(See definition)
The idea of a process in which societies or individuals become better – how convenient. What if individuals do not want to become better? What if individuals think that things are only getting worst and they used to be happier before?
Certainly we now know much more than the people back in the 19th century, who knew more than those from the 17th, 15th, 13th. Certainly progress has lead to us being more informed of the complications the progress itself has created all around the world. Certainly we have discovered many scientific facts we used to not know and many ways to implement them practically in order to make our lifes more comfortable. I am the last person to imply that this is bad, morally reprehensible or undesirable. We have no choice but to assume that the people in the 23th century will know more and will know better than us how to use the cumulative knowledge. (unless a war over oil puts an end to all progress ofc :)
But if we would agree that the only factual and provable knowledge is mathematical knowledge, how do we judge philosophical or particularly moral ideas? We can only prove mathematically that we have enhanced our methodological approach – that is analysis, generalization, typology, etc. We can judge a specific moral idea either from the point of view of its perception in different hystorical contexts by different people or groups, which is relative and does not say much about the idea itself, or from the point of view of... morality. Is our morality subject to progress? Has it improved due to the cumulative knowledge of the centuries? Have we discovered new facts, dependencies, cause-effect relations? Maybe we have. Can we prove it mathematically? I doubt it.
So of what does the cumulative knowledge consist? First, of science i.e. mathematics. Its second ingredient, though, is pure prejudice.
YOU see, Sir, that in this enlightened age I am bold enough to confess that we are generally men of untaught feelings, that, instead of casting away all our old prejudices, we cherish them to a very considerable degree, and, to take more shame to ourselves, we cherish them because they are prejudices; and the longer they have lasted and the more generally they have prevailed, the more we cherish them. We are afraid to put men to live and trade each on his own private stock of reason, because we suspect that this stock in each man is small, and that the individuals would do better to avail themselves of the general bank and capital of nations and of ages. Many of our men of speculation, instead of exploding general prejudices, employ their sagacity to discover the latent wisdom which prevails in them. If they find what they seek, and they seldom fail, they think it more wise to continue the prejudice, with the reason involved, than to cast away the coat of prejudice and to leave nothing but the naked reason; because prejudice, with its reason, has a motive to give action to that reason, and an affection which will give it permanence. Prejudice is of ready application in the emergency; it previously engages the mind in a steady course of wisdom and virtue and does not leave the man hesitating in the moment of decision skeptical, puzzled, and unresolved. Prejudice renders a man's virtue his habit, and not a series of unconnected acts. Through just prejudice, his duty becomes a part of his nature.
Edmund Burke, 18th century
So poor St. Thomas indeed didn't know a shit about differential calculus, but what do we know of morality and the ways of living together such as he did not, regardless of the fact whether he would agree or oppose it? It is always the same dozen of simple things, things before and beyond mathemathics, things that get no influence of such events as falling apples and Copernican shift-aways. The same simple things we always return to.
And a bit off-topic, but I love this text:
Perhaps what liberalism aspires to marry with liberty is not so much prosperity as progress. Progress means continued change for the better; and it is obvious that liberty will conduce to progress in all those things, such as writing poetry, which a man can pursue without aid or interference from others: where aid is requisit and interference probable, as in politics, liberty conduces to progress only in so far as people are unanimous, and spontaneously wish to move in the same direction. Now what is the direction of change which seems progress to liberals? A pure liberal might reply, The direction of liberty itself: the ideal is that every man should move in whatever direction he likes, with the aid of such as agree with him, and without interfering with those who disagree. Liberty so conceived would be identical with happiness, with spontaneous life, blamelessly and safely lived; and the impulse of liberalism in the beginning, to give everybody what he wants, in so far as that is possible, would be identical with simple kindness. Benevolence was one of the chief motives in liberalism in the beginning and many a liberal is still full of kindness in his private capacity; but politically, as a liberal, he is something more than kind. The direction in which many, or even most, people would like to move, fills him with disgust and indignation; he does not at all wish them to be happy, unless they can be happy on his own diet; and being a reformer and a philanthropist, he exerts himself to turn all men into the sort of men he likes, so as to be able to like them.
George Santayana, The Irony of Liberalism