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I'm trying to understand Wittgenstein, but two of his most oft quoted statements seem to me to be implying contradicting things. I understand that later Wittgenstein did refute a lot of his earlier ideas, but these statements both come from the Tractatus.

The statements are:

4.1212 What can be shown, cannot be said.

and

5.6 The limits of my language mean the limits of my world.

The first statement seems to imply that Wittgenstein believes there are things that we can know (and be shown), but that we cannot say (express in our language). However, the second statement seems to imply that if we cannot express it in our language, then it cannot be known (be a part of our world).

Can someone clarify this for me?

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    You've got to be very careful with paraphrasing! It is not at all the same thing to say that a proposition can be known and that a state of affairs is a part of our world. There is a very crucial relation of demonstration or standing in for that constitutes a substantial theory of connecting these things in Wittgenstein's work. – Paul Ross Aug 9 '14 at 9:28
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This is undeniably difficult. The section at 4.1212 onwards is where he gives his take on the internal/external relations doctrine. The holding of internal relations cannot be asserted by propositions, but rather shows itself in the propositions (in den Saetzen), by an internal property of the proposition which presents a state of affairs. A property is internal if it is unthinkable that its object does not possess it (4.123).

He also says (4.121) that propositions cannot represent logical form, which mirrors iself in propositions. “That which mirrors itself in language, language cannot represent”. A proposition shows the logical form of reality, or exhibits it (er weist sie auf).

So in this sense, what can be shown (logical form, internal structure etc) cannot be said.

Passing to “The limits of my language mean the limits of my world”. I imagine he means, consistent with what he says above, is that whatever falls within the limits of our language includes all that can be said. What can be shown, however lies outside our language, or perhaps ‘at the limit’.

Note also his remark later on at 5.6331 about the form of the visual field – hard to explain without his diagram, which shows the eye and the visual field on the page itself. He means that the eye itself would never appear in the visual field. “The subject does not belong to the world but it is a limit of the world”.

So in summary, “What can be shown, cannot be said” and “The limits of my language mean the limits of my world” are not necessarily contradictory, if ‘what can be shown’ is at the limits of language and the world.

Note also, if what can be known is limited to what is said by a proposition, rather than what is shown, then there are things that can be shown, but which we cannot be said to know. If that is the case, his first statement does not imply there are things that we can know (and be shown), since what is shown is unknowable, in the sense we cannot say what it is, in a proposition of the form 'S knows that p'.

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I haven't done a huge amount of reading, but read and think I understood the Tractatus [like 7 years ago]

The first statement seems to imply that Wittgenstein believes there are things that we can know (and be shown), but that we cannot say (express in our language). However, the second statement seems to imply that if we cannot express it in our language, then it cannot be known (be a part of our world).

Let's go back to the two passages:

4.1212 What can be shown, cannot be said.

5.6 The limits of my language mean the limits of my world.

You've glossed "show" as "know" and then "world" as "possible knowledge". This obviously isn't helpful for you.

I would actually read 5.6 as meaning that what I cannot say I cannot say* is in my world, and then read 4.1212 as meaning that some things cannot be said. The only corollary of that is: there are some things that I cannot say are in my world - I cannot say everything is a "fact" [see 1].

I hope I'm not too rusty...

  • If he meant that what I cannot say is not actually in my world, then not only is anything we are shown outside our world, but because I cannot say that it is false that colourless green clouds sleep furiously, so in my world it is not actually false that colourless green clouds sleep furiously, and so it is true that colourless green clouds sleep furiously.
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I do not see any contradiction in the Wittgenstein's statements you have given, but it would appear that statement 4.1212 could be 'improved' by saying "What can be shown, needs not be said", for the obvious reason that what is demonstrated can be apprehended by the senses, therefore becomes more memorable by virtue of being seen rather than by sounds/words. But with Wittgenstein one has to be doubly aware that he uses language with an intense precision, so that first 'natural' reactions by readers are likely to be misplaced. The use of 'shown' and 'said' are left without contexts, and this could imply a meaning which is difficult to fathom (and I am not trying to give a Derridean rendering of the sentence). Statement 5.6 does not seem to me to contain any noticeable contradiction. It could be interpreted variously, but given Wittgenstein concentration on Language (among other things), we could venture to say that the limitations of my knowledge regarding language (my mastery of it) also limits the extent of my mental/intellectual world, and possibly even the knowledge of the world surrounding me. This, because thought, perceptions and analyses are normally manifested through mental processes that depends on words/language for their quality and exactness. A more limited grasp of my language would affect the quality of those mental processes and their expression..

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