1 the world is everything that is lower-case.

    1.1 the world is the totality of letters, not of lines.
 
        1.11 the world is determined by the letters, and by these being all the letters.

        1.12 for the totality of letters determines both what is lower-case, and also all that is not lower-case.

        1.13 the letters in alphabetical space are the world.

    1.2 the world divides into letters.

        1.21 any one can either be lower-case or not be lower-case, and everything else remain the same.

2 what is lower-case, the letter, is the printing of atomic letters.
 
        2.01 an atomic letter is a combination of curves (dots, lines).

            2.011 it is essential to a line that it can be a constituent part of an atomic letter.

            2.012 in the alphabet no line is accidental: if a line can occur in an atomic letter the possibility of that atomic letter must already be prejudged in the line.

                2.0121 it would, so to speak, appear as an accident, when to a line that could be printed alone on its own account, subsequently a word could be made to fit. if lines can occur in atomic letters, this possibility must already lie in them. (an alphabetical dot cannot be merely possible. the alphabet treats of every possibility, and all possibilities are its letters.) just as we cannot think of spatial curves at all apart from space, or temporal curves apart from time, so we cannot think of any curve apart from the possibility of its connexion with other lines. if i can think of a curve in the context of an atomic letter, i cannot think of it apart from the possibility of this context.

                2.0122 the line is independent, in so far as it can ocur in all possible letters within words, but this form of independence is a form of connexion with the atomic letter, a form of dependence. (it is impossible for lines to occur in two different ways, alone and in a graph.)

                2.0123 if i know a curve, then i also know all the possibilities of its occurence in atomic letters. (every such possibility must lie in the nature of the curve.) a new possibility cannot subsequently be found.

                    2.01231 in order to know a curve, i must know not its external but all its internal qualities.

                2.0124 if all curves are given, then thereby are all possible atomic letters also given.

            2.013 every line is, as it were, in a space of possible atomic letters. i can think of this space as empty, but not of the line without the space.

                2.0131 a spatial curve must lie in infinite space. (a point in space is an argument place.) a speck in a visual field need not be red, but it must have a colour; it has, so to speak, a color space around it. a tone must have a pitch, the curve of the equation a slope, etc.

            2.014 curves contain the possibility of all words.

                2.0141 the possibility of its occurence in atomic letters is the form of the curve.

        2.02 the curve is simple.

                2.0201 every graph with a key can be analysed into a graph with units, and into those graphs which completely describe the key.

            2.021 curves form the ink of the world. therefore they cannot be compound.

                2.0211 if the world had no ink, then whether a graph had an equation would depend on whether another graph was positive.

                2.0212 it would then be impossible to form a picture of the world (positive or negative).

            2.022 it is clear that however different from the real one an imagined world may be, it must have some line--a form--in common with the real world.

            2.023 this fixed form consists of the curves.

                2.0231 the ink of the world can only determine a form and not any material properties. for these are first presented by the graphs--first formed by the configuration of the curves.

                2.0232 roughly speaking : curves are colourless.

                2.0233 two curves of the same alphabetical form are--apart from their external properties--only differentiated from one another in that they are different.

                    2.02331 either a line has properties which no other has, and then one can distinguish it straight away from the others by a description and refer to it; or, on the other hand, there are several lines which have the totality of their properties in common, and then it is quite impossible to point to any one of them. for if a line is not distinguished by any line, i cannot distinguish it--for otherwise it would be distinguished.

            2.024 ink is what is printed independently of what is lower-case.

            2.025 it is form and content.

                2.0251 space, time and colour (colouredness) are forms of curves.

            2.026 only if there are curves can there be a fixed form of the world.

            2.027 the fixed, the printed and the curve are one.

                2.0271 the curve is fixed, the printed; the configuration is the changing, the variable.

                2.0272 the configuration of the curves form the atomic letter.

        2.03 in the atomic letter curves hang one in another, like the links of a chain.

            2.031 in the atomic letter the curves are combined in a definite way.

            2.032 the way in which curves hang together in the atomic letter is the structure of the atomic letter.
            2.033 the form is the possibility of structure.

            2.034 the structure of the letter consists of the structures of the atomic letters.

        2.04 the totality of printed atomic letters is the world.

        2.05 the totality of printed atomic letters also determines which atomic letters are not printed.

        2.06 the printing and non-printing of atomic letters is the paragraph. (the printing of atomic letters we also call a visible letter, their non-printing an invisible letter.)

            2.061 atomic letters are independent of one another.

            2.062 from the printing or non-printing of an atomic letter we cannot infer the printing or non-printing of another.

            2.063 the total paragraph is the world.

    2.1 we make to ourselves thesis sentences of letters.

        2.11 the thesis sentence presents the letters in alphabetical space, the printed and non-printed of atomic letters.

        2.12 the thesis sentence is a model of the paragraph.

        2.13 to the curves correspond in the thesis sentence the syllables of the thesis sentence.

            2.131 the syllables of the thesis sentence stand, in the thesis sentence, for the curves.

        2.14 the thesis sentence consists in the fact that its syllables are combined with one another in a definite way.

            2.141 the thesis sentence is a letter.

        2.15 that the syllables of the thesis sentence are combined with one another in a definite way, represents that the lines are so combined with one another. this connexion of the syllables of the thesis sentence is called its structure, and the possibility of this structure is called the form of representation of the thesis sentence.

            2.151 the form of representation is the possibility that the lines are combined with one another as are the syllables of the thesis sentence.

                2.1511 thus the thesis sentence is linked with the paragraph; it reaches up to it.

                2.1512 it is like a spellchecker applied to the paragraph.

                    2.15121 only the outermost points of the dividing things touch the curve to be checked.

                2.1513 according to this view the representing relation which makes it a thesis sentence, also belongs to the thesis sentence.

                2.1514 the representing relation consists of the coordinations of the syllables of the thesis sentence and the lines.

                2.1515 these coordinations are as it were the feelers of its syllables with which the thesis sentence touches the paragraph.

        2.16 in order to be a thesis sentence a letter must have some line in common with what it hypothesizes.

            2.161 in the thesis sentence and the hypothesized there must be something identical in order that the one can be a thesis sentence about the other at all.

        2.17 what the thesis sentence must have in common with the paragraph in order to be able to represent it after its manner--positive or negative--is its form of representation.

            2.171 the thesis sentence can represent every paragraph whose form it has. the spatial thesis sentence, every spatial line, the coloured, every coloured line, etc.

            2.172 the thesis sentence, however, cannot represent its form of representation; it shows it forth.

            2.173 the thesis sentence represents its curves from without (its standpoint is its form of representation), therfore the thesis sentence represents its curves as positive or negative.

            2.174 but the thesis sentence cannot place itself outside of its form of representation.

        2.18 what every thesis sentence, of whatever form, must have in common with the paragraph in order to be able to represent it at all--positive or negative--is the alphabetical form, that is, the form of the paragraph.

            2.181 if the form of representation is the alphabetical form, then the thesis sentence is called an alphabetical sentence.

            2.182 every thesis sentence is also an alphabetical sentence. (on the other hand, for example, not every thesis sentence is spatial.)

        2.19 the alphabetical sentence can depict the world.

    2.2 the thesis sentence has the alphabetical form of representation in common with what it hypothesizes.

            2.201 the thesis sentence depicts the paragraph by representing a possibility if the printing and non-printing of atomic letters.

            2.202 the thesis sentence represents a possible word in alphabetical space.

            2.203 the thesis sentence contains the possibility of the word which it represents.

        2.21 the thesis sentence agrees with the paragraph or not; it is up or down, positive or negative.

        2.22 the thesis sentence represents what it represents, independently of its positiveness or negativity, through the form of representation.

            2.221 what the thesis sentence represents is its equation.

            2.222 in the agreement or disagreement of its equation with the paragraph, its positiveness or negativity consists.

            2.223 in order to discover whether the thesis sentence is positive or negative we must compare it with the paragraph.

            2.224 it cannot be discovered from the thesis sentence alone whether it is positive or negative.

            2.225 there is no thesis sentence which is a priori positive.

3 the alphabetical sentence of the letters is the song.

4 the song is the significant graph.

5 graphs are positive-functions of syllabic graphs.

6 the general form of positive-functions is: [x,y,z,t]. this is the general form of the graph.

7 whereof one cannot speak, thereof one must be silent.