LITMIR.BIZ

      Notes

       Table of Contents

      1. To the words analysis and synthesis a two-fold meaning is commonly given; for the synthesis is either qualitative, a progress in a series of subordinates from the reason to the consequence, or quantitative, a progress in a series of coordinates from the given part through its complements to the whole. Similarly, analysis, taken in the first sense, is a regress from the consequence to the reason, but in the latter meaning a regress from a whole to its possible or mediate parts, that is, to the parts of parts; hence it is not a division but a subdivision of the given composite. Synthesis as well as analysis are here taken only in the latter sense.

      2. Those who reject the actual mathematical infinite do not take much trouble. They frame a definition of the infinite from which they can shape out some contradiction. The infinite is said by them to be a quantity than which none greater is possible, and the mathematical infinite the multiplicity—of an assignable unit—than which none greater is possible. Having substituted greatest for infinite they easily conclude against an infinite of their own making, as a greatest multiplicity is impossible; or, they call an infinite multiplicity an infinite number, and show this to be absurd; which is plain enough, but a battle with their own fancy only. But if they would conceive of a mathematical infinite as a quantity which being referred to measure as unity is a multiplicity greater than all number; if, furthermore, they would take note that mensurability here denotes only the relation to the smallness of the human intellect, to which it is given to attain to a definite concept of multiplicity only by the successive addition of unit to unit, and to the sum total called number only by going through with this progress within a finite time, they would gain the clear insight that what does not fall in with a certain law of some subject does not on that account exceed all intellection; since an intellect may exist, though not a human one, perceiving a multiplicity distinctly by a single insight, without the successive application of measurement.

      3. Something is considered theoretically when we attend only to what belongs to the thing; practically, when we view what by liberty should be in it.

      4. Höhere Mechanik, p. 354.

      5. Simultaneous facts are not such for the reason that they do not succeed each other. Removing succession, to be sure, a conjunction is withdrawn which existed by the time-series. Yet thence does not originate another true relation, the conjunction of all things in the same moment. For simultaneous things are joined in the same moment of time exactly as successive things are joined in different moments. Hence, though time is of but one dimension, still the ubiquity of time, to speak with Newton, by which all things sensuously thinkable are some time, adds to the quantity of actual things another dimension, inasmuch as they hang, so to speak, on the same point of time. For designating time by a straight line produced infinitely, and the simultaneous things at any point of time whatever by lines applied in succession, the surface thus generated will represent the phenomenal world, both as to substance and accidents.

      6. As the necessity of conceiving space as a continuous quantity is easy to demonstrate, I pass it by. It is a consequence from this that the simple in space is not a part, but a limit. A limit generally, is that in a continuous quantity which contains the limited portion. Space not the limit of another is a solid. The limit of a solid is a surface, of a surface the line, of a line the point; hence there are three kinds of limits in space, as there are three dimensions. Two of these limits, the surface and the line, are themselves spaces. The concept of limit enters into no quantity besides time and space.

      7. The moments of time do not appear to follow one another, since if they did another time would have to be premised for the succession of moments; but by sensuous intuition the actual things appear to descend, as it were, through a continuous series of moments.

      8. The use of this criterion is fruitful and easy in distinguishing principles which enunciate laws of sensuous cognition only from those prescribing besides something concerning the objects themselves. If the predicate be an intellectual concept, its reference to the subject of the judgment, though this subject be thought of as an object of sense, always denotes a mark belonging to the object itself. If the predicate be a sensuous concept, then, since the laws of sensuous cognition are not conditions of the possibility of things themselves, it is not valid as to the subject of the judgment conceived intellectually, and hence it cannot be enounced objectively. Thus in the common axiom whatever exists is somewhere, as the predicate contains conditions of sensuous knowledge it cannot be enounced as to the subject of the judgment, namely, anything existing, generally; hence this formula as an objective rule is false. But converting the proposition, so as to make the predicate an intellectual concept, it becomes perfectly true; thus: whatever is somewhere, exists.

      9. Space and time are conceived as comprehending in them all things in any way offered to the senses. Hence, according to the laws of the human mind, the intuition of nothing is given except as contained in space and time. To this prejudice another may be compared which is not properly a spurious axiom but a play of the fancy, and which may be set forth in the general formula: In whatever exists are space and time, that is to say, every substance is extended and continuously changed. But though people of dense conception are bound firmly by this law of imagination, even they see readily that it pertains only to the efforts of fancy, shadowing forth to itself the appearance of things, not to the conditions of existence.