Karl popper

13thNovember 2020

one of the greatest philosophers of science of the 20th century […] also a social and political philosopher of considerable stature, a self- professed critical-rationalist, a dedicated opponent of all forms of scepticism, conventionalism, and relativism in science and in human affairs generally and a committed advocate and staunch defender of the ‘Open Society’

Thornton, S.Karl Popper, The Stanford Encyclopedia of Philosophy

Karl Popperon the Stanford Encyclopedia of Philosophy

An increasingly isolated figure due to his combative personality and his strong claims in favor of his philosophy.

19thNovember 2020

The formulation of the problem

The traditional formulation of the scientific method takes for granted what should be discussed instead, therefore it is defined as anuncriticalformulation.

Popper offers acriticalreformulation, which aims to get to the roots of traditional formulation and analyze what’s taken for granted.

According to Popper, the traditional formulation has two main roots:

The Common sense view

This view takes for granted that beliefs and regularities are justified by repeated observations.

There’s nothing in our mind that doesn’t come from experience, nevertheless we form expectations about things that are yet to happen.

It’s taken for granted that observations,if repeated, are enough.

Hume’s problem

In Hume, two problems face each other, and there’s a conflict between the two:

The logical problem

Expectations have no logical justification. Induction doesn’t bring to truth.

The psychological problem

We form expectations as a matter of habit.
Hume is forced to embrace a kind of irrationalist epistemology: repetition alone isn’t a valid argument.

The lunatic who believes that he is a poached egg is to be condemned solely on the ground that he is a minority

B. Russell,A History of Western Philosophy, 1945

Popper’s critical formulation

From the logical point of view, Hume is right: there are several problems in the interpretation of induction.
Nevertheless, the psychological side of Hume’s reasoning is not shared by Popper: we don’t form expectations and beliefs from repetitions. We don’t have to wait for a repetition of occurrence or concurrence of events to give birth to expectations. Even Hume acknowledges this: there are cases in which a singular observation is enough to form an expectation.
Popper believes Hume is struggling in grasping the psychological argument.

The example of puppies sniffing a cigarette:
after sniffing it once, they behave confused and agitated as the first time even if they see one.

In Hume repetition is defined by similarity and resemblance of occurrences, but Hume doesn’t realize that repetitions and occurrences are interpretedby us, we respond to situationsweinterpret to be similar.

The logic behind the point Popper is making:

The kind of repetition envisaged by Hume can never be perfect; the cases he has in mind cannot be cases of perfect sameness; they can only be cases of similarity.They are repetitions only from a certain point of view[…]. But this means that, for logical reasons, there must always be a point of view – such as a system of expectations, anticipations, assumptions, or interests – before there can be any repetition;which point of view, consequently, cannot be merely the result of repetition

Repetitions occur only from the individual point of view.Beforeany repetition to happen, there’s a point of view which supposes it.

We need to replace this “rather naive” idea with the idea that events we react to by interpreting them from the start, involving several particulars related to the individual.

There’s a kind ofinfinite regressin Hume’s psychological theory.

  • we actively impose regularities upon the world
  • we try to discover regularitiesand similarities
  • without waiting for the premises, we jump to conclusions, which we will discard later if they get contradicted

We, as humans, always proceed bytrial and error.

??? These interpretations are then the same from individual to individual, so they regard man in general, or are they subjective?

Man has an inborn propensity to look for regularities, yet they might be mistaken, and not valida priori

This is something similar to Bacon’s interpretation, but the difference between Popper and Bacon lies in thetesting:
to Bacon such testing is inductive, to Popper instead it’s by falsifying errors.


This matter has a critical relevance if it’s brought to light Popper’s aim:

in science this attitude of imposible regularities is applied. Still, acting uncritically on this propensities would make us dogmatic creatures. We don’t need to go against the propensity itself, but we need to get prepared to confront it when new discoveries or points of view or interpretations.

This is the form that within science this procedure of acting by trial and error is following.

What in everyday lives is trial and error, becomes in science a matter ofconjectures and refutations.

Popper’s strategy

Can we reformulate the psychological problem so that we can understand where it’s wrong and then rebuild all the methods all at once?

Popper wants to find a direction which takes a different path not only respectively to Hume’s one, but to induction in general.

The logical error behind repetition

Can an affirmative claim such asX is truebe justified by empirical reason?
Obviously, we can’t inductively conclude this according to Hume.

Popper’s reformulation:
Can the claimX is true or false, orit is true or false that Ybe justified by empirical reasons?

Since falsity is the other side of the coin The answer here could be yes: sometimes we can conclude with logical certainty thefalsehoodof something.

The process Popper uses is not induction anymore, but deduction.
It follows a crucial question: can we makea deductive use of experience? Popper starts from Hume by confuting its philosophy, but getting gradually away from it, embracing deduction.

To understand Popper’s argument, the concept ofmaterial implicationneeds to be understood.

A parenthesis on !Material implication

Modus ponens

The use of material implication can be described asmodus ponens(short formodus ponendum ponens, “the method of affirming by affirmation”), the mode of affirming the antecedent.

NOTE: This argument must not be confused with the method of affirming the consequent, which is a fallacy.
If 3 + 2 = 5
3 + 2
(Of course, 5 isn’t only the sum of 3 + 2 but also 4 + 1, for example)


An example of whymodus ponensisn’t suited for Popper’s purposes:

  • If there is flash of light there is a clap of thunder
  • There is a flash of light

Therefore, there is clap of thunder

In this case, not necessarily every time there is a flash of light is because it’s caused by a thunder.

Modus ponensis not the deductive procedure Popper has in mind, it’s easy to fall in the problem of induction again.

Modus tollens

Modus tollensis an opposite logical format which seems to be more suitable: short formodus tollendum tollens, it’s the method of denying by denial.

It operates bydenying the consequent.

Note: again, a fallacy would be to deny the antecedent:
if P, then Q

All dogs have four legs
Mules are not dogs
Mules don’t have four legs

Whymodus tollens

There are two main types of logical statements:

  • singular existential statements, assertions about the existence of some particular thing. They areobservational statements, for exampleThere is an x that is a swan, and x is white
  • universal statements, assertions that categorize all instances of something.

it’s not possible to infer universal statements from observational statements; inductively it may be possible, but it would be invalid.

Instead, by usingmodus tollens, we can with certainty falsify a universal statement starting by an observation which make it false.
If I can deny the consequent, I get a true statement. I conclude with certainty something just by applying ordinary deductive logic.

Can wevalidly(instead of invalidly) infer a universal statement from an observational statement?


U -> O

The process of falsification:

  1. start with a hypothesis, a universal statement (U)
  2. make a prediction about a certain singular happening. (U->O)
  3. observation that contradicts the expected condition (!O,potential falsifier)
  4. falsify the initial hypothesis (!U)

With logic of falsification, it’s possible to draw conclusions with absolute certainty.

It’s a matter of deductive logic: we’re bound to falsify something when we’re presented with a contradiction.

Experience is used as a test to prove that my previous universal statements arefalse.

An example:if all swans are white, then this swan must also be white
this swan is black
Therefore, not all swans are white

In this way we can create an argument from experience:

  • we have a deductive argument which uses experience to test the validity of a universal statement, only in a negative way.
  • the singular observational statement is thepotential falsifierfor the universal statement it refers to

It doesn’t matter how many instances in favor of a theory we have, if we counted on there, we would fall in an inductive circularity.
It’s sufficient to have a falsifying statement or observation to definitely eliminate a theory, by proving its falsity withdeductive certainty.

Popper’s solution

Infinitely many instances aren’t enough to positively prove a universal statement for sure, while with falsification it’s necessary only one to prove its falsity.

The original problem of induction is the problem of justifying induction, […] If you answer this problem by saying that what is called an ‘inductive inference’ is always invalid and therefore clearly not justifiable, the following new problem must arise: how do you justify your method of trial and error? Reply: the method of trial and error is a method of eliminating false theories by observation statements; and the justification for this is thepurely logical relationships of deducibilitywhich allows us to assert the falsity of universal statements if we accept the truth of singular ones.

The problem of demarcation

What identifies science is the use of a method. Such method is empirical.

Induction has always played a rather central role in science, since it’s a method based on experience. The existence of a method in science is often advocated to distinguish what is science and what’s not.

Relying too much on scientific procedures (empirical, inductive processes) may make scientists fall into dogmatism; this would make them desperate to confirm their theories, scientists lose their critical approach.

The difference between science and pseudo science for Popper lies in the need to find confirming evidence.

While pseudo-scientists are desperate to confirm their thesis, actual scientists provide risky and bold predictions which are very likely to be falsified.

Instead of using criticisms to confute their theses, pseudo-scientists include them in their theories to avoid possible objections; they fight for the truthfulness of their statements. Observations which threaten their theories are used to enforce them instead of questioning them.
Why should we believe this? Popper points out that actually Freud never tests his theories.

Fundamentally, Popper highlights a difference inattitude.

A perfect example of a true scientist is Einstein; he promoted a completely different approach:

  • he made a courageous prediction in advance of evidence…
  • …hence he had a serious risk of being refuted

If observation shows that the predicted effect is definitely absent, then the theory is simply refuted. The theory is incompatible with certain possible results of observation – in fact with results which everybody before Einstein would have expected. This is quite different from the situation I previously described, when it turned out that the theories in question were compatible with the most divergent human behaviour, so that it was practically impossible to describe any human behaviour that might not be claimed to be a verification of these theories.

Conjectures and Refutations, p.56

Furthermore, truly scientific theories arecorroborated, not proved, by evidence

the degree of corroboration […] is just a report about the state of discussion at time t.

Objective Knowledge, p.19

We can’t be sure something is true, but we certainly know for sure that at the given time the given theory is not false.

It’s reasonable to accept a theory becausenot yet refuted. We may never know it, but we need to attach corroboration. Now it’s corroborating, but if something comes up, I need to be ready to drop it.

If we actually succeed in falsifying a conjecture, it means the given theory has empirical content. What’s wrong with pseudo-sciences is reinterpreting all potential falsifiers in such a way they become a support for their theories, but they never test anything.

The hallmark of genuine science is itsrefutability,testabilityorfalsifiability.


  • Inductive method is a myth
  • the actual procedure of science is theorizing, jumping to conclusions, and prove them later
  • repetition has to be used only at the time of testing a conjecture
  • falsification, rather than induction, has to be used as the right criterion of demarcation

In finding the right criterion of demarcation we find the correct way to make the argument from experience work.


Next topic:Post-Popperian interpretations



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