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I am stuck over whether these statements are true:

First: "If an argument is invalid, any argument of that logical form must be invalid."

Second: "There may be invalid argument with inconsistent premises."

I thought that both of them are false but I'm not sure. Can you correct me if I'm wrong?

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  • The technique of counter example is what you first question proves. That is if your argument is valid then I can change the content to any topic I desire with the same form and my new argument must ALSO BE VALID regardless of the subject matter. Think about how often something can be true in one subject but false elsewhere. It can happen and often. One counter example proves the truth is not 100 percent. At best you have a half truth. The 2nd question is confusing. Yes you can have an invalid argument with inconsistent premises but not sure that is what you really mean. Clarify. – Logikal Aug 23 '20 at 2:43
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Hint for the first question:

An argument scheme being valid means that all instances of sentences of this form are valid; if the form is invalid, then not all instances are valid. According to this definition, could it be the case that there exist valid instances of an invalid form?

Hint for the second question:

An argument is valid iff in all structures, either at least of the premises is false or the conclusion is true, and invalid iff there exists at least one structure (a counter model) under which all premises are true but the conclusion is false. If the premises are inconsistent, i.e. true in no possible structure, can there be such a counter model that makes the premises true and the conclusion false?

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  • then the first question is FALSE i.e we can find counterexample but the answer of second must have been true i.e we can find an example for invalid argument with inconsistent premises. Am i right? – Bulbasaur Aug 23 '20 at 7:42
  • Your first answer is correct. Though note that we only might find a counter example in the general case; it could still be that the invalid argument is indeed not only invalid in some, but possibly even all instances. For the second one, by a counter example I mean a counter valuation that proves the invalidity of the argument, which makes the premises true but the conclusion false. If there is no interpretation which makes the premises true because they are inconsistent, can there be an interpretation which makes the premises true but the conclusion false? – lemontree Aug 23 '20 at 7:45
  • then there is a possiblity when all premises are inconsistent, there may be invalid argument,so the second is true. Thanks for your helps – Bulbasaur Aug 23 '20 at 7:53
  • No. If the premises are inconsistent, then this means there is no way to make all of them true, so in particular there is no way to make the premises true but the conclusion false, so the argument can not be invalid. An argument with inconsistent premises is said to be vacuously valid. See also here: philosophy.stackexchange.com/q/75605/23223 – lemontree Aug 23 '20 at 7:59
  • @lemmontree, if an argument is NOT valid then we have two options: either the argument is invalid or meaningless. By meaningless I mean the language being used doesn't meet proper syntax to count for any type reasoning. Here is an argument with inconsistent premises: if outer space aliens exist, then 4 is an even integer. There are no existing outer space aliens. Therefore 4 is not an even integer. That example is fallacious correct? So we can have an invalid argument with inconsistent premises. – Logikal Aug 24 '20 at 18:31

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