I have been reading and thinking about the nature of science, and its definitions, for a long time - probably since I saw Bronowski's TV programme The Ascent of Man in 1972.
Any comprehensive definition must be minimal - in particular there is no characteristic scientific method, nor mode (i.e. Popper was wrong, although interesting and useful) - nor does science have any essential attribute of being self-correcting, nor is science necessarily observational or empirical.
And so on.
So what made the difference between science and what went before?
This is the idea: Science came from philosophy and philosophy from theology - by a process of specialization - a part coming off from the whole, and being pursued autonomously as a social system.
Theology is a social system that aims to discover the truth; and which puts the truths of divine revelation first and reason subordinate (if at all); philosophy aims to discover truth (or used to) but puts reason first - but remains (in its early phases) constrained by revelation.
Then science broke-off from philosophy by eliminating divine revelation as an allowable explanation.
So science is a specialized social system, based on reason, but which excludes all reference to divine revelation.
But what is special about being a social system?
Mainly time and effort, in a co-operative sense (although the cooperation can be between just a few people).
So science is simply some people devoting time and effort to investigating the world using reason and excluding reference to divine revelation.
Naturally, since Science excludes divine revelation, science can have no formal impact on theology, nor can it have any formal impact on philosophy.
Yet, apparently, science has substantially impacted on theology and philosophy - it is, for example taken to have discredited Christianity.
How did this perception arise?
1. Science as (until recently) been perceived as in enabling (somehow, indirectly) humans to increase power over nature (this perception may be subjective/ delusional, or false, as it often is now - or it can be all-but undeniable).
Yet science is (or rather was) successful mainly because a lot of smart people were putting a lot of effort into discovering truth.
(And now that people don't try to discover truth, they don't discover it - naturally not.)
2. Sheer habit. People trained and competent in the (wholly artificial) scientific way of thinking, which a priori excludes religious explanations, leads to human beings who habitually exclude divine explanations.
And it turns out that habit is very powerful as a socialization device.
Such that people trained in an artificial (hence difficult) and socially-approved specialized mode of thinking, eventually do not notice the exclusions of their mode of thought, and assume that their mode of thought is the whole thing; assume that that which was excluded a priori has instead been excluded because it was false.
A mistaken inference - but mainstream in modernity.
NOTE ADDED: in sum, to put it another way, progress in science was essentially a consequence of the quality and quantity of man-hours dedicated to the aim of discovering truth about the world using reason and excluding religious explanations.
When the most able truth-seeking people with leisure from subsistence increasingly shifted their interest, activity and effort away from theology into philosophy (from, say, the twelfth century onwards in the West) and then from philosophy into science (from, say, the seventeenth century) - this shifted achievement in the same direction.
And when the most able people with leisure from subsistence increasingly shifted their interest, activity and effort away from truth-seeking and into other things (especially careers) (from, say, the early-middle twentieth century) this shifted achievement into... well, bureaucracy and media distractions.