Page 1 (ii)

Kann ich den Raum in rationalen Zahlen abbilden so kann ich ihn auch in irrationalen Zahlen abbilden. Und ist die eine Abbildung gegeben so ist damit auch schon die andere Art der Abbildung gegeben.

Nun frägt es sich: Gibt es eine bevorzugte, etwa besonders unmittelbare, Art der Abbildung? Ich glaube nein!

Jede Art der Abbildung ist gleichberechtigt.

Wie läßt sich aber eine Entscheidung darüber denken welcher Art die Kontinuität des Gesichtsraumes ist?

I can represent space in rational numbers so I can also represent it in irrational numbers.
And the one representation is given so the other way of representation is also already given.

Now the question arises: Is there a preferred, roughly (a) particularly immediate, way of representation? I think not!

Every way of representation has equal rights.

How can a decision be made about which way the continuity of visual space is?

O.K. I'm not really happy with this translation, but I'll go ahead and post it. Here are some of the questions I have about it:

(1) I don't know what to do with 'so' in the first two sentences. The only conjunctive meaning that my dictionary (the Oxford Duden) has is 'however,' but that doesn't seem to fit. I don't know if the English 'so' is a permissible translation, and I'm not sure that works either.

(2) In the third sentence, the clause before the semicolon is literally something like 'Now it asks itself.' I'm assuming this is idiomatic. I also didn't know what to make of the clause between the commas.

(3) Finally, as you can see, I am puzzled by the last sentence. Literally, I arrived at the mangled 'How can a decision think itself...' Unless we're talking about the Unmoved Mover, this can't be right.

The general point seems to be this: We have two different ways of representing space, viz., with rational or irrational points. Neither of these has a claim over the other. So how are we to choose between them when representing the continuity of visual space? As I don't know what these two ways of representing space amount to, I'm not sure what's at stake here.

By the way, the title of the last post should have been 'Page 1 (i).' This post covers the rest of page 1. I also noticed that the dates don't proceed down the page numbers in a linear way, e.g., the last post translates material from February 2nd, and this post translates material from the 4th. But then on page 2, there's more material from the 2nd followed by more material from the 4th. I don't know if this was an editorial decision (for some reason of which I'm unaware), or if Wittgenstein wrote across both pages. The version I have also begins with page 1, goes on to page 2, then skips to page 4, returning to pages 3 then 5. I have no idea what's going on, but I'm looking into it.

Page 1 (i)

Wittgenstein's first entry is on February 2, 1929. It consists of two questions:

Ist ein Raum denkbar der nur alle rationalen aber nicht die irrationalen Punkte enthält?

Und das heißt nur: Sind die irrationalen Zahlen nicht in den rationalen bereits präjudiziert?

Is a space thinkable that only contains all the rational but not the irrational points?

And that only means: Are the irrational numbers not already prejudged in the rational?

If I had to guess (and I do have to because my mathematical training is sorely lacking), I'd say that a rational point is a point that is fixed by rational numbers, and an irrational point is a point that is fixed by irrational numbers. (If that's right, I suppose a problem with irrational points would be that their exact positions can't be given.)

In the Notebooks Wittgenstein says,

So it looks as if the existence of the simple objects were related to that of the complex ones as the sense of ~p is to the sense of p: the simple object is prejudged [präjudiziert] in the complex. (p. 60)

And in the Tractatus,

In logic nothing is accidental: if a thing can occur in an atomic fact the possibility of that atomic fact must already be prejudged [präjudiziert] in the thing. (2.012)

The former concerns the internal relation between a complex and its constituents. The later, the internal properties of objects. But what does it mean to ask whether the irrational numbers are prejudged in the rational? That the former are internally related to the latter?

Philosophische Bemerkungen

Wittgenstein completed the Tractatus in August of 1918. From then until February of 1929, Wittgenstein produced no philosophical writing (aside from a few letters to Russell and Ogden explaining parts of the Tractatus). In January of 1929 he returned to Cambridge to work with Frank Ramsey, and shortly thereafter, began to record his philosophical thoughts in notebooks. The first of these notebooks was titled "Philosophische Bemerkungen" (MS 105 in von Wright's catalogue).

With this blog, I plan to translate MS 105 at the slow but steady pace of one page a week. I will also comment on or ask questions about the translated passages. My reason for doing this is twofold: (1) to work on my German (so corrections are welcome), and (2) to better understand Wittgenstein's philosophical concerns in 1929.