FREEDOM.
101. An action, which is not determined by some other action, is free. God is free, because apart from him there is none other action.
102. Man, as being an image of God, is likewise free; as being an image of the world he is devoid of freedom. Man is, therefore, in his primary commencement or principle free, but not in his end or object to be attained. In the resolution Man is free, in the execution he is not free. The mathematician can select at pleasure any proposition; but having selected it, must solve it in accordance with necessary laws and with definite numbers and figures. Man is a twofold being, compounded of freedom and necessity.
RETROSPECT.
103. Hitherto we have considered simply the arithmetical relations of the primary act and of the universe. We have shown, to wit, that all ideas fluctuate simply under the forms of numbers; that everything was comprised in the 0 + -. Time was only the active series of numbers; motion was the actual arithmetical calculation, namely, the process of reducing numbers to absolute identity, to zero.
104. Life is moreover only a mathematical problem, which, the higher it ascends, approaches so much the nearer to absolute zero in its attainment of the infinity of numbers, becomes so much the more endowed with life.
105. Arithmetic is the science of the second idea, or that of time and motion, or of life; it is, therefore, the first science; mathematics not only begins with it, but creation also, with the becoming of time and of life. Arithmetic is, accordingly, the truly absolute or divine science, and therefore everything in it is also directly certain, because everything in it resembles the Divine. Theology is arithmetic personified.
106. Hence it follows in the most perfect manner, that every science, if it would possess certainty, must resemble arithmetic. Now a science always implies a science treating of certain objects; all certain objects must, therefore, resemble the objects of arithmetic; or all objects, of whatever denomination, whether natural or spiritual, must correspond to arithmetical objects, consequently in idea be numbers, an actual arithmetical problem, as it were the numbers of motion, of life.
107. A natural thing is nothing but a self-moving number; an organic or living thing is a number moving itself out of itself, or spontaneously; an inorganic thing, however, is a number moved by another thing; now, as this other thing is also a real number, so then is every inorganic thing a number moved by another number, and thus ad infinitum. The movements in nature are only movements of numbers by numbers; even as arithmetical computation is none other than a movement of numbers by numbers, but with this difference, that in the latter this operates in an ideal manner, in the former after a real.
c. FORM, SPACE. (Third form, of the Primary Act.)