# A statement that is always true, but not a tautology?

Given I hand in a manuscript and the comment of the reviewer would be "You did not take in consideration to potential influence of this variable" the reviewer would be correct. However, my issue lies with the fact this is always true. Considering all possible existing variables the statement "you did not include the potential influence of this variable" is always correct. However, it is not a tautology neither is it an argument, so what is it?

• Maybe a trivial statement? Commented Jun 6, 2022 at 11:09
• In the field of mathematics it would be deemed a tautology by definition of always being TRUE but this context is not universal outside of math. In philosophy a tautology has another context: a relationship between propositions where both hold the same truth value. That is both propositions are equivalent or both are absolutely identical. The proposition "all s are p" is identical to "no s is non p". They are not just equivalent. There is a distinction between identical & equivalent propositions. All equivalent propositions are not identical. Sentences can be different & have the same meaning. Commented Jun 6, 2022 at 11:16
• Sentences are not propositions. The sentence "you are fired" is completely different wording from "your employment service are no longer required any longer." Either one states you are terminated from employment there. So the sentences are not identical in words nor in the length. "All cats are cats" is identical to " all cats are cats." If one is true the other must hold the same value. This is the principle of Identity. 2+2= 4 = 8-4. The math statements are equivalent not identical as in the numerals. 2+2= 4 = 2+2 is identical. Both examples are tautological in mathematics. Hope that helps. Commented Jun 6, 2022 at 11:23
• If I understand correctly this only works by invoking our finitism compared to infinity. It not always true “you did not consider this variable” because you could redo your manuscript to consider it. What might be better is “you did not include some variable”. This kind of thing crops up a lot. Kolmogorov said “no step in an algorithm can take infinitely long (paraphrased)” and we’d all have no problem saying “no utterance will ever contain all the integers”. I think they are not tautologies because we could find reality has no actual infinity. Tautologies can’t be possibly wrong. Commented Jun 6, 2022 at 12:44
• @MauroALLEGRANZA thank you I will have a look in to the definition and application. Commented Jun 6, 2022 at 18:44

the reviewer would be correct. However, my issue lies with the fact this is always true.

I think the word you are looking for is truism: which is a notion that has to do with cogency, not so much with logical validity (and even less with formal logic).

In your example, whether the reviewer's comment is or is not a "truism", so a fallacious vs a valid objection, depends on whether and to which degree the "potential influence" s/he mentions has (not) anything substantial/relevant to it.

This makes me think of the challenge of negative facts in how we account for truth. The list of things you have not taken account of, is basically infinite. But of course a contextual implication here that is unspoken, is that this specific variable you should have considered. So an argument is being made, and presumably by someone with a syllabus, who knows what knowledge or standards of writing get a pass.

• There is "teaching to the test", and there is also "studying the prof". Commented Nov 3, 2022 at 23:05

If a statement is always true, but it is not a tautology (where a tautology is a statement or expression that is always true, irrespective of whether its variables are true or false), then it must be a necessary truth (a statement that is true in all possible worlds is a necessary truth).

While a tautology is true in virtue of its logical form (if p then p is always true because p can be either true or false while the expression remains true), a necessary truth is true because it cannot, under any conditions whatsoever, be false.

• What is necessary is never untrue. Commented May 10 at 12:57

I don't personally interpret the word 'tautology'as a proposition that is always true. Some statements are simple, and some are compound. Only a compound statement can denote a tautology. In the case of the simple statement "1+1=2" the proposition it denotes is always true, but I don't consider it a tautology, because it's referrer is a simple statement. On the other hand, (If A then B) iff (not A or B) denotes a tautology, because it's compound AND all the components of its truth vector are true. That is, the entries in all the rows under the statement are 1's.

Since you aren't dealing with a tautology, the word you are searching for is an eternal truth, or an eternal fact.