Having had some time to think about it: I think I can give a fuller answer to your question.
A theory Science would never be able to prove:
A Theory Science would never be able to disprove.
They kind of amount to the same thing.
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A theory that cannot be
proven is one that is not testable or has been tested to wildly divergent results like, say, Cold Fusion.
Fusion is a kind of nuclear reaction that, according to conventional thinking, only occurs at high temperatures and pressures such which are not available on Earth (but which are quite normal inside stars.)
So far Cold Fusion (the idea that fusion
can take place at not only Earth-bound pressures but at room temperature), to date, has not been proven. But then nor to my knowledge has it been 'disproved.' Scepticism is high, however, for as I tried to explain in my original post, the repeated poor experimental data suggests that as a theory it is wrong - or to be more specific - that the theory of high temperature/high pressure fusion cannot account for it. So perhaps the phenomenon
is real but if it is then so far experimental data just isn't there to lend credibility to such an alternative viewpoint. But then perhaps the right experiment that provide such convincing (read repeatable, objective, falsifiable) data that
would prove it, hasn't been done yet. But any research scientist is going to want to think long and hard before taking up a career trying to prove the theory of Cold Fusion.
This explains why science tends towards conservatism - to be an outcast and right - you need to be awfully sure of your facts.
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A theory that can't be
disproved, however, is different. It's hypothesis is not
able to be proven false because it does not submit to testing. Whereas the theory of Cold Fusion, for all it's faults, is still scientifically testable because as a theory of energy production tests can and have been conducted but to dissapointing results. So it can, in theory be falsified.
A theory that cannot be disproved doesn't even go that far. It's claims and theories are not even able to be tested, right or wrong.
A cogent example from modern times would be Intelligent Design.
I.D is a recent mutation of Creationism (the idea that Life, the Universe and Everything was - and depending on your view - still is being created by a Divine Supernatural Intellect.)
Intelligent Design, because it is so desperately unoriginal, borrows a lot of scientific terms and phrases and tries to appear scientific-by-proxy. However, ultimately, it's hypothesis is unfalsifiable because it crosses from Empiricism (Natural) to Theology (Supernatural) in search of an explanation. And not by accident either.
Carl Sagan famously remarked: "extraordinary claims require extraordinary evidence"
Bearing that in mind: the claims of the Intelligent Design fringe claim that there are instances of biological complexity so complex that the 'bottom-up' theory of incremental evolutionary development by natural selection cannot account for them. Therefore, they conclude they must have been designed and that therefore this designer is the Judeo-Christian God Yahweh and the Creation Process is the one described in Genesis page 1.
This is, to put it mildly, the end of inquiry. It is in short to say: 'We can't explain it, therefore God did it.'
There may be examples of complexity in nature which are yet to be fully understood but the track record of evolutionary biology is quite good on this part. As a theory it has an empirical basis, extraordinary explanatory power, and as of last century is understood in light of the genetic theory of transmission of inherited characteristics. So far it's hypothesis, predictions, and evidence and conclusions have withstood scrutiny.
The claim however that the complex 'whatever-it-is', which Creationism would argue was a magically conjured into existence by an all-powerful deity, is not able to be investigated because (often by their own admission) God is defined to be something outside of the 'normal', physical (i.e empirical) universe.
As a theory or a claim to truth, something stating that that something is 'outside' the universe but somehow able to affect change and cause 'inside' the universe is not able to be investigated and therefore not able to be either falsified or for that matter verified.
The strategy of the so-called 'God of the Gaps' is one that when you think about it, is ultimately doomed but for now this argument says: whatever science cannot explain, must *therefore* be God at work. As a theory that is inherently untenable. To return to Sagan: it would require extraordinary evidence not just "because the bible says so."
And this is why, no matter what they may say, the claims of the I.D.ots are categorically
not based on science. In fact they are antithetical to it because they purposefully try to operate outside of science while simultaneously claiming not to be. This makes them hypocrites as well.
In either case, as I tried to outline above, the fault lies with not so much the rational of science of the scientific
method but the premises of the theories it sets out to test.
If the premises (fusion at room temperature or 'God did it') are flawed, a theory will either be unable to be proven or unable to be disproved.
Science is and will remain only a method for conducting thought. Where it scores over faith or philosophy or alchemy is that it looks at the world we inhabit and tries to understand it: this has led to some extraordinary claims (like Quantum theory) but this theory in particular has to it's credit extraordinary evidence, satisfying Sagan's scepticism.
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It is instructive to remember that 'prove' originally meant 'to test'
as in
"It is the exception that proves the rule."
This does not mean, just in case like me you'd ever stopped to wonder,
'it is the exception to the rule that demonstrates the rule is correct.'
Which would be nonsensical (Think about it).
Rather if you read it as:
'it is the exception that tests the rule' - it makes far more sense.
Either the exception is not governed by that rule or the rule is flawed.
'Proof' in logic and mathematics has another more refined and specific application which boils down to the the outcome following from the premise.
Hope that helps.
LJ.