ABSTRACT
You can’t talk generally in sentential logic, be it classical or nonclassical. Something more is needed.
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In the previous chapter, we examined the logical theories that resulted from dropping the completeness and consistency constraints on atomic sentences. We did so while examining only the most basic connectives. In this chapter, we extend this examination to the richer syntactic setting of first-order logic. In Chapters 8-13, we performed a similar examination for the classical theory, but pursued it in stages: first we allowed atomic innards, then we added equality, finally we added quantification. Here we will skip to the end, as these syntactic elements should be wellunderstood by now (and if they’re not, now’s a great time to go review them!).
