# Is this argument about the disjuncive syllogism valid and sound?

If some arguments of the form disjunctive syllogism have false premises, then some arguments with false premises are deductively valid. Some arguments of the form disjunctive syllogism have false premises. So some arguments with false premises are deductively valid.

This argument is valid but unsound.

Is the above statement true?

• Some ideas ? Your thought ? Feb 17, 2020 at 8:45
• The argument is valid; see Modus Ponens. Feb 17, 2020 at 9:03
• I agree it is valid but I am just unsure if it is unsound @MauroALLEGRANZA
– L0J0
Feb 17, 2020 at 9:37
• Is it true that "some arguments with false premises are deductively valid" ? Feb 17, 2020 at 9:43
• When you say "if ... then" are you just stating a material implication, or something else like a logical implication? (see the first 4 paragraphs of my answer here on the way material implication doesn't really correspond to our ordinary use of if-then statements even though it's sometimes written that way). Also, if you're using a material implication, you have to specify the domain of discourse, in this case the collection of "arguments" that the are being discussed (is that argument above one of them? It's not itself a disjunctive syll.) Feb 18, 2020 at 6:12

## 1 Answer

There is perhaps a hidden premise that all arguments of the form disjunctive syllogism are valid. That said,

"If some arguments of the form disjunctive syllogism have false premises, then some arguments with false premises are deductively valid" is true,

"Some arguments of the form disjunctive syllogism have false premises" is true, and

"Some arguments with false premises are deductively valid" follows by modus ponens.

This would suggest that your argument is both valid and sound. There is one little catch, however. You say "false premises" plural. If by this you mean an instance of disjunctive syllogism both of whose premises are false, then this is not possible. Disjunctive syllogisms have the form A or B; not A; therefore B. For the first premise to be false, A must be false, and hence the second premise is true. If that is your intended meaning then "Some arguments of the form disjunctive syllogism have false premises" is false, and so the argument would not be sound.