Branches of Science: Formal, Empirical, and Their Methods

Posted on Nov 22, 2024 in Philosophy and ethics

1. Classification of Science

The sciences are divided into two groups:

• Formal Sciences: These do not refer to facts or experience. This group includes only two sciences: mathematics and logic. For example, the statement x + y = 25 is a mathematical statement that does not give us any information about reality. Its truth depends on deduction, not on correspondence with experience. Variables like x and y are placeholders, not representations of real-world objects. The method used is the deductive method.
• Empirical Sciences: Unlike formal sciences, these refer to facts or make assertions about the world. For example, the statement “Earth orbits the Sun” is empirically verifiable. Empirical sciences include all sciences except mathematics and logic and have three characteristics:
  1. Practicality: Their purpose is practical; knowledge is sought for its usefulness.
  2. Experimental: Their method is based on experimentation.
  3. Mathematization: They use mathematical language.
  They are divided into two groups:
  • Natural Science: Its subject is nature (e.g., Physics, Chemistry, Biology, Astronomy).
  • Social and Human Sciences: Its subject is the human being (e.g., Psychology, Sociology, History, Geography).
  The empirical sciences use two methods: the inductive and hypothetico-deductive.

  ¹Empirical: Pertaining to or based on experience.

2. The Origin of Sciences

2.1. Formal Sciences

In the fourth century BC, Greek philosopher Euclid compiled in a treatise called The Elements all the mathematical knowledge of the Western world at that time. He also created Geometry, which is still studied today. In the same century, Logic was born in Greece with Aristotle’s Organon, the first known treatise on logic.

2.2. Empirical Science

Physics, the model natural science, appeared in the West with Aristotle, who wrote about motion. He proposed a geocentric system, where Earth was the center of the universe. Copernicus (1473) later corrected this, establishing a heliocentric system. Galileo (1564-1642) stated that the Earth moves, and Newton (1642-1727) wrote about mechanics. Einstein’s Theory of Relativity marked another major change in physics. Most social sciences originated in Greece but became scientific in the nineteenth century when they began using the scientific method.

3. The Deductive Method

The deductive method, used in Formal Sciences, proceeds logically from universal to particular. For example:

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.

The conclusion necessarily follows from the premises. Mathematics and logic are axiom systems, composed of self-evident axioms and theorems deduced from axioms or other theorems. These sciences have a high degree of certainty because their statements are either axioms or theorems. The deductive method does not rely on experience; it starts with general statements, which are never empirical.

4. Inductive Method

Typical of empirical science, the inductive method formulates general statements from specific experiences. For example, a scientist observes ten black ravens and concludes that all ravens are black. The observations are private, but the conclusion is general.

5. The Problem of Induction: Falsificationism

The inductive method has a problem: how can we be sure that all members of a class have a property observed only in some? We cannot be absolutely certain. Popper argued that a general statement cannot be empirically verified but can be refuted (falsification). A general statement stands until refuted (e.g., finding an orange raven). All empirical science statements are based on the inductive method and are not entirely certain. They are conjectures, provisional until proven false. Scientific laws and theories are falsifiable; we must accept the possibility they are false. According to Popper, the scientific method does not provide absolute certainty; we accept conclusions until proven otherwise. Criticisms of falsifiability include:

• It applies to isolated statements, not theories.
• A theory is abandoned only if there is a better replacement.

²Refute: To contradict or challenge with arguments.
³Check: To prove the truth of something doubted.

6. The Hypothetical-Deductive Method

This method, typical of empirical sciences, combines deduction and induction. It has five steps:

1. Observation of phenomena: A natural phenomenon occurs (e.g., lightning).
2. Hypothesis: A tentative explanation is proposed (e.g., lightning occurs when clouds collide).
3. Deduction of consequences: If the hypothesis is true, certain consequences should follow (e.g., colliding clouds should produce lightning).
4. Experiment: The phenomenon is reproduced in a laboratory to test the consequences (e.g., colliding clouds to see if lightning occurs).
5. Formulation of the law: If the hypothesis is supported, it becomes a law (e.g., “lightning occurs when clouds collide”).

⁴A theory is a set of interconnected laws.

7. Law and Theory