Not an easily summarized topic, but this should give you a general idea.
There were two main facets of early modernity's empiricism: a proposal of hypotheses with the intention of corroborating intuitions, enabling the positing of progressive theory, and a critical dismantling of previous theories, providing a recursive niche for improvement. These complementary aspects of science were consistently inculcated at university and infused themselves into the general intellectual climate as modern skepticism, what could be called systematic doubt, and what came to be much later known in the 20th century as positivism, the pursuit of comprehensive theories as well as precepts to guide subsequent development.
The philosophical underpinnings of science, a foundation still under construction in the Early Modern 17th century, tended to adopt one of two general approaches in taking the not yet synthesized skeptical or positivist turn, either rationalist, essentially falling in line with an analysis based on pure conceptualization traceable all the way back to Plato's abstract, Socratic dialecticism, or a materialist strategy founded primarily on observation of the natural world more in likeness to the thinking of Aristotle. Philosophers, with the newly coalescing scientific instincts of their cultural milieu, mused from a starting point of mental ideations or physical facts, usually attempting to either construct a complete system, or deconstruct knowledge in order to reach explicit recognition of what can be known with certainty.
The first major grappling with ontology of history can probably be attributed to the German Georg Hegel, who at the start of the 19th century postulated an abstract concept of spirit as the general mechanism of temporal change; the essence of this view was expounded in Phenomenology of Spirit. His theorizing's central tenet was that history is dialectical: a novel manifestation of 'spirit' - spontaneous impetus - comes into being, a 'thesis', which then prompts responsive impetus, an 'antithesis', finally resulting in 'synthesis', the combinatorial form of a new thesis out of which the process continually reasserts itself. In this schema, our history is like parallel movement steadily expanding in width, drawing more and more of existence under its influence, into the scope of its relatively systemlike, interweaving, temporal strands of substantiality. Propagating threads of spirit bind into an enlarging whole as internal conditioning occurs until they achieve a sort of organized equilibrium, which draws growing swaths of the environment into its mutating general form, just as dialectical communication in pursuit of truth increases the breadth and alters the configuration of human knowledge.
In the 20th century, a philosophy by which to understand the nature of human knowledge was still being pursued, and American philosopher Willard Quine made eminent contributions in this area. He formulated a positivist concept influenced by Wittgenstein's vision of logic, theorizing the episteme as a gigantic mutating web of interrelated beliefs and theories. Quine addressed the nature of truth with a concept of 'confirmational holism': verifying hypothesis or theory in one area of our body of knowledge changes, even if only slightly, the general structure of the whole, especially beliefs in closest proximity to it. He regarded math as "indispensable" to epistemic progress, one of the most important types of conceptualizing in our attempts to process information and make sense of reality.
Contemporary science's reply to Humean skepticism, the uncertainty involved in any extrapolation from past conditions or integration of dispersed information, is statistics. This field supplies techniques for quantifying probability of error in the relationship of any particular datum to any potential geometric model of a data set, making decisions about how to fit figures to information much more exact as deviations are pooled mathematically and processed collectively according to well-defined standards. General implications of spatially and temporally complex or large-scale math for hypotheses and theories have thus become much easier to assess, corroborated or controverted with greater overall precision.
Descartes' skeptical challenge to rationality has been met by the central scientific tradition of peer review. Once a research project has been completed, academics present their work at conventions; attendees ask questions, getting as much clarification and further analysis as desired. Results are also published in journals so the whole scientific community has an opportunity to reflect upon and discuss new facts and theories as well as incorporate ideas into their own professional endeavors. This collectivity is massive triangulation to the most valid perspective on reality; "I think, therefore I am" is blown up to massive proportions, as "We can agree, therefore we know". It is not a perfect system, for groupthink and irrational bandwagons occasionally take hold, in addition to personal rivalries and the occasionally crucified reputation, but science often involves real honesty, transparency and accountability, a combination fostering as much intellectual integrity as any subculture has yet achieved.
The observational side of positivism has matured in the context of science as an implementing of progressively more technologically advanced instruments, enlarging the scope of human perceptivity so that we simply have more information at our disposal, increasing efficacy of theoretical modeling and enriching our image of the world. The conceptual side of positivism has crystallized into the scientific method, an analytical procedure that is essentially recursion producing ever more potent hypotheses as investigators design an experiment, collect data, process results, draw conclusions, and utilize those conclusions to make further predictions, modifying theory as they go. The method has been clarified and generalized to such an extent that it is simple enough for even schoolchildren to grasp, and students are typically instilled with this mode of thinking at a very young age.
Hegel's vision of history is coming to fruition in the context of Quine's confirmational holism: research trajectories of all the many scientific fields are starting to interact with each other, sharing their theoretical paradigms and information so that the episteme is becoming more integrated. The first examples of this movement were contributions of biochemistry to medicine, then neuroscience to psychology; these interdisciplinary efforts have been spectacular successes, giving inspiration to astrophysics (astronomy and physics), biogeochemistry (biology, geology, chemistry), environmental science (ecology, politics, economics, sociology), ethnic studies (anthropology, sociology, psychology), quantum biology (physics, biology, chemistry), with many more instances as well as all their subdivisions.
Modern empiricism has synthesized conception and observation, our rationality augmented by math and our perception enhanced by technology, instating a culture of technical method with seemingly unlimited potential to harness natural environments. Empiricism has settled into three main scientific fields: physical matter, individual psychology in humans and additional organisms, and the study of societies; nature as inanimate, intentional, and collective. In the context of human decision-making and public policy, these domains - material, mental, and cultural - are starting to blend into consciousness of the future as universal in its human meaning, a species-wide sphere of action characterized by intrinsic mutuality of progress.
How could you not agree? lol