5. Time and Space¶
Core Argument¶
In his philosophy of nature, Herr Dühring launches a polemic against his predecessors, denouncing them as charlatans, and proposes a “law of definite number”. He argues that infinity, conceived as an unlimited numerical series, possesses only one direction; a retrogressive infinity would require a counted infinite series, which he deems a contradiction. From this, Dühring concludes that the chain of causes must have a beginning—a final cause—and that the number of all independent things, including the smallest particles, must be definite. All actual division therefore has a limit, necessitating atoms; all periodical processes must have begun; and all differentiation must originate in a self-equal state. This state could exist from eternity only if time were not composed of real parts.
Engels demonstrates that Dühring’s arguments are copied verbatim from Kant’s First Antinomy of Pure Reason (1781), which presents both the thesis that the world has a beginning in time and space and the antithesis that it does not, as an insoluble contradiction. Dühring suppresses the antithesis. Engels argues that real infinity in time and space has no end in any direction, unlike a series starting from a first term. The “counted infinite series” is a contradictio in adjecto, presupposing a beginning. Infinity is a contradiction, an unending process. Dühring’s self-equal initial state, containing no change, cannot generate motion without an external “initial impulse”—a reintroduction of God.
Dühring admits that absolute identity cannot itself produce transition to change, nor can absolute equilibrium pass into motion. He offers three arguments. First, he claims the difficulty is the same for any small link in the chain of existence. Engels counters that natural science explains transitions between links as transfer or transformation of prior motion, never as motion arising from nothing; the issue here is precisely motion from immobility, that is, from nothing. Second, Dühring invokes a “bridge of continuity”. Engels retorts that the continuity of immobility consists in not moving; without an act of creation, nothing can come from nothing, not even a mathematical differential. Third, Dühring notes that present-day mechanics cannot explain the transition, but suggests the mechanical theory of heat may provide a bridge, though processes take place “somewhat in the dark”. Engels concludes that Dühring leaves us in the dark, having produced only lame, false arguments. Despite this, Dühring claims to have provided real content for the idea of self-equal stability from the behaviour of matter and mechanical forces. Engels notes one consolation: Dühring asserts that the mathematics of other celestial bodies rests on no other axioms than our own.