1

On p22 in The Big Questions by Solomon:

A tautology is a trivially true statement. Some examples:

A man is free if he is free.

You can't know anything unless you know something.

I wouldn't be here if I hadn't arrived.

Are these four statements all tautologies?

Business is business.

Boys will be boys.

"A rose is a rose is a rose." (Gertrude Stein)

"Become who you are." (Friedrich Nietzsche)

9
  • The source is not a book about formal logic. See Glossary, page 434 (10th ed): "tautology: A trivially true statement, or a statement that is necessarily true by virtue of its form." Thus, the author write both usages: the common one as well as the "technical" one used in formal logic. Sep 12, 2023 at 12:44
  • And see page 20: "A common way in which philosophical claims can turn out to be trivial is when they express what logicians call tautologies: for example, “A is A.” A tautology is a statement that is so necessarily true, so obviously correct, that a statement claiming the opposite would be self-contradictory." In this statement the author links the two meanings. Sep 12, 2023 at 12:47
  • 2
    Maybe the aim of the author is to teach us how to identify the two usages... but I'm a little bit concerned: "I wouldn't be here if I hadn't arrived." is NOT a tautology in the formal logic sense. Sep 12, 2023 at 12:51
  • See G.Stein's Rose is a rose is a rose is a rose for context: the original was part of a poem; thus not a tautology. Sep 12, 2023 at 13:56
  • 1
    I'm not sure of your background but I would suggest looking at some of the tools for English to Logical statement translation: English to Logic cs.miami.edu/home/geoff/Courses/TPTPSYS/Practicum/… Sep 13, 2023 at 16:11

3 Answers 3

6

"Business is business" means in order for a business to be successful it is necessary to do things that may hurt or upset people.

"Boys will be boys" means being rough or noisy is part of the male character.

(Both of the above are highly dubious claims: The first may be true to some degree, but suggests that working towards being successful makes it "ok" to harm others, which is highly questionable. The second is, at best, perpetuating stereotypes that are only true on average, that are learnt behaviour or that aren't accurate at all, and at worst, is used to excuse harmful behaviour, e.g. abuse, neglect or violence, just because it was perpetrated by a boy or man. But that's an aside.)

"Rose is a rose is a rose is a rose" is part of a poem to express that simply using the name of a thing already invokes the imagery and emotions associated with it.

"Become who you are" cannot be a tautology, because it's a command, not a statement, but it may seem paradoxical, in the sense that you already are who you are. Although it actually seems to mean that you should "be(come) your best self" by reflecting on your short-comings and overcoming your flaws.


So, while these may seem like tautologies when considering the words as written, the deeper meanings behind these sayings are clearly not tautological.

2
  • I would have answered that the statement "Business is business" is a tautology because I am unfamiliar with the deeper meaning and am only aware of the statement as written. If understanding a deeper meaning is required before determining whether a statement is tautology, how can I ever identify one with confidence? Sep 13, 2023 at 14:14
  • 5 = 5 is a tautology. However, it's not a tautology if, in a deeper context, the statement really is 5 apples = 5 oranges. IMHO. Tautolgies should only be applied to a statement as written. Sep 13, 2023 at 14:45
2

A man is free if he is free.

A tautology of the form: P→P

You can't know anything unless you know something.

Suppose Kx means 'x is a known proposition' and we're just talking about everything, this says: (∀x¬Kx ∨ ∃xKx) which with quantifiers exchanged amounts to (¬∃xKx ∨ ∃xKx) A tautology.

I wouldn't be here if I hadn't arrived.

A tautology like the first, without mincing the meaning too badly, this says: (¬P→¬P) (it might have some tensed/modal meaning too, but then it won't be a tautology.

Business is business.

Kind of a weird thing to consider. It might mean P therefore P. It might mean: ∀x(Bx→(x=x)) (where B means 'x is business' this says if anything is business it is identical to itself.)

It might mean: ∀x(Bx→Bx) with a meaning analogous to the first tautology again. The problem here is that we're considering an idiomatic expression, something like an exclamation rather than a statement (the truth-evaluable stuff of logic.) Then it's not a tautology.

Boys will be boys.

Again an idiom, or something. Strictly parsed it might be like, where Bx means 'x is a boy', t and t' are times, and x<y is a relation and means 'x is later than y' and Lxy is a relation and means 'x is located at y', and finally we're talking about everything:

∀x∀y(x=t ∧ By ∧ Lyt → ∃z(z=t' ∧ t'<t ∧ Lyz))

Or something funky like that, without modifying the logic too much. Not a tautology in quantified predicate logic. In tense logic it's not good either, basically: p→F(p) (Being a boy implies future boyhood) Kind of confusing overall.

"A rose is a rose is a rose." (Gertrude Stein)

Where Rx means 'x is a rose', and we're talking about everything: ∃x∃y∃z(Rx ∧ Ry ∧ Rz ∧ x=y ∧ y=z)

Not a tautology. Charitably we might wonder if it means everything is identical to itself, in which case it is a tautology, one of the laws of thought.

"Become who you are." (Friedrich Nietzsche)

An imperative, not a truth evaluable statement.

Final thoughts: Forgetting about the little semantics I've done for the logical expressions, just look at the expressions here and think: is there an interpretation (and domain) for these symbols that could make them false? A tautology's truth will come from the fixed logical meanings of the connectives or quantifiers or identity. Hence logical truth.

4
  • Your snalysis of G.Stein's verse is debatable... The original play on the ambiguity between the proper name Rose and the common name rose. Thus, simplifying it to "Rose is a rose", its formalization will be rose(Rose) which is not a tautology. Sep 12, 2023 at 17:41
  • If instead we stay with the version used above by the author and the OP, we have "A rose is a rose:, that is "for every x (if rose(x), then rose(x))" , which is a valid formula of predicate logic. Sep 12, 2023 at 17:43
  • Sorry, I'm not familiar with Stein (is she riffing on Shakespeare?) I took it that it was a common noun because the sentence uses 'rose' and not 'Rose.' The initial capitalised Rose could be a name, I guess! If Rose is a rose then definitely, rose(Rose). But if its just the common noun I think my analysis actually needs a disjunctive modification: ∀x∀y∀z Rx & Ry & Rz, implies x=y or x=z or y=z. This now says there's at most two rose things. Not that great even modified. I think that your reading: forallx(rose(x) implies rose(x)) is good as a tautology. Sep 12, 2023 at 18:01
  • 1
    Regarding "Business is business", using your B(x) predicate it is simply: ∀x(Bx ⇔ Bx)$ Sep 18, 2023 at 9:03
1

There are two approaches to your question regarding tautolgies:

Evaluating a statement literally (by syntax): Business is business -> Business = business. Syntactically or literally tautological

Evaluating a statement by semantics (symbolic or metaphoric)

"Business is business" means in order for a business to be successful it is necessary to do things that may hurt or upset people.

Semantically (metaphoric or symbolic), not a tautology.

Special thanks to Michael Carey at Math SE and all the other nice people who answered and commented.

https://math.stackexchange.com/q/4770142/1068723

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .