# If this world is the only possible world, what does that mean for validity in logical arguments?

Validity is usually defined in terms of possible worlds. More specifically, an argument with premise set S and conclusion C is said to be valid if and only if there is no possible world with all the members of S true but C false. But, what if this world, the actual world, is the only possible world, as I and many others believe? Then all sorts of arguments that are intuitively invalid would be valid. In fact, all arguments with a true conclusion would be valid, since there is no other world where the conclusion is false. So, does this mean that actualism implies that validity is "trivialized" in this way? And have any philosophy books or papers argued for this analysis?

• Nothing. One can describe validity in terms of "possible worlds" (more commonly called models), but has to be very careful with selecting the class of "possible worlds" to match the standard notion. It makes no difference what they believe exists, validity is not tied to that. Shapiro in Logical consequence: Models and modality discusses what happens when the class of models is badly selected, it is related to Etchemendy's criticisms of Tarski's semantic validity. – Conifold Jul 21 at 1:15
• There's also a whole competing school of thought that proposes a proof-theory-centric view of logical consequence (and its associated validity notions), which would seem to circumvent this "possible worlds" objection even if it could be made substantial. See e.g. plato.stanford.edu/entries/logical-consequence/… – Paul Ross Jul 21 at 14:37
• Your understanding of validity is incorrect from the philosophy point of view. What you are referring to is the Mathematical logic or Computer Science context of validity. You can find logical arguments that are valid but actually false in this world. Validity doesn't guarantee truth in this world. For example, this is valid: All snakes are cats. All dogs are snakes. Therefore all dogs are cats. If you understand logical form you will see this is an AAA syllogism in the first figure which must be valid. Soundness means the premises must be true & the conclusion must be true plus being valid – Logikal Jul 21 at 17:33