forall x : Calgary Remix An Introduction to Formal Logic by P. D. Magnus, Tim Button, with additions by, J. Robert Loftis, remixed and revised by

Aaron Thomas-Bolduc and Richard Zach.

From the introduction:

As the title indicates, this is a textbook on formal logic. Formal logic concerns the study of a certain kind of language which, like any language, can serve to express states of affairs. It is a formal language, i.e., its expressions (such as sentences) are defined formally. This makes it a very useful language for being very precise about the states of affairs its sentences describe. In particular, in formal logic is is impossible to be ambiguous. The study of these languages centres on the relationship of entailment between sentences, i.e., which sentences follow from which other sentences. Entailment is central because by understanding it better we can tell when some states of affairs must obtain provided some other states of affairs obtain. But entailment is not the only important notion. We will also consider the relationship of being consistent, i.e., of not being mutually contradictory. These notions can be defined semantically, using precise definitions of entailment based on interpretations of the language—or proof-theoretically, using formal systems of deduction.

Formal logic is of course a central sub-discipline of philosophy, where the logical relationship of assumptions to conclusions reached from them is important. Philosophers investigate the consequences of definitions and assumptions and evaluate these definitions and assumptions on the basis of their consequences. It is also important in mathematics and computer science. In mathematics, formal languages are used to describe not “everyday” states of affairs, but mathematical states of affairs. Mathematicians are also interested in the consequences of definitions and assumptions, and for them it is equally important to establish these consequences (which they call “theorems”) using completely precise and rigorous methods. Formal logic provides such methods. In computer science, formal logic is applied to describe the state and behaviours of computational systems, e.g., circuits, programs, databases, etc. Methods of formal logic can likewise be used to establish consequences of such descriptions, such as whether a circuit is error-free, whether a program does what it’s intended to do, whether a database is consistent or if something is true of the data in it….

Unfortunately, formal logic uses “true” for a conclusion that is valid upon a set of premises.

That smearing of “true” across formal validity and factual truth, enables ontologists to make implicit claims about factual truth, ever ready to retreat into “…all I meant was formal validity.”

Premises, within and without ontologies, are known carriers of discrimination and prejudice. Don’t be distracted by “formal validity” arguments. Keep a laser focus on claimed premises.