Scientific Methodology and the Classification of Knowledge

Definition and Nature of Science

Science is a systematic set of propositions and a logical sequence that has been sufficiently verified.

Classification of Scientific Disciplines

The sciences are classified in many ways: human sciences as opposed to theological science, and the science of ideas as opposed to facts. Also, sciences can be classified according to what they study (the subject) or pursuant to the end with which they study it.

Theoretical vs. Practical Sciences

From the point of view of the purpose, theoretical sciences are directed toward knowledge, and practical sciences direct knowledge toward action.

Formal, Natural, and Social Sciences

In light of its object, the categories include:

• Formal Science and Logic: These are mathematics. They study concepts, relations, and ideal models for each type of content. In many cases, we can isolate a form to study regardless of its contents.
• Natural Sciences: These study physical and natural beings.
• Social Sciences: These study human behavior and its creations. They have also been called "cultural studies" or "human sciences."

Scientific Methods and Procedures

The different sciences have different methods or procedures to expand their knowledge.

The Inductive Method

The inductive method is a type of inference that enables us to move from the observation of particular cases to general statements. It allows us to move from the discovery of a constant ratio between two phenomena to the affirmation of a universal relationship, which can be expressed by a law.

However, this method raises many problems. To be absolutely safe, you should examine all possible cases, which is often unsustainable.

The Deductive Method

The deductive method is a type of inference that enables us to derive from given propositions (called "premises") another proposition called a "conclusion."

Sciences are systems of truths. Each science has its own criteria for measuring the strength of its evidence. Not all sciences are equally secure; physical theories can be better substantiated than the hypotheses of the social sciences.

Mathematics: A Pillar of Formal Science

As a great creation of intelligence and an example of a formal science, we will focus on mathematics. Under the name "mathematical disciplines," we include algebra, mathematical analysis, geometry, etc.

From a philosophical perspective, we see mathematics as one of the great wonders of human intelligence. They are a language that allows us to calculate, speak of reality in a precise and effective way, and invent new concepts. Thanks to mathematics, the natural sciences (especially physics) have been able to develop theories with great precision and make great discoveries.

Originally, mathematics was invented to solve problems. All cultures have things they need to calculate. Just as with letters of the alphabet we can write all possible words, in mathematics, something similar happens.

The Role of Formal Systems

A system is a set of related elements. The formal sciences (mathematics and formal logic, which studies the correct ways of reasoning) analyze and construct formal systems using a deductive method.