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Since I don't have any philosophy background, please answer as simply as you can! Thank you!

mohammad-ghasemi
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    This is rather a question for etymologists. My opinion is that 'false' is an un-nuanced.. bare status.. whereas untrue is slightly pejorative... Meaning 'a lie'.. or possibly an accidental mistake. Either way... Untrue is a more emotive word. – Richard Dec 06 '18 at 00:54
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    I wonder if there may be some distinction between false and untrue if one considers paradoxes. The paradox would not definitely be false. Perhaps the most it would be is untrue. – Frank Hubeny Dec 06 '18 at 01:14
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    This may be a duplicate: https://philosophy.stackexchange.com/q/38542/29944 – Frank Hubeny Dec 06 '18 at 01:22
  • Quoting from a comment in the other post: 'Google "law of excluded middle"' – Tim kinsella Dec 06 '18 at 02:51
  • See dictionary : [untrue](https://www.merriam-webster.com/dictionary/untrue) : not according with the facts : FALSE. – Mauro ALLEGRANZA Dec 06 '18 at 07:08
  • Consider the following view. We map True to 1(T=1) and False to 0(F=0). In a discret binary set that only contains 1 an 0, Untrue (U≠1) is always 0. In this case untrue=false. However we can imagine a Set that contains all real numbers between 0 and 1. Keeping the same mapping F=0, T=1 and U≠1. U can now be any number from 0 to 1 exept 1 (0<=U<1). We can further see that we could also exclude False and still not have an empty set for U. Untrue itself still is a binary operator but allows to model non binary cases by not equating nearly true results with false. – CaZaNOx Dec 06 '18 at 22:31
  • I forgot to spell it out clearly that untrue is refereing to True. By negating it it gets defined as it's logical opposit and therefore is deductivly derrivable. While false and true are technically speaking just assignments that are not necessarily deductivly derrivable from each other. You could obviously argue that False has to be understood as the logical opposit and can therefore be seen as Untrue. However what you are doing in this case is assigning False to Untrue to create this relation. This assignment is not obviously correct as seen in the example above. – CaZaNOx Dec 06 '18 at 22:51

2 Answers2

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I went to the market where I ate an apple.
Did I go to the market?
"Yes" = true
"No" = false
"I ate an apple" = untrue

Untrue is equivalent to the expression "that's not even wrong!"

EternalPropagation
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mohammad-ghasemi, welcome to PSE.

A dictionary will tell you that 'untrue' = 'false'. But your question is about conceptual distinctions expressed in ordinary language. A dictionary does not always do justice to such distinctions. Nor is the matter to be settled by saying by the principle of bivalence in logic that there are only two truth values - true and false - so that 'untrue' can only mean 'false'. Ordinary usage is the key here, neither dictionaries nor logical principles. It's a question of how a language community uses language.

I think we use 'false' when we want to assert the contradictory of a true statement or at least of a statement we take to be true. 'I met X last week' (true); 'I did not meet X last week' (false). The sentence 'I met X last week' is at least by ordinary language standards not vague, ambiguous, lacking in a unique meaning. So if it is true, there is a clear contradictory,' I did not meet X last week', which is false.

In contrast we use 'untrue' when e.g. vagueness creeps in. In a familiar example, due to JL Austin, 'France is hexagonal'. I don't want to say simply that this statement is false, because there is a vague sense in which France is hexagonal. So instead of saying, 'It's false that France is hexagonal', I say 'It's untrue that France is hexagonal' - meaning that it is not strictly (geometrically) true that France is hexagonal but not simply (in common sense, everyday terms) false either.

'False' indicates definite, unqualified error; 'untrue' suggests that the statement does not have a unique meaning and cannot be endorsed as it stands. So I might say, 'France is hexagonal' is untrue because it is not geometrically hexagonal but it is approximately hexagonal on the map. 'Untrue' qualifies my rejection; 'false' does not.

In referring to vagueness I have in mind only one way in which the false/ untrue distinction might come into play. This is not a full account; I'm sure other angles are possible.

Geoffrey Thomas
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