• Banno
    2.9k
    On the introduction of a name for something logically simple, a definition is not possible. There is nothing for it but to lead the reader or hearer, by means of hints, to understand the words as is intended.
    Nice. Thanks.
  • Srap Tasmaner
    1.9k

    LW tends to talk about the logical constants this way too. I can't remember if that's in Frege, but it might be.
  • Posty McPostface
    3.9k
    Sorry, @Srap Tasmaner; but, I'm at a loss here as what to say. I'm reading the companion provided by another member here, that seems to clarify all these issues. I'm somewhat slow to read it, and it's taking a lot of time to cover everything up until picture theory of meaning.

    It's a really good companion, from what I gather. If you're interested in it helping us guide through the Tractatus, let me know.
  • Srap Tasmaner
    1.9k

    Been away for a few days, so I'll try to get back into this.

    We're going to work on logical space some more?
  • Posty McPostface
    3.9k
    Been away for a few days, so I'll try to get back into this.

    We're going to work on logical space some more?
    Srap Tasmaner

    Glad you're back.

    It's a crapshoot. Do you think we need a companion to help guide us? As I'm reading the Routledge one provided in the first page of this thread, I feel like it can only help us along the way.
  • Banno
    2.9k
    We're going to work on logical space some more?Srap Tasmaner

    That'd be pleasing. What do we find in logical space?
  • Posty McPostface
    3.9k
    What do we find in logical space?Banno

    Substance.
  • Banno
    2.9k
    The facts in logical space are the world.

    No substance. Facts and logical operators.
  • Posty McPostface
    3.9k


    2.021 Objects form the substance of the world. Therefore they cannot be compound.

    2.024 Substance is what exists independently of what is the case.

    A substance is something which remains the same thing through change, although change is ambiguous here and rather irrelevant according to Wittgenstein. Substance is what is constant across all possible differences in the atomic facts.
  • Banno
    2.9k
    A proposition determines a place in logical space.
    SO propositions are found in logical space.

    3.42 A proposition can determine only one place in logical space: nevertheless the whole of logical space must already be given by it. (Otherwise negation, logical sum, logical product, etc., would introduce more and more new elements in co-ordination.) (The logical scaffolding surrounding a picture determines logical space. The force of a proposition reaches through the whole of logical space.)
    There's already a holism coming through here.
  • Banno
    2.9k
    But
    2.0231 The substance of the world can only determine a form, and not any material properties. For it is only by means of propositions that material properties are represented—only by the configuration of objects that they are produced. 
  • Posty McPostface
    3.9k


    2.025 It is form and content.

    The thinking here is something like this. There must be something common, something constant across all possible alternative scenarios. This is (at least close to) what is known traditionally as substance. But what is actually required, according to Wittgenstein, is a common form. What might be meant by ‘form’ here? The notion of form has already been introduced in the idea of the form of an object: it is the ways in which that object can combine with other objects to form atomic facts. Wittgenstein introduces a related notion in connection with atomic facts:

    2.032 The way in which objects hang together in the atomic fact is the structure of the atomic fact.

    2.033 The form is the possibility of the structure.

    Form and content become the substance of logical space. (sorry, other way around)
  • Posty McPostface
    3.9k
    Think about it in Kantain terms. There cannot be objects or facts or things without logical space.
  • Posty McPostface
    3.9k
    And finally,

    2.0211 If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true.

    2.0212 It would then be impossible to form a picture of the world (true or false).
  • Posty McPostface
    3.9k
    The structure of an atomic fact is something contingent: it is the fact that its constituent objects are actually combined in the way they are. The atomic fact’s form is quite different: it is (as it were — the reason for this caution will have emerged by the time we have reached the end of the book) the fact that the constituent objects can be arranged like that. This latter ‘fact’ — the form of the atomic fact — clearly has its roots in the form of the constituent objects, since ‘objects contain the possibility of all states of affairs’ (2.014). So there can only be a fixed form, common to all possible worlds, if the objects whose form is the root of the form of atomic facts are also common to all possible worlds. This is why substance is both form and content. It is form, because the form of atomic facts — the possibility of there being such facts — is what is common to all possible worlds. And it is content, because the form of atomic facts is carried in the form of their constituent objects, so there must be things as well as forms, if there are to be the appropriate forms. Hence Wittgenstein says:

    2.026 Only if there are objects can there be a fixed form of the world.

    2.027 The fixed, the existent and the object are one.

    I'm quoting at leisure from the Routledge companion to the Tractatus. Sorry.
  • Srap Tasmaner
    1.9k
    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?

    I think the latter is what's in the text, but I don't know how to understand that. Surely these obtainings and non-obtainings are not entities of some kind in addition to the atomic facts themselves. So I want to say it's the former, the atomic facts themselves, obtaining or not, that are the elements of logical space.
  • Posty McPostface
    3.9k
    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?Srap Tasmaner

    As far as I understand, Wittgenstein uses the terms existent and non-existent, so we might want to stick with that; but, yes-I think so.
  • Srap Tasmaner
    1.9k

    Yes, what? There were two options.
  • Posty McPostface
    3.9k
    So I want to say it's the former, the atomic facts themselves, obtaining or not, that are the elements of logical space.Srap Tasmaner

    Sorry for being ambiguous. I meant to affirm the former you're talking about.
  • Banno
    2.9k
    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.
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