Pete Mansell makes many interesting points in his recent post. I won't deceive the other list members by failing to admit that Pete and I have discussed these issues many times over the years !
I think Pete is right to draw the attention of us all to the ambiguity of the term "science"; from its Latin derivation, it can be used to describe any attempt to know. The scientific method, involving repeatable & public experimentation, is a special case.
I agree with Pete that mathematics is not a science. It is an invention, though theorems are discovered within the context of an invented mathematical formalism. This is a controversial view, I'm told, and one that I've floated in Commensal previously. The question arises as to why mathematics is so effective in describing certain aspects of the world. It is not clear why this should be the case if it is purely a human invention. Applications of mathematics are discovered, sometimes before the formalism is invented.
I wonder whether there's too much of a bias towards the mathematical sciences in Pete's thoughts - he refers to geology as a science, made use of by evolutionary theory. But, according to his definition, is geology even a science ? Again it may make use of the sciences of physics and chemistry, but other aspects are more akin to history; in the way the geological column is constructed for instance.
Pete makes reference to "theories of the origins of the human species". While I have no ideological objection to treating human evolution in the same breath as animal evolution, human evolution is a particularly difficult area because of the diversity of theories and the paucity of the fossil evidence. Fossilisation is a rare event, and humans are less likely to get themselves fossilised than marine or amphibious animals, at least until the time of ritual burial, which is a very recent invention.
Pete refers to the choice between "not disproved" theories as "just" a matter of personal judgement. "Just" is a dangerous word. This approach would leave any opinion in history (say) similarly exposed to private choice. I would say, moreover, that experiments are possible in historical sciences. We can create a theory and then subsequently note further evidence for that theory as it turns up. As evidences (or counter-examples) arise, they confirm (or falsify) the theory.
I'm afraid my "dream theory" is not yet formulated. However, I do recognise a great difference between the use of Occam's Razor and Pascal's Wager. The purpose of Occam's Razor is to remove ad hoc-ness; to remove those superfluous elements of theories that are not central, indeed are not necessary, and will become hostages to fortune if allowed to remain. So many things might be true - we're limited only by our inventiveness - that to clarify matters we must reject all those for which there is no positive evidence. Pascal's Wager is more dangerous. Maybe if two theories appeared equally probable (however we measure this - but "not disproved yet" is hardly a leveller), it would be perverse to choose the least appealing or personally disadvantageous, but equal probability is hardly likely.
I was not impressed by the attempt to keep things simple by leaving only one unknown, namely "God". God is not a simple concept, but is a way of packaging up all mystery into a single term.
Also, I'm not sure invoking causa sui, or whatever the Spinosist term is, is going to get us far when the majority of scientists (other than a few hidden-variable die-hards) have abandoned causality in the quantum world. When we get right back to the beginning, quantum rules rule !
The problem with "non-disproved" theories, is just when are they disproved ? Biblical Fundamentalists, when confronted with a seemingly insuperable obstacle, defer to future research in the hope that the issue may yet be resolved. In a sense this is true of all theories and all disciplines, except those few without anomalies that are thoroughly worked out. The question is (and for this the "dream theory" is required !), how do we rank the "not disproved" theories and choose between them ? Theories die for lack of adherents and opposition dies with the opponents. For instance, I'm informed that Ernst Mach never accepted the atomic hypothesis, much as Einstein was never happy with quantum mechanics. The problem is that none of us ranks all "not disproved" theories equally, or we'd be prey to all sorts of conspiracy theories or wild speculations. Conspiracy theories are virtually impossible to disprove because their proponents invoke yet another layer of cunning on the part of the authorities. As I asked in the first post to this list, has man really been to the moon ? We aren't justified in believing something just because it hasn't been disproved to our satisfaction, especially (again referring to my earlier post) since we won't even be cognisant with all the pro and con data, but have to rely on the summarising and opinions of others.
Finally, with respect to what is taught to children. It is an unfortunate practical fact that much school work has to be taught simplistically, since we just don't have time to discuss what Johnny thinks happened at the Battle of Hastings. It's there in a book. OK, we can give the impression of allowing students to "research" topics, but from what I've seen the references are spoon-fed. Even at tertiary level, it's there in the books. If someone wants seriously to research the issue, then that's up to them as a professional or amateur scholar, but for the generality of students facts have to be learnt and crammed into some overall world-view. This is not rote learning, because the interrelations have to be noted, common themes picked up, the flow of history (in this case) understood. Of course, there are two sides to every story; and, it is said, history tends to be written by the victors. So, scientific textbooks are written by the winners, or at least their camp followers. In this case, the winners tend to have right on their side.
Pete bemoans the possibility of children of a certain persuasion being forced to recite antithetical dogma. I would suggest this happens in the home as well - children pick up or are fed ideas second hand from their parents; until, that is, they are teenagers when they pick them up from even more dubious sources. I dare say it's the parents in Kansas who are upset by the teaching of evolution, not the children. If fundamentalist parents are worried about their children's minds being poisoned, they can counteract this at home, but at least then their children have heard both sides. Children of non-Christian parents should also be exposed to religious traditions, including those traditions' theories of origins - though not in as much depth as evolutionary theory, if only because these theories themselves are not as substantial.
Interestingly, an approving quotation from Theodosius Dobzhansky appears in a review of Steve Jones' new book Almost like a Whale in this week's Economist; "Nothing in biology makes sense except in the light of evolution". Another review in the same magazine (of Matt Ridley's Genome : the Autobiography of a Species in 23 Chapters) starts ... "Biology is rapidly becoming as "hard" a science - in all senses - as physics" (referring to the success of genetics, and of mapping the human genome, the subject of the book). These sources are not quoted as proof-texts !