If all the premises of an argument are true, is the argument logically valid?


Where an argument is said to be logically valid "if and only if it is not possible for the premises to e true and the conclusion false".

I know that the argument is indeed logically valid if all the premises are logically true, through I am confused if the same reasoning applies to 'true' premises, because it is possible for all the premises to be true but for the conclusion to not follow from them--in such a case, is the argument valid?

Cassidy Parong

Posted 2015-01-09T22:28:19.663

Reputation: 55

possible duplicate of logical form of the definition of validity

– virmaior – 2015-01-11T23:55:31.160



It is easy to come up with a set of premises that are all true, or logically true, but have the conclusion drawn from them be invalid. The most obvious way would be by not having a full enough set of premises. It would not be fair to say...

All humans are primates. All primates are mammals. Therefore all mammals are orange.

The conclusion is not explicitly derived from the premises, but can still be presented in this way.

Chris C.

Posted 2015-01-09T22:28:19.663

Reputation: 11


It's trivially easy to come up with an invalid argument with either conditionally true or logically true premises --just attach it to a false conclusion.

On the other hand, every argument that ends with a logically true conclusion is valid, regardless of the premises.

If you carefully reread the definition you provided, you will see how both the statements above follow from it.

Chris Sunami supports Monica

Posted 2015-01-09T22:28:19.663

Reputation: 23 641


Consider the argument with no premises and the conclusion "the sky is red". All the premises are (vacuously) true --- and surely "logically true", whatever you might mean by that --- but surely the conclusion is false and the argument is not valid.

This is no better than R. Barzell's example, but it's even simpler. And it addresses your distinction between "true" and "logically true", by providing a list of premises all of which are true, all of which are logically true (again, whatever that means), all of which are false, all of which are logically false, and all of which have property glarb, whatever that might be.


Posted 2015-01-09T22:28:19.663

Reputation: 847

1Although nobody thinks that there can be arguments without premises. And if there are no premises, why on earth would the premises be true? That sound weird. – Lukas – 2015-01-10T10:39:10.563

3Of course there are arguments without premises. A valid argument consists of a set of premises and a list of statement, each of which is either a premise or a valid inference from earlier statements. Nothing in that definition says that the set of premises has to be non-empty. There is thus exactly one valid argument (along with a great number of invalid arguments) with no premises. – WillO – 2015-01-10T14:29:00.923

please show me the source according to which the set of premises can be non-empty – Lukas – 2015-01-10T16:58:12.543

@Lukas: You mean empty, not non-empty. I also think you've got the burden of proof backwards. If we've established that people are omnivores, and I draw the conclusion that Joe is an omnivore, and you claim that people named Joe don't count as people, then it's your job to explain why not. If an argument starts with a set of premises, and I construct an argument with an empty set of premises, and you claim that empty sets of premises don't count as sets of premises, then it's your job to explain why not. What is your source for the assertion that the set of premises must be non-empty? – WillO – 2015-01-10T17:27:44.070


@Lukas: If nevertheless you inisist on a specific source, try the first sentence of the Wikipedia page on formal proof: http://en.wikipedia.org/wiki/Formal_proof .

– WillO – 2015-01-10T17:29:27.967

It doesn't say there that the set of premises can be empty. Pick up any logic textbook, it will tell you that there has to be at least 1-2 premises, depending on the author – Lukas – 2015-01-10T18:06:00.083

1@Lukas: It also doesn't say there that the number of premises can be exactly two. Do you conclude that the number of premises can't be exactly two? – WillO – 2015-01-10T19:58:54.720

You really are wrong at least as long as standard logic is assumed. Validity is a relation between the premises and the conclusion. Without premises, the concept of validity doesn't even applies. Stating just one sentence is no argument. – Lukas – 2015-01-10T22:28:42.067

1@Lukas: You are just making this up. You can make up any rules you want, but that doesn't mean the rest of the world has to follow them. An argument starts with a set of premises. It is nowhere explicitly stated that the number of premises can be even; nevertheless, the number of premises can be even. It is nowhere explicitly stated that the number of premises can be prime; nevertheless, the number of premises can be prime. It is nowhere explicitly stated that the number of premises can be zero; nevertheless, the number of premises can be zero. (CTD) – WillO – 2015-01-11T00:04:46.797

(CTD) Why on earth should we impose an extra restriction just because you randomly demanded it? Telling me I can't use the empty set of premises is like telling me I'm not allowed to use exactly five premises. You can play by any rules you want to, but you can't just declare them arbitrarily and ask others to play by them. I won't discuss this further. – WillO – 2015-01-11T00:08:38.623