After two weeks straight of posting daily, I unfortunately missed out on yesterday. Not to worry though, today’s topic will hopefully be interesting enough to make up for it. Over the past few days I’ve been speaking about formal logic, particularly sentence logic, as I’m being taught through Teller’s Logic Primer. Today I’m going to introduce one new concept which are the final ones to understand before we look at how arguments are structured in sentence logic and how we can use it to create arguments. The symbol we will be discussing looks like this “AↄB” where A and B are two sentences with a true/false value.
This little symbol which looks like a backwards “c” is the conditional connective. A connective connects two different sentences and this one does so in an interesting way. We could “translate” AↄB into English by saying “If A then B” or “A. Therefore B.” as explained in the book. This symbol allows us to express the idea of the conditional in sentence logic. Before, we could only say “and”, “or” and “not”. We’ve know added “if” to our repertoire. So how do we use this? Let’s come up with two example sentences. A will represent the phrase “I like chocolate” and B will represent the phrase “I will buy chocolate”. If we transcribed the above into English we’d get the sentence: “If I like chocolate, then I’d buy chocolate”. Now let’s say I add two negations, one to to “A” and the other to “B” like so: “~Aↄ~B”. With that change we’re now saying: “I do not like chocolate, therefore I will not buy chocolate”.
Each connective gives back a true or false values based on the sentences it’s connecting. The conditional connective will give us a true value in every scenario except when B is false. I hope you’ve enjoyed this look into a new connective and are excited because I’m going to be talking a bit about how you can write simple deductive arguments based on Teller’s book soon!