Can an argument be valid even though one of its premises is false?

Curious 05/08/2018. 5 answers, 1.746 views
logic validity soundness

Is it possible for an argument to be valid by virtue of its logical form, but contain a false premise ? In other words, can a premise be false even though the argument itself is logically valid ?

Thanks in advance!

(For context: The initial question was if an argument can be false even though it "seems true" in terms of it's logical form. The question is better asked this way: can the propositions contained in an argument be false even though the argument itself is logically valid.)

5 Answers

Bram28 05/08/2018.

First: we don't really say that arguments are true or false. Statements are true or false, but arguments have different kinds of properties.

One of those properties is, as you are obviously aware of, validity. However, another important property is well-foundedness, which means that the premises are true (or, for more practical everyday purposes, plausible or acceptable).

Well-foundedness is important, because if I am allowed to just assume anything as my premise, I can (validly!) argue for anything. For example:

"All dogs are purple. Foofy is a dog. Therefore, Foofy is purple"

This argument is logically valid, but not well-founded. And indeed, as such it is a bad argument.

... which is probably just what you were looking for when you said you wanted a valid but 'false' argument. Indeed, instead of saying that arguments are true or false, you can say they are good or bad (and of course anything in between: pretty good, pretty bad, ho-hum, excellent, terrible, etc.)

A special kind of 'bad' argument is something like this:

"Bananas are yellow. Therefore, bananas are yellow"

Interestingly, this argument is logically valid, and its premises are true (well, not in my local supermarket, which for some reason thinks that I would like to purchase their still green bananas, but you get the point). However, it is what you will recognize as a circular argument ... which is bad. OK, but why exactly is it bad? Well, think about it: why would someone be looking for an argument as to whether bananas are yellow or not? Presumably it is exactly because such a person doesn't know whether bananas are yellow or not. And we really shouldn't be assuming something that, to this person, is not acceptable ... which is another reason why for real life purposes, it may be more useful to define well-foundedness as 'the premises are acceptable' rather than 'the premises are true'.

Geoffrey Thomas 05/08/2018.

Yes :

Premise : All dogs are mortal (true)

Premise : All birds are dogs (false)

Conclusion : All birds are mortal (true)

The argument is valid because there is a correct relation between premises and conclusion. This is not because the conclusion is actually true but, crucially, because granted the premises the conclusion must follow even though one of the premises is false.

As noted in the answer above, an argument itself is never said to be true or false : truth and falsity belong only to the premises and the conclusion. Arguments are only valid or invalid, depending on how premises and conclusion are related. If we cannot affirm the premises and consistently deny the conclusion, the argument is valid.

Zibbobz 05/08/2018.

It sounds like you are trying to ask if you can have logical premises that are false, yet support an argument that is true - in other words, an example of presenting facts that lead to a true statement, but the facts themselves are wrong.

This is entirely possible - the other answers provided give absurd examples of demonstrably false things, but they still logically lead to the argument presented being true, and the argument is true.

Take @Bram28 's purple dog for example - assume that what actually happened is that someone has poured purple paint on a cat named Floofy, and the damp cat looks like a small dog. This means the Argument (Floofy is Purple) true, but the premises (All dogs are purple/Floofy is a dog) false.

PeterJens 05/08/2018.

The question is too imprecise.

The premise establishes the area being discussed. If the premise is conditional to the validity of the logic of the argument, then it must be true for the logic to be valid. There are an infinite number of premises that could be invented for anything but only ones relevant to the logic need to be applied.

So for a logical argument to be valid all the assumptions and premises used need to be quantified and be valid for the logic to hold true. In practical terms people make mistakes, get the wrong premises, but are still correct in their logic, because it is founded on valid premises which are not specified. You could argue the argument is then invalidated because the correct premises where not stated. So it depends on what is actually being reviewed, the argument or the argument with its complete set of premises.

BradC 05/08/2018.

(Promoting this from @MauroALLEGRANZA's comment, since it deserves a full answer.)

Yes, an argument can be valid but still not be sound.

This is primarily a matter of terminology:

A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.

A deductive argument is sound if and only if it is both valid, and all of its premises are actually true. Otherwise, a deductive argument is unsound.

The following is a valid argument:

  • All dogs hate cats
  • Fluffy is a dog
  • Therefore, Fluffy hates cats.

Its only a sound argument if both premises are true. I can tell you that they are not, since Fluffy is my hamster.

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