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No arguments with false premises and a true conclusion are valid for If an argument is valid and the premises are true, then it's a sound argument. no arguments with mood and figure IAI-4 are arguments with false premises and a true conclusion and some arguments with mood and figure IAI-4 are not valid.

How would I put this in standard logical form? I am so beyond confused.. What are the instances? thank you.

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    Arguments with false premises and a true conclusion can be valid. All birds fly; all flying things have feathers; therefore, all birds have feathers. I think what you meant to say is that no argument with true premises and a false conclusion is valid.
    – Bumble
    Commented Sep 17 at 14:51
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    Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
    – Community Bot
    Commented Sep 17 at 16:34

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No arguments with false premises and a true conclusion are valid.

This is not correct; see Deductive arguments for relevant definitions.

An argument is (formally) valid when it is not the case that the premises are all true and the conclusion false.

Sound means that the argument is both valid in form and has no false premises.

This definition implies that an argument with contradictory premises is always valid (Ex falso).

Regarding Syllogistic, the "mood" IAI-4 (in the fourth figure) has been called Dimatis.

It is simply AII-1 in the first figure (Darii) with the two premises interchanged. From a modern point of view, the order of the premises is not relevant for the validity of the argument.

How would I put this in standard logical form?

The standard representation is: SiM, MaP ⊢ SiP,

that is: ∃x(Sx ∧ Mx), ∀x(Mx → Px) ⊢ ∃x(Sx ∧ Px).

IAI-4 is a valid argument: thus, all its instances must be of two types:

  • either with true premises (sound), in which case the conclusion is also true: there is a Philosoper that is Greek; every Greek is Human. Therefore: there is a Philosopher that is Human; or
  • with false premises (unsound), in which case the conclusion can be true without invalidating the general argument: there is a Philosoper that is Greek; every Greek is Male. Therefore: there is a Philosopher that is Male.
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