Begriffsschrift (English) by Gottlob Frege

By Gottlob Frege

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G. on paper, and proceed to prove the judgment by showing, through the use of the diagram, how the angles must add up to 180 degrees. The specific procedure is well discussed at A 7 1 3 - 2 4 / B 741-52, from which the following is an extract: [The geometrician] at once begins by constructing a triangle. Since he knows that the sum of two right angles is exactly equal to the sum of all the adjacent angles which can be constructed from a single point on a straight line, he prolongs one side of his triangle and obtains two adjacent angles, which together are equal to two right angles.

A716-17/B744-5) The essential ingredients in this example are, I think, these. ) are ones that we devise for ourselves, entirely a priori, 'without having borrowed the pattern from any experience' (A 713/B 741). Second, although the figure (the triangle) which we draw on paper is, of course, an empirical one, the way that we use the figure in the demonstration is entirely 21 CRITIQUE OF PURE REASON independent of any of the contingencies of this particular drawn figure (its size, the colour of the drawn lines and so on).

Time contains only relations, three of them: 'succession, coexistence, and that which is coexistent with succession, the enduring' (B 67). What this comes to is that everything that appears to us, whether in space or as a mere modification of the subject's own thoughts, must do so under the aspect of time, and in accordance with one or more of these three time relations. For instance, when we experience spatial objects, and their states, we must always perceive them as coexisting or in succession (with their substance remaining - enduring - throughout any change).

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