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Is it correct to say that validity tout court (as opposed to formal validity) is a pre-theoretical notion? This would be the reason why we say things like: «predicate logic can account for the validity of this argument, but not propositional logic». We can say this because validity is an intuitive, pre-theoretical notion ("In every imaginable situation in which the premises are true it is impossible for the conclusion to be false"). What do you think?

Thanks a lot

Fisher

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    «predicate logic can account for the validity of this argument, but not propositional logic» : this is related to the different +expressive power* of propositional logic compared to first-order logic. Every (propositional) tautology is valid, but not vice versa: $\forall x (x=x)$ is *valid* but not tautological. – 2017-02-12
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    And yes: the concept of "vaid argument" was defined firstly by [Aristotle](https://seop.illc.uva.nl/entries/aristotle-logic/#SubLogSyl); various "formal systems" (starting from A's syllogistic) has been defined in order to "capture" the intuitive notion. – 2017-02-12
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    Relative toe.g. the first-order langugae, we have a formal definition of *validity*; the Completenes theorem for FOL shows that various formal systems (Hilbert-style, Natural Deduction, Tableau) fully capture the formal notion of validity. – 2017-02-12
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    See also Peter Smith, [Squeezing arguments](https://pdfs.semanticscholar.org/0b9e/1ea5ea281173d80abf48d42695a2dd480ca2.pdf) (2010) – 2017-02-12
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    Ok, but mine was a broader, philosophical question: can we say that validity preexists formal validity? In other words, I think that if predicate logic had never been introduced we would still say that a given argument is valid (although not FORMALLY valid). – 2017-02-12
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    Ok so the answer is yes; your second comment is what I was after :-) – 2017-02-12
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    Yes and no; A's logic is *formal*: syllogistic "figures" are schematic. A's theory is a full-blown theory. So I would say that A's theory is about formal validity. Of course, it is not a [formal system](https://en.wikipedia.org/wiki/Formal_system) or *calculus* developed with mathematical tools. – 2017-02-12
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    Ok, so it's not that straightforward. Anyway, regarding A's logic, I think you should say it's SEMIformal. – 2017-02-12

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