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Is it possible to know the truth value of a statement without knowing any information about that statement?

If no, then to me that would imply that truth values are not absolute and depend on how we interpret the language or symbols that the statement contains. Without knowledge of the statement itself, its truth value is not an inherent property that can be determined, but a consequence of the meaning applied to the statement.

If yes, then to me that would imply that truth values exist independently of our knowledge of the objects or ideas in question. The next question would be whether or not we can access these values despite our ignorance. In a poetic way, "Does truth bear witness to itself?" If I know nothing of mathematics or its symbolic language, can I still know the truth value of "1+1=2" And more to the point, can the following statement ever be true? "I don't know what it is, but I know it's true simply because it's true. I may not know how I know that it is true, or why it is true, but it's congruent with everything else I know to be true."

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    Wouldn't your first sentence be a better title for this question than the current title? The current title is a very different question than the first sentence, i.e. the title is asking whether or not unknown (Statements? Propositions?) have truth values, and the first sentence is asking if we can know the truth value of a statement without knowing anything about the statement. The title doesn't say anything about people knowing the truth value, which make them very different questions. – Not_Here Sep 7 '18 at 22:56
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    We presumably know that the statement is a statement, so "any" in "without knowing any information" better be qualified. Once it is the question will likely answer itself, we know A → A without much information, for example. Your inferences from yes and no answers are rather odd. Just because truth values in some cases can be determined "independently of our knowledge of the objects or ideas in question" does not mean they can always be, and just because some truth values depend on interpretations does not mean all of them do. Finally, "what do you think" questions are off-topic here. – Conifold Sep 7 '18 at 23:03
  • @Not_Here I changed it. Do unknown statements have truth values? Maybe I should make that the question instead. But the original intent of the question was to know if truth values can be accessed by our knowledge faculty without any data or information that would otherwise be needed to prove them. – lurker Sep 8 '18 at 1:17
  • In my dreams it is true. – Seraphina Sep 14 '18 at 6:49
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According to Frege's Theory of Sense and Denotation sentences have sense and denotation (or reference; see : Über Sinn und Bedeutung).

The sense (its "meaning") is a thought, its conceptual content: what we have to grasp in order to understand the sentence.

The denotation is its truth-value.

In order to determine the reference of a sentence, i.e. its truth-value, we have to understand it, i.e. we have to grasp the thought expressed by the sentence: its sense.

In conclusion, according to Frege's theory, it is not possible to know the truth value of a statement without knowing its sense.


Similarly, see Wittgenstein's Tractatus :

4.063 in order to be able to say, ‘ “p” is true (or false)’, I must have determined in what circumstances I call ‘p’ true, and in so doing I determine the sense of the proposition.

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    I do not think the conclusion is right. Frege says that sense determines truth value, he never says the converse. Moreover, he says that to understand the sense of a sentence we must understand the sense of its constituents (compositionality). But one can tell the truth value of “The Evening Star is the Evening Star” without any understanding of what the “The Evening Star" is. More generally, Frege's sense is supposed to be a descriptive truth-condition, and one can easily determine truth value sometimes without understanding the description. – Conifold Sep 10 '18 at 5:36
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Suppose P is a true statement....

In the context of this hypothetical argument, the only thing we know about P is that it is true, and anything that is a consequence of that fact.

Whether knowing "P is true" counts as "knowing information about P" I'll leave up to your definition of what the latter phrase means. However, I imagine "yes, it does" holds for the more useful notion of "knowing information", for which the answer to your title question is "no", but for fairly trivial reasons.

  • Ooh, this is a nice take - does the act of quantifying over true statements require the possibility of sentences having truth values independent of their informational content? – Paul Ross Sep 9 '18 at 12:54
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I'm assuming a reading of the question that goes ".. without knowing any other information about the statement", because if knowing its truth value counts as "knowing information", then the question becomes trivial, in the sense that such a situation cannot arise, due to internal contradiction: to know its truth value would imply knowing information about it, under that interpretation, so the situation of knowing the former but not the latter can't arise.

On that interpretation, I suspect the answer is "yes", because you can know a truth value without other information about the actual statement itself (as distinct from the medium it's embedded in). For example, if I give you a sealed envelope and tell you it contains a true statement.

What you can't necessarily do is verify the truth value of the statement, without at least some further knowledge beyond a bare statement of its truth value. But that's a whole other question...

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I would say it is impossible to not know anything about a given statement. At the very least, we know what language it is in. If we don't know that, then we cannot understand it, and consequently cannot assess its truth value, because we don't understand its meaning - and, of course, do not know even if it is a statement at all.

All statements, however, are highly dependent of pragmatics. Take for instance a trivial statement, that is trivially true, like,

The sky is blue.

It is easy to see that this is "true" in an abstract sense (the Earthan sky is usually blue, at least during the day). But exactly because of its triviality, it is unlikely that we will hear it as a statement about an inherent property of the sky.

It is contextually used as a synonym to "the sky is clear" (and that because of a quirk of English language; in Portuguese for instance there are two distinct statements, "o céu é azul" - the sky is usually blue -, and "o céu está azul" - the sky is now blue -), with two distinct meanings, that cannot be used interchangeably).

It is also used as a benchmark for the truth value of other statements, often hyperbolically ("The Mariners will win this game, as sure as the sky is blue", meaning we are very sure that the Mariners will win the game).

But it is untrue whenever we are not talking about the Earthan sky on daylight (the sky is pink on Mars, and black on Moon, and even on Earth, at night), and in an habitual aspect (it is grey when it rains, and pink-and-orange at dawn, for instance).

Those issues are usually disambiguated by context, both linguistic (what are we talking about) and extra-linguistic (where we are, and when). Which means that the context usually offers us the necessary information about the statement; when it doesn't, ambiguity arises, and, with it, sophisms, jokes, and misunderstandings.

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