• Srap Tasmaner
    1.9k
    There are facts that represent other facts. They do this, roughly, by their elements being arranged the same way the elements of the facts represented are. This is pretty intuitive. But it also leads directly to the point that a representing fact, a picture, cannot have as an element any of these: something that indicates it is a picture, something that indicates what fact it is a picture of, something that explains how it represents what it represents, any indication that it is a picture at all. None of those are present in the fact represented, so there is no element in what is represented for any such element of the picture to correspond to. (If there are such things, they will have to be immanent in the picture, but not an element.)

    Thus we get 2.172: "The picture, however, cannot represent its form of representation; it shows it forth." (More below.)

    We're still working through whether and how pictures are veridical. We begin with pictures tied to facts and reality. Thus at 2.15: "That the elements of the picture are combined with one another in a definite way, represents that the things are so combined with one another." That's are. No question that the elements of a picture are combined in a definite way. Of course they are. So what does a picture represent? Obviously a veridical picture shows things combined as they are. What about a non-veridical picture? Doesn't it show things combined in a way that they aren't? (More on this in a moment.)

    We get the rest of the terms we need in the remainder of 2.15: "The connection of the elements of the picture is called its structure, and the possibility of this structure is called the form of representation." Structure makes perfect sense, but form of representation is the possibility of this structure? And then in 2.151 he says: "The form of representation is the possibility that the things are combined with one another as are the elements of the picture."

    So this is what 2.172 says the picture cannot represent. It represents a possible situation in logical space, atomic facts existing or not, and it represents (vorstellen this time instead of darstellen) that things are combined the way its elements are, but it does not represent the possibility of itself having the structure it shows the things it represents having.

    The form of representation is the possibility of this fact, the picture, having a certain structure; what's notable about this structure is that its elements can be coordinated with the things it represents. This is the representing relation. The representing relation is what makes a fact a picture, and this relation is immanent in the picture. (Evidently pictures are not signs at all, are not arbitrary — that will come later. Pictures are models.)

    All this leads up to 2.17: "What the picture must have in common with reality in order to be able to represent it after its manner — rightly or falsely — is its form of representation." So its form of representation — the possibility of the picture having the structure that it does, its elements being combined as they are — this possibility is what the picture has in common with reality.

    So now we can come back to the true and false problem. We can look at this backwards: what the picture does not represent, it cannot get wrong; what no picture represents is its own form of representation. This it cannot help but get "right". But what is it?

    ((Timeout. Possible that "form of representation" is not the best translation here. P&M use "pictorial form" which is scarcely better. The key word here is Abbildung which seems to cover lots of stuff related to projection — reproductions (as of pictures), mappings and such in mathematics. As a matter of fact, it seems likely that this idea of projection — from what is represented to the picture — is exactly what's missing here. LW has all these descriptions that run from the picture to reality — the feelers and all that — but almost nothing in the other direction, which is quite strange.))

    It seems like he was on the verge of saying that a picture has the same structure as what it represents, but he doesn't — he says it has in common with what it represents this form of representation, or projection or mapping. So we can conclude that this possibility of the structure the picture has is also a possibility found in what is pictured.

    Remember my marbles? Physically sorting the red and blue marbles into separate boxes is a way of physically representing the logical partition of the marbles by color, using the marbles themselves. The physical arrangement of them into separate boxes creates a correspondence, a systematic correspondence like a mapping or a projection, between how the marbles are combined or separated and the logical partition. This is a physical model of a logical possibility. That's suggestive anyway.

    I'll stop here and wait for your input, @Posty McPostface. Need clarity on the form of representation, and then we'll make some sense of the true and false business. Maybe that won't be clear until we push into 3 and propositions.
  • unenlightened
    2.4k
    This, I think, is what the Tractatus is doing.


    Print_Gallery_by_M._C._Escher.jpg

    Some interesting mathematical messing with the picture here, but probably a side issue, except to note that they manage to fill in the blank spot, and it contains the whole picture again, twisted upside-down, and so ad infinitum.

    There is a sense in which this is an impossible picture, and thus 'meaningless' in Witty-speak, and another sense in which it is a necessarily incomplete and distorted representation of the reality that we we see that we are part of. I think this goes some way to explain the difficulty of pinning down the relation of world and logical space - gallery and picture.
  • Posty McPostface
    3.9k
    I'll have to get back to you in a while Srap, that's a lot to cover, and really hope someone else can chime in also...

    =]
  • Posty McPostface
    3.9k
    @Srap Tasmaner, before we move on, I feel as though it's important that we still need to cover one important topic to understand the importance of the picture theory and everything else that follows. Namely, I want to delve a little more deeply into 'logical space' and the possible configurations that can be obtained from the arrangement of objects in it. In fact I would want to go as far back and cover some more of Frege, just to give some more backdrop on everything that follows from it, which is a lot. But, that might be too much to ask for, so I'm just going to stick with logical space until I feel that we've adequately covered it to entertained where and how pictures derive their meaning from, in logical space.

    Just to start out in case anyone is interested, here are some useful links:

    http://www.autodidactproject.org/other/wolniewicz1.html
    https://www.quora.com/What-is-Wittgenstein-s-Logical-Space


    I'll read up on it, and delve more into this aspect as time allows me to. I should have everything ready by the end of this week, as I'm still composing everything.

    Sorry for this snag, although an important one we ought to cover.
  • Posty McPostface
    3.9k
    Any input from you, Srap, welcome. If you think it's not worth doing, let me know and we can brush this aside.
  • litewave
    306

    I see that Wittgenstein regards only one possible world as actual. Does he also explain what makes a possible world actual?
  • Posty McPostface
    3.9k


    It is already apparent that Wittgenstein's idea aims at the construction of a geometrical representation for the logic of propositions, and that his "logical space" is an abstract space like the "phase‑space" of physics or the "sample‑space" of the theory of probability. And this leads immediately to the next and most essential question: what are to be the points of this abstract logical space?

    The right answer: to this question has been already given by Stenius (Wittgenstein's 'Tractatus', 1960): every point in logical space is the representation of a possible world! (Stenius' answer is not the only one that has been suggested, but none of the others will do as an interpretation of Wittgenstein's position.) Let's call these worlds "logical points". We have thus:

    Logical space = the totality of logical points,

    The logical the set of logical points which
    place of “p" = would make the proposition "p" true.

    One point in logical space is designated: it represents the actual world. (Since each possible world is incompatible with every other the designated point is unique.) Of course, we do not know its exact position; but if we know a proposition "p" to be true, we know the designated point to lie in that area of logical space which is the logical place of "p". Thus we have:

    "p" is true = the designated point is contained in the logical place of "p".

    According to Frege the denotation of a proposition is its truth‑value; according to Wittgenstein the denotation of a proposition is its logical place (= a set of possible worlds). And 'this makes clear, why formula (F) has to be rejected.

    I believe the answer is presented in the above quote from the website you referenced. I see now that I'm going to have to delve into Stenius' interpretation of the Tractatus. Dang...
  • litewave
    306
    I believe the answer is presented in the above quote from the website you referenced. I see now that I'm going to have to delve into Stenius' interpretation of the Tractatus. Dang...Posty McPostface

    Well, it just says that the actual world is represented by a designated point in logical space. But why is this point designated?
  • Posty McPostface
    3.9k
    Well, it just says that the actual world is represented by a designated point in logical space. But why is this point designated?litewave

    Just think of it as an observer that obtains a specific reality from what they observe, the world. Yeah, it's getting mystical and solipsistic here. As the author notes in that referenced text, this isn't subjective idealism, but closer to objective idealism of Plato and Leibniz.
  • litewave
    306
    Just think of it as an observer that obtains reality from what they observe, the world. Yeah, it's getting mystical and solipsistic here.Posty McPostface

    Was Wittgenstein a modal realist like David Lewis, that is, did he believe that all possible worlds are just as real as the actual one and the actual one is simply the possible world in which we happen to live? I see that in the article you linked, reality is identified with the totality of all possible worlds (the logical space).
  • Posty McPostface
    3.9k


    I think that can't be true because reality obtains from atomic facts and the various possibilities they can configure in to give rise to states of affairs in logical space. Wittgenstien doesn't talk about modalities in the Tractatus per the previous posts I made from the Scott Soames book.

    My personal opinion is that possible realities branching out and diverging from the actual world kind of fade off and become meaningless. Take it for what's that worth, just an opinion. It kind of sounds like a consensus based objective idealism of sorts, which gets deeply elaborated on in his Investigations...
  • litewave
    306
    My personal opinion is that possible realities branching out and diverging from the actual world kind of fade off and become meaningless. Take it for what's that worth, just an opinion.Posty McPostface

    Ok, that's a common intuitive view although upon reflection I fail to see why a particular possible world should be more real than others, or what it would even mean...
  • Posty McPostface
    3.9k
    although upon reflection I fail to see why a particular possible world should be more real than others, or what it would even mean...litewave

    I think it's about which view is closest to reality. The second link I provided talks about homomorphic and isomorphic states of affairs or realities. I think it all comes down to a pragmatic coherentist view in regards to possible worlds and their relationship with the world.

    Edit: Under Fregian logic, I don't think there's room for isomorphic propositions. So my bad.
  • Banno
    2.9k
    Thus we get 2.172: "The picture, however, cannot represent its form of representation; it shows it forth." (More below.)Srap Tasmaner

    Hence showing as opposed to saying is one thing that Wittgenstein carried from the Tractatus into the Investigations.
  • Posty McPostface
    3.9k
    And we still haven't touched the realm of nonsense. Ehh...
  • Srap Tasmaner
    1.9k

    And he got it from Frege.
  • Banno
    2.9k
    Interesting. Where? I'd like to read it.
  • Srap Tasmaner
    1.9k

    It's at least in "Concept and Object" (maybe that's "function"): he tries several ways of explaining the difference between a concept (or function) and an object, explains the trouble with talking about concepts (you're forced to talk about them as if they're objects), and then finally says, I can't tell you the difference but I can show you. And then that's pretty much the point of the predicate calculus: you can see the difference.
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