# Are there modern approaches to logic that aren't *grounded* in math?

Are there any modern approaches to logic that are non-mathematical in nature or not grounded in math?

The introduction to Thoughts, Words and Things, referenced in this answer, contains an interesting passage about the history of logic and how modern readers link logic and the foundations of math.

Readers coming at this material from the point of view of modern logic may be surprised to find very few of what are sometimes called “logical results” — that is, theorems about interesting general logical truths. In fact, you may think what we are doing isn’t really "logic" at all, but more philosophy of language, or even philosophy of mind or epistemology. Why then call it logic? The short answer to this of course is that they called it "logic," and they got there first! A less contentious response would be to point out how much the close connection between logic and the foundations of mathematics in the recent period has shaped our view of what logic is, to the point of making it hard sometimes for us to think of logic in any other terms.

I've seen other comments elsewhere about the success of the mathematical approach to studying logic and how it revolutionized the field, but this passage has a rather different tone. It suggests but does not directly claim that conflating an application of logic and logic itself obscures some important and interesting ideas.

I've really enjoyed learning bits and pieces of traditional syllogistic logic, particularly the pieces that differ radically from mathematical approaches as I understand them, such as not including syllogisms with weaker-than-possible conclusions from the set of valid syllogisms, and not having syllogisms with inconsistent premises.

• It is hard to understand what "non-mathematical" approaches, as you understand them, are. I thought I understood it (what used to be called "logic" and is now renamed into "epistemology") until the last paragraph. Excluding weaker-than-possible conclusions or inconsistent premises are studies of interesting subsystems of a grand system, a perfectly mathematical enterprise. There are relational extensions of the syllogistic, for example, radically different from the predicate calculus (referenced here), would that be "non-mathematical"? Jan 21 '21 at 4:21
• @Conifold the last paragraph was meant to indicate an example of properties that can be accounted for when viewed through the lens of mathematics, but suggest, at least to me, a different heritage. Jan 21 '21 at 4:42
• Perhaps the different heritage is that traditional logicians tried to stay closer in form and motivation to natural language and reasoning rather than giving them up for more technical benefits. If that's what it is perhaps what you are looking for goes under "natural logic" and "semantics of natural language". References I linked are of this sort. Jan 21 '21 at 4:50
• Logic is not "grounded" in mathematics: but, as well as many other fields of inquiry (physics, economy) the mathematical tool-set greatly improved the study of logic. Jan 21 '21 at 9:08
• Mathematics is an enormously great source for representing various definitive concepts when studying logic and similar ideas. It's more a tool with which you can express abstract quantities, draw implications, identify functions, generalise relationships, plot data, extrapolate results, rigorously prove conjectures, organise and communicate information with strong clarity, etc. To me, the question asked is analogous to "Are there approaches to language that is not grounded in writing?" Jan 21 '21 at 19:00