# What is the name of this fallacy? (not A imples the value of B is unknown, therefore A)

Does the following fallacy have a name?

If A were not true then it would be impossible to determine whether B is true or not, therefore A is true.

It sounds like a pretty silly argument when written explicitly, but I've come across it in science from time to time. It sometimes happens that if one assumes a hypothesis (A) to be true, then one can make progress on some important unanswered question (B). This sometimes leads the hypothesis to be treated as a principle (i.e. a postulate that must be accepted without explanation). It can then become difficult to question A, because this also means questioning all the progress that has been made towards B under the assumption that it's true.

I note that this form also comes up quite often as a (perfectly valid!) step in solving logic puzzles. Its validity in this case comes from knowing the puzzle has a unique solution, so one can correctly conclude that it won't be left unknown. Please note though that this point about logic puzzles is just an observation - my question is about the situation in the paragraphs above, which are about the cases where we do not know the problem has a solution, so we cannot correctly make this inference.

I guess it's a form of appeal to consequences, but I'm wondering if it has a more specific name.

It also seems related to the streetlight effect, though it's perhaps even stronger.

• The logical structure is modus tollens: ~A → ~B, B ⊢ A, and as you said, it's a valid logical principle. If the major premise is true, and B can be determined, then it follows that condition A was met. Your questioning the argument doesn't involve a fallacy; rather, it sounds like you're just doubting the truth of the major premise, i.e. doubting that A actually is necessary for determining B. – user3017 Jan 8 '18 at 9:15
• It's not modus tollens. "If A were not true then it would be impossible to determine whether B is true or not" is quite a different thing from "~A → ~B", which would be "If A were not true then (we would know that) B is not true" – Nathaniel Jan 8 '18 at 9:58
• As stated it is an enthymeme, logically incomplete. I suppose the argument fully runs : If A were not true then it would be impossible to determine whether B is true or not; but it is possible to determine whether B is true or not : therefore A is true. – Geoffrey Thomas Jan 8 '18 at 10:02
• @PédeLeão ah, I see what you mean, thank you. There's a couple of subtle points here though. In the case of solving a logic puzzle this is all fine and correct of course, but my main interest is in the cases where this arises in science, in which we don't generally have C, so we can't make that inference. The other point is, in general the statement ~A → ~C is dependent on there not being any other competing hypotheses or evidence that would imply B or ~B, so the implication in ~A → ~C is somewhat weak. – Nathaniel Jan 8 '18 at 10:34
• I feel you've drawn attention to one of the central problems of philosophy or at least one its greatest dangers for philosophers, which is buying into axioms and beliefs without proper justification and with insufficient scepticism. . . . – PeterJ Mar 10 '18 at 12:46

There is no name for the fallacy involved here, so you're not missing one and no-one can tell you what the name is. The argument you cite is invalid but not all types of invalid argument embody specific, named fallacies. So far as I know there is no specific name for the fallacy embodied here.

But it is easy to see what is wrong. The argument is missing a minor premise.

As it stands :

'If A were not true then it would be impossible to determine whether B is true or not, therefore A is true'

is invalid. : from (a) 'If A were not true then it would be impossible to determine whether B is true or not', it does not follow that (b) 'A is true'. (a) could be true, and (b) false : and this is impossible in the case of a valid argument. In no valid argument can the premises (a) be true and the conclusion (b) false.

But your argument is an enthymeme, an argument with a suppressed minor premise. The suppressed - unstated - premise is : 'It is possible to determine whether B is true or not'. Put that in, and you get a valid form of argument :

If A were not true then it would be impossible to determine whether B is true or not; but it is possible to determine whether B is true or not : therefore A is true.

So, yes, it is fallacious as it stands; but no, it is not fallacious if we add the suppressed premise. And no, there is no name for this fallacy.

The argument is valid if the tacit premise is "It is not the case that it is impossible to know the truth value."

The first premise is not negative. Let S equal the phrase "A is not true." The second premise is the phrase "It would be impossible to know whether B is true or not." The tacit premise would be expressed as "It is not the case that it is impossible to know whether B is true or not". The conclusion must follow that it is not the case A is true or A must be false. Premise alignment makes the argument form a Modus Tollens to get the denial of the antecedent as a conclusion.