Let's say you say this country thought that this country was evil.

This is neither false or true, because it's not like every people in the country had the same opinion. Maybe it's 70%, but using the term country here makes the statement inaccurate, but not entirely untrue. What do you call these type of statement, or something between truth and lie?

  • The example you gave can be true or false. Countries are usually defined by their institutions e.g. government. Analyzing if the actions and/or policies of an institution is enough to determine if it is immoral. It should be noted that an institution can be immoral without every member being immoral (e.g. slaves in slavery). I did not put this as an answer because you are asking a perfectly valid question, but gave a flawed example. – E Tam Apr 29 at 4:09
  • A proposition is a statement that's either true or false. A statement doesn't have to be a proposition. For example, "Look out!" is neither true nor false. It's not a proposition. It's just a statement. – user4894 Apr 29 at 4:38
  • There are lots of things that are neither true no false for different reasons, your example falls under the broad category of "opinion". There are also intermediate truth values, truth value gaps, and statements that are not meant to be true or false at all, like questions and commands. – Conifold Apr 29 at 5:22

In systems of formal logic, you can go from having two truth values (True or False) to infinitely many truth values. If something is neither True or False, it can be deemed as Indeterminant. One type of infinitely many-valued logic is Fuzzy logic. It is a logic that assigns a value from 0 to 1, where 0 is completely false and 1 is completely true. This logic can express partial truth.

  • People always bring up fuzzy logic but it does not actually work for any kind of logical reasoning. Consider that A∧A is supposed to be equivalent to A. – user21820 May 1 at 3:32
  • @user21820, your comment is irrelevant to my post and the original question. I was only using fuzzy logic as an example of a logic with infinitely many truth values. I was not talking about the utility of fuzzy logic or its effectiveness in solving problems. – Anon1313 May 2 at 2:07
  • My comment is relevant because the asker explicitly asks about statements ostensibly about the real world. By mentioning fuzzy logic in your post, you are implying that it can be used to deal with real-world statements of the kind in the question with unclear truth value, which is wrong. – user21820 May 2 at 13:11

There are several ways in which a statement can be neither true nor false:

  • Indeterminant with an assigned truth value between 0 and 1.
  • Probabilistic, expressing a probability that it might be true. Such statements are common in quantum physics, as exemplified by Schroedinger's cat.
  • Paradoxical, such as "this statement is untrue".
  • Meaningless, often defined as unprovable, untestable or unfalsifiable.

Not sure if I have missed any out.

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