On Some Logical Properties of ‘Is True’

I think that it is very proper to include a paper about truth in a volume dedicated to Jaakko Hintikka even if it does not deal directly with his highly original ideas about this topic that are related to IF logic. This essay considers the problem of truth in a conservative way, so to speak way. I will focus on properties of the predicate ‘is true’ derived from very elementary logical insights. It is convenient to start with Frege’s view (see Frege 1979a, Frege 1979b) that logic is the science of truth. This thesis should be understood to mean that logic concerns formal principles of truth (the distinction between formal truth and material truth was very common in German philosophy of the 19 century). Putting this in more contemporary terminology, formal truth consists in truth defined by purely structural criteria and transmitted by principles of logical entailment (logical consequence) as codified by logical calculus. These principles always guarantee the truth of conclusion if premises are true; technically speaking, logical entailment preserves truth, that is, transmits it from premises to conclusion. Is the view that logic is the science of truth the only possibility? Surprisingly enough, the answer is no, because it is not difficult to define the consequence relation as preserving falsehood (see also Wolenski 1995). Consider the formulas