Logic, philosophy of logic, metalogic

The business of philosophy of logic, as I understand it, is to investigate the philosophical problems raised by logic – as the business of the philosophy of science is to investigate the philosophical problems raised by science, and of the philosophy of mathematics to investigate the philosophical problems raised by mathematics.

A central concern of logic is to discriminate valid from invalid arguments; and formal logical systems, such as the familiar sentence and predicate calculi, are intended to supply precise canons, purely formal standards, of validity. So among the characteristically philosophical questions raised by the enterprise of logic are these: What does it mean to say that an argument is valid? that one statement follows from another? that a statement is logically true? Is validity to be explained as relative to some formal system? Or is there an extra-systematic idea that formal systems aim to represent? What has being valid got to do with being a good argument? How do formal logical systems help one to assess informal arguments? How like ‘and’ is ‘&’, for instance, and what should one think of ‘p’ and ‘q’ as standing for? Is there one correct formal logic? and what might ‘correct’ mean here? How does one recognise a valid argument or a logical truth? Which formal systems count as logics, and why?