Formal and Empirical Sciences: Methods and Theories
Formal and Empirical Sciences
There are two kinds of science:
- Formal Science: Deals with symbols and their relationships, not with facts and events in the world. Its content is based on logic and mathematics, and it doesn’t have an empirical connection to reality.
- Empirical Science: Deals with reality and has empirical content that emerges from observation. It is divided into two types:
- Natural Science: Deals with natural reality (e.g., physics).
- Social Science: Deals with social and human reality (e.g., history).
The Scientific Method
The scientific method concerns the best way to achieve success in explaining the facts around us. Throughout history, various methods have been used:
- Deductive Method: Extracts particular data from a conclusion. This method is primarily applicable to formal sciences.
- Inductive Method: Draws a general conclusion from specific data. After observing many cases, we assume the same will occur in similar cases. It provides general principles but has the problem of validating these principles.
- Hypothetico-Deductive Method: Combines the inductive and deductive methods. It consists of:
- Observation of reality and problem formulation.
- Hypothesis formulation: Proposing a coherent and consistent explanation.
- Deduction of consequences: Extracting consequences if the hypothesis is true.
- Hypothesis testing: Checking if the predicted consequences occur through observation and experimentation.
- Hypothesis refutation: Rejecting the hypothesis if the expected consequences are not met.
- Hypothesis confirmation: Confirming the hypothesis if the expected consequences are met.
- Obtaining results: Formulating a new law or confirming an existing theory.
Hypotheses, Laws, and Theories
Scientific Hypothesis
A hypothesis is a probable explanation of a phenomenon. To contribute to explaining reality, a hypothesis must be tested through:
- Verification: Ascertaining the truth of a hypothesis by checking if it aligns with observed facts.
- Falsification: Testing the hypothesis by searching for facts that prove it false. If no such facts are found, the hypothesis is considered true.
Scientific Law
When a hypothesis has been thoroughly tested and not falsified, it can be considered a scientific law. A law is a universal proposition that describes what happens in reality.
Scientific Theory
Science aims to explain reality as broadly as possible. Scientific laws are interconnected, forming compact systems called scientific theories.
Considerations on the Progress of Science
Karl Popper: The Continuing Progress of Science
Falsificationists, like Popper, believe that no theory is definitively true, as it could be falsified in the future. When a theory replaces a falsified one, it represents significant progress.
Thomas Kuhn: Scientific Revolutions
Kuhn argues that scientific progress doesn’t always follow the falsificationist model. Theories are not immediately abandoned when falsified. Anomalies within a scientific paradigm might lead to a crisis and a scientific revolution.
Paul Feyerabend: Epistemological Anarchism
Feyerabend argues that there’s no inherent progress in science and that it’s not superior to other forms of knowledge. He questions the scientific method’s effectiveness.
The Truth
Throughout history, “truth” has referred to both propositions and reality. Greek philosophers sought truth as identical to reality, while also considering it a property of true statements.
Subject and Object
The notions of subject and object relate to the question of truth. Truth can be subjective, depending on the individual’s perspective.
Reality and Truth
Greek philosophers viewed truth as identical to reality, which was associated with permanence. Hebrews, on the other hand, viewed truth as faithfulness and trustworthiness.
Proposition and Truth
- Truth as Consistency: When propositions don’t refer to reality, truth lies in their coherence.
- Truth as Correspondence: Truth exists when there’s a fit between what is (the object) and what is said (the subject’s expression).
- Pragmatic Theory of Truth: A statement is true if it’s useful and effective in solving problems or meeting needs. Truth is provisional and related to practice.
Richard Rorty: Narrativity and Objectivity
Rorty argues that humans make sense of life by placing it in a broader context through narrating their contributions to a community (solidarity) and discovering their relationship with nonhuman reality (objectivity).
Differences Between Mathematical Objects and Ideas
Plato considered mathematical entities as copies of ideas, ontologically inferior. Mathematical objects allow for multiple interpretations, unlike ideas. Mathematics relies on axioms that are not always justified.