I also find much of the article dense, but here's my attempt at a summary. Logicians like the idea that words and phrases have "meanings" or "references." Lik

I also find much of the article dense, but here's my attempt at a summary. Logicians like the idea that words and phrases have "meanings" or "references." Like, "my computer" should be interpreted, when I say it, as referencing a particular gadget that I own. If you sit around and speculate about such references, you might wonder, for example, what the reference of "the unit sphere" is. Your Platonist friends will tell you that the reference is to an actually existing abstract object, or something like that. The question of truth values seems to revolve around the question of the reference of a claim such as "Socrates is mortal." And the proposed answer is that this claim is a kind of name referring either to "the Truth" or "the False." Note that this is how you tend to think of such claims when you work in predicate logic: the term Mortal(Socrates) is assumed to have the value True or False. A quote cited by the article, by Jan Łukasiewicz (incidentally the inventor of "Polish notation"): "All true propositions denote one and the same object, namely truth, and all false propositions denote one and the same object, namely falsehood. I consider truth and falsehood to be singular objects in the same sense as the number 2 or 4 is. … Ontologically, truth has its analogue in being, and falsehood, in non-being. The objects denoted by propositions are called logical values. Truth is the positive, and falsehood is the negative logical value. … Logic is the science of objects of a special kind, namely a science of logical values." These thoughts about meaning were fundamental to the development of mathematical logic. Frege's notion of truth values was a prerequisite for his development of formal first-order logic and second-order logic, and algebraic logic in general (Boole's algebraic logic is an early version).