What is the law of contradiction? The law of contradiction states: A concept itself cannot at the same time contain two or more mutually contradictory meanings, and if a certain concept contains two contradictory meanings, then that is regarded as a logical error. A contradictory concept cannot simultaneously have both sides correct or both sides incorrect, and the correct one is, and can only be, one of those two. Its formula is A is not equal to not-A. Kant has enumerated the four following antinomies (maodun sixiang):[4-408] The world’s time has a [p. 245] beginning and an end, and is limited in space; the world has no beginning or end in time, and also is limitless in space. This is the first of them. In the world everything is constituted of simple matter (cannot be re-divided); in the world there are no simple things, everything is complex (can be re-divided). This is the second of them. In the world there exists free causation; in the world there is no freedom, everything is inevitable. This is the third of them. In the world there exists a certain inevitable essence (biran de shizhi), in the world nothing is inevitable, everything is accidental. This is the fourth of them. Kant gave these irreconcilable and mutually opposed principles the one title of “The Second Law of Contradiction”. However, he stated that these were only contradictions in man’s thought, in the real world they really did not exist. According to the law of contradiction in formal logic, these contradictions were thus a mistake, and had to be rejected. However, in reality, thought is a reflection of things. There is not one thing which does not contain contradiction, and because of this, there is no concept which does not contain contradiction. This is not an error in thought, but precisely where thought is correct, and the law of the unity of contradictions of dialectical logic is founded on this base. It is only with formal logic’s rejection of the contradictory law of contradiction that it becomes really incorrect thought. The law of contradiction in formal logic is only a manifestation of the negative of the law of identity, and it functions as a supplement to the law of identity, the purpose of which is to consolidate the law of identity’s so-called a concept is equal to itself, A is equal to A.
What is the law of excluded middle? The law of excluded middle states: Of the two opposite meanings of a
concept, the correct one must be one or the other, for it is not possible for both to be incorrect, or to rush to a third as the correct meaning. Its formula is “A is equal to B, or not equal to B, but cannot be equal to C”. They do not realize that things and concepts are developing, and in the process of development of things and concepts, not only are their internal contradictory elements made manifest, but these contradictory elements can be removed, negated, and resolved to become a third thing which is not-A and not-B, change to become a new and higher thing or concept. Correct thought should not exclude the third factor, should not exclude the law of the negation of the negation.
According to the law of the excluded middle, in the contradiction between the proletariat and the bourgeoisie, the correct one is either the former or the latter. It cannot be a society without classes. However, it is a fine thing that the process of social evolution does not stop at class [p. 246] struggle, but progresses towards a proletarian society. China and Japanese imperialism are in a state of contradiction. We oppose the invasion of Japanese imperialism, but we do not agree that a post-independence China must remain forever in a state of hostility with Japan. We advocate that through national revolution and a revolution within Japan, the two nations will reach a stage of free association. The same applies to the opposition between bourgeois democracy and proletarian democracy; a higher stage to both of them will be the epoch in which there will be no states and no governments, and this will be arrived at through proletarian democracy. The law of excluded middle in formal logic also supplements its law of identity, which only recognizes the fixed condition of a concept, and which opposes its development, opposes revolutionary leaps, and opposes the principle of the negation of the negation.
It can, therefore, be seen that all the laws of formal logic oppose contradictoriness and advocate the characteristic of identity, oppose development and change of concepts and things, and advocate their solidification and immobility. This is in direct opposition to dialectics.
Why do formal logicians advocate these things? Because they observe things separate from their continual mutual function and interconnections; that is, they observe things at rest rather than in movement, and as separate rather than in connection. Therefore it is not possible for them to consider and acknowledge the importance of contradictoriness and the negation of the negation within things and concepts, and so they advocate the rigid and inflexible law of identity.
Dialectics on the other hand observes things in movement and in connection, and is in direct opposition to the law of identity of formal logic, advocating rather the revolutionary law of contradiction.
Dialectics considers that the contradictions in thought are none other than the reflection of objective external contradictions. Dialectics does not ritualistically adhere to two principles which appear externally to be in a state of mutual conflict (for example, the many antinomies raised by Kant in his four contradictory principles and to which I referred above), but sees through to a thing’s internal essence. The task of dialecticians is to perform the task that those formal logicians have not carried out – study of an object – to concentrate attention on finding out the strength of its contradictions, the tendency of the contradictions, the aspects of the contradictions, and the fixity of the contradictions’ internal relations. The external world and man’s thought are both in motion and are dialectical; they are not static and metaphysical. For this reason, the revolutionary law of contradiction (namely the principle of the unity of contradictions) therefore occupies the principal [p. 247] position in dialectics.
The entirety of formal logic has only one nucleus, and that is the reactionary law of identity. The entirety of dialectics also has only one nucleus, and that is the revolutionary law of contradiction.
Does dialectics oppose the identity of things or concepts? It does not. Dialectics recognizes the relative identity of things or concepts. Why then does dialectics oppose the law of identity of formal logic? It is because the law of identity of formal logic is an absolute law which rejects contradictions. Dialectics acknowledges the identity of things or concepts, but asserts that they simultaneously contain contradictions and are interconnected; this kind of identity indicates the interconnection of contradictions, it is relative and temporary. Since the law of identity of formal logic is an absolute law which rejects contradictions, it cannot but advance the law of excluded middle which opposes one concept changing into another concept, or one thing changing into another thing. Dialectics on the other hand regards the identity of a thing or concept as temporary, relative and conditional; because the struggle of contradictions guides the regularities (guilüxing) of change and development of a thing or a concept, such struggle is forever absolute and unconditional. Because formal logic does not reflect a thing in its true condition, dialectics cannot allow its existence. There is only one scientific truth, and that truth is dialectics.
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Mao is referring here to the conflicts of the transcendental ideas from the