Scientific knowledge is normally divided into two large blocks, formal sciences and factual sciences. The first are all those disciplines of an abstract nature and that do not deal with facts, such as mathematics and logic. The second are those that refer to empirical or factual facts.
General considerations
Biology, history, chemistry, psychology or geology are factual or empirical disciplines, since in all of them concrete facts or data are studied.
Biology studies the simple structure of matter (the cell) and how this basic unit develops to form living organisms.
History refers to something concrete, the set of historical events. Chemistry focuses on the molecular mechanisms that build reality.
Psychology studies human behavior.
Finally, geology describes the phenomena that take place 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 a reference some kind of real phenomenon. In other words, humans, animals, or molecules are observable realities.
Real phenomena can be explained, predicted, classified or discovered. In this sense, factual sciences are always related to experience.
Factual sciences versus formal sciences
A mathematical formula is valid regardless of experience. However, all mathematical formulation is applicable to real phenomena. A logical reasoning is a set of axioms and signs that have nothing to do with material reality or with the temporal dimension of events, but it is a formal structure that can be projected onto all kinds of realities.
The formal sciences are applicable to the empirical world and, in parallel, the empirical is explainable through a formal language.
The hypotheses of mathematics are tested from proofs, while the hypotheses of any factual discipline are tested from some empirical data. The truth criterion of mathematics is the internal coherence of a reasoning or theorem and the truth criterion of an empirical science is based on the evidence of the facts.
In short, in formal sciences reasoning is demonstrated (for example, the Pythagorean theorem) and in factual sciences laws are confronted with a part of reality (for example, the laws of genetic inheritance are applicable to all living organisms ).
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