## Ongoing Tractatus Logico-Philosophicus reading group.

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"A proposition determines a place in logical space."

SO propositions are found in logical space.

Is that what 3.4 says?
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Gee, thanks.
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Logical space contains propositions connected by logical operators. When those propositions are facts, logical space is the world. The truth or falsehood of a (atomic) fact changes nothing else in logical space - that is, they facts are independent one of the other.

SO logical space is a grammatical system. Substance provides the interpretation of that logical system. That interpretation is in the form of facts.

I'm in agreement here. I just wanted to highlight that there is no infinite regress here, which presupposes substance in the form of atomic facts composed of objects (or vice-versa), meshed together giving rise to facts through the structure of logical form, which all takes place in logical space. So, in every possible world, objects obtain (are existent to use W's terminology) equally, and all propositions are equal in merit (jumping ahead a little).

SO, do we now move on to logical form or facts? I feel as though we've covered facts already so many times... We can also mention modality, which Wittgenstein talks about a little in terms of what is possible and necessary.

Edit: Rejigged the wording a little.
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I'm going to upload the companion I'm using, which is excellent. Anyone else welcome to refer to it too, as we go along. Any other companions welcome.
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I hope this clarifies the issues we've been having about states of affaris and atomic facts, @Srap Tasmaner

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Are the elements of logical space obtaining and non-obtaining atomic facts, or are the elements of logical space the obtaining and the non-obtaining of atomic facts?

To answer this better here is a passage from the companion I'm using, which should clarify the issue:

The remainder of the 2.01's (up until 2.0141) are concerned with the relation between objects and atomic facts; and Wittgenstein returns to the topic in the 2.03's. Wittgenstein is concerned to explain here certain complicated relations of dependence and independence. Objects are both, in one sense, dependent on, and, in another sense, independent of, atomic facts. Atomic facts are, in a sense, dependent on objects, despite themselves being the most basic organic unities in the world.

Objects have to be, in a sense, independent of atomic facts, if we are to make sense of the idea that atomic facts are composed of objects. They are independent of atomic facts in the following sense. Objects appear in combination with one another, in atomic facts, but the very same objects could have existed even if those particular atomic facts had not existed. Suppose that there is an atomic fact that Bill is to the left of Ben, in which the objects Bill and Ben stand in relation to each other. Bill and Ben could have existed, even if they had not stood in that particular relation to each other (if Bill had been to the right of Ben, for example). The crucial point here is that atomic facts are contingent: they are what is actually the case, but might not have been. The independence of objects from atomic facts consists in this: the existence of objects does not depend on what is actually the case, but simply on what is possible.
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Cool. I've been reluctant to rely on an interpreter because, well, what an interpreter gives you is an interpretation. But I'm coming around. We'll just treat Michael Morris as a virtual participant in our little group. He doesn't get the last word, but he gets a word, and that's bound to be helpful.

I want to talk about these two, which should be a way into logical form:

3.1431 The essential nature of the propositional sign becomes very clear when we imagine it made up of spatial objects (such as tables, chairs, books) instead of written signs.

The mutual spatial position of these things then expresses the sense of the proposition.

3.1432 We must not say, “The complex sign ‘aRb’ says ‘a stands in relation R to b’”; but we must say, “Thata’ stands in a certain relation to ‘b’ says that aRb”.

One natural way to approach representation is in terms of things: a picture that shows things that actually exist is on its way to being a true picture; if it shows them related as they are in reality, or better, were at a specific time and place, then it's true. There's some of this in TLP, because we get the correspondence between the elements of the picture and the components of the facts it presents.

But what LW says is that the picture represents its sense. And in 3.1431 the arrangement of some physical things can express the sense of a proposition — and I think here we're not talking about propositions about those tables, chairs and books. I think the example we want is something more like this: you're explaining, say, how a figure can be translated in plane geometry, but drawing it on a blackboard with multiple chalk colors is just a confusing mess, so instead you cut out a shape, lay it on a piece of graph paper and then slide it from one position to another. This would be a way of using things to say what you can also say in (x, y) notation. Both are models. Both express the sense of a proposition.

What's puzzling though is that we seem to still need the isomorphism between the elements of a model and some special designated objects — which gets to my confusion over @Banno's remarks. The model is a model of something: it agrees or disagrees with what it models, represents it rightly or falsely. Do we say that what is modeled also expresses the sense of a proposition, and that the model and what is modeled agree if they express the same sense?
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The model is a model of something: it agrees or disagrees with what it models, represents it rightly or falsely. Do we say that what is modeled also expresses the sense of a proposition, and that the model and what is modeled agree if they express the same sense?

Well, going back to 1.1, The world is the totality of facts, not of things.

So, no. Pictures don't represent things, but facts.

About sense, I'm not quite there yet.
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isomorphism

This could use some expanding on. What do you think?
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This could use some expanding on.

I mean what LW means when he talks about correspondence:

2.13 To the objects correspond in the picture the elements of the picture.
3.2 In propositions thoughts can be so expressed that to the objects of the thoughts correspond the elements of the propositional sign.
3.21 To the configuration of the simple signs in the propositional sign corresponds the configuration of the objects in the state of affairs.
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About sense, I'm not quite there yet.

We already know that "how things might stand in logical space" — what atomic facts obtain and what don't — is the sense of a picture, and thus the sense of a proposition. This is what is expressed and what is asserted to be the case.

If I assert that the cat is on the mat, what I assert is that a certain state of affairs obtains, that such-and-such is how things stand in logical space. That's the sense I'm expressing. Is there an identification of facts (broadly) and senses in the offing here? "That the cat is on the mat" is a fact, and it's a sense I can represent, express, model. The question is whether this cat's being on this mat is itself an expression of the sense of the proposition that the cat is on the mat.

Propositions and reality are said to share the logical form. Some facts are isomorphic to other facts given the right mapping (the logical form of representation). But there's some trouble here about "sense": are we saying that we get these correspondences because there are underlying structures in common, or do we in essence just project linguistic structure onto reality? We're accustomed to saying that a proposition expresses something about the world. But there's an option here to say that the fact itself is an expression of the same thing, the sense, that the proposition expresses.

Is my puzzlement clear yet?
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I'm not quite sure; but, I have the feeling that Wittgenstein deviated from Frege and Russell. I don't think there is much isomorphism due to not associating a fact, or 'that' sentence with anything else than elements in reality. Notice using 'reality' here, instead of 'world'.

Take 2.1513 for example:

According to this view the depicting relation which makes it a picture, also belongs to the picture.

2.151 The form of representation is the possibility that the things are combined with one another as are the elements of the picture.
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I'll get back to you on that.
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Take:
2.1513 According to this view the depicting relation which makes it a picture, also belongs to the picture.
2.172 The picture, however, cannot depict its form of depiction; it shows it forth.

And, the version of Wittgenstein's stipulative isomorphism becomes clear.

So, hence saying and showing are not the same, or where one finds oneself at the limit of saying, then showing becomes necessary.
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The world is structured in a certain way: (a) it divides into facts; and (b) facts have a certain structure of their own.

When we come to talk about sense-- pictures, thoughts, propositions-- we note that these are also structured in a particular way: the picture and the propositional sign are facts that each have a structure that mirrors the structure of facts, or, rather, possible facts, ways things might be, and either are or aren't. This is their sense. It is what they say. (What they cannot say, what is not part of the sense of a picture or a proposition, is the logical form itself, which they show.)

In "practical" or operational terms, this being the case means that learning about the structure of models is learning about the structure of facts and the world. Else representation is impossible. I guess the question is whether saying that facts have logical form amounts to saying facts have propositional form, are the expressions of propositions, rather than saying propositions also have logical form.
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It's possible that this amounts to an ontological question, and Morris suggests that TLP is deliberately neutral on ontology, in at least some respects.
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Is my puzzlement clear yet?

So, as promised, I'm returning to this post. Yet, I'm not entirely sure what the question is. If you could possibly specify further what you are asking, I might be able to answer better.

My impression is that sense arises out of modality of possible configurations of atomic facts. Nothing more or less. Logical form is inherently expressed through this modality. I know it sounds like something what Kripke might possibly say; but, it seems correct.
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the picture and the propositional sign are facts that each have a structure that mirrors the structure of facts, or, rather, possible facts, ways things might be, and either are or aren't. This is their sense.

Yeah, this I agree with.

It is what they say. (What they cannot say, what is not part of the sense of a picture or a proposition, is the logical form itself, which they show.)

Yes, they complement one another. What isn't said is said through what can be said. Kinda tautologous.

I guess the question is whether saying that facts have logical form amounts to saying facts have propositional form, are the expressions of propositions, rather than saying propositions also have logical form.

Thank you for participating in this (nearly) abandoned reading group for the matter.
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Banno says logical space is populated by propositions. I thought it was populated by possible facts. Propositions have a structure that mirrors the structure of facts, so maybe this makes little difference, in one sense. BUT-- IF a propositional sign, which is a fact that has the form, the structure of another fact, can consist of any sorts of things, not just entities we're accustomed to thinking of as symbols, THEN might we not say the fact itself is in effect a propositional sign, a perceptible expression of a proposition?

That seems slightly crazy, but it dissolves the difference between me and Banno (and it's terribly important we do that). It does mean thinking of propositions as something a bit different from, you know, sentences we assert.

Not clear to me yet. Rest of the book will make it all plain as day, I'm sure.
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Good discussion. (I skimmed a little.)

Here's a point against my suggestion: you would have to say that the projection of the fact onto itself is trivial.
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This is from the Morris companion:

The proposition is what we have when we have a string of signs with the range of possible grammatical combinations fixed. It is, therefore, only the constituents of a proposition — rather than a mere propositional sign — which can be correlated with items in reality. In effect, a proposition is a certain kind of sign with the syntax fixed. Contrary to some modern uses, syntax brings in more than what we are given with the mere signs: we can have two examples of the same sign, which have different syntax; syntax provides us with the range of combinations.
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Yeah but that misses the whole issue by talking about signs.
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Yeah, I leave it to Banno to clarify the issue.
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Well the way I've done this we do get a solid distinction we can work with, between trivial and non-trivial mappings or projections.

It is curious to think of a possible fact actually obtaining as a possibility being expressed. The projection we need, the form of representation, would be a mapping onto substance.

Not sure if the projection is going in the direction W wants though...
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Oh, and "expressed" can be glossed as "becoming perceptible by the senses," like a propositional sign. That's cool.
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Yeah, I leave it to Banno to clarify the issue.
:wink:

I would have thought that things like "Pp" and "PPp" were our symbols. Allow them to picture the world, then they have what we would now call an interpretation, in terms of what WItti called substance, and they become propositions. The ones that are true are facts.
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I would have thought that things like "Pp" and "PPp" were our symbols

So how do you read 3.1431?
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