Meaning and Argument Book

This is a very nice treatment on basic classical logic with a strong focus on language and translation. New logical notations are always motivated by being needed to represent expressions in natural language not capable of being represented in the notation presented thus far. This creates a very nice pedagogical approach where, beginning with propositional logic, the logical language is extended in several iterations all of which start with showing how some sentences in natural language can be represented in the logical notation developed so far, and ending with some sentences not capable of being treated, leading to the next iteration in which new notational capabilities are introduces to allow further capabilities. This leads to a richer and richer logical language, from propositional logic, via monadic predicate logic (here called property predicate logic), polyadic predicate logic (relational predicate logic) up to predicate logic with identity.

The path from basic propositional logic up to predicate logic with identity seems fairly standard for introductory logic texts, but the heavy use of language not only as a tool for creating examples, a pedagogical tool, but as a way of motivating the continuing expansions of the logical language, is seemingly less common. This focus on language is pretty far reaching. Much time is spent discussing the proper logical form for various grammatical forms (the subject of definite descriptions and Russell's treatment of them in terms of logical form is one example). All of this is very interesting and might be a good way to understand the use of the logical language for those who have trouble seeing the motivations behind the formalisms when reading more strictly technical texts (I will be the first one to admit that my experience with introductory logic texts written by mathematicians can be rather puzzling), but the focus on language might be a bit too heavy for am introduction to logic. Including the appendix, the text comes to 355 pages, which seems a bit excessive considering how little of actual logic it contains. There is no discussion of proof systems other than truth trees (semantic tableaux), there is virtually nothing about semantics for logic (only a few words are dedicated to extracting counter models from open truth trees, which gives some sense of what a model is, but not a single word is dedicated to hinting at even the existence of the field of model theory), and nothing (as far as I can remember, but feel free to correct me if I am mistaken) is said about richer logical languages. The last chapter talks about verb modifiers and towards the end semms to hint a little bit towards modal logic (when talking about the "event approach" and mentioning that the example "The president possibly lied to the people" is probably best rephrased as "It is possible that the president lied to the people" before trying to figure out how it could be formalised in logic) but it is never mentioned explicitly. (Modality is mentioned in the appendix, but only as a feature of natural language, there is no mention of modal logic.)

These things single it out as an introductory text in my experience. It seems that the heavy focus on natural language and translations made sure there was no room to even mention some more advanced topics in logic, some metalogical results and some richer logical systems (I don't believe second order logic is mentioned either). This is surely a conscious decision, but I'm not sure it's the right one for an introductory course to logic, even if it is taught in a philosophy department (and surely not if it is taught in a mathematics or computer science department).

Perhaps it is better seen as a book filling a niche. Since the other introductory texts I have encountered do treat other logical systems, several different proof systems and some metalogical results (or at least mention them), there might be need for a logic text that ignores these in favor of more linguistic focus. At my university, there is a program in philosophy and linguistics and perhaps this is a perfect introductory text in logic for them.

In any case, the seemingly negative opinions expressed above are only slightly and hesitatingly negative, they should perhaps be seen more as a form of pusslement over the approach taken in this book than a dismissal of it.