# Is there a category for statements that are never true?

I studied logic and found no category for statements that are not impossible but never true (e.g. "The earth is flat.") to differ them from statements that could be true ("I'm wearing blue shoes.") or that were or are occassionally true ("I drink beer."). Why not? Wouldn't it be hepful to classify not only what is necessarily true and false but also what is or was always or never true or false? I don't think it's the same as a contradiction (e.g. "The small house is larger than the big house.") since a contradiction is false in relation to itself and per definition false whereas a statement that was never true is not impossible and could have been true of another world ("The stock market gained 500 % today").

• Isn't it simply a false proposition? – stevebot Dec 11 '13 at 21:06
• Statements that are never true are generally called official statements. ;) – EvilSnack Feb 11 '20 at 3:20

Tense Logic makes this distinction. In tense logic, there are all of the typical logic connectives plus 4 modal operators {P, F, H, and G} defined as follows:

• Px = "x was true at some time"
• Fx = "x will be true at some time"
• Hx = "x has always been true"
• Gx = "x will always be true"

To use the example you've given of "The earth is flat," we could express it like so:

``````Lx = x is flat   and    e = Earth

~P(Le) ^ ~F(Le)   // It's not the case that the Earth was flat at some time,
// and it's not the case that the Earth will be flat at some time.
or

H(~Le) ^ G(~Le)   // It has always been the case that the Earth is not flat,
// and it will always be the case that the Earth is not flat.
``````

You may also want to explore Modal Logic (from which Tense Logic is an extension). In Modal Logic there are Necessary Truths (things that must be true in all possible worlds), Possible Truths (things that may or may not be true in a given possible world), and Contingent Truths (things that happen to be true in our world but are not necessary). Your examples could all be considered false contingent truths.

• How do you know ~F(Le) is true? – Lukas Dec 12 '13 at 8:22

The way "The earth is flat" differs from "I'm wearing blue shoes" is that the latter sentence includes an indexical: "I." An indexical is a term that can change its reference based on the context in which it's uttered. "You" is another example, as are "this" and "nearby." Sentences containing indexical terms take on different truth-values in a more obvious way than sentences like "The earth is flat" do. But even a sentence like that can vary in truth-value. Suppose I like going to a bar called "the earth." Maybe for some reason I want to say that it's flat, not rectangular like some other bars. My point is that other than that one contains indexicals, there's no difference between the sentences in terms of the relationship between their structures and truth. That is unlike a logical contradiction, which has a structure that makes it false. A false proposition, on the other hand, as stevebot notes, is simply false, because we say that different utterances of sentences (or instances of them in different contexts) sometimes express different propositions, which are true, or false, or possibly something intermediate.

I think you got the notion of contradiction kind of wrong. "There exists a horse and there does not exist a horse" is a contradiction, but not in relation to itself and not per definition. They are never true.

Your example, "The earth is flat", is not never true. It is just not true here, but possibly true.

To clarify your question you should define the scope of "never". Either it means our world, then the simple actual true/false suffices. Or you understand it modally, then something that is necessary false is never true.

Adding to what @Lukas said, I think the only statement I can think of that never is true is "This statement is false", and that's known as the liar paradox.

• What about: "There exists a squared circle", on my book its never true and necessarily false. – Lukas Dec 12 '13 at 8:20