Is this a mathematical statement?

Question

Is this a mathematical statement:

Suppose this statement is false.

I know what a mathematical statement is: it's either true or false. But the suppose is what's confusing me.

I think the effect of “suppose” is to make the sentence into a command, rather than a statement; commands are not normally understood to be either true or false, and are not normally understood to be statements. (Compare “Don't go in there!” where nothing is being stated.) Even an utterance like “Suppose that $x>3$” is not itself a statement; the statement “$x>3$” is only a component of the complete utterance. But I think you would get better and more authoritative answers in a forum about linguistics or perhaps philosophy. — MJD, May 21 '14 at 19:47
In mathematics, whenever you see the word "suppose", it typically signals the start of a proof by contradiction. — Paul Hurst, May 21 '14 at 19:55
@Paul I disagree with your characterization. It sometimes signals a proof by contradiction, but more often not. I would guess that the most common use of ‘suppose’ is merely to introduce the conditions of a problem or to establish names for previously unnamed entities. For example, “Suppose that the cyclic group $G$ acts on a set $S$ and $g_1$ and $g_2$ generate $G$.”. A search on this web site for ‘suppose’ produces many examples, very few of which seem to have anything to do with proof by contradiction. — MJD, May 21 '14 at 20:01
@MJD On the whole I agree with you. The sentence itself is an instruction/command rather than a statement or proposition. It is therefore not the kind of statement which has a truth value, and as an instruction is therefore incoherent (in referring to itself as true) rather than untrue. — Mark Bennet, May 21 '14 at 20:28

score 0 · Answer 1 · answered Jan 10 '18 at 12:06

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No, it is not Because it is not declarative but Imperative The word "suppose" is imperative and this statement is not mathematical at all.

answered Jan 10 '18 at 12:06

Nitin Kumar

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score 0 · Answer 2 · edited Jun 12 '20 at 10:38

Is this a mathematical statement:

Suppose this statement is false.

No. I can't imagine anything like this statement in a formal mathematical proof.

It would be more clearly meaningless if it had been instead, "Suppose this statement is true." That would clearly be a non-statement. We would not be able to infer anything from it. And changing "true" to "false" is not going to suddenly imbue it with meaning.

score 0 · Answer 3 · answered May 22 '14 at 03:43

I started this as a comment but it got too long.

"Suppose" works like, "let's consider that this something is true regarding the premise." You see, this statement, by itself, isn't a premise. Your sentence, "Suppose this statement is false," would introduce some constraint or condition regarding the premise.

A premise might be, $n^2+n$ is even $\forall \: n \in \mathbb{N}$. From there, one might begin the proof by, suppose $n^2+n$ is not even. From there, the proof would work through the steps and arrive at a conclusion. (in this case, the conclusion would contradict the supposition because $n^2+n$ is indeed even $\forall \: n \in \mathbb{N}$.

Is this a mathematical statement?

3 Answers3