If you accept truthmakers, and two further principles, then you can maintain that a deductive argument is valid just in case the truthmakers of its premises suffice to make true its conclusion. Or as David Armstrong puts it in Sketch of a Systematic Metaphysics (Oxford UP, 2010), p. 66,
In a valid argument the truthmaker for the conclusion is contained in the truthmaker for the premises. The conclusion needs no extra truthmakers.
For this account of validity to work, two further principles are needed, Truthmaker Maximalism and the Entailment Principle. Truthmaker Maximalism is the thesis that every truth has a truthmaker. Although I find the basic truthmaker intuition well-nigh irresistible, I have difficulty with the notion that every truth has a truthmaker. Thus I question Truthmaker Maximalism. (The hyperlinked entry sports a fine photo of Peter L.)
Armstrong, on the other hand, thinks that "Maximalism flows from the idea of correspondence and I am not willing to give up on the idea that correspondence with reality is necessary for any truth." (63) Well, every cygnet is a swan. Must there be something extramental and extralinguistic to make this analytic truth true? And let's not forget that Armstrong has no truck with so-called abstract objects. His brand of naturalism excludes them. So he can't say that there are the quasi-Platonic properties being a cygnet and being a swan with the first entailing the second, and that this entailment relation is the truthmaker of 'Every cygnet is a swan.'
The Entailment Principle runs as follows:
Suppose that a true proposition p entails a proposition q. By truthmaker Maximalism p has a truthmaker. According to the Entailment Principle, it follows that this truthmaker for p is also a truthmaker for q. [. . .] Note that this must be an entailment. If all that is true is that p --> q, the so-called material conditional, then this result does not follow.
I would accept a restricted Entailment Prinicple that does not presuppose Maximalism. To wit, if a proposition p has a truthmaker T, and p entails a proposition q, then T is also a truthmaker for q. For example, if Achilles' running is the truthmaker of 'Achilles is running,' then, given that the proposition expressed by this sentence entails the proposition expressed by 'Achilles is on his feet,' Achilles' running is also the truthmaker of the proposition expressed by 'Achilles is on his feet.'
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