Claims, sentences, and truth-conditions

So far we’ve spoken about arguments as collections of claims. This is pretty intuitive, but we need to look a little more closely at what we mean by ‘claim’.

The term ‘claim’ is actually non-standard: it’s more usual for logicians to talk in terms of statements or propositions. Let’s clarify.

Consider a simple argument:

1. If Fatima is a counsellor, then she will have been trained to stay calm under pressure.
2. Fatima is a counsellor.
3. So, Fatima will have been trained to stay calm under pressure.

Here, it’s very plausible that, if the premises are true, the conclusion will have to be true too. It’s plausible this is a valid argument. Note that in this case it seems clear what the claims are. In particular, it’s clear from what sentences are written down what claims are involved (at least, once we’re clear about who we’re talking about). But — and this is the key point for what we’re interested in right now — this isn’t always the case.

Consider the sentence ‘I am hungry’. If you utter this sentence, what is said will be true if and only if things are a particular way: you are hungry. But if I utter it, what is said will be true if and only if things are a different particular way: I am hungry. We would both use the same sentence to make utterances, but we’d make different statements and express different propositions (or claims). We can understand the difference here in terms of truth: it would take one thing to make your statement true, and another different thing to make my statement true. We can put this more precisely by introducing the idea of truth-conditions. The truth conditions of a statement are just the conditions under which it is true (how things have to be for it to be true). For example …

• Your utterance of the sentence ‘I am hungry’ is true if and only if you are hungry (at the time you make the utterance).
• My utterance of the sentence ‘I am hungry’ is true if and only if I am hungry (at the time I make the utterance).

Are you comfortable with the idea that the same sentence can express different claims? If you have questions about this issue, please raise them in Comments.