undecidable true statements, and undecidable false statements. The orientation of those four categories to the whole set of well-formed strings depends only on the specific axioms of the grammar. Godel showed decisively that the superset of all possible axiomatic orientations is not
constructable, *not* (given Mathematical Platonism) that it doesn't *exist*. I don't think it is unreasonable to posit that for each grammatical string severally there exists a set of axioms in which that string is a theorem or a negative theorem, and such a result is not excluded (so far as I can tell) by Godel's findings.