Scientific knowledge is normally divided into two large blocks: the formal sciences and the factual sciences. The former are all disciplines of an abstract type that do not deal with facts, such as mathematics and logic. The second refer to empirical or factual facts.
General considerations
Biology, history, chemistry, psychology, and geology are factual or empirical disciplines, all of which study hard facts or data.
Biology studies the simple structure of matter (the cell) and how this basic unit evolves to form living organisms.
History refers to something concrete, the set of historical facts. Chemistry is focused on the molecular mechanisms that make up reality .
Psychology studies human behavior.
Finally, geology describes the phenomena that occur in the different layers of the earth.
Consequently, these disciplines are factual because their object of study is something concrete, objective and measurable.
They have as reference some kind of real phenomenon. In other words, humans, animals and molecules are observable realities.
Real phenomena can be explained, predicted, classified or discovered. In this sense, the factual sciences are always related to experience.
factual sciences versus formal sciences
A mathematical formula is valid regardless of experience. However, every mathematical formula can be applied to real phenomena. A reasoning logic is a set of axioms and signs that have nothing to do with the material reality or the temporal dimension of events, it is a formal structure that can be projected onto any kind of reality.
Formal sciences are applicable to the empirical world and, in parallel, the empirical is explainable through a formal language .
Mathematical hypotheses are tested on the basis of proofs, while the hypotheses of any factual discipline are tested on some empirical data. The truth criterion of mathematics is the internal coherence of a reasoning or theorem, whereas the truth criterion of an empirical science is based on the evidence of facts.
In summary , in the formal sciences reasonings are demonstrated (eg the Pythagorean theorem) and in the factual sciences the laws are confronted with part of reality (eg the laws of genetic inheritance are applied to the set of living organisms).
