Interesting non-mathematical tautologies

Question

Are there any interesting examples of tautologies that are not mathematical? Something non-trivial like

It is raining or it is not raining.

I can't come up with one nor have I found any on the internet.

Example: the mathematical statement of the mean value theorem is a tautology, but it's a mathematical one with a lot of information inside. And it's not apparrent that the statement of the mean value theorem is a tautology.

By "interesting" I probably mean just that: a tautology "with a lot of information inside" without it obviously being a tautology. But then, wouldn't it then be considered mathematical becuase of its complexity? 🤔

Here is the definition of "mathematical" I am using (taken from here):

Mathematics is the domain of inquiry where logical reasoning is the sole methodology. That is, a question is a mathematical question if and only if it can (in principle) be settled by logical reasoning alone.

Answer 1

Tautologies constrain the space of possible true statements: all true statements must comport with all tautologies, and all tautologies are true statements. Often the addition of "... even when" or "... including" makes them more useful. Tautologies are useful for...

• Avoiding cognitive errors, e.g.: Reality is reality; descriptions are descriptions. As more commonly phrased: the map is not the territory.

• Avoiding logical fallacies, e.g.: What's true is true, even when it's unpopular.

• Employing scientific models consistently, e.g.: The rate of change of distance measured by an observer with respect to time measured by that observer is the rate of change of distance measured by an observer with respect to time measured by that observer, even when the cause is modeled as cosmic expansion.

• Attaching intuitions to abstractions, e.g.: An observer is always stationary in the observer's own reference frame because wherever you go, you're always right there.

Answer 2

A tautology is trivially true but there can be an underlying or dual meaning behind non-mathematical tautologies:

Boys will be boys: a superficial tautology that describes a male who is or does something childish or immature.

You do what you have to do: a superficial tautology that describes a person always acting in their best interests.

Some others:

• A kiss is just a kiss.
• Sometimes, a cigar is just a cigar.

I find these interesting and non-trivial and they contain more information than contained in the tautology by itself.

There are some tautologies that might, arguably, be considered redundancies:

• Free gift
• Joint collaboration
• safe haven
• new innovation

Not very interesting from a philosophical perspective. These would be better suited to psychology (sales and marketing).

Answer 3

No such thing. A formula is a tautology just in case it is true in all models, e.g. a truth of logic. Many of these will seem trivial to you, though some are surprising, e.g. in classical logic, for instance, it is a tautology that for any two sentences, either one of them implies the other or vice versa. However, in the more technical sense of 'trivial', all tautologies are trivial.

Answer 4

“The whole is greater than the part”. It’s Euclid’s (at least in his Elements) but it’s not solely mathematical imo. Something like, “what is is, and what isn’t isn’t” is also an informative tautology a la Parmenides and Eleatic monism but that one may be a bit less obvious. That sect thought it showed the ease humans can double speak and saying anything about non existence is questionable to them. They certainly found it interesting.