Different Logical Systems Can Be Used to Model Different Fragments of Natural Language
When I was teaching logic I would sometimes get students who had some prior exposure to the subject and often it was an exposure to Aristotelian logic. I had several students who were taught the subject in Catholic high schools, and some homeschooled students said that they had to learn categorical logic as part of their “classical” homeschooling education program.
One of the unfortunate consequences of this early exposure is that many of these students associated all of logic with the one formal system that they were taught.
As a result, some of these students had a distorted view of what logic really is and how it works.
The key idea that I want students to understand, on the issue of how logic relates to language, is that different logical systems represent different fragments of the logical structure of natural human language.
What do I mean by a “fragment”? I mean a subset, a partial description, not the whole picture.
To see what I mean, let’s take a look at the three systems of logic that most students are introduced to in an introductory symbolic logic class, and say a few words about the kinds of logical properties of language that each is capable of modeling.