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FORMAL SCIENCE IS THE ONE THAT STUDIES IDEAL OBJECTS, THAT IS, CONSTRUCTIONS THAT ALWAYS ARE, TO A CERTAIN IMAGINARY EXTENT, SERVE TO THINK THE ORDER OF THE REAL They do not exist in a specific space and time but help to delimit the confusing aspect that they present things when we first see them. It should be clarified that this is one way of looking at things and not the only one possible. Formal science thinks about the archetypes that will drive any experience.
How do they do it without the ground of experience? Through deductive proofs from axioms. The axioms form the undoubted basis of what we start from. The demonstration must be structured in absolute conformity with them. In Modernity, the prestige of these sciences increased because, despite the fact that it was experienced ad nauseam, experimentation alone was not enough to substantiate it and give it objectivity.
On the other hand, the development of science required a logical-mathematical demonstration. To address the issue, we have summarized the essentials of "Formal Science and Factual Sciences", by Silvia Rivera.