In section 14 of The Logic of Scientific Discovery Popper discusses the use of universal and individual names or concepts in singular and universal statements.

He starts with a pretty straightforward explanation by way of example: 'dictator', 'planet' and 'H2O' are universal names, 'Napoleon', 'Earth' and 'The Atlantic' are individuals. Individuals are defined by proper names. A temporal description can also constitute an individual concept (so, "goat" versus "the goat that was at 20 degrees longitude west and latitude north at 3:00pm on July 24th 2015"). Individual concepts may be of elements and classes (Popper's dog (individual) is a member of the sub-class Austrian dogs (individual) is a member of the class of mammals (universal)). He then offers a definition:

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

He says that this distinction is indispensable if "we are not to blur the corresponding distinction between universal and singular statements."

He then says one cannot identify an individual concept by all of the universal properties it holds as this merely describes the class to which it belongs (even it is the only element in that class), and one cannot define a universal by all individuals belonging to it as this describes a class and not a universal.

Here is where I come to trouble. Popper then says that:

"It is therefore not possible to abolish the distinction between individual and universal concepts with arguments like the following of Carnap's: '...this distinction is not justified...because every concept can be regarded as an individual or universal concept according to the point of view adopted'. Carnap tries to support this by the assertion '...that all so-called individual concepts are names of classes, just like universal concepts.' This last assertion is quite correct, as I have shown, but has nothing to do with the distinction in question."

To me it seems Popper is either making a semantic ruling or making a metaphysical statement. If the only reason you cannot refer to Napoleon without his name is because Popper has defined doing as such as referring to the class to which he belongs and not to him, hasn't he presupposed metaphysically that there is a Napoleon in a deeply existential sense?

What if this metaphysics is incorrect, and there are only classes of different orders? Does that negate the possibility of validly making universal versus singular statements?

Am I misunderstanding something fundamental here?

Thanks in advance for any help.

1 Answer 1


The background of Popper's discussion is Rudolf Carnap's Der logische Aufbau der Welt (1928), Engl.transl.1967.

[§ 1] The word "object" is here always used in its widest sense, namely, for anything about which a statement can be made. Thus, among objects we count not only things, but also properties and classes, relations in extension and intension, states and events, what is actual as well as what is not.

[§5] Since we always use the word "object" in its widest sense (§1), it follows that to every concept there belongs one and only one object: "its object" (not to be confused with the objects that fall under the concept). In opposition to the customary theory of concepts, it seems to us that the generality of a concept is relative, so that the borderline between general and individual concepts can be shifted, depending on the point of view.

[§158] Concepts are usually divided into individual concepts and general concepts; the concept Napoleon is an individual concept; the concept mammal, a general concept. From the standpoint of construction theory, this division is not justified, or, rather, it is ambiguous, since every concept, depending upon one's point of view, can be considered either an individual concept or a general concept. We have stated this earlier (§5) and have derived from it the justification for speaking of the object which corresponds to a given concept. [...] In the ordinary view, some of the concepts in this example [i.e. the dog (species) is a class to which my dog Luchs belongs] would have to be called individual and others general. But each of them (except for the last one) is constructed as a class or relation extension, and each of them is an element of the preceding class or a term of the preceding relation extension; thus, each of them is a generality of other objects. What is the reason that, in the ordinary view, e.g., the species dog and the sense quality brown are considered something general while the dog Luchs, and a given world point, and a given experience are considered something individual, and that frequently only the latter are called "objects", while the former are called "mere concepts"?

According to Popper, this approach, considering the distinction between individual and universal concepts as conventional is wrong.

There are "real" individuals, like Napoleon, and they are used to define individual concepts; the concept "Napoleon's generals" is obviously the name of a class with more than one individual, but it is an individual concept because we cannot define it without using a proper name: Napoleon.

Popper's critique is related to abstraction and the possibility of an inductive reasoning: if there is a "break" between individuals and universals, we cannot "generalize" from a collection of individual cases to a general statement a law.

  • Just to make sure I get this: Commented Apr 26, 2016 at 10:51
  • Popper is saying that if instead of the statement "Napoleon lost at Waterloo in 1815" you say "x=short Corsican generals born 1769 and later exiled to an island --> x lost at Waterloo in 1815" you are then sneaking in inductive logic because you are using a statement regarding the individual case "Napoleon" to infer something about the class to which he belongs? Commented Apr 26, 2016 at 10:58
  • @washboardalex - I do not think that way... Carnap's book is quite difficult and the link with induction is indirect: It seems to me that Popper is interested to "restore" the distinction between individual/universal (that in C's book seems to be superseded) and I personally think that this issue is related to P's rejection of induction: induction is not a "logical grounded" way to move from empirical (individual) facts to general (uinversal) laws. Commented Apr 26, 2016 at 14:00
  • Hmm...OK, I will continue the struggle with this book. Thanks very much for your help Mauro. Commented Apr 27, 2016 at 1:24
  • @washboardalex - you are welcome. Commented Apr 27, 2016 at 6:13

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