Is this kind of conditional sentence grammatically correct?

If x weren't y, I couldn't -insert verb- z but I can -insert verb- z, therefore x is y.

As requested, here is an example for complete sentence:

If I weren't rich, I couldn't afford this house but I can afford this house; therefore, I am rich.

I have one more question: Is the italic part of example sentence necessary?

  • I'm only asking about grammar.
    – Donatello
    Jul 19 '15 at 14:37
  • I'd put a semicolon, or at least a comma, after the first z; otherwise it's fine. Jul 19 '15 at 14:40
  • I think 'true' might be meaningful here in one of its definitions, but the question is not clear enough to be sure. Donatello, could you please append to your question a sentence/proposition that instantiates x, y and z and the missing verb. That would turn it into an English Language question. Otherwise it should be on the Linguistics SE. Jul 19 '15 at 14:42
  • @chaslyfromUK, I edited my question.
    – Donatello
    Jul 19 '15 at 14:56
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    I would put some punctuation (comma, semicolon, or period) before "but", but otherwise it seems valid. (And punctuation is not technically "grammar", according to many.) The italicized phrase is not grammatically necessary, and the sentence is OK (understandable) without it, but it may be useful to maintain clarity in slightly more complex sentences.
    – Hot Licks
    Jul 19 '15 at 15:21

It is grammatically correct, except that you probably need a full stop before but. At the very least you need a semicolon there. Was there anything specific that you thought might be ungrammatical about your sentence? The italicised part is not necessary (but it is perfectly fine).

It is not, however, correct in formal logic.

If it weren't raining, there wouldn't be a puddle. But there is a puddle; therefore it is raining.

In formal logic, that conclusion is invalid, because one cannot draw any conclusions based on the consequence; only from the antecedent can one draw conclusions, and only if it is true (then the consequent must also be true). Purely as an illustration: if this example were in the real world, there could be a puddle but without any raining (it could be a garden hose).

However, there is in real language a very strong implication that antecedent and consequence correlate. So your implication is perfectly fine in a normal context (outside formal logic).

In general, a statement can be syntactically correct but logically incorrect, or even nonsense. Consider Chomsky's famous sentence:

Colorless green ideas sleep furiously. [syntactically perfect, but nonsense]

*Furiously sleep ideas green colorless. [syntactically flawed, and equally nonsensical]

  • I think your analysis has got tangled up in the negatives. Your syllogism (and OPs) are entirely valid, since in formal logic "If A, then B" means "Either B or not A". Drawing a conclusion from the antecedent (such as "It is raining; therefore there is a puddle") is something first-year students learn to avoid. Jul 20 '15 at 16:18
  • @TimLymington: Drawing a conclusion from a material implication is possible if and only if the antecedent is true (then the conclusion is that the consequent must be true). The OP was drawing a conclusion from the consequent, which is invalid. I did the same (invalid) thing in my example, as intended. So I don't see any problems... Jul 24 '15 at 1:39
  • The conclusion in your example is not only valid but the only conclusion that can validly be drawn from the premisses; a garden hose could render the antecedent false without affecting the validity of the argument. You may be thinking of "But it is raining: therefore there is a puddle", whch is common but invalid. And what I meant by 'tangled up in the negatives' is neatly shown by your statement that "If it weren't raining" is true if it is not raining. Jul 24 '15 at 10:18
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    If we leave out the subjunctive (which actually I think important) your conclusion is merely restating the premise, not deducing (If not raining then no puddle. Given not raining, no puddle.) Yes, of course I disagree: I repeat that formal logic holds that "If A then B" is equivalent to "B or not A". "If it is raining there is a puddle. There is no puddle: therefore it is not raining" is probably the simplest valid argument imaginable. Jul 24 '15 at 23:03
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    @TimLymington: I think this is rather basic formal logic, and neither of us is stupid; therefore, one of us must have been staring at this for too long, semantic satiation... Jul 25 '15 at 2:17

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