On Strict and Numerical Universality by Flemming Steen Nielsen

Popper on Strict and Numerical Universality

by Flemming Steen Nielsen


In his article, ”Evolutionistiske forklaringer og kritikken af historicismen” (Evolutionary explanations and the Critique of Historicism) (1), professor Mogens Blegvad raised a series of searching objections to Karl Popper’s famous critique of Historicism (2) – objections which any future treatment of historicism would do well to take into consideration. Not least, Blegvad described and criticised those of Popper’s arguments that are based upon his distinction between on the one hand stricly universal law-statements and singular statements of individual fact on the other. In the following (3) I shall attempt to clarify this distinction of Popper’s – a distinction absolutely central to his thought, but never really treated as such by his commentators and critics. Hopefully this could provide a basis for a detailed reply to some of Blegvad’s objections.


The main sources of the subject are Popper’s works Logik der Forschung (1934) and Die beiden Grundprobleme der Erkenntnistheorie (written before Logik der Forschung but published in incomplete form as late as 1979). Die beiden … must be considered the best of these and gives us by far the the most complete description we now have of Popper’s views on the subject. Very naturally I shall base the following primarily on this work.

The first of the two problems of epistemology that Popper discusses in his book is the problem of induction, which he treats by first presenting his well-known falsificationist and fallibilist solution and then giving very detailed logical and transcendental critiques of various alternative solutions under the following five headings: (1) naïve inductivism, (2) strict positivism, (3) apriorism, (4) probability positions and (5) pseudo-sentence positions (”Scheinsats-Positionen”). He argues that the first four can be explicated and criticized in terms of a formulation of the problem of induction which in a traditional manner distinguishes between ”general” (”allgemeine”) and ”particular” (”besondere”) propositions. In connection with the fifth position, however, he finds it necessary to subject this very distinction to a closer examination. The expression ”pseudo-sentence positions” refer to epistemological positions which in order to circumvent the problem of induction assert that law-statements are not genuine sentences with truth-values, but instead a kind of ”formulae for the construction of singular sentences” (in analogy with propositional functions), or ”tools or instruments for the construction of prognoses, which cannot be true, false, or probable, but at most more or less useful.” (4)

To be able to examine the scope and validity of this view, Popper asserts, it is necessary to introduce a distinction between two kinds of synthetic, universal statements. The following example could illustrate this distinction:

(a) The trajectory of all stone’s throws (Steinwürfe) are parabolae, …

(b) the trajectory of all stone’s throws that have hitherto been measured are parabolae. (5)

There has been a tendency – not least in Classical Empiricism and Logical Positivism – to overlook the difference between these two kinds of statement, i.e. the difference between universal law-statements and empirical generalisations; but Popper in this respect like so many other respects follows Immanuel Kant. Like Kant, Popper insists that this distinction is indispensable for any attempt to characterize the theoretical, nomothetic sciences in an adequate way. Kant speaks about ”strenge Allgemeinheit” in the first case, and ”komparative oder angenommene Allgemeinheit” in the second. (6) Popper’s terminology is as follows: Statement (a) in our example is a (synthetic) strictly universal statement; statement (b) is a (synthetic), numerically universal statement. As we shall see, numerically universal statements strictly speaking are singular statements. (7)

Why do for instance Logical Empiricists overlook or reject the distinction? Popper’s explanation is that they tend to accept only such distinctions as can comfortably find expression in the their favoured logic, i.e. the logic of Principia Mathematica: ”Die Logistik”. But the distinction beween strict and numerical universality cannot be expressed in this Logistik, Popper insists. In our example both statements can be formalized as the so-called ”general” or ”formal implication”:

(Ax) (Fx  Gx). (9)

From a purely logical point of view the lack of the distinction is of no importance according to Popper; but for the purposes of epistemology and scientific methodology we most certainly need both kinds of statement.

As the statements both can be formalized as general implications, i.e. statements about all members of a class, of course the difference between tham cannot be a question of logical form. So it must be a question of (logical) ”content”, i.e. a difference between the concepts involved? In the statements. This means that we must similarly distinguish between universal and individual concepts. This distinction is, according to Popper, ”unambiguous and absolute.” (10)


It may surprise that Popper considers the distinction ”unambiguous and absolute”. An obvious objection would be the following: There is at least one sense of ”unambiguous” in which it would seem quite absurd to label it unambiguous. For is it not a fact that what in one context functions as an element of a class, i.e. as an individuum, in another might itself function as a class? If that is the case, would it not be more correct to characterize the distinction as ”relative”? Popper’s reply to this objection is: ”True, but irrelevant!”. A more thorough analysis of such terms as ”class”, ”element”, ”universal” etc. will make clear why:

The most important source of confusion in connection with these terms is that we confuse three different distinctions, namely those between (i) class and element, (ii) class and subclass, and (iii) universals and individuals.

Ad (i) It must be admitted that the distinction class/element is relative in exactly the above sense. For instance, the concept ”iron” could be viewed as a class of physical bodies with certain properties in common. On the other hand, any of these bodies can be viewed as elements of the class ”iron”. But ”iron” can of course in another context be viewed as an element, namely as an element of a higher class ”metal”, where ”metal” is the class of classes of certain physical bodies [the following manner of exposition is mine, not Popper’s]:


metal – iron – a piece of iron


Such a string of class/element-related concepts we call a type hierarchy. Popper gives us the following example:

Type hierarchy (the example taken from Carnap, though somewhat changed): ”My dog Lux” is an element of the class ”dogs living in Vienna”, that class itself an element of the class of ”dog-classes in Vienna”; ”my dog Lux” is, however, also a class, namely, whose elements are ”the states of the dog Lux”; a single ”state of Lux” is (according to Carnap) ”a class whose elements are points in the world of experiences” etc. (11)

Ad (ii) The distinction between class and element must not be confused with another distinction, namely that between class and subclass (Überbegriff/Unterbegriff), a distinction which is also relative:


mammals dogs the dogs of Vienna


A string of class/subclass related concepts is called a hierarchy of concepts (”Begriffshierarchie”):

Hierarchy of concepts: ”In Vienna living Alsations”; ”in Austria living Alsations” etc. … ”in Austria living dogs”; ”dogs” … ”mammals” … ”animals”.- All these classes are of the same type, which can be seen from the fact that my dog Lux is an element of any of these classes. (Or from the fact that you can construct the general implication: ”x is a Viennese dog” generally implies ”x is an animal”.) (12)

Ad (iii) The third distinction, that between universal and individual concepts cannot be illustrated in a similar manner as the two others. Examples are:


naval battle the battle of Trafalgar
star Sirius
needle this needle

It is Popper’s thesis, then, that this distinction is unambiguous and absolute in exactly the sense in which the two others are not so. It ”cuts through” the type- and concept-hierarchies in an unambiguous manner:

Right through the types and the extensions runs a boundary in such a way that it runs through every type so that every type is divided by it into two parts. This boundary divides the whole system of concept extensions into two, namely the domain of universals (examples: ”the race of dogs”, ”A large, brown dog”) and the domain of individuals (examples: ”the races of dogs in Vienna”; ”my dog Lux”).
Each of the two domains contains type hierarchies, contains classes and elements; and each of the domains contains concepts of greater and smaller extent.
This boundary between universals and individuals is according to the present point of view unequivocal: Whereas one and the same concept in different contexts can function as a class or an element, as well as as a broader or a narrower class, we must be able to answer the question whether it is a universal or an individual unambiguously. (13)

What this last assertion means I shall discuss in quite a detailed manner in section VII. But first I shall present something the Popper never gives us, namely a systematic illustration of the way in which the distinction universal/individual cuts through the two other distinctions:

A. Type hierarchy of universals:

¬¬¬¬_ _ _ _ _
_ _ _ _ _
”metal” as a class of classes of bodies
”iron” as a class of physical bodies
a physical body as the class of its states
the states of a class of molecules
_ _ _ _ _
_ _ _ _ _

B. Concept hierarchy of universals:

_ _ _ _ _
_ _ _ _ _
body of metal
body of heavy metal
body of iron
body of cast iron
_ _ _ _ _
_ _ _ _ _

C. Typehiearchy of individuals

_ _ _ _ _
_ _ _ _ _
the animal classes of Vienna
dogs living in Vienna
my dog Lux
the states of Lux
_ _ _ _ _
_ _ _ _ _

D. Concept hierarchy of individuals
_ _ _ _ _
_ _ _ _ _
in Europe living mammals
in Austria living Mammals
in Austria living dogs
in Vienna living dogs
_ _ _ _ _
_ _ _ _ _


The distinction universal/individual cannot be defined in a non-circular way, Popper admits. Accordingly, he considers these concepts ”indefinable, logical primitives”. Nevertheless, it is possible to set up a ”simple and unambiguous criterion” for the application of them. There is an old logical rule to the effect that a given individuum cannot be characterized without the use of proper names or expressions functioning as proper names. This means that the individuum cannot be adequately characterized by general terms, but that proper names will have to be used. Universal concepts (Universalbegriffe) can therefore be defined as concepts which can be defined without the use of proper names, and individual concepts (Individualbegriffe) as concepts that need at least one proper name for their definition.

The term ”proper name”, however, is itself indefinable, he admits, but it is possible to say quite a lot about how to use it in a fruitful and satisfactory way:

A proper name is a sign which if necessary can be directly attached to the object (for instance like a dog tag) and which if necessary is used once and for this object only. (If the object is such that an actual attachment is impossible – for example a name of a country and things like that – the proper name nevertheless can be ascribed to the nation’s borders; or it can be defined by veritable proper names like ”The Conference of February 8., 1893” [….]). Proper names are at the same footing as (demonstrative) references like ”this dog”, ”today” etc. 14)

Two ”guiding propositions” can be formulated in order to make quite precise the relation of irreduceability among universals and individuals:

(1) An individual object cannot unambiguously be characterized in its individuality by universal concepts alone, i.e. without proper names.
(2) A universal cannot be defined solely by proper names or by a class of individual concepts.


Guiding proposition (1) can be explained in the following manner: Let’s take the individual thing ”Lux”. If we attempt to characterize the dog Lux in general tems – i.e. universals – we soon discover that what we end up with will always be a class – not an individuum. We might try describing Lux as a poodle, a black poodle, a two years old poodle etc.; but unless we use proper names the result will always be a class. In fact, even if we narrow our description so much that only a single dog (or even no single dog) actually exists, we will only have arrived at a ”kind” of objects – a class!

By contrast, we can easily characterize an object in an unambiguous manner if we introduce proper names og terms functioning as proper names, for instance ostentative expressions. For instance, we can refer to it by applying expressions like ”Lux”, ”my dog Lux”, ”the dog which in 1930 carried dog tag no. 17948” etc. Even if we make use of space/time coordinates the use of proper names is implied:

Especially definite specifications of space and time make unambiguity possible. This is an important point. One must not overlook the fact that it must be specifications of a particular place or a particular moment of time; these again always involve proper names. The point of origin of a space/time coordinate system can only be determined by proper names (for example Greenwich or the Birth of Christ) or – what is actually the same – by direct (”demonstrative”) reference. (Only a reference to an ”individual coordinate system” specified in this way could work as ”principium individuationis”). Also, a particular human being, for instance Napoleon, can be characterized in an unambiguous way by giving his place and time of birth: but thereby individual concepts are being used. (15)

Two important aspects of Popper’s concept of an individual concept might seem to conflict with ordinary usage. First, he stresses that an individual concept according to his chosen way of speaking doesn’t have to be a well-defined physical body. Thus he considers ”The Battle of Waterloo” an individual concept , whereas ”iron cube with sides of 1 cm” is a universal concept. (16) Secondly, an individual concept need not refer to single ”objects”. ”All persons leaning out of a window in Copenhagen just now” or ”all persons who have ever been leaning out of this window” are individual concepts according to his definition. They need proper names or indexical terms to be formulated.


Analogously, according to the second guiding proposition universal concepts cannot be defined by proper names or by reference to a specific class of individuals. This principle is of the greatest epistemological importance – not least because it implies that even if universals may stand in a class/element-relation to individuals they cannot be ”reduced to” or ”constituted by” concrete classes of individuals.

Although we find this point expressed both in Die beiden … and in Logik der Forschung, I prefer illustrating it by the far more elegant and clear treatment in the important article ”The Demarcation Between Science and Metaphysics” from 1955. (17) Here Popper has collected his arguments against Rudolf Carnap’s various theories of demarcation and meaning. In his critique of what he calls ”Carnap’s first theory of meaninglessness” Popper attempts to show that Carnap presupposes a particular, extremely simple kind of radical nominalism which can be shown to be untenable. According to this, all non-formative words (i.e. all words which are not logical constants) are names. This implies that not only proper names like ”Fido” are names, but that even a word like ”dog” strictly speaking is a kind of name, namely the name of, for instance, Fido, Candy and Tiffin. In a language constructed according to this assumption the meaning of general terms is given by an enumeration of the individual things denoted, i.e. through an enumerative definition. However, such a language can be shown to be totally inadequate as the language of science, Popper objects. This is because it has the absurd property that all its sentences are analytic – either analytic truths or contradictions. No synthetic sentence can be formulated in it, simply because the truth or falsity of all its sentences can be decided by a simple inspection of the enumerative definitions giving the meaning of the non-logical words used:

That this is so may be seen from our example. ”Fido is a dog” is true because Fido was one of the things enumerated by us in defining ”dog”. As opposed to this ”Chunky is a dog” must be false, simply because Chunky was not one of the things to which we pointed when drawing up the list defining ”dog”. Similarly, if I give the meaning of ”white” by listing (1) the paper on which I’m now writing, (2) my handkerchief, (3) the cloud over there and (4) our snowman, then the statement ”I have white hair” will be false, whatever the colour of my hair may be.
It is clear that in such a language hypotheses cannot be formulated. It cannot be a language of science. And conversely, every language adequate for science must contain words whose meaning is not given in an enumerative way. Or, as we may say, every scientific language must make use of genuine universals, i.e. of words, whether defined or undefined, with an indeterminate extension, though perhaps with a reasonably definite intensional ’meaning’. (18)

This also shows that any attempt to define universals enumeratively from individuals is doomed to failure. Let me add here that it would be no use to try a definition like such as ””dog” =def. ”Fido, Candy, Tiffin and all things similar to these”. For even a cat or a turtle are similar to Fido, Candy and Tiffin in some respects, of course. And a suggestion like ””dog =def. ”Fido, Candi, Tiffin and all things similar to these in respect to dogness” would of course lead us right back into the use of a universal concept.

These considerations are also destructive of any idea of a ”logical process of abstraction” which is supposed to make it possible for us to move from individual to genuinely universal concepts, although of course there is a method by which we can construct classes through ”abstraction” (- but these classes will remain individual concepts). (19) In fact we would do well to stop talking about a ”method of abstraction” or a ”process of abstraction” and to speak instead of a problem of abstraction in analogy with the classical problem of induction. The problem of induction arises from the relationship between singular end strictly universal statements. Strictly universal statements, according to Popper, are such that only involve universal concepts. Singular statements are such that involve at least one individual concept. The problem of abstraction, accordingly, is a problem about the relationship between universal and individual concepts. Both problems underline the hypothetical, tentative, almost groping nature of human knowledge. In science we work with genuine, strictly universal law-statements. These cannot be verified from our singular, experiental statements. Analogously, we have to make use of genuine, universal concepts; but we have no method – by way of ”reduction”, ”constitution”, or ”explication” – for once and for all securing an entire arsenal of absolutely unambiguous and, at the same time, concretely applicable universal concepts.


Now let us return to the question about what Popper might mean by characterizing the distinctions between universal and individual concepts – as well as that between universal and singular statements – as unambiguous. Some of his formulations might give the impression that what is meant is that a simple inspection of what we could call ”the grammatical character” of a given formulation makes it possible for us to decide once and for all whether a statement is strictly universal or not. The frequent talk of ”proper names” points towards an interpretation like that. Despite the somewhat heavy-handed formulations used by Popper when introducing the distinction in a general way, many of his later formulations make it clear that he has a more subtle view in mind. Far from maintaining that the grammatical form unambiguously reveals the universal or individual character of a statemement, he is quite aware that interpretation involving context almost always is necessary.

For instance, he points out, it is not possible simply to say whether a word like ”pasteurized” is an individual or a universal concept; for of course it can function as both:

”Pasteurized” can be defined either as ”treated according to Louis Pasteur’s instructions” (or something like that), or as ”heated to 80 degrees Celsius and kept at that temperature for ten minutes”. By the first definiton ”pasteurized” is an individual concept; by the second it is a universal concept. (19)

So context is decisive: In a historical discussion of the historical development of medical science, the expression might well be used as an individual concept, while in a theoretical discussion of the resistance of various micro-organisms it would be natural to use it as a universal concept. Another of Popper’s examples is the following, which introduces what we might call ”intended meaning”:

The use of the word ’mammals’ as an example of a universal name might possibly cause misunderstanding. For words like ’mammal’, ’dog’, etc., are in their ordinary use not free from ambiguity. Whether these words are to be regarded as individual class names or universal class names depends upon our intentions: it depends upon whether we wish to speak of a race of animals living on our planet (an individual concept), or of a kind of physical bodies with properties which can be described in universal terms. (20)

Both examples show that when Popper characterizes the distinction between individual and universal concepts as unambiguous he certainly does not think of ”unambiguity of a formulation” – a kind of unambiguity which would make it possible for us unambiguously to decide the question by sheer inspection of sentences. On the contrary, both ”pasteurized” and ”mammal” are ambiguous in that sense. We might express this important difference by saying that while the distinctions admittedly are ”grammatically ambiguous”, they are asserted by Popper to be ”logically unambiguous”. Exactly for that reason it is important to distinguish between their strictly universal and their individual uses. Popper might be said to defend the logical distinction by simply challengeing any opponent to explicate these and similar examples without applying it. In fact, this is exactly what Popper does in the epistemologi, methodological and metaphysical parts of his philosophy. Let me conclude this paper by illustrating this by offering a few more examples.


In The Poverty of Historicism Popper stresses the importance of distinguishing between theoretical and historical sciences. Theoretical physics is, of course interested in finding and testing universal laws; the historical sciences are interested in actual, singular, or specific events, rather than in laws and generalisations. (21) A historical explanation takes all kinds of universal laws (for instance those of economics) for granted when attempting to explain its singular statements. Both kinds of science use the hypothetical-deductive model when trying to offer, test, and predict causal explanations:

In the sense of this analysis, all causal explanations of a singular event can be said to be historical in so far as the ’cause’ is always described by singular initial conditions. And this agrees entirely with the popular idea that to explain a thing causally is to explain how and why it happened, that is to say, to tell its ’story’. But it is only in history that we are really interested in the causal explanation of a singular event. In the theoretical sciences, such causal explanations are mainly means to a different end – the testing of universal laws. (22)

The distinction is also, as might be expected, of great importance in connection with Popper’s discussion of the question whether the Theory of Evolution gives us reason to believe that there is such a thing as a law of evolution. Here Popper distinguished between (a) a theory about what might be called ”the Darwinian or Neo-Darwinist mechanism of evolution” and what he calls (b) ”the hypothesis of biological evolution” as a theory about an individual, though enormously complex occurrence. (23) (b) is not, as many seem to believe, a universal law, as many believe. Rather it must be viewed as a rather complex singular historical statement quite analogous to, for instance, ”Charles Darwin and Francis Galton had a common grandfather”. So even if an expression like ”all vertebrates” might look like a universal concept, in this context it is used as an individual concept, for ”all vertebrates” refers only to all vertebrates existing on Earth – ”… rather than to all organisms at any place and time which have the constitution which we consider as characteristic of vertebrates”. (23)

What we call the evolutionary hypothesis is an explanation of a host of biological and paleological observations – for instance, of certain similarities between various species and genera – by the assumption of the common ancestry of related forms. This hypothesis is not a universal law, even if certain universal laws of nature, such as laws of heredity, segregation, and mutation, enter with it into the explanation. It has, rather, the character of a particular (singular, specific) historical statement. (24)

This view of Popper’s might be seen as challenging anybody who disagrees to develop a version of the hypothesis of evolution in a form not using ”proper names or terms functioning as proper names”.

An analogous situation is found in a well-known cosmological debate between Popper, Adolf Grünbaum, and others. (25) At a particular stage of the discussion, Popper defends the use of egocentric particulars such as ’I ’, ’here’, and ’now’. Admittedly, they do not have a place in theoretical physics in a narrower sense; but this doesn’t mean that they don’t rightfully belong in cosmology:

”The present state of the surface of the moon suggests that …” is a phrase which is fully legitimate in science, though it is not likely to occur in theoretical physics. ”The present age of the universe” is a perfectly good term in cosmology, and one which it would be quite unnecessary and pedantic, if not downright misleaning, to replace by ”the age of the universe on October 14, 1970”. In other words, the past, present and future are perfectly good terms in cosmology and astronomy, two excellent examples of (to some extent historical) physical sciences. It is fully legitimate to remind the astronomer that what he observes, in certain cases, is the state of star 1,000 years ago, or of a gallaxy 100,000 years ago, where ”ago” is just a synonym of ”before the present”. The fact that these notions do not occur in theoretical physics, and that we replace them by names and dates in history, does not show that they are to be expunged.
Nor are they expungeable. It is perfectly true that astronomers can use coordinates instead of speaking of the Great Nebula in Andromeda. But the coordinates go back to the axis and equator of the Earth, to here-and-now terms. (The Earth changes its axis in time; and although we may speak of the north pole as the sky on ”October 14, 1970” we must not forget that ”October 14, 1970”, though in many respects preferable to ”now”, refers to a zero date which is highly conventional and anthropomorphic. Nobody claims to know even the precise year of the birth og Jesus Christ.)
Thus my thesis is that notions like ”the present” are needed, if not in theoretical physics, at any rate in physical science. But I want to claim even more. Theoretical physics uses all the time spatiotemporal variables; and without applications in which these variables are specified (in the last instance with the help of ”here and now”), they would have no reasonable function whatsoever. (26)

The importance of Popper’s distinction is seen elsewhere in his philosophical writings. To mention only a few examples, the impossibility of reducing strictly universal law-statements to a finite number of singular statements is of course decisive for his epistemological deductivism and fallibilism. The distinction is also used by him in his arguments concerning free will. (27) Likewise, of course, in his critique of determinism and in his radical emergentism with its daring idea that our natural laws might not, after all, be strictly universal because they after all seem to be the result of an ’evolution’ of our individual, open universe. (28)



Translated with some changes from: ”Begrebet streng universalitet hos Karl Popper”, FILOSOFISKE STUDIER, vol. 9, Copenhagen 1987, pp. 125-142, Copenhagen 1987.

Dedicated to Mogens Blegvad

(1) FILOSOFISKE STUDIER, vol. 5, Copenhagen 1982, pp. 7-32.

(2) See especially Karl Raimund Popper: The Poverty of Historicism, 1944-45, 1957; K.R.Popper: The Open Society and Its Enemies, 1945.

(3) A shorter version of this paper was read at the Polish/Danish philosophical seminar, Copenhagen 1983.

(4) K.R.Popper: Die beiden Grundprobleme der Erkenntnistheorie. Aufgrund von Manu-skripten aus den Jahren 1930-33 herausgegeben von Troels Eggers Hansen, Tübingen 1979, p. 159 ff.

(5) Ibid. p. 228.

(6) Immanuel Kant: Kritik der reinen Vernunft, 2. Aufl. 1787, p. 3.

(7) In Logik der Forschung, § 13 Popper uses the expression ”spezifische Allgemeinheit” for Kant’s ”strenge Allgemeinheit”. In the English version (The Logic of Scientific Discovery, 1959), he prefers the expression ”strict universality”.

(8) See for instance Rudolf Carnap: ”Eigentliche und uneigentliche Begriffe”, Symposion Vol. I, 1927; Der logische Aufbau der Welt, 1928, p. 213.

(9) Logik der Forschung, § 14.

(10) Die beiden Grundprobleme, p. 234.

(11) Ibid. pp. 233-34.

(12) Ibid. p. 233.

(13) Ibid. p. 234.

(14) Ibid. pp. 234-35.

(15) Ibid. pp. 235-36.

(16) Die beiden Grundprobleme, pp. 238-41; Logik der Forschung, 4. Ausg. 1971, pp. 27-28.

(17) K.R.Popper: Conjectures and Refutations, 1963, Ch. II.

(18) Conjectures and Refutations, p. 226.

(19) Logik der Forschung, p. 37 note 1.

(20) The Logic of Scientific Knowledge, p. 59.

(21) The Poverty of Historicism, pp. 143-147.

(22) Ibid, p. 144.

(23) Ibid. p. 107 note.

(24) Ibid, § 30. For a closer treatment of this distinction as well as the problem of the respective falsifiability of these two kinds of ”theory of evolution”, see my ”Karl Poppers som evolutionistisk filosof”, (”Karl Popper as an Evolutionist Philosopher”) in: Niels Bonde, Jesper Hoffmeyer and Henrik Stangerup: Naturens historiefortællere, II: Udviklingsideens historie, Copenhagen 1987, Ch. 15.

(25) Adolf Grünbaum: ”Popper’s Views on the Arrow of Time” and Popper: ”Grünbaum on Time and Entropy” in Schilpp (ed.): The Philosophy of Karl Popper, p. 775 and p. 1143.

(26) Ibid. p. 1143.

(27) For instance, Die beiden Grundprobleme der Erkenntnistheorie, Dritte Auflage pp. 481 ff; The Open Universe, pp. 41 ff, pp. 128 ff.

(28) The Open Universe, p. 143.

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Flemming Steen Nielsen: A Personal Recollection of Popper

From: Sandhedens Sider, Institute of Philosophy, Copenhagen, Autumn 1994

Happy Acquaintance With a Difficult Person
In memoriam Karl Raimund Popper, 26.7.1902-17.9.1994.

By Flemming Steen Nielsen

One morning a few weeks ago my friend Troels Eggers Hansen (theoretical physicist, editor of Karl Popper’s Die beiden Grundprobleme der Erkenntnistheorie) telephoned to tell me that our friends in London had called to inform us that Popper had just died. The conversation which followed was not, of course, a particularly cheerful one. On the other hand it was not dominated by grief – rather by a quiet sadness and a strange feeling of emptiness (’one somehow feels like an orphan’ as Troels put it). After all it could hardly be considered very tragic when a person dies at the age of 92 – of sound mind till the end, and after an extremely eventful and productive life. Starting out as an out-of-work school teacher around 1920 and ending up a friend of and discussion partner with many of the world’s most brillant scientists; the creator of philosophical arguments and theories of wide-ranging importance; the inspiration of statesmen and cultural celebrities; knighted and highly decorated by nations and universities; and, not least, loved and admired by his many readers – this must surely have been a good life. The following days many thoughts and images whirled around in our heads: About the joy, many years earlier, of discovering the works of this amazing thinker; about the exciting days when ’a new Popper’ appeared in the bookshops or arrived by mail with his signature; about the fascination of meeting him in person etc. So when Sandhedens Sider asked me to write a few pages on the occasion of the death of this strikingly original philosopher I decided to offer some hints about those thoughts and images rather than attempting a solemn obituary.


On my way to a summer holiday tour in Jutland in June 1961 I looked in at the Institute of Philosophy, then situated at Copenhagen Cathedral Square, to look for one more book to bring with me (- I already brought Viktor Kravchenko’s I Chose Freedom, (1946)). Here I came across a stout volume with the title The Open Society and Its Enemies, (1945). Who could resist a title like that? Not I, and so I brought that one too. Incidentally, Popper’s book complemented Kravchenko’s splendidly, so every day during the two weeks’ tour from one beautiful Jutland locality to another, some chapters of the one were read in combination with some chapters of the other. The horrible experiences of a Russian engineer under Stalin’s terror and his later escape to the West made acutely real and concrete the bloodshed and sufferings caused by the totalitarian state. And Popper’s diagnosis of the collectivist and utopian ideas from more than 2000 years’ philosophical tradition, which have constantly been used as standard ammunition against liberty and democracy – and resulted in world wars and tyranny – was enough to remove from my mind the few remnants of utopianism and ’philosopher king’-ways of thinking that might have survived many years’ discussions with my father or my wonderful history teacher at school.
Apart from the book’s passion and moral force – an emigrant to New Zealand, Popper began writing on the day of Hitler’s inclusion of his native Austria into the German Reich and finished the book during the War – it was its manner of arguing that made an impression on a young philosophy student. The book showed that it is indeed possible to do philosophy the old way: attacking important metaphysical, moral and political problems with substantial, general arguments. You have to remember that at the time of my first reading it there was a strong tendency within the Anglo-Saxon and Scandinavian countries to remove philosophy from its original cosmological and ethical context and into one of two directions: (1) Viewing it as ’linguistic analysis’; i.e. treating it as the study of pseudo-problems originating in a perverse misuse of ’ordinary language’ – problems that could only be cured, not solved, by a sort of linguistic psychoanalysis (see Ernest Gellner’s critical diagnosis of the phenomenon in his brillant Words and Things from 1959). Or (2) replacing philosophy by the construction of formal systems representing scientific theories and the ’evidence’ supporting them – often resulting in desperate inductionist or confirmation-logical attempts to clarify that elusive relation of ’support’. How refreshing on this background to encounter a philosopher who took a stance against these tendencies and explicitly chose to do philosophy in the traditional manner!
The Open Society shows how important the theory of knowledge is to political philosophy according to Popper. If, for instance, you accept an epistemology according to which we are able to reach authoritative, apodictic knowledge about both descriptive and normative questions you will quite naturally tend towards elitist and anti-democratic ways of thinking. If you reject the idea of expertise concerning normative questions, but all the same believe in the possibility of apodictally certain and detailed knowledge about societal processes, then what Popper dubs holistic utopian engineering, or at least central planning of the economy, will seem within reach and basically desirable – and the possible advantages of the rule of law and market economy will become invisible. And thus it is evident how indebted his philosophy of the open society is to the well-known ideas of his epistemology and philosophy of science. His view of knowledge as basically a trial-and-error process, his fallibilism, his model for testing, explanation and prediction, and his view of rationality as comprehensive critical discussion – all are ingredients of his critique of totalitarianism, revolutionism and historicist prophecy as well as his arguments for democracy, individualism and political reformism.


I had the priviliege of living at the old ”kollegium” (students’ dormitory) Regensen at the time. On returning there after my tour I told the other members of our ’Regens-club’ (a sort of small beer and debating society) – a physicist, a mathematician, an astronomer, a historian and a literature guy – about Popper, and we decided to study his Logic of Scientific Discovery (1934, 1959) together. One thing strikes me when I think back to our discussions about that book. The objection which nowadays in broad circles is considered an absolutely devastating refutation of it, and which has given rise to a series of ’new and better’ philosophies of science, never had an important place in our discussion. I’m referring to the objection that Popper’s view of testing as attempted empirical falsification af strictly universal theories, must be wrong because it is just as impossible to falsify a theory as to verify it – all because of the point made by Popper himself that it is impossible to give unambiguously applicable criteria for certain and unrevisable verification of observation statements (because they themselves must refer to strictly universal laws). We were aware of this objection, but did not take it seriously. As we read Popper’s book, it attempted to give a Logic of Science, i.e. a set of abstract rules and proposals for how we can make our theories as critisizable as possible, how we can compare their informative strength, which objections concerning initial conditions and auxiliary theories are relevant in a discussion about concrete test results, etc. etc. The analogy to the regulative application of formal logic’s schemata and principles to discussions in general seems clear. For this purpose we found Popper’s version of the hypothetico-deductive method eminently superior to for instance positivist-inductivist or con-ventionalist models of scientific debate. What we certainly could not read from the text was that it (1) presumed to describe how and why actual scientists actually choose or chose to believe in individual theories; nor (2) that it pretented to give us a set of unambiguous criteria to tell us when a given empirical theory is conclusively falsified. Could Popper really be supposed to think that he had given us a kind of touchstone – a veritable ’philosopher’s stone’ – which would make it possible for us to go around from laboratory to laboratory and authoritatively and conclusively in-form scientists about which particular experimental results must be considered firm and final, and consequently which theories are falsified once and for all? Of course not.
Popper also gave os (in ”Appendix X” as well as in the article ”Science: Conjectures and Refutations”) a psychological and logical critique of Hume’s idea of repetition as a basis for induction, as well as an effective, rational strategy against various phenomena we considered pseudo-scientific, for instance astrology, para-psychology, and Freudianism. Until then we had been forced to take shelter in the usual positivist critique that these theories couldn’t be verified empirically – some-how hoping that their proponents would not point out to us that neither could the best physical theories! Now we could attack them by arguing that they did not specify any possible phenomenon which – according to the theory itself – could not happen; or we could at least challenge their proponents to identify at least one possible event that they themselves would admit to be a decisive falsification of their theory if it ever happened.


Some years later I wrote Popper to tell him about my interest in his ideas as well as a little about the state of philosophy in Denmark. His reply was extremely kind and encouraging, although he gave me a – probably well-deserved – rap on the knuckles for a youthfully arrogant remark I had made about Niels Bohr’s philosophical efforts. Popper had met Bohr in Copenhagen at a congress in 1936 and had had a somewhat overwhelming conversation with him about the interpretation of Quantum Mechanics. This led him to characterise Bohr as ”… everything a great man should be!”
In the summer of 1967 Troels and I finally got the opportunity to meet Popper at a congress for Logic, Methodology, and Philosophy of Science in Amster-dam. At the opening cocktail party we went around eagerly looking for him – com-paring the many new faces with our only source: a perfectly awful portrait from a book about Popper, which made him look very angry and strangely Prussian. A poor little man who had some resemblance to this portrait, got visibly flustered by our youthful interest and almost fled the scene. Later we found out that he was an extremely nice professor fra Roumania, otherwise having a perfectly wonderful time in beautiful, free Amsterdam. Little did we know that Popper never attended occasions like that, but only lectures, seminars etc., where a total ban of smoking could be effectively upheld. Allergy or no allergy,- as one of his colleagues at the London School of Economics once told me with a wry smile, Popper’s insisting on his right to avoid tobacco smoke had at least excused him from taking part in countless dull faculty meetings.
Then came the great moment when we would be able to see and hear our hero. Strangely enough, Popper had been given the honourable task of giving the plenum talk. ’Strangely enough’ because the congress to our great surprise proved to be dominated by a not very pleasant cliquishness – a remarkably scientistic at-mosphere, as if we were a gathering of Logical Positivists in the Thirties. Incessantly, the tough-minded ’real’ philosophers distanced themselves from all the ’metaphys-icians’ (to be pronounced with a sneer) and all the formal-logical illiterates, i.e. more or less all other schools of philosophy.
Perhaps a brief remark may help to explain what followed: as hinted at in my title, Popper was by many of his philosophical colleagues thought to be a particularly difficult person. Bill Bartley’s article ”Ein schwieriger Mensch” elabor-ates upon this and explains it by the fact of his being extremely critical of his opponent’s often very superficial interpretations of his writings and by his never compromising in theoretical debates in order to politely smoothe out what he thought were genuine disagreements. In this particular gathering his conviction that he had ’killed Positivism’ hardly made things easier, of course (see his intellectual autobiography Unended Quest (1976), Section 17). His habit of mischievously doing the exact opposite of what his audience expected may have played a role, too.
For no sooner had the rather short man with the strongly marked features and a gentle smile sat down in front of the hundreds of participants before he started something like this: ’Today I’m going to set forward and defend a metaphysical theory in important ways similar to Plato’s Theory of Ideas and Hegel’s doctrine of the Absolute Idea.’ A shiver went through the audience and eyes glazed. ’What’s going on? Is he making fun of us?’ people seemed to ask. Well, he wasn’t; and for the first time we heard about Popper’s metaphysical theory of the three worlds: World 1, the physical world; World 2, the mental world; and World 3, the world of abstract entities and theories like for instance the natural numbers. These World 3-en-tities are created by World 2, i.e. our thoughts and our imagination; but when they have been thus created they possess a certain autonomy and objectivity. For instance, we evidently cannot place the prime numbers where we want them. Theories about World 1, too, are World 3-entities, but can be used to influence the physical world (think of nuclear physics and Hiroshima) – though not directly, only via World 2.
Next day I introduced myself to him. Great was my astonishment when he was immediately quite clear about who I was and about the content of our letters. ’Let’s get out of here’, he said, crinkling his nose at the tobacco smoke in the foyer of Hotel Krasnapolsky. He then took a firm grip of the sleeve of my jacket and led me out into the sunshine. So here I was, with this famous, busy and much sought after celebrity firmly attached to my sleeve, walking briskly round and round the central square of Amsterdam, with his eyes permanently fixed on me as he asked questions about my interests and plans, criticised my ideas, made suggestions, joked – as if the whole situation was the most natural thing imaginable. When, after about an hour, he was fetched for other duties by Imre Lakatos who in those days rather humbly functioned as a kind of secretary to him, the young Danish philosopher was sweaty and exhausted – the 65 years’ old still quite fresh and brimming over with energy.
On this as on other occasions I met him – in his and Lady Poppers beautiful home Fallowfield in Buckinghamshire, at the L.S.E., or elsewhere – Popper never wasted time on small talk or polite conversation: ’Here is some tea and some pastry, what’s the situation about drugs and Danish youth?’; or, ’Let’s get away from all these people, what do you say about Lakatos’ statement that Newtonian me-chanics is no more falsifiable than Freud’s psychoanalysis?’ these were typical Popper openings. A difficult person? Not in my experience. Perhaps a bit intense and demanding, in fact wonderfully so!
The delight of discovering Popper the philosopher was of course primarily one of living with his books – but also one of teaching his ideas. In Denmark we have been a handful of persons who by teaching his views at universities, peoples’ universities, peoples’ high schools, and also through various publications have done our best to make sure that his ideas did not remain unknown in this country. Already in the beginning of the seventies we must have had a certain succes. For when we made an official proposal that Popper should receive the Sonning Prize (’for Contribution to European Culture’), there was great support from many sides. He received the prize during his particularly successful and pleasurable stay in Copenhagen in 1973. At a solemn occasion in the University’s ’Solennitetssal’, professor of philosophy Mogens Blegvad gave an impressive motivation speech about Popper’s many contributions to European thought (’very well-informed’, Popper whispered to me). His own lecture was formed as a critique of the then as now extremely influential ideas of closed conceptional frameworks, the incommensurability of paradigms, and cultural relativism. The publication of Popper’s that comes closest to that lecture is the article ”The Myth of the Framework” from E.Freeman’s Schilpp-volume (see below). He also gave a seminar on the subject at the Institute of Philosophy.
Popper gladly accepted an invitation from my wife and me to take part in a less solemn occasion in our new home – not least because I mentioned to him that he could meet many students and others who actually knew his ideas, but had not been present at the grand dinner at the Hotel D’Angleterre or similar gatherings. Fortunately it was a lovely, sunny day as there would hardly have been room for all invited indoors. Popper went round for some minutes’ talk with almost every one present and seemed to enjoy himself enormously. During his four day’s stay in Copenhagen he gave the impression of being grateful for his reception in Denmark as well as for the considerable sum of money involved. His attitude to the honour and the host country was markedly different from that of two other philosophers who had received the prize: the Norwegian Arne Naess (Sonning Prize 1977) who not even gave a lecture or a seminar, and Bertrand Russell (1960) who wrote a friend before going to Copenhagen, ’We’re just going over to pick up the money and come straight back again.’ (R.Crawshay-Williams: Russell remembered, Oxford 1970, pp. 127-28).


Apart from the moral and intellectual strength of his critique of totalitarianism, collectivism, historicism, and utopianism (a critique which made many of my students burst out: ’If only I had known these arguments when I was on the defensive during discussions with my Marxist friends or fellow students!’) the aspect of Popper’s philosophy that has especially made an impression on the general public is that he was an ’old-fashioned’, rarely very technical thinker of the kind that non-professional philosophers are attracted to. His philosophical writings have a science-oriented but also common-sense character which makes it a pleasure to teach them. His approach is, as he often stressed himself, basically an ontological one: Is there, apart from material things, also such a thing as consciousness – if, indeed, there is such a thing as matter at all? Has the world always existed or has it had a beginning? Is it divinely created or perhaps just evolved from nothing? Does human consciousness have en influence on physical or economic reality, or is it in every detail determined by these? Do we have free will? Is our biological evolution teleologically directed towards a perfect final state; is it determined by an absolute ’law of evolution’, or is it a process of ’emergence’ involving real novelty? Do ’time’s arrow’ and the given ’now’ have ontological reality or are they the result of a human Anschauungsform? etc. etc.
But how can Karl Popper, being a well-known proponent of Positivism, express an interest in such metaphysical questions as these? – you might ask. In fact, Popper is not a Positivist at all. On the contrary, he is one of the greatest and most explicit critics of that philosophy. Not only does he refute Logical Empiricism’s criterion of meaningfulness with devastating reflexivity-arguments, but his view of scientific theories as systems of strictly universal statements makes evident the futility of its probability-inductivist attempts. A large part of his works are on metaphysics: In The Self and Its Brain (1977), (another lovely title, I think!) he critizises different versions of materialism and develops his interactionist Three World-Theory as well as giving interesting hints about how we humans have to ’learn to become selves.’ In The Open Universe (1982) and Quantum Theory and the Schism in Physics (1982) he takes on determinism: There is ample room for rational, free acts in a universe that shows its fundamentally creative and open character every time a new argument, a new work of art, a new theory, even a new piece of prediction, is created; for aren’t we ourselves a part of the Universe? In Realism and the Aim of Science, (1983) Unended Quest (1976), and Objective Knowledge (1972) he defends philosophical realism against phenomenalism, instrumentalism, relativism etc. In A World of Propensities (1990) we find an elegant survey of his view of objective probability and of his evolutionary metaphysics and theory of knowledge.
His views on evolution make his deductictivist theory of knowledge perfectly understandable. According to Popper’s version of Neo-Darwinism our bio-logical evolution is such that, at no point in Evolution, a ’direct (’Lamarckian’) instruction’ takes place from Nature to organisms. Analogously, we humans have no ”hotline” to reality in itself or to any other ’source of knowledge’. We have to do with a secular view of human knowledge, you could say. Mankind is episte-mologically alone in the world: we can never receive instruction or communication ’from outside’ to the effect that this or that set of statements are irrevocably true and certain or even that this particular theory is inductively probable to a certain degree. What, then, would be the rational strategy if this is our situation? Free critical dis-cussion of (logically speaking) freely invented hypotheses – metaphysical as well as scientific – but, importantly, a discussion not allowing typically ’philosophical’ objections to the effect that the opponent’s thesis has not been proven. For the demand for proof and the ideal of perfect certainty entail either logical circularity or infinite regression or irrational adherence to fundamental dogma. ’Apodictic certainty’ is not something inherently desirable, but something we can always get hold of, for instance through passionate subjective belief, effective censorship, immunisation of paradigms, or whatever. Paradoxically, if we strive to understand Reality, we will have to make do with fallible hypotheses and the critical comparison of fallible hypotheses.


In his later years, Popper concentrated his efforts in the fields of evolutionary epistemology and objective indeterminism; but his worries concerning the fate of Mankind led him now and then to speculations about politics and social matters. Among university philosophers he soon lost whatever influence he might have had (very little, he sincerely thought); but in broader intellectual circles he increasingly acquired the status of a sort of wise old man who was always worth listening to, not least because he – whether as a lecturer or as an interviewee – was often ready with surprising and often provoking statements. For example, he never accepted the common talk of the West’s, and especially USA’s, ’cultural imperialism’. That Western Civilisation in important respects is ’objectively superior’ to other cultures could be rationally argued, he said, as well as seen from the fact that individuals all over the world adopt it to an increasing extent or even vote for it ’with their feet.’ There is no question of compulsion there.
The greatest dangers for world peace, he argued, is the growing number of well-armed pocket-dictatorships (he unhesitantly supported the role of Western countries in the First Gulf War) and the spread of plutonium and nuclear scientists from the former Soviet Union. We must create international task-forces to fight this particular problem; and, in general, democracies must be ready to ’go to war for peace,’ as he put it. Areas of Free Trade is a good thing and ought to be steadily extended for the sake of peace and prosperity; but new, big state-constructions such as an European Union are definitely harmful.

There is some encouragement to be derived, I think, from the fact that one of the last tasks of this great philosopher of freedom was overseeing one more edition of The Open Society and Its Enemies – in Russian.

Further references.
Bartley, W.W.Bartley III: ”Ein Schwieriger Mensch: Eine Porträtskizze von Sir Karl Popper”, in: Nordhofen. E. (ed.): Physiognomien: Philosophen des 20. Jahrhunderts in Portraits, 1980.
James, Roger: Return to Reason. Popper’s Thought in Public Life, 1980.
Nielsen, Flemming Steen: ”En kritik af den totalitære statstanke”, in: Svend Erik Stybe (ed.): Politiske ideologier, 1972.
– – : ”Karl Popper som evolutionistisk filosof”, in: Hoffmeyer & Stangerup (eds): Naturens historiefortællere II: Fra Darwins syntese til nutidens krise, 1987.
– – : ”Begrebet streng universalitet hos Karl Popper”, in: Filosofiske Studier fra Filosofisk Institut, København Universitet, bd. 9, 1987.
Karl Popper: Conjectures an Refutations, 1963.
– – : ”The Myth of the Framework”, in: E.Freeman (ed): The Abdication of Philosophy. Essays in Honour of Paul Arthur Schilpp, 1976.
– – : In Search of a Better World, 1990.

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Railway lines of thought

One of the themes which I developed some years ago concerned the way ideas take hold and exert an influence on our thoughts and our research projects which is very hard to identify, to subject to critical appraisal and to change. I used the term “railway lines of thought” to capture the image of a vehicle that has to stay “on track” more or less regardless of the  wishes of the passengers.

The late Liam Hudson dropped onto the same theme in his wonderful book The Cult of the Fact and he gave me permission to reproduce several chapters on my web site. This material is now an appendix to the collection “Jacques Barzun and Others“. I urge you to read it!

Here is the Preamble to convey the flavor.

This is a book about professional psychologists and the visions they pursue. It expresses a growing dissatisfaction with the self-consciously scientific psychology in which I myself was trained – an activity that, increasingly over the last ten years, has taken on the air of a masquerade. It has been written in the hope that, somewhere behind the paraphernalia of false science and apparent objectivity, there lies the possibility of a more genuinely dispassionate study of human nature and human action.

Such a book is bound to some extent to be autobiographical; and it is bound also to concern itself not simply with the ‘facts’, but with the unspoken assumptions that we all use when deciding which facts are interesting, and which trivial, a bore…One must question not so much what university teachers think they teach, nor what students think they are learning, but the more subterranean traffic in ideals and prejudices that all powerful teaching institutions create, and that governs thereafter the intellectual lives their products lead.

In attempting this, I have set myself to transgress certain barriers that at present hem in academic discussion, and render much of it inconsequential. Each of these barriers takes the form of a distinction, persuasive but false. The first is that between Science and Art: my belief, unfashionable though this may still be, is that all arguments bearing on human life deserve to be heard within the same arena of debate. The second is between the Serious and the Frivolous: we are moving, if the tastes of the student body are any guide, from an era in which wit, like Art, has been seen as an irrelevant frill, into one – at once gloomier and more Teutonic – in which wit is outlawed as an affront to moral rectitude. The systematic, technical and cheerless are automatically preferred to the literate and humane. Although this new Calvinism satisfies simple psychic needs, I have written in defiance of it – also on the chance that the tide of piety is one that can still be turned.

Lying behind these false distinctions, and serving to unite them, is a further and more general distinction, itself false: that between Style and Content. In the entrenched sciences, it is possible to transmit the truth in prose that is as crabbed as it is evasive. But where foundations are shakier, style not merely limits what we find it natural to express; it is, in important respects, the very essence of that expression. For it is through our style, our mode of address, that we transmit all those messages that lie beyond the literal meaning of our utterance. And it is precisely on such ‘meta-messages’ that the focus of this book lies.

My account begins, conventionally, with the circumstances of its own conception. Also, less conventionally, with a foray into literary criticism, and into the history of a particular myth. This may seem at first sight irrelevant, a diversion. But if I have judged matters aright, this brief literary exploration heralds my main theme – Myths, Ancient and Modern – and also serves to identify the metaphorical nature of its own motive force: the spring that moves the mechanism along. My assumption is that human thought, before it is squeezed into its Sunday best, for purposes of publication, is a nebulous and intuitive affair: in place of logic there brews a stew of hunch and partial insight, half submerged. And although we accept that our minds’ products must eventually be judged by the puritan rules of evidence and insight – the strait gate through which they must pass – we seem in practice to draw what inspiration we possess from a hidden stockpile of images, metaphors and echoes, ancient in origin, but fertile and still growing. This work is no exception. Its energy is drawn from a clutch of human sentiments that, over and again down the centuries, have found expression in potent, metaphoric form. What these sentiments are, and what their relation is to a putative science of human life, should with luck become clearer as the narrative progresses.

To begin with, though, the story is simple enough – in fact, it has about it the beguiling air of a fable. In it, the intrepid young psychologist is packed off by his mentors across the deserts of ignorance and superstition. In mid-journey, with rations running low and a dead-line approaching, this outrider of the rational order is set upon – or so it seems – by the agents of unreason. Bloodlessly, as on the silver screen, his assailants tumble to the ground. But the dead will not lie still. They dust themselves down, and demand to be heard. Our hero finds that parley he must, and around the camp-fire all wax philosophical.

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Popper vs von Mises on the philosophy of science


A long thread on the Critical Rationalist facebook page began by drawing on  von Mises’s criticism of Popper in The Ultimate Foundation of Economic Science “he [von Mises] addressed the claim of Karl Popper that scientific propositions must be falsifiable. Although Popper was not a positivist, he intended his falsification criterion to separate scientific from non-scientific statements.”

That is not a helpful statement without providing an account of the problem situation which the positivists and Popper addressed. For the positivists, the use of the inductive method was a distinctive feature of science, but Popper considered that induction was logically incoherent.  Instead, he was looking for a convention make a clear distinction between (a) theories that claimed to be scientific (due to their alleged basis on evidence) which are nevertheless not refutable and (b) theories that do lay themselves open to falsification (in principle).

As described in The Guide to The Logic of Scientific Discovery,  he made a significant departure from the usual approaches to decide these matters, either by logical analysis or by observation of the way scientists work (the naturalistic approach). He articulated the “rules of the game” or “conventions” approach. This is closely related to his rejection of certainty as an aim of science . He introduced the theme of conjectural knowledge as a permanent feature of scientific theories and not a transient situation or a “bug” in a new theory, to be superseded by further investigation and “confirmation”.

His criterion of demarcation is a proposal for an agreement or convention. He noted that his convention will be rejected by people who think that science can generate a system of “absolutely certain, irrevocably true statements”.

The test for his proposals is to examine their logical consequences, and to explore their fertility in solving problems in the theory of knowledge and scientific investigation. Essentially, it is a test of practice and practical results.

One of the practical implications of  Popper’s criterion is that it can be used early in an argument to discover where the various parties stand on the use of evidence in the debate. It also prompts scientist to be constantly mindful of the importance of testing, with all that implies for the design of experiments and the attitude adopted towards adverse findings.

Popper’s program was radically different from the positivists, a fact obscured by people who can only see Popper’s falsifiability criterion as a rival of the positivists criterion of MEANING  (they royally confused the issue by taking up testability as a criterion of meaning, as though Popper was working on the same problem).

Part of the problem here is the great significance ascribed to Science in the wake of Newton, when Science gained the reputation for finding ultimate truths. Previously the terms science or scientific merely implied  systematic investigation with a view to  obtaining useful principles, and so there was the science of angling and every other thing.

Part of the power of Popper’s program was to get away from the hopeless quest of the positivists/empiricists for a criterion of meaning (or cognitive significance) and the attempt to save inductive logic. The falsifiability criterion had logical coherence which the verification  criterion lacked, and although falsification could not be decisive in practice, it did have the practical effect of pointing up the need for more critical attention to conventions to guide scientific practice (hence the program charted by Ian Jarvie).

One more important point: the focus of critical discussion for Popper was/were the laws of science, expressed as universal generalizations. That is what makes the logic of testing so strong (compared with verification).  I don’t understand how  a pure logical analysis  can demonstrate  that both the verification criterion and the falsifiability criterion are worthless.   What is the point of Popper’s demarcation principle, given the larger contours of his program? Where is the universal statement that is tested by the basic statement “there is a chair in this room”? Is it a universal statement of any interest in the real world of scientific investigation?

This is the original argument.

In point of fact, the criterion is worthless, since every statement comes out verifiable under it. Suppose that “p” is a non-controversially verifiable statement, e.g., “there is a chair in this room.” Let us take “q” to be a statement logical positivists reject as meaningless. A good example is one that Rudolf Carnap held up to ridicule when he called for an end to metaphysics. He cited the following from Martin Heidegger’s Being and Time (1927): “The not nothings itself.” I shall not attempt to explain this: one can see why Carnap presented it as a paradigm instance of a meaningless statement.

Does the verification principle eliminate it? Surprisingly, it does not. From p, we deduce p or q. (This step is non-controversial.) Assuming that a logical consequence of a verifiable proposition is itself verifiable, (p or q) is verifiable. Further, if p is verifiable, then the negation of p is verifiable; this principle seems difficult to question. Now, consider this argument:

p or q not -p ______ q
This argument is valid, and each of its premises is verifiable. Then, q is a logical consequence of verifiable propositions, and it, too, is verifiable. Clearly, if the verification criterion cannot eliminate “the not nothings itself,” it is not worth very much.

A falsification criterion fairs no better. If p is falsifiable, then (p and q) is falsifiable. Once more, not-p should be falsifiable if p is, though Karl Popper has implausibly denied this. By an argument parallel with that for verification, we conclude that q is falsifiable.

One might think that this is a mere trick, readily avoidable through slight modification of the principle. There have been many attempts to formulate a criterion that comes up with the “right” results, but so far all have failed to withstand criticism.

What is the “right result”  or the criterion for a “right result”?

Looked at in the context of testing (universal) scientific theories, what is wrong with the principle of falsifiability in logic and in practice for working scientists?  With scientifically relevant statements in place of the ps and qs in the argument above would the result still look like a knockdown victory over Popper’s arguments?
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Non-justificationism: A distinction that makes a difference

When the linguistic philosophers inspired by  Ryle, Wittgenstein and Austin ruled the roost in some universities, notably Oxford, critics sometimes referred to “distinctions that don’t make a difference”. What about the distinction between justificationism and non-justificationism? A critic of Popperism in the Critical Café (email list)  was prepared to read widely and he complained that the Popperians were the only people in the world who used this term non-justificationism. He wondered why we should be bothered with it, given that it was not a topic of interest or concern in the wider philosophical world. That was a decade or so ago and the ensuing discussion did so little to change the minds of the critics that some of us have not been back to the Café on a regular basis since that time. I suppose we decided that life is too short to spend a lot of it engaging with people who appear to be completely closed to the ideas of critical rationalism. I will add to this later and I just want to put this ball in play before I go out. The point is to take up a challenge that Bruce and I offered to each other, to be more hospitable to critical visitors to the site and take some time to explain more carefully the things that we have been taking for granted for a long time. Things like non-justicationism, inductivism  objective knowledge.


to be continued

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Updating the Popper Guides and Misreading Popper

I am preparing to publish Misreading Popper and some other of my ebooks as print-on-demand paperbacks. This facility is available through a publishing associate of Amazon called CreateSpace.

There are still people out there who want books to hold in their hands and I want  to give them that opportunity at a price  that is not much more than the ebook

The reason for this notice is to ask people to let me know about (a) mistakes of all and any kind that you have noticed and (b) any kind of improvements that you think can be made. Please use my email address for this,  not the comments here. The email is rchampATbigpondDOTnetDOTau

The order of publication will probably be

Misreading Popper

Reason and Imagination

The five guides in one volume.

So please focus on those books if you can find the time to dip into some of them again (or even for the first time!).

The full set.


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Hans-Joachim Niemann on Karl Popper, biology and evolution

A copy of Karl Popper and the Two New Secrets of Life has arrived, courtesy of the author. This books is a fine addition to Popperian exegesis,  just when you thought the  cottage industry on the intellectual development of KRP was running out of material.  Check it out on Amazon, I agree with Luc Castelein that it is a five star performance! Unlike some of the over-priced books on the market this one is affordable and real value for money.

I am short of time and I would like to do a slow read, chapter by chapter to explain the new information and the insights of this wonderful book, but I will have to spread this over several days or even weeks.

There is a handy summary.

The story of how humans and all living things came into existence is told in two widely believed versions: the Book of Genesis and Darwin’s Origin of Species. It was the philosopher Karl Popper who presented us with a third story, no less important. His New Interpretation of Darwinism denies the creative power of blind chance and natural selection and establishes knowledge and activity of all living beings as the real driving forces of evolution. Thus, spiritual elements are back in the theory of evolution, and in Popper’s view “the entire evolution is an adventure of the mind.”

In this book, Hans-Joachim Niemann establishes Karl Popper as an eminent philosopher of biology. In the first chapter, biographical details are unearthed concerning how Popper’s biological interests were inspired by a biological meeting in the old windmill at Hunstanton in 1936. The second chapter focusses on the year 1986 when Popper, in several lectures, summarized the results of his life-long biological thinking. The most important of these, the Medawar Lecture given at the Royal Society London, was lost for a long time and is now printed in the Appendix. A new world view begins to emerge that is completely different from Creationism or Darwinism.

Twenty years after Popper’s death, the last chapter looks back on his biological thoughts in the light of new results of molecular biology. His then attacks on long-lasting dogmas of evolutionary theory turned out to be largely justified. The new biology seems even well suited to support Popper’s endeavour to overcome the gloomy aspects of Darwinism that have made organisms passive parts of a machinery of deadly competition. Neither blind chance nor natural selection are the creative forces of all life but knowledge and activity. How they came into existence is still a secret and a worthwhile research programme.

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The debacle of philosophy in the 20th century

Can philosophy progress, or is there an eternal  dialogue on fundamentals that just keeps the issues in play without resolving any of them and moving on, like the successful natural sciences?  Unlike the progress of science,  there are signs of decline in philosophy judging from some of the schools of thought that achieved great prestige in the 20th century.

This situation could be seen as a comedy or a farce, but it should be seen as a tragedy because ideas have consequences and bad ideas are likely to have bad consequences. Some examples are Heidegger’s phenomenology, Sartre’s existentialism, Wittgenstein in both his early and later stages and the logical positivists/empiricists

On the bright side

Of course there are alternatives to the bad philosophers and a some  good philosophy may be done by people who have a notional allegiance to some of the defective movements such as “linguistic philosophy” inspired by Wittgenstein in his second phase.

Phillip Kitcher is reviving the science and practice-oriented philosophy of the pragmatists (Peirce and Dewey) and there are the critical rationalists.

I have taken out most of the post because I want to use some of it for a magazine. It will be substantially different but there is some overlap and I don’t want to prejudice their policy of publishing original work.

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Topics and themes

Planning a paper version of  Reason and Imagination  I have made some minor improvements and Bruce made a major suggestion, to have a new Introduction to spell out the six themes that I have used to introduce the guides and Misreading Popper.

This reminds me of some wise words from C Wright Mills on the treatment of themes and topics in writing a book. He talked about  themes and topics (a distinction which he attributed to a great editor, Lambert Davis).  A topic is a subject which might be treated in a chapter of the book. The order of chapters brings up the issue of themes.

“A theme is an idea, usually of some signal trend, some master conception, or a key distinction, like rationality and reason, for example. In working out the construction of a book, when you come to realise the two or three, or as the case may be, the six or seven themes, then you will know that you are on top of the job. ”

These themes will keep turning up in connection with the different topics, they may appear to be repetitious, they may at first be confused and poorly formulated.

“What you must do is sort them out and state them in a general way as clearly and briefly as you can…cross classify them with the full range of the topics…At some point all the themes should appear together, in relation to one another…maybe at the beginning of the book, certainly near the end…It is easier to write about this than to do it, for it is usully not so mechanical a matter as it may appear…Sometimes you may find that a book does not really have any themes. It is just a string of topics, surrounded of course by methodological introductions to methodolgy, and theoretical introductions to theory. These are indeed quite indispensable to the writing of books by men without ideas. And so is lack of intelligibility”.

So in addition to the introduction to the six themes (1) conjectural knowledge, (2) objective knowledge, (3) no obsession with terms,  (4) the social turn (‘rules of the game’), (5) revival of metaphysics and (6)  significance of evolution I will need to look at each paper to see if it will help to identify how one or more of the themes occur in that chapter.

Or maybe the Introduction can flag the way the themes are related to particular topics in each chapter.


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Papineau on Popper

A student who is studying Popper in London  sent this paper by David Papineau for comment.

His immediate task is to write a paper on induction so I will not dwell on other matters except to suggest that Popper deserves some credit for writing one of the great books of political philosophy in the 20th century and also his “three world” theory is exciting and fertile.

It will help to get clear about the several things which travel under the label of induction.

1. Inductive discovery of  regularities (sometimes unhelpfully called laws), like the sun rises every morning in the east.

2. The (subjective) belief that the sun will rise every morning in the east.

3. Inductive proof of the law or the belief, by observing the sun rising in the east.

4. The shift to probabilities after Hume’s critique has been taken on board and people accept that you can’t actually have inductive proof. So inductive logic becomes the matter of putting probability values on theories (not to be confused with the probability of events or the probability values assigned in statistical analysis  to indicate the probability that the result could have come about by accident rather than a genuine causal relationship).

5. The assertion that induction means the belief that there are regularities in the world, so the future will be like the past, as long as the laws or regularities persist. This has got nothing to do with discovery, or testing, or probabilities and it tends to be the last resort of inductivists when the  other forms of induction are criticized.  It is better described as a metaphysical theory about the world.

After various critiques of the CERTAINTY of scientific knowledge and induction were accepted, the core of the program of inductivism became the quest for inductive probabilities.  In recent decades it seems that Carnap’s quest for objective probabilities had been given up and the core these days is Bayesian subjectivism


In paragraph 5 he wrote “Popper’s philosophy of science centres on his rejection of inductive reasoning. This is the kind of reasoning by which we judge that some hitherto observed pattern will continue to hold good in the future“.

That is induction of the fifth type identified above – the belief in regularities in the world.  Did Popper reject the idea that there are regularities in the word? For him the theoretical or generalizing sciences were all about the quest for (true) laws of nature, that is regularities (or propensities) for systems to behave in particular ways.

That is a metaphysical idea about the way the world works in general, it has nothing to say about the methodology of science or epistemology (how we learn and test our ideas).

Moving on to para 7 we find explicit criticism of Popper’s strategy of conjectures and refutations because it “can only deliver negative knowledge. It shows certain scientific theories are false, but it never shows that any theory is true”.



Papineau mocks Popper by producing two examples of theories – that cigarettes cause lung cancer and matter is made of atoms. What sort of theories are these?  Not all smokers contract lung cancer, so clearly the proposition that cigarettes cause lung cancer is not a universal law. Similarly, atoms are very complex phenomena and they might well be explained in terms of force fields, not the  little billiard balls  of classical atomic theory.

The causes of lung cancer and the structure of matter are much more complex than the picture painted by Papineau, there are many conjectural elements and more work remains to be done. The theory of conjectural knowledge is not demolished by reference to cigarettes causing cancer and the atomic theory of matter.

Moving on to para 11 and 12 Papineau attacks Popper’s demarcation of scientific propositions on the basis of testability. He did not take account of the historical problem situation that created the issue of demarcation: that was the aim of the logical positivist to eliminate metaphysics using the demarcation principle of  VERIFICATION and also the hallmark of science was THE METHOD OF INDUCTION, BASED ON EMPIRICAL DATA, EVIDENCE OR SENSE EXPERIENCE.

Popper argued that the principle of verification could not work (eventually that turned out to be undeniable despite major efforts by the positivists and logical empiricists to use it) and neither would inductive logic to either PROVE  theories to be true or to make them PROBABLE  (with a numerical p  value).

Note that we are  talking about general, explanatory theories that explain how things work, not just statements about things that exist like black swans or atoms.

Popper suggested that to should use evidence to test our theories (because we cannot verify them) and this proposal has two advantages over the positivists.

1. It makes us check to see whether evidence can be brought to bear in the argument that we are having. It may be that the theory at stake is in principle not testable, that does not mean that it is meaningless or trivial, it just means that criticism has to proceed using criteria other than evidence.

2. It liberated the positivists from the quest to eliminate metaphysics  (by making it meaningless) by finding an empirical criterion of meaning.  But they did not want to be liberated and so wasted some decades until nowadays metaphysics has made a comeback to the point where Popper’s theory of metaphysical research programs may be taken seriously.

Papineau went on to write (para 12) that Popper could not say that physics is less speculative than astrology because he cannot claim that atomic theory  is firmly established by a large amount of evidence (as the inductivists claim). And so Popper “is stuck with the non-problem of explaining why some speculations are better than others”.

That is not difficult: we favour theories that are  better tested, that explain more, that predict more accurately, that lead to fertile research programs.



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