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Research Methodology
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Fundamentals of research methodology. Source: Wikipedia (CC BY-SA 4.0).
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Read the full theory →The scientific method: foundations, evolution, and validity criteria
- Scientific method: methodology for obtaining knowledge through observation, measurement, and experimentation.
- Validity characteristics: falsifiability, reproducibility, and repeatability.
- Main techniques: deduction, induction, abduction, and prediction.
- Objective: minimize the scientist's subjectivity.
- Variability by science: experimentation is not possible in theoretical physics; history is non-repeatable.
- Empirical sciences: perfect knowledge does not exist; theories are always refutable.
- Formal sciences: proofs are valid only within their axioms.
- Popper's Criterion: falsifiability replaces verification (seeking the exception instead of total corroboration).
- Scientific practice: theories often persist in the face of anomalies through ad hoc hypotheses until their eventual abandonment.
Scientific revolutions and paradigm shifts according to Kuhn
- Scientific revolution: change of paradigm (theoretical framework of reference).
- Paradigm: general theory with an established fundamental core.
- Scientific progress: the ability to generate new avenues of research and hypotheses.
- Old theories: lose their status as current science but maintain historical value or utility in limited fields.
- Research: requires a funded team, a renowned expert, and an established method.
- Validation: requires publication in specialized journals and acceptance by the scientific community.
- Patents: 20-year right for practical or technical applications.
The scientific method as a mechanism against cognitive biases
- Scientific method: postulation of hypotheses and verification by experimentation.
- Cognitive biases: physiological and intrinsic mental processes that cannot be eliminated.
- Function of the method: offsetting biases by discarding false hypotheses through evidence.
- Nature of science: neither absolute nor dogmatic; it is revisable and based on the empirical method.
- Validity criterion: depends on the strength of the evidence verified.
- Refuted result: the hypothesis must be discarded or modified.
- Biases in science: affect hypothesis generation but are filtered out during the contrast of results.
- Critical thinking vs. Scientific method: critical thinking is less rigorous because the scientific method requires reproducibility.
Cognitive limits and the role of chance in the scientific method
- Limitation: The empirical method is restricted by the cognitive capacities of the human species.
- Proposal: Combine the scientific method with an evolutionary-random approach to overcome cultural frameworks.
- Nature of biases: They are variable, non-uniform, and based on probabilities, not certainties.
- Function of the scientific method: Master tool for testing hypotheses and discarding false ones.
- Chance rate: Between 33% and 50% of scientific discoveries are fortuitous.
- Antifragility: The scientific method is antifragile because it benefits from randomness and error.
- Origin of discovery: Begins with the identification of persistent and systematic failures in experiments.
- Validation: Unexpected failures drive the search for theoretical explanations and interdisciplinary collaboration.
Relationship between science and mathematics
- Science: the process of evaluating models (formulas, simulations, steps) against the observable
- Similarity: both disciplines distinguish the known from the unknown
- Model requirements: they must be internally consistent and falsifiable
- Conjecture: a mathematical statement that has not yet been proven
- Proof: grants 'immortality' to the mathematical statement
- Interaction: time emerged in science and is used in mathematics (e.g., Poincaré conjecture)
- Unreasonable effectiveness: Eugene Wigner's concept regarding the relationship between mathematics and reality
- Postmodernist view: mathematics as a result of human and cultural limitations (Chaitin and Lakoff)
- Common method: use of iterative and repetitive steps in problem-solving (Pólya)
Philosophy and methodology of mathematics and science
- Pólya: Understanding (reformulate), Analysis (plan), Synthesis (expose), and Review (re-examine)
- Gauss: Method of tangible systematic experimentation
- Lakatos: Mathematics is not perfect; it is improved through contradiction, criticism, and revision
- Counterexample: If one appears, the theorem must be adjusted or extended
- Lakatos: Mathematical knowledge is based on heuristics and thought experiments
- Exact sciences: Defined by the capacity to infer truths with certainty
- Key function: Creation of formal systems of inference and scientific models
- Numerical analysis: An essential tool for scientific models on computers
- Main branches: Mathematical analysis, numerical analysis, and statistics
- Logical empiricism: Science is a logical-mathematical unit for interpreting reality
- AI and deep learning: Non-numerical models that mimic neural networks and allow for self-programmed actions
Philosophical foundations and critiques of the scientific method
- Basis of the scientific method: objective reality, accurate human perception, and rational explanations.
- Methodological naturalism: the framework that underpins scientific practice.
- Kuhn: The scientific method varies historically and his observations are sociological in nature.
- "Theory-laden" observation: observation depends on the conceptual framework and the preconceptions of the observer (Hanson).
- Kuhn (1961): Theory precedes the experiment and dictates the form of measurement.
- Feyerabend: Denies a universal method; maintains that scientific progress sometimes requires violating methodological norms.
- Science wars: conflict between postmodernism (science as discourse) and scientific realism (science as fundamental truth).
- Karl Popper: Questions the existence of a unique or generic scientific method.
Flashcard preview (6 of 35)
- 01
In the scientific method, what seeks to minimize the influence of the scientist's subjectivity?
The rules and principles of the scientific method.
- 02
In the human and social sciences, why is the requirement of reproducibility and repeatability not applied?
Because phenomena are, by their essence, unrepeatable (e.g., history).
- 03
In the empirical sciences, is the verification of "perfect knowledge" possible?
No (every theory remains open to being refuted).
- 04
According to Popper, what criterion replaced the verification criterion to validate a scientific theory?
The criterion of falsifiability.
- 05
In the formal sciences, within what framework are proofs generated through mathematical deductions?
Within the system defined by certain axioms and inference rules.
- 06
According to Kuhn, what produces the advancement of science through revolutions?
A paradigm shift.
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