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According to Wittgenstein's tractatus,

  • A fact is composed of atomic facts.
  • An atomic fact corresponds to an elemental proposition. (Picture theory)
  • A proposition is a series of elemental propositions connected by logical connectives such as ∧, ∨ and ¬. The truth value of a proposition is determined by the truth values of its elemental propositions and can be calculated by using the laws of logic.
  • Thus, a fact is representable by a proposition.

So it seems like to me that Wittgenstein assumes that:

  1. All facts(propositions) are either true or false, and,
  2. The laws of logic are valid.

Here is my question. Does Wittgenstein think that the above assumptions hold because they are the nature of the universe, or because they are the way humans perceive the world? Plato claimed the former, Kant claimed the latter. Where would Wittgenstein stand?

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  • A fact can be false?
    – David Gudeman
    Aug 19, 2021 at 15:40
  • I’ll have a fuller answer soon, but just to note that tractarian Facts are not the sort of thing that can be true or false - they just are the case, and reality is only composed of (positive) facts! This change of emphasis is important because, as he says, the Fact (rather than the object) is the fundamental building block on which everything else stands.
    – Sofie Selnes
    Aug 19, 2021 at 15:55
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    Bearn has an insightful discussion of this in Waking to Wonder, p.67ff. Wittgenstein analogizes laws of logic to laws of ethics, they are not claims but commands. Commands can be neither true/false nor valid/invalid, but breaking logical ones leads to the text losing sense. If we say that it is our practices that make it so then the next question will be what it is in the world that makes our practices that way. And vice versa, what it is in our practices that makes the world show itself thus. Ultimately, the question should be not answered but silenced, solution is in vanishing the problem.
    – Conifold
    Aug 20, 2021 at 0:20
  • Bearn, Waking to Wonder
    – Conifold
    Aug 20, 2021 at 0:21
  • The laws of logic are presupposed by Wittgenstein, in the same sense that the laws of addition and subtraction are presupposed in maths. If the first doesn't work, anything subsequent becomes impossible, and then Wittgenstein (and everyone else) would be incapable of even the most basic forms of reasoning. Logic is axiomatic. You might as well ask why people assume they can breathe.
    – Ted Wrigley
    Aug 21, 2021 at 5:41

1 Answer 1

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(1) Propositions can be true or false. Facts are states of affairs in the world that true propositions correspond to. (2) The assumptions you listed (i.e. propositions are either true or false, and the laws of logic are valid) aren't assumptions in Wittgenstein's Tractatus. They're definitions. If a statement is not either true or false, it's not a proposition. If a rule of inference ("law of logic") isn't valid, it's not a rule of inference ("law of logic"). "Valid" is defined as truth-preserving. He uses truth-tables to demonstrate which rules of inference are valid. The ones that don't pass the truth-preservation test don't get to be laws of logic. So it doesn't have to do with the nature of the universe or with the way humans perceive the world. It just follows from the rules of the game he constructed. Logic and math don't describe reality; they're constructed languages for performing operations on representations of reality. If a given representation represents reality accurately, the valid logical and mathematical operations that we conduct on those accurate representations will never produce any inaccurate representations.

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