The argument is almost valid.
The argument is neither valid nor invalid.
The argument must be valid.
The argument must be invalid.
The argument may be either valid or invalid.
  • 2
    The last option - "The argument may be either valid or invalid" - is the correct answer. When trying to determine the validity of an argument in logic, the truth of a premise is a non-factor. Logic is concerned about whether or not an argument would effectively transfer truth from its premises to the conclusion if the premises were true. – Christian Dean Feb 2 at 5:28
  • 1
    There is an intriguing subtlety to this question: My first reaction is the same as @ChristianDean, but then the Question is really asking if untruth is "effectively transferred from premises to conclusion". – christo183 Feb 2 at 11:03

First, one should understand what "valid", "true" and "sound" mean when it comes to argumentation.

Truth means, roughly speaking, that the proposition matches a state of affairs in an actual world.

Validity means that the collection of all the premises entails the conclusion. That is, given the premises are true the conclusion must be true.

Soundness is when an argument has True premises, True conclusion AND is valid, so Truth + Validity = Soundness

Back to your question, given an argument has false premises and a false conclusion, it does not necessarily follow that the argument is valid or invalid.

Let us consider an example, suppose that "Unicorns exist" is a false premise. And suppose that "if Unicorns exist then they have 2 horns" is also a false premise (since we know by definition, that a Unicorn has 1 horn, not 2).

From these 2 false premises, we can form this valid argument, which is in the form of a Modus Ponens.

  • Premise 1 : If Unicorns exist, then Unicorns have 2 horns [false, by definition]
  • Premise 2 : Unicorns exist [false, probably by induction]
  • Conclusion : Therefore, Unicorns have 2 horns [false]

As you can see, the argument is valid, although the three premises are false (where the first conditional is false by definition, the second premise is probably false by induction)

You can change the first premise to obtain :

  • Premise 1 : If Unicorns have 2 horns, then Unicorns exist [false]
  • Premise 2 : Unicorns exist [false, probably by induction]
  • Conclusion : Therefore, Unicorns have 2 horns [false]

It is obvious that the first premise is false, if Unicorns have 2 horns, it does not imply that they exist or not.

Now this argument is of the form : If P then Q, Q therefore P which is a formal fallacy called Affirming the consequent, which makes our second argument invalid.

So far we have seen two arguments with all premises and conclusion false, one of them is valid and the other invalid.

So, truth or falsehood of premises, or the conclusion or both, does not necessarily make the argument valid or invalid.

So, your answer is the last option:

The argument may be either valid or invalid.
  • I edited the answer to include the case where the argument is invalid. – SmootQ Feb 3 at 15:26

The argument may be either valid or invalid.

Logic deals with forms of reasoning or logical form. For example :

  1. No A is B

  2. Some C is B

  1. Some C is not A

This logical form is valid - deductively valid - because it would be contradictory for 1. and 2. to be true, and 3. false whatever premises A, B and C stand for. 1. and 2., the premises, logically imply the conclusion, 3. The content of 'A', 'B' and 'C' doesn't matter.

It is logical forms, then, that are valid : and you cannot know anything about the logical form of an argument from the mere fact that the premises and conclusion are all false.

Clearly, then, we need to know the logical form of the argument, not just the falsity of premises and conclusion :

  1. All cats are purple animals (F)

  2. All purple animals have four eyes (F)

  1. All cats have four eyes (F)

Here the premises and conclusion are all false but the argument's logical form is valid. The conclusion is not logically independent of the conclusion; the premises logically imply the conclusion. Said another way, it is self-contradictory to affirm the premises and to deny the conclusion.

By contrast :

  1. New York is the capital of the USA (F)

  2. The San Andreas Fault is in Tennessee (F)

  1. The 16th President of the United States was born in 1811 (F)

is invalid. The truth-value of the premises (F) is independent of the truth-value of the conclusion (F). The premises do not logically imply the conclusion. The argument's logical form is invalid.

Moral of all this :

FFF tells you nothing about logical form, which alone determines the validity of an argument. We need to know the logical form of the argument and not just the truth-value of premises and conclusion.

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