Summary: The Logic of Scientific Discovery by Karl Popper

• The book challenges the traditional view of scientific method as a process of observation, hypothesis, and confirmation, and argues that this view is based on flawed inductive logic.
• The book proposes a new view of scientific method based on deductive logic, which emphasizes the role of falsification. A scientific statement is one that can be potentially falsified by empirical evidence, and a scientific theory is one that has survived repeated attempts of falsification.
• The book also discusses the concepts of probability, causality, quantum physics, and the demarcation between science and non-science, showing the relevance and applicability of his philosophy to various domains of human knowledge.

The Logic of Scientific Discovery (1935) is Karl Popper’s classic work on the purpose of science and knowledge. Scientists should test their theories not to verify them, but to falsify them, and hence become even more accurate.

Who is it for?

• Scientists interested in the big picture
• Philosophers curious about scientific method
• Logic lovers

Dive into a classic of twentieth-century scientific philosophy.

Picture this. It’s a lovely morning in your small hometown, and you’ve decided to go for a short stroll along the river. As you’re walking along, soaking up the warm summer sun, a beautiful white swan comes swimming around the nearest bend.

And oh, look! Just behind it is yet another white swan!

And then another!

You, being a ponderous, scientific sort, notice a common theme. All of these swans are white. And because these are the first swans you’ve ever seen, it’s easy to formulate a little theory: all swans must be white.

Then, almost right on cue, a fourth swan turns up. Lo and behold, it’s also white. Well, that just proves it! This theory is quickly becoming fact.

But . . . hold on. How do you know a fifth swan won’t turn up that’s black? Or pink? It’s impossible to discount that possibility – however unlikely it is.

Oh, dear! And here you thought you were just going on a calm, uncomplicated walk in the sunshine. Yet unwittingly, now surrounded by this concerningly large number of swans, you’ve stumbled across one of the trickiest questions in twentieth-century philosophy.

How can we ever truly prove a theory to be correct?

Luckily, this summary to Karl Popper’s philosophical classic, The Logic of Scientific Discovery, aims to solve this very question.

Be it white swans or any other hypotheses you’ve been brewing on the side, you’re about to find out why your theories might not be as airtight as you once thought.

Scientists should use deduction not induction, and aim to falsify – not prove – their theories.

Okay, to start with, let’s go back to those swans.

On your walk back from your riverside stroll, you get to thinking. How are you going to explain your new findings that all swans are white to the world?

It shouldn’t be too hard. The evidence is on your side. You took a limited and specific data set – four swans, in fact, practically a flock – and you drew a reasonable theory from it. Every swan you’ve seen has been white. So, therefore, it’s only natural, to theorize that all swans are white.

It’s airtight, surely even Popper would be on your side.

This is an example of inductive reasoning, or simply induction, and Popper opposes it strongly. The problem is that we’re using singular statements, like “This swan is white,” to prove universal statements, like “All swans are white.” Logically speaking, Popper argues this approach simply isn’t valid. It’s always possible that a black swan – or a pink one, or a yellow one – might have come swimming around that corner. That applies if you’ve seen four swans, or 40, or all the swans you can imagine. A black swan could always appear.

Here’s a question, though: What would happen if a black swan actually did turn up?

Well, that would disprove the theory that all swans were white. So there’s an asymmetry to the logic here: specific statements can’t prove universal ones, but they can disprove them.

That’s an important point when it comes to Popper’s preferred scientific method – known as deduction.

Rather than starting with specifics, deduction starts with universals and examines the relationships between them to see what other logical conclusions can be drawn. You might say, for instance, that all birds can fly, and also that swans are birds – and hence, you can deduce that swans can also fly.

That’s logically valid, Popper says, but that doesn’t mean it’s necessarily true. Rather, a good scientist would be constantly on the lookout for anything that goes against their hypothesis.

They’d be looking to falsify their own theories. For instance, if they found out about a nonflying bird like a penguin. That specific case falsifies the general statement that all birds can fly.

That shouldn’t be a disappointing result for a scientist: in fact, it should be exciting. It’s an intriguing new piece of information that will cause them to formulate a better, more accurate theory. Instead of “All birds can fly,” maybe it’s “All birds have wings.” And then, they’ll be looking everywhere for a bird with no wings to try and then falsify that statement.

In this way, falsifiability is a big deal for Popper. It’s even what he calls the criterion of demarcation: the simple fact that distinguishes science from nonscience. A statement is only scientifically valid, he says, if it can potentially be falsified. Otherwise, you’re not dealing with science at all, but rather with something much vaguer: metaphysics.

Deciding which theories to accept isn’t strictly logical.

There’s absolutely nothing wrong with saying “All swans are white” in the first place. The mistake is to think this is true simply because you’ve seen a few white swans on your local river. Instead, you have to accept that your statement that “All swans are white” is only a guess.

But, even then, we’re not out of the woods yet. That can still be picked apart by Popper. Because in order to still have that theory, guess or not, you have to think about how you even came up with that in the first place. How did you get the idea to suggest that all swans were white?

That might sound like a trivial question, but it’s not. Remember that Popper rejects induction very firmly: the existence of a few white swans isn’t enough to justify the general statement. So there isn’t actually any logical basis at all for coming up with a theory like your swan theory – or, for that matter, even more legitimate scientific theories like gravity, or relativity! It’s basically guesswork.

For Popper, coming up with a theory relies on a small but vital leap of faith, an act of imagination. He calls it psychologism – and it’s something logic simply can’t account for. And as such, it’s essentially outside the scope of what he discusses in his work: Popper’s concern is with the logical processes that you subject a theory to – in other words, all the stuff that happens after you’ve come up with a theory. But he happily accepts this moment of imagination as a crucial first step. We just have to remember that that’s all it is.

A slightly illogical leap of faith is also involved when it comes to deciding which theories to accept as true. We can’t use only our own experiences to decide what to accept, because that would be inductivism – instead, we simply have to make a decision.

It’s a bit like how a jury works in court. A jury is asked to determine what happened in a particular case. All it has to go on is the available evidence about the case, and a pre-existing set of rules – the law. A jury’s verdict is accepted as fact – but of course, if more evidence had come to light, they might have reached a different verdict. Is a jury’s verdict the actual truth? It’s probably more accurate to describe it as close as we can possibly get to it.

So, even though science aims for objectivity, it’s essentially like a jury’s verdict. It doesn’t really deal in absolutes – it just makes the best guesses it can, based on the evidence available.

Probability statements are of limited use to science.

For this next section, we’re going to deal with probability. Because when addressing the idea of statements being either true or false, it’s crucial to also factor in the role that probability might play in our reasoning.

Take a six-sided die, for example. Say you want to roll a six. Your probability of throwing a six is one in six. So, let’s pretend we roll a die 600 times? You’d likely end up with approximately 100 sixes – but would it be exactly that? Likely not. You might have, let’s say, 103 sixes rolled instead.

So should you revise your starting theory, and say that the probability of rolling a six is actually 103 out of 600? No, because our first statement was a numerical probability statement, calculated mathematically, rather than through experiment. Assuming the die is fair, the probability of throwing a six remains one in six. The previous 600 throws don’t affect that probability at all.

And what that means is crucial for Popper: probability statements are not falsifiable. Maybe if we could actually roll a die an infinite number of times, things would be different – but we can’t. We simply can’t truly put probability statements to the test.

What role do probabilities have in science, then? Popper, falsification fanboy that he is, says, not much. Most of the time, as they’re not falsifiable, they simply don’t have a role.

There are some occasions where probabilities really do have a role in theories – Brownian movement is one example, which is about how particles move in a fluid. That movement of liquid is somewhat random, so some deviations from average results are very much expected. But in a case like that, the variation becomes part of the theory itself – it’s hard-wired into the theory. So overall, a theory like that can, in fact, be falsified: it would be proved wrong if the results fell outside the window of acceptable outcomes. So, because it’s falsifiable, it then belongs in science.

Popper also makes another point about probability that throws a fascinating perspective on his views in general. What’s the difference, he asks, between predicting the orbits of the planets and predicting a throw of a die?

You’d probably respond that throwing the die is pure chance, whereas the planets move in a regular pattern. But Popper says that actually, the two scenarios are much more similar than you think.

Why? Because it’s all about initial conditions. We know the initial conditions in which the planets move very precisely through observations over many centuries. But precisely what movements go on inside someone’s fist as they shake a die? What are the exact properties of the surface they’re throwing onto? Throwing a die seems random, but only because we have such poor knowledge of the conditions. If we knew all that in detail, we’d be able to predict the outcome just as accurately as where Mars will be next Friday. And that would definitely help in a casino.

Popper disagreed with Heisenberg’s uncertainty principle.

There are some things, though, that we genuinely have no choice but to be uncertain about. At least, according to the physicist Werner Heisenberg.

In quantum mechanics, Heisenberg’s famous uncertainty principle is all about the limits of what we can know. At a subatomic level, the more accurately we know where a particle is, the less accurately we know its momentum. The most famous example of this is if we simply observe a particle at the subatomic level: this causes a small exchange of energy with the particle, which affects the way it behaves.

In other words, there really are hard limits on exactly what we can know. It’s not possible to continue getting more and more accurate in our measurements over time. It’s only ever a matter of approximation.

Given what you’ve already heard about Popper’s views on probability, it’s easy to see why he was uncomfortable with Heisenberg’s conclusions. Popper believed that scientists should be constantly modifying their theories to make them more and more accurate as they accumulate more information and knowledge – but Heisenberg says no, at a certain point that just isn’t possible.

To cut a long and complicated story short, Popper disagreed so adamantly with Heisenberg’s arguments, that in The Logic of Scientific Discovery he actually proposed an experiment designed to falsify Heisenberg’s uncertainty principle. But Popper’s efforts came in for criticism too, including from Albert Einstein. And, in later editions of his book, he modified his position on this.

It’s funny, really, when you stop to think about it – from one perspective, Popper and Heisenberg aren’t so far apart. What they have in common is an acceptance that it’s essentially impossible to know anything with 100 percent certainty. It’s just that, while for Heisenberg that puts a limit on what scientists can hope to achieve, Popper says scientists should never stop in their search for ever-greater accuracy.

Science isn’t about seeking truth – it’s about seeking ever greater accuracy.

For this last section, let’s zoom out a little, and think about what Popper’s ideas really mean. And let’s forget about swans this time – I think you’ve got the picture with those. So, here’s another scenario for you.

Let’s say, tomorrow morning, the sun doesn’t rise. It just stays dark all day. We’re assuming, for the purposes of this, that you don’t live in the Arctic circle where this is actually plausible – just imagine something happens that’s completely out of line with what you’d expect of the natural world.

Assuming all the scientists manage to find their way to the lab, what should they do?

It wouldn’t be enough simply to explain why, in this one instance, the sun hadn’t risen. The scientists would have to go right back to the drawing board and adjust all their existing theories about the way the world works in order to account for this one day’s peculiar events.

They’d need to find new scientific laws that explained not only the present but the past too – new laws that fit with all the evidence they had available.

That one day when the sun didn’t rise would be enough to falsify our current scientific theories. But remember, even once the scientists had made the necessary adjustments and come up with more accurate theories, every day that the sun either did or didn’t rise in accordance with those theories wouldn’t prove those theories to be true – because that would be inductive reasoning.

What those days would do is corroborate the theories – but that’s much weaker. It’s effectively just saying that there wouldn’t be any reason for the scientists to be concerned.

The moral of the story is that science is always uncertain and tentative. Science isn’t knowledge. It isn’t truth. It’s just as close as we can get to it. And when we encounter a result that falsifies what we think we already know, that’s something to get excited about – because it means we can come up with new theories that are ever so slightly better.

So what’s the aim of science, then? It isn’t to uncover absolute truth – because that’s impossible. And after all, it’s always possible that a black swan will come gliding down that river, or that the sun won’t rise tomorrow, and in that case, we’ll have to go back to the beginning and revise our theories from scratch.

The aim of science is simply to become ever more accurate: and to do it better each time.

Final Summary

The key message in these summaries is that:

Scientists should aim to falsify their theories rather than verify them. In doing so, they can revise their theories and make them more accurate. It’s a mistake to think that science will ever uncover the absolute truth about how the world works. The aim should be to simply do a little bit better every time we learn something new.

To implement this into your daily life, here’s a quick piece of actionable advice to take with you: Falsify your own opinions.

Popper’s focus is on dense and complex scientific topics like quantum mechanics – but really what he’s talking about is an attitude that can apply in far less academic situations too.

So next time you form an opinion about something – whether you’re scrolling through Twitter or listening to a podcast – don’t look for evidence that verifies your view, look for data that falsifies it. That way, rather than getting excited when you see yet another tweet that confirms what you already think, you’ll take an interest in something that challenges your views, and in doing so pushes you to find a better, more inclusive worldview.

About the author

Karl Popper (1902–94) was one of the twentieth century’s major philosophers, specifically working on the philosophy of science. He began his career in Vienna, his birthplace, and emigrated first to New Zealand and then to the United Kingdom in the 1930s. As well as The Logic of Scientific Discovery, which he wrote while still in Vienna – although he revised it several times later on – another of his well-known works is The Open Society and Its Enemies.

Sir Karl Raimund Popper, FRS, rose from a modest background as an assistant cabinet maker and school teacher to become one of the most influential theorists and leading philosophers. Popper commanded international audiences and conversation with him was an intellectual adventure—even if a little rough—animated by a myriad of philosophical problems. He contributed to a field of thought encompassing (among others) political theory, quantum mechanics, logic, scientific method and evolutionary theory.

Popper challenged some of the ruling orthodoxies of philosophy: logical positivism, Marxism, determinism and linguistic philosophy. He argued that there are no subject matters but only problems and our desire to solve them. He said that scientific theories cannot be verified but only tentatively refuted, and that the best philosophy is about profound problems, not word meanings. Isaiah Berlin rightly said that Popper produced one of the most devastating refutations of Marxism. Through his ideas Popper promoted a critical ethos, a world in which the give and take of debate is highly esteemed in the precept that we are all infinitely ignorant, that we differ only in the little bits of knowledge that we do have, and that with some co-operative effort we may get nearer to the truth.

Nearly every first-year philosophy student knows that Popper regarded his solutions to the problems of induction and the demarcation of science from pseudo-science as his greatest contributions. He is less known for the problems of verisimilitude, of probability (a life-long love of his), and of the relationship between the mind and body.

Popper was a Fellow of the Royal Society, Fellow of the British Academy, and Membre de I’Institute de France. He was an Honorary member of the Harvard Chapter of Phi Beta Kappa, and an Honorary Fellow of the London School of Economics, King’s College London, and of Darwin College Cambridge. He was awarded prizes and honours throughout the world, including the Austrian Grand Decoration of Honour in Gold, the Lippincott Award of the American Political Science Association, and the Sonning Prize for merit in work which had furthered European civilization.

Karl Popper was knighted by Queen Elizabeth II in 1965 and invested by her with the Insignia of a Companion of Honour in 1982.

Genres

Humanities, Logic, Food Science, Philosophy, Science, Classics, History, Popular Science, Academic, Sociology, Research

Table of Contents

TRANSLATORS’ NOTE
PREFACE TO THE FIRST EDITION, 1934
PREFACE TO THE FIRST ENGLISH EDITION, 1959

PART I Introduction to the Logic of Science

1 A Survey of Some Fundamental Problems
1 The Problem of Induction
2 Elimination of Psychologism
3 Deductive Testing of Theories
4 The Problem of Demarcation
5 Experience as a Method
6 Falsifiability as a Criterion of Demarcation
7 The Problem of the ‘Empirical Basis’
8 Scientific Objectivity and Subjective Conviction

2 On the Problem of a Theory of Scientific Method
9 Why Methodological Decisions are Indispensable
10 The Naturalistic Approach to the Theory of Method
11 Methodological Rules as Conventions

PART II Some Structural Components of a Theory of Experience

3 Theories
12 Causality, Explanation, and the Deduction of Predictions
13 Strict and Numerical Universality
14 Universal Concepts and Individual Concepts
15 Strictly Universal and Existential Statements
16 Theoretical Systems
17 Some Possibilities of Interpreting a System of Axioms
18 Levels of Universality. The Modus Tollens

4 Falsifiability
19 Some Conventionalist Objections
20 Methodological Rules
21 Logical Investigation of Falsifiability
22 Falsifiability and Falsification
23 Occurrences and Events
24 Falsifiability and Consistency

5 The Problem of the Empirical Basis
25 Perceptual Experiences as Empirical Basis: Psychologism
26 Concerning the So-Called ‘Protocol Sentences’
27 The Objectivity of the Empirical Basis
28 Basic Statements
29 The Relativity of Basic Statements. Resolution of Fries’s Trilemma
30 Theory and Experiment

6 Degrees of Testability
31 A Programme and an Illustration
32 How are Classes of Potential Falsifiers to be Compared?
33 Degrees of Falsifiability Compared by Means of the Subclass Relation
34 The Structure of the Subclass Relation. Logical Probability
35 Empirical Content, Entailment, and Degrees of Falsifiability
36 Levels of Universality and Degrees of Precision
37 Logical Ranges. Notes on the Theory of Measurement
38 Degrees of Testability Compared by Reference to Dimensions
39 The Dimension of a Set of Curves
40 Two Ways of Reducing the Number of Dimensions of a Set of Curves

7 Simplicity
41 Elimination of the Aesthetic and the Pragmatic Concepts of Simplicity
42 The Methodological Problem of Simplicity
43 Simplicity and Degree of Falsifiability
44 Geometrical Shape and Functional Form
45 The Simplicity of Euclidean Geometry
46 Conventionalism and the Concept of Simplicity 8 Probability
47 The Problem of Interpreting Probability Statements
48 Subjective and Objective Interpretations
49 The Fundamental Problem of the Theory of Chance
50 The Frequency Theory of von Mises
51 Plan for a New Theory of Probability
52 Relative Frequency within a Finite Class
53 Selection, Independence, Insensitiveness, Irrelevance
54 Finite Sequences. Ordinal Selection and Neighbourhood Selection
55 n-Freedom in Finite Sequences
56 Sequences of Segments. The First Form of the Binomial Formula
57 Infinite Sequences. Hypothetical Estimates of Frequency
58 An Examination of the Axiom of Randomness
59 Chance-Like Sequences. Objective Probability
60 Bernoulli’s Problem
61 The Law of Great Numbers (Bernoulli’s Theorem)
62 Bernoulli’s Theorem and the Interpretation of Probability Statements
63 Bernoulli’s Theorem and the Problem of Convergence
64 Elimination of the Axiom of Convergence. Solution of the ‘Fundamental Problem of the Theory of Chance’
65 The Problem of Decidability
66 The Logical Form of Probability Statements
67 A Probabilistic System of Speculative Metaphysics
68 Probability in Physics
69 Law and Chance
70 The Deducibility of Macro Laws from Micro Laws
71 Formally Singular Probability Statements
72 The Theory of Range

9 Some Observations on Quantum Theory
73 Heisenberg’s Programme and the Uncertainty Relations
74 A Brief Outline of the Statistical Interpretation of Quantum Theory
75 A Statistical Re-Interpretation of the Uncertainty Formulae
76 An Attempt to Eliminate Metaphysical Elements by Inverting Heisenberg’s Programme; with Applications
77 Decisive Experiments
78 Indeterminist Metaphysics

10 Corroboration, or How a Theory Stands up to Tests
79 Concerning the So-Called Verification of Hypotheses
80 The Probability of a Hypothesis and the Probability of Events: Criticism of Probability Logic
81 Inductive Logic and Probability Logic
82 The Positive Theory of Corroboration: How a Hypothesis may ‘Prove its Mettle’
83 Corroborability, Testability, and Logical Probability
84 Remarks Concerning the Use of the Concepts ‘True’ and ‘Corroborated’
85 The Path of Science

APPENDICES
i Definition of the Dimension of a Theory
ii The General Calculus of Frequency in Finite Classes
iii Derivation of the First Form of the Binomial Formula
iv A Method of Constructing Models of Random Sequences
v Examination of an Objection. The Two-Slit Experiment
vi Concerning a Non-Predictive Procedure of Measuring
vii Remarks Concerning an Imaginary Experiment

NEW APPENDICES
*i Two Notes on Induction and Demarcation, 1933-1934
*ii A Note on Probability, 1938
*iii On the Heuristic Use of the Classical Definition of Probability
*iv The Formal Theory of Probability
*v Derivations in the Formal Theory of Probability
*vi On Objective Disorder or Randomness
*vii Zero Probability and the Fine-Structure of Probability and of Content
*viii Content, Simplicity, and Dimension
*ix Corroboration, the Weight of Evidence, and Statistical Tests
*x Universals, Dispositions, and Natural or Physical Necessity
*xi On the Use and Misuse of Imaginary Experiments, Especially in Quantum Theory
*xii The Experiment of Einstein, Podolsky and Rosen. A Letter from Albert Einstein, 1935

INDICES, compiled by Dr. J. Agassi
Name Index
Subject Index

Review

The Logic of Scientific Discovery is a philosophical work that challenges the traditional view of scientific method as a process of observation, hypothesis, and confirmation. Popper argues that this view, based on inductive logic, is flawed and leads to dogmatism, pseudoscience, and untestable theories. Instead, he proposes a new view of scientific method based on deductive logic, which emphasizes the role of falsification.

According to Popper, a scientific statement is one that can be potentially falsified by empirical evidence, and a scientific theory is one that has survived repeated attempts of falsification. Popper also discusses the concepts of probability, causality, quantum physics, and the demarcation between science and non-science.

The Logic of Scientific Discovery is a seminal and influential book that has shaped the philosophy of science and the practice of scientific research. Popper’s ideas are original, rigorous, and provocative, challenging many established notions and assumptions in the history and philosophy of science. His critique of induction and verificationism exposes the limitations and problems of these approaches, and his defense of falsification and deductive logic offers a more rational and objective way of testing and evaluating scientific theories.

His book also addresses many important topics and questions in the fields of logic, mathematics, physics, psychology, sociology, and ethics, showing the relevance and applicability of his philosophy to various domains of human knowledge. The book is not an easy read, as it is dense, technical, and complex, requiring some familiarity with logic and scientific terminology.

However, it is also clear, coherent, and well-structured, presenting its arguments with examples, diagrams, and appendices. The book is a must-read for anyone interested in the nature and methods of science, as well as the epistemological and ethical implications of scientific inquiry.