The Crisis in Psychology

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16 is not only the addition of 16 unities, it is also the square of 4 and the biquadrate

of 2 . . .. Only even numbers can be divided by two . . .. For division by 3 we have

the rule of the sum of the figutes. . .. For 7 there is a special law.. .. Zero destroys

any other number by which it is multiplied; when it is made divisor or dividend with

regard to some other number, this number will in the first case become infinitely large,

in the second case infinitely small [Engels, 1925/1978, pp. 522/524].

About both concepts of mathematics one might say what Engels, in the words of

Hegel, says about zero: “The non-existence of something is a specific non-existence”

[ibid., p. 525], i.e., in the end it is a real non-existence. [7] But maybe these qualities,

properties, the specificity of concepts as such, have no relation whatsoever to reality?

Engels [ibid., p. 530] clearly rejects the view that in mathematics we are dealing

with purely free creations and imaginations of the human mind to which nothing

in the objective world corresponds. Just the opposite is the case. We meet the pro-

totypes of each of these imaginary quantities in nature. The molecule possesses

exactly the same properties in relation to its corresponding mass as the mathemati-

cal differential in relation to its variable.

Nature operates with these differentials, the molecules, in exactly the same way and

according to the same laws as mathematics with its abstract differentials [ibid., p. 531].

In mathematics we forget all these analogies and that is why its abstractions turn

into something enigmatic. We can always find

the real relations from which the mathematical relation . . . was taken . . . and even

the natural analogues of the mathematical way to make these relations manifest [ibid.,

p. 534].

The prototypes of mathematical infinity and other concepts lie in the real world.

The mathematical infinite is taken, albeit unconsciously, from reality, and that is why

it can only be explained on the basis of reality, and not on the basis of itself, the

mathematical abstraction (ibid., p. 534).

If this is true with respect to the highest possible, i.e., mathematical abstraction,

then bow much more obvious it is for the abstractions of the real natural sciences.

They must, of course, be explained only on the basis of the reality from which they

stem and not on the basis of themselves, the abstraction.

2. The second point that we need to make in order to present a fundamental

analysis of the problem of the general science is the opposite of the first. Whereas

the first claimed that the highest scientific abstraction contains an element of reality,

the second is the opposite theorem: even the most immediate, empirical, raw, sin-

gular natural scientific fact already contains a first abstraction. The real and the

scientific fact are distinct in that the scientific fact is a real fact included into a

certain system of knowledge, i.e., an abstraction of several features from the inex-

haustible sum of features of the natural fact. The material of science is not raw,

but logically elaborated, natural material which has been selected according to a

certain feature. Physical body, movement, matter—these are all abstractions. The

fact itself of naming a fact by a word means to frame this fact in a concept, to

single out one of its aspects; it is an act toward understanding this fact by including

it into a category of phenomena which have been empirically studied before. Each

word already is a theory, as linguists have noted for quite some time and as Po-

tebnya [1913/1993] has brilliantly demonstrated. [8]

Everything described as a fact is already a theory. These are the words of

Goethe to which MUnsterberg refers in arguing the need for a methodology. [9]

When we meet what is called a cow and say: “This is a cow,” we add the act of

thinking to the act of perception, bringing the given perception under a general