Course: Logic: The Language of Truth

But now we hit another problematic feature of natural languages. Suppose someone said: It’s not the case that it’s raining and it’s warm What would they be saying? Under what …

One of the key things we’re going to be doing in this course is introducing carefully defined symbols to help us be clear about what’s going on with claims and …

We now have two sentence-operators in our formal language: ampersand (‘&’) and tilde (‘~’). This highlights the possibility of having sentences which contain two sentence operators. (That possibility was present …

Having unpacked what we mean by ‘arguments’, we’re now in a position to outline what logic is, in the sense in which we’re interested in it in this course. Logic …

The result of applying tilde to a sentence is the negation of that sentence. The negation of a sentence is true when that sentence is false, and false when that …

You might be a bit worried about the possible gap between what’s said (explicitly, by the sentence used) and what’s merely suggested. It might seem like we can never be …

In this step, we’ll look at an idea from philosopher Paul Grice on how the kind of ‘getting a message across’ that we’ve been looking at works. Grice suggested that …

Let’s develop these ideas around distinguishing between what sentences mean and the messages we get across by saying them. We’ll start with a rough sketch of the distinction between semantics …

In this step we’ll start to look at some interesting ideas clustering around a suggestion originally made by philosopher Paul Grice. In this and the next few steps, we’ll look …

So, do we have a real mismatch case? Have we found that ‘and’ doesn’t have the same meaning as ‘&’ (in the sense of expressing the same truth-conditions), or that …

We’re now in a bit of an awkward position. On the one hand, we have some cases that seem to be mismatches. On the other, we’ve just seen that there’s …

We know what the truth-table is for ‘&’ — because we just defined it (once and for all) using that truth-table. The question we’re looking at now is whether the …

When you first start making truth-tables for complex sentences, it can be a little puzzling seeing what order to do your workings. This video shows a helpful way to identify …

We’ve said that it looks like ampersand is close in meaning to the sentence connective ‘and’ in English. But how can we test this idea? Before we look further at …