The Logic of Scientific Discovery

1. Science as a Process of Conjecture and Refutation

I suggest that it is the task of the logic of scientific discovery, or the logic of knowledge, to give a logical analysis of this procedure; that is, to analyse the method of the empirical sciences.

The core of scientific progress. Popper reframes science not as a quest for verification, but as a continuous cycle of proposing theories and rigorously attempting to refute them. This process of conjecture and refutation is the engine that drives scientific advancement. It emphasizes critical thinking and the willingness to abandon even cherished ideas in the face of contradictory evidence.

The scientist's role. Scientists should actively seek out evidence that could disprove their theories, rather than trying to confirm them. This critical approach is essential for identifying weaknesses and paving the way for better explanations. The goal is not to defend a theory, but to test its limits and find its flaws.

Embracing error. Error is not a failure, but an opportunity for learning and growth. By acknowledging and correcting our mistakes, we can refine our understanding of the world and move closer to the truth. This iterative process of trial and error is at the heart of scientific progress.

2. The Problem of Induction and the Deductive Method

Now it is far from obvious, from a logical point of view, that we are justified in inferring universal statements from singular ones, no matter how numerous; for any conclusion drawn in this way may always turn out to be false.

The limits of inductive reasoning. Popper challenges the traditional view that science relies on induction, the process of generalizing from specific observations to universal laws. He argues that no matter how many confirming instances we gather, we can never be certain that a universal statement is true. This is because a single contradictory observation can always overturn it.

Deduction as the alternative. Popper proposes a deductive method of testing theories. Instead of trying to prove a theory true through induction, scientists should deduce testable predictions from it. If these predictions are found to be false through observation or experiment, the theory is falsified.

The asymmetry of falsification. While no amount of evidence can definitively prove a theory true, a single piece of contradictory evidence can definitively prove it false. This asymmetry between verification and falsification is the foundation of Popper's approach to scientific method.

3. Demarcation: Distinguishing Science from Metaphysics

The problem of finding a criterion which would enable us to distinguish between the empirical sciences on the one hand, and mathematics and logic as well as ‘metaphysical’ systems on the other, I call the problem of demarcation.

Defining the boundaries of science. The problem of demarcation is to establish a clear line between what constitutes empirical science and what belongs to other domains, such as mathematics, logic, or metaphysics. This is crucial for ensuring that scientific inquiry remains grounded in testable claims about the world.

Positivism's failed attempt. Positivists sought to define science by its reliance on inductive methods and its reducibility to sense experience. However, this approach fails because scientific laws and theories cannot be logically reduced to elementary statements of experience.

A new approach needed. Popper argues that a suitable criterion of demarcation must be based on the unique characteristics of empirical science, rather than on a naturalistic attempt to define its essence. This requires a convention or agreement about what constitutes empirical science.

4. Falsifiability as the Criterion of Demarcation

In other words: I shall not require of a scientific system that it shall be capable of being singled out, once and for all, in a positive sense; but I shall require that its logical form shall be such that it can be singled out, by means of empirical tests, in a negative sense: it must be possible for an empirical scientific system to be refuted by experience.

The hallmark of empirical science. Popper proposes falsifiability as the criterion of demarcation. A system is scientific if it is capable of being refuted by empirical tests. This means that the system must make predictions that can be shown to be false through observation or experiment.

Asymmetry between verification and falsification. Universal statements can never be derived from singular statements, but they can be contradicted by singular statements. This asymmetry is crucial for understanding the role of falsifiability in science.

Evading falsification. It is always possible to evade falsification by introducing ad hoc hypotheses or changing definitions. However, Popper argues that the empirical method excludes precisely these ways of evading falsification. The aim is to expose systems to the fiercest struggle for survival.

5. The Empirical Basis: Testing Singular Statements

If falsifiability is to be at all applicable as a criterion of demarcation, then singular statements must be available which can serve as premisses in falsifying inferences.

The foundation of testing. Falsifiability relies on the existence of singular statements that can serve as premises in falsifying inferences. These singular statements, which Popper calls "basic statements," describe specific events or observations.

The role of perceptual experiences. Perceptual experiences are closely connected to basic statements, but they cannot logically justify them. Statements can only be justified by other statements.

Distinguishing psychology from logic. It is important to separate the subjective experiences or feelings of conviction from the objective logical relations among scientific statements. Subjective experiences can never justify a statement.

6. Objectivity and Inter-Subjective Testability

I shall therefore say that the objectivity of scientific statements lies in the fact that they can be inter-subjectively tested.

Justifiability independent of whim. Scientific knowledge should be justifiable independently of anyone's whim. A justification is objective if it can be tested and understood by anyone.

Inter-subjective testing. The objectivity of scientific statements lies in the fact that they can be inter-subjectively tested. This means that other scientists can repeat the experiments and observations to verify the results.

Repeatable experiments. Only when events recur in accordance with rules or regularities, as is the case with repeatable experiments, can our observations be tested by anyone. This is essential for convincing ourselves that we are not dealing with a mere isolated coincidence.

7. Methodological Rules as Conventions

Methodological rules are here regarded as conventions. They might be described as the rules of the game of empirical science.

Rules of the scientific game. Methodological rules are conventions that guide the practice of empirical science. They are not part of pure logic, but rather rules of the game that scientists agree to follow.

A supreme rule. The supreme rule of empirical science is that the other rules must be designed in such a way that they do not protect any statement in science against falsification. This ensures that scientific systems remain open to testing and revision.

Value of methodological investigations. Methodological investigations may help to clarify the logical situation and solve problems that have hitherto proved intractable. They can also help us to detect inconsistencies and inadequacies in older theories of knowledge.

8. Theories as Nets: Rationalizing the World

Theories are nets cast to catch what we call ‘the world’: to rationalize, to explain, and to master it. We endeavour to make the mesh ever finer and finer.

Tools for understanding. Theories are not mirrors reflecting reality, but rather tools we use to understand and interact with the world. They are systems of signs and symbols that help us to rationalize, explain, and master our environment.

The pursuit of finer meshes. The goal of science is to create theories with ever finer meshes, capable of capturing more and more of the world's complexity. This involves constantly refining and improving our theoretical systems.

Universal statements. Scientific theories are universal statements that apply to all times and places. They are not merely descriptions of particular events, but rather attempts to formulate general laws that govern the behavior of the universe.

9. Causality, Explanation, and Prediction

To give a causal explanation of an event means to deduce a statement which describes it, using as premises of the deduction one or more universal laws, together with certain singular statements, the initial conditions.

Deductive explanation. A causal explanation involves deducing a statement describing an event from universal laws and singular statements (initial conditions). The universal laws provide the general framework, while the initial conditions specify the particular circumstances.

Components of causal explanation. A complete causal explanation requires both universal statements (hypotheses of the character of natural laws) and singular statements (initial conditions). The prediction describes what is usually called the 'effect'.

Rejection of the principle of causality. Popper excludes the 'principle of causality' from the sphere of science, regarding it as metaphysical. He proposes a methodological rule that we are not to abandon the search for universal laws and a coherent theoretical system.

10. Strict Universality vs. Numerical Universality

We can distinguish two kinds of universal synthetic statement: the ‘strictly universal’ and the ‘numerically universal’.

Two types of universal statements. Strictly universal statements apply to any place and any time, while numerically universal statements refer only to a finite class of specific elements within a finite spatio-temporal region.

Strict universality as a convention. The question of whether the laws of science are strictly or numerically universal cannot be settled by argument. It is a matter of agreement or convention.

Methodological implications. Popper argues that it is both useful and fruitful to regard natural laws as synthetic and strictly universal statements. This is to regard them as nonverifiable statements which can be put in the form: 'Of all points in space and time it is true that...'.

11. Universal Concepts and Individual Concepts

An individual concept is a concept in the definition of which proper names (or equivalent signs) are indispensable. If any reference to proper names can be completely eliminated, then the concept is a universal concept.

Distinguishing concepts. Universal concepts can be defined without the use of proper names, while individual concepts require proper names or their equivalents in their definitions. This distinction is fundamental for understanding the difference between universal and singular statements.

Spatio-temporal coordinates. Individual names often appear in the guise of spatio-temporal coordinates. This is because the application of a spatio-temporal system of coordinates always involves reference to individual names.

The problem of universals. The attempt to identify an individual thing merely by its universal properties and relations is foredoomed to failure. Such a procedure would describe not a single individual thing but the universal class of all those individuals to which these properties and relations belong.

12. Falsifiability and the Growth of Knowledge

The root of this problem is the apparent contradiction between what may be called ‘the fundamental thesis of empiricism’— the thesis that experience alone can decide upon the truth or falsity of scientific statements—and Hume’s realization of the inadmissibility of inductive arguments.

Resolving Hume's problem. The problem of induction arises from the apparent contradiction between empiricism and the inadmissibility of inductive arguments. This contradiction disappears if we admit as empirical also statements which are decidable in one sense only—unilaterally decidable and, more especially, falsifiable.

The method of falsification. The method of falsification presupposes no inductive inference, but only the tautological transformations of deductive logic whose validity is not in dispute. This allows us to test scientific statements by systematic attempts to falsify them.

The growth of knowledge. By embracing falsifiability, we can create a framework for understanding the growth of knowledge. Science advances not by accumulating confirming instances, but by proposing bold conjectures and subjecting them to rigorous testing.

Last updated: February 26, 2025