The op makes a distinction between convictions that can be confirmed empirically “out in the world” and convictions that cannot.
For example, a considerable chasm once existed between astronomers who embraced the “steady state” model of the universe and astronomers who embraced the “big bang” model instead. Today that gap has virtually disappeared. Almost all astronomers/astrophysicists agree the big bang model makes the most sense. By far.
Consider this from Bill Bryson:
[b]Alan Guth’s inflation theory…holds that a fraction of a moment after the dawn of creation, the universe underwent a sudden dramatic expansion. It inflated----in effect ran away with itself, doubling in size every 10 to the minus 34th power seconds. The whole episode may have lasted no more than 10 to the minus 30th power seconds----that’s one million, million, million, million, millionths of a second—but it changed the universe from something you could hold in your hand to something at least 10,000,000,000,000,000,000,000,000, bigger. Inflation theory explain the ripples and eddies that make our universe possible. Without it, there would be no clumps of matter and thus no stars, just drifting gas and everlasting darkness.
According to Guth’s theory, at one ten-millionth of a trillionth of a trillionth of a trillionth of a second gravity emerged. After another ridiculously brief interval it was joined by electro-magnetism and the strong and weak nuclear forces—the stuff of physics. These were joined an instant later by swarms of elementary particles----the stuff of stuff. From nothing at all, suddenly there were swarms of photons, protons, electrons, neutrons, and much else—between 10 to the 79th power and 10 to the 80th power of each, according to the standard Big Bang theory.[/b]
And this is true, astrophysicists insist, because it is reflects the most reasonable manner in which to explain why the universe exist as it does today.
But suppose instead we consider the moral arguments of those who insist that spending on space exploration should cease until we have solved more pressing problems right here at home. Is this a rational [ethical] point of view? Is there a way for philosophers to establish this? To establish it, in other words, in the manner in which science has established the rationality of big bang theory?
No, in my opinion, there is not.
And even if down the road the big bang theory is modified or shunted aside by a more rational argument still, the rationality will be subject to rigorous peer review and able to be or not to be replicated by others based on hard data.