# Is this a logical fallacy?

I’m thinking of a mistake in reasoning where, if you take two propositions that alone are false, you assume that their conjunction must be false as well. I think this is the logical form: If x does not imply z, and y does not imply z, then (x&y) does not imply z.

It can work in some situations: Brian is not my friend; Megan is not my friend; therefore Brian and Megan together are not my friends. But obviously it falls apart fairly quickly: a lit match alone cannot cause an explosion; a barrel of oil alone cannot cause an explosion; therefore a lit match combined with a barrel of oil cannot cause an explosion.

Is this a logical fallacy, or some other type of error? Either way, does it have a name? I’ve looked through the lists of fallacies on wikipedia and elsewhere and I didn’t recognize it in any of them.

Sorry, I completely messed up the first sentence: you’re not assuming the propositions themselves are false (obviously if one or both of the conjuncts is false then the conjunction will be false too), but you’re making the assumption that since neither x nor y alone imply conclusion z, then the conjunction of (x&y) can’t imply z either.

Doesn’t ring a bell. Have you found an example of someone using this reasoning?

I think you’re misunderstanding the idea of a conjunction.

In your example: a lit match alone, and a lit match combined something else, are two totally different things, and no logical inferences can be brought from one to the other.

You’re also misunderstanding “imply”. I suggest you stick to statements of the form “If x, then y” and see what happens.

There are some things in the OP that aren’t completely clear, but I thought it was fairly obvious the idea was to ask whether there is a special term for the following kind of invalid inference:

Premise 1: not-(if X then Z)
Premise 2: not-(if Y then Z)
Conclusion: not-(if (X and Y) then Z)

-FrL-

If I understand correctly, another way to word the OP’s fallacy is:

1. It is possible to have x without z.
2. It is possible to have y without z.
3. Therefore, it is possible to have both x and y without z.

And this is, indeed, a fallacy—i.e. an invalid argument. The combination of x and y (like the OP’s example of the lit match and the barrel of oil) could cause/imply/necessitate z.

Whether there’s a name for this particular fallacy, or it’s equivalent to one that has a name, I don’t know.

And now, I’m not so sure of what I said in my previous post (that it’s an invalid argument). Framing the premises as Frylock did (which I think is correct), and taking the logical connectives “not,” “and,” and “if-then” in their standard meanings, there seems to be no way the premises could both be true and the conclusion be false. (The only way both premises could be true, if I’m figuring it correctly, is for X and Y both to be TRUE and Z to be FALSE; but then the conclusion would also be true.)

I think the confusion comes because the conjunction—the “and” in logic—doesn’t carry any meaning of “interaction” or “cooperation” between X and Y, just that X is true and, separately but simultaneously, Y is true.

I’m not a logician, but that matches what one told me at one point.

That’s the way I read it, too – you can easily simultaneously have a lit match and a barrel of oil without having an explosion. The fallacious element here is disregarding the possibility of emergent new phenomena arising from a combination of the parts, and thus I’d call it an instance of the fallacy of composition. Every part has the property of ‘not causing an explosion’, but the whole need not.

Sorry, that’s a valid inference!

What’s invalid is

Premise 1: not for all x (if Px then Rx)
Premise 2: not for all x (if Qx then Rx)
Conclusion: not for all x (if (Px and Qx) then Rx)

A counterexample* to the inference (in colloquial english for comprehensibility’s sake…)

P1. Just because something is male, that doesn’t make it a father.
P2. Just because something is a parent, that doesn’t make it a father.
C. Just because something is a male parent, that doesn’t make it a father.

*An argument following the logical form just given, where the premises are true, but the conclusion is false. If there is such an argument, then the logical form is invalid.

ETA: Ah, I see someone already spotted that the first inference is valid. I was hoping to have come back to the thread before anyone noticed. Damage control!

You’re right, the ‘barrel of oil’ example doesn’t work. Sorry, I’m trying to come up with an example off the top of my head and I’m not very good at it!

Here’s another stab: assume for the sake of argument that if a car is moving down a hill without any brake fluid then it will crash.

1. ‘The car is moving down the hill’: even if this statement is true, it’s not sufficient to mean the car will crash, because it might still have working brakes.
2. ‘The car has had its brake fluid drained’: even if this statement is true, it’s not sufficient to mean the car will crash, because it might not be moving.
Conclusion: THEREFORE, ‘The car is moving down the hill and has had its brake fluid drained’: even if this statement is true, it’s not sufficient to mean the car will crash.

That conclusion is false, because as we agreed for the sake of argument, a car moving down a hill without brake fluid will crash. Is that better? Is there a name for it?

That example looks like the same thing I was looking for as well. Any name for it, or is it such poor reasoning it’s not worth a name?

A. Asprin won’t end my migraines.
B. Tylenol won’t end my migraines.
C. Caffeine won’t end my migraines.

You’re confusing “and” with “or.” A B or C wiill not end my mirgraines, yet A & B & C will end my migraines.

I agree with **Frylock **that it is most similar to the fallacy of composition. You are inferring that because A is not F, and B is not F, that (A&B) is not F.

Going back to the original formulation in the OP, I think this is a variation on confusing necessary & sufficient conditions.

Having a lit match AND having a barrel of oil are both *necessary *conditions to having an explosion (in the simplified world framing the example situation). But they are not *sufficient *conditions. And a syllogism constructed just of those two conditions and a conclusion doesn’t give us any info about *which *other conditions are required to add up to sufficient for the conclusion, nor *what *the state of those conditions are. And as a result, they tell us nothing about the state of the conclusion.
Turning to Frylock’s very well-formed example about male parentage, the specific terms chosen (male + parent = father) work because (at least for common usages of the terms), the conditions given are both necessary *and *sufficient. More than that, they are all-covering; there are no other possible conditions relevant to the question of what constitues a father.
Going back to oil & matches, or other more complex ideas, the collection of sufficient conditions may not be a simple collection. IOW, it may not be just a matter of “check all 4 of these boxes and you’ll have outcome X”.

Real-world situations can be more like “If (A & B & C), or (A & D & E), or (D & F & not-G) then (after the passage of time Q), outcome X is assured. There are also another 100 possible comnbinations of difficult-to-identify factors which could accelerate, prevent, or cause outcome X.

You’re gonna have a hard time writing a Philosophy 101 sylogism or proof which accurately captures that concept. As a result, I don’t see a named fallacy there, other than the fallacy of *inappropriately applying logic algebra to the real world * (one I just made up).

May I ask the OP why they are concerned to find a name for this fallacy? If it has come up in an argument with a friend, for example, the thing to do is what Frylock did: actually demonstrate why this template of reasoning is not in general valid.

There’s no need to to search for a specific name, so that one can throw down the red card with a whistle while linking to a page on “The Fallacy of the Morchivicated Exponential” or what have you. The number of ways to make erroneous leaps of inference is potentially infinite; they haven’t all been assigned specific labels, nor would there be any great benefit in carrying out such a categorization.

I was wondering if it has a name. Are you saying it doesn’t have a name? That would be more helpful than telling me about the benefits of naming fallacies.