An appeal to authority is valid when
* The cited authority has sufficient expertise.
* The authority is making a statement within their area of expertise.
* The area of expertise is a valid field of study.
* There is adequate agreement among authorities in the field.
* There is no evidence of undue bias.

The proper argument against a valid appeal to authority is to the evidence. However, a reasonable layperson would be very cautious in challenging a brain surgeon on the proper techniques in brain surgery.

Mesk

So most individuals on both sides of this debate rely instead largely on the mainstream media, popular science publications, and scientific blogs to build their knowledge.

Mainstream media is considered a secondary source.

NATIONAL ACADEMY of SCIENCES: "The theory of evolution has become the central unifying concept of biology and is a critical component of many related scientific disciplines. In contrast, the claims of creation science lack empirical support and cannot be meaningfully tested."

The evidence relevant to evolutionary theory is largely tucked away in the academic literature, which is (a) difficult to access without institutional subscriptions, and (b) exceptionally difficult for the layperson to penetrate, given the jargon and assumed background knowledge that permeates every scientific paper.

How do we know what we know?

Scientific evidence consists of observations that can support or counter a specific scientific hypothesis.

Many aspects of science can be easily confirmed. We can repeat the experiments of Galileo, build a telescope and see the phases of Venus. Like Faraday, we can make an electric motor to demonstrate the relationship between electricity and magnetism. We can make a microscope, just as Leeuwenhoek did, and rediscover tiny animacules swimming in a single drop of water. We can see the spectrum of the Sun by using a prism, just as Newton did.

Or we can take a hike, examine the geologic column, and verify the maps of geologists, such as those of William Smith "” perhaps even finding a few common fossils. And after having reasonably verified these observations, we can have confidence in the findings of geology, paleontology, and the succession of fossils.

It is the repeatability of scientific observations that allows us to have confidence in our conclusions.

Agreed. The Bayesian approach seems much more in tune with our basic intuitions about how evidence for a theory or group of theories is weighed. As a formal statistical methodology, though, it is only somewhat recently (~6-10 yrs?) that it's becoming mainstream–at least in my field. So as I was going through school, I got to hear a lot of the older profs express their various reservations about it. The Bayesian vs. Likelihood debate was always interesting to me b/c it's one of the most clear-cut cases where people's philosophy (in this case, there philosophical views on statistics) have an easily observed impact on how they conduct and judge practical research.

"…I do think it's an eloquent account of how science (in fact, I would say scholarship, even belief in general) actually works, both for the individal and for the scholarly community;…"

That's why the old 'Extreme Claims require Extreme Evidence' chestnut is true in a subjective sense, but useless as an argument for or against a position. Take the claim of a miracle, for instance. The ardent materialist needs absolutely undeniable evidence for a miracle to a degree which he would never demand for anything else; a single miracle would require him to reevaluate his entire worldview (i.e. 'miracle' has a tiny prior probability). Meanwhile for a Christian, belief in a miracle would require solid evidence (as miracles are rare), but nothing like the evidence demanded by the materialist, because it sits comfortably within his existing framework of belief (i.e. has a higher prior probability).

Which is to say that 'Extreme claim' is in the eye of the beholder, as is 'Extreme evidence'. Ultimately I think a grand mistake so many people make is to believe that there is some objective, 'netural' position from which we should all attempt to evaluate observations as evidence for and against positions. There is no such objective, neutral position. Everything we evaluate, we evaluate from our own network of beliefs and assumptions, and there is nothing 'neutral', or 'objective' about that.

For the record, my pessimism was somewhat exaggerated, but I do feel that most people express undue confidence in the probability of their current opinions being ultimately correct, and of the opinions of their opponents being fundamentally wrong. I also think the emphasis on an "advocacy" style of debate increases this effect, by forcing people to polarise their opinions. The reason I like TT is that most people here are closer to the middle than on any other evolution/creationism/ID forum I've ever visited, making it (occasionally) possible for constructive dialogue to take place.

Would you consider this pessimistic conclusion an informed opinion?

I'm actually starting to reach the pessimistic conclusion that none of us have the requisite knowledge to have an informed opinion about anything.

Would you consider this pessimistic conclusion an informed opinion?

It's the above fragment of the Bayesian approach that makes it unpalatable for many scientists. There are some limited circumstances where one might have approximate knowledge of the probability distribution for the theory itself (e.g. the probability that the theory 'George is HIV positive' may be approximately the frequency of HIV in the relevant population for George) but in most cases the priors are pulled out of the researcher's you-know-what. Alternatively, they are considered uniformly probable, in which case the Bayesian approach is effectively the same as using Maximum Likelihood, which most folks are comfortable with b/c there are no priors.