2. What is a Claim, or Statement?

Arguments are made up of "claims", or "statements". In this section I want to say a few words about what this means and why it's important for logic.

Here's a definition you might see in a logic text:

A claim is a sentence that can be true or false (but not both).

Actually in logic texts the more commonly used term is "statement" or "proposition". These are all intended to mean the same thing. A claim, or a statement, or a proposition, is a bit of language whose defining characteristic is that it makes an assertion that could be true or false but not both.

The "true or false" part of this definition expresses a principle of classical logic that's called the Principle of Bivalence. This principle asserts that a claim can only assume one of two truth values, "true" or "false"; there's no third option like "half-true" or "half-false", or "almost true".

The "but not both" part of this definition expresses a different principle of classical logic called the Principle of Non-Contradiction. This principle states that a claim can't be both true and false at the same time, it's either one or the other. To assert otherwise is to assert a contradiction.

(Actually there are systems of logic where both the Principle of Bivalence and the Principle of Non-Contradiction are relaxed. Logicians can study different systems of reasoning that don't assume these principles. But in classical logic they hold, and in what follows we're going to assume that they hold.)

Now, you might ask why defining claims in this way is important. Here are two reasons.

(1) Not all sentences can function as claims for argumentative purposes.

For example, questions don't count as claims, since they don't assert anything that can be true or false. If you have a question like "Do you like mushrooms on your pizza?", that's a request for information, it doesn't assert that such-and-such is true or false.

Another type of sentence that doesn't count as a claim is a command, or an imperative, like "Step away from the car and put your hands behind your head!". That's a request to perform an action, it makes no sense to ask whether the action or the command is true or false.

So, not every bit of language counts as a claim, and so not every bit of language can play the role of a premise or a conclusion of an argument.

Here’s a second reason why this definition of a claim is important.

(2) The definition gives us a way of talking about clarity and precision in our use of language.

This is because in saying that a sentence can function as a claim in an argument, what we're saying is that all the relevant parties, both the person giving the argument and the intended audience of the argument, have a shared understanding of the meaning of that sentence.

In this context, what it means to understand the meaning of a sentence is to understand what it would mean for the sentence to be true or false. That is, it involves being able to recognize and distinguish in your mind the state of affairs in which the sentence is true from the state of affairs in which the sentence is false.

So, in the context of logic and argumentation, for a sentence to be able to function as a claim, for it to be able to function as a premise or a conclusion of an argument, there has to be a shared understanding of what the sentence is asserting.

Consequently, if the sentence is too vague or its meaning is ambiguous, then it can't function as a claim in an argument, because in this case we literally don't know what we're talking about.

The requirement that a sentence be able to function as a claim is not a trivial one. It's actually pretty demanding. Not all bits of language make assertions, and not all assertions are sufficiently clear in their meaning to function as claims.

This is important. Before we can even begin to ask whether an argument is good or bad, we need to have a shared understanding of what the argument actually is, and this is the requirement that you're expressing when you say that an argument is made up of claims that can be true or false.

What this means in practice is that, ideally, you want everyone to have a shared understanding of what the argument is about and what the premises are asserting. If people can't agree on what the issue is, or what's being asserted then you have to go back and forth can clarify the issue and clarify the arguments so that all parties finally have a shared understanding of the argument.

Only then can you have a rational discussion of the strengths and weaknesses of the argument.

Questions and Comments

1. Sometimes a statement can be expressed using a question, can’t it?

That’s true. A good example is “rhetorical questions”, which are really statements.

For example, if you ask me whether I’m going to study for the final exam, and I look at you say “What do you think I am, an idiot?”, I’m not actually asking whether you think I’m an idiot. It’s a rhetorical question, used to (sarcastically) assert the statement “Yes, I’m going to study for the final exam”.

This example illustrates a general point, that identifying arguments in ordinary language requires paying attention to rhetorical forms and stylistic conventions in speech and in writing. A complex writing style, or a failure to understand the rhetorical context in which an argument is given (for example, failing to recognize SATIRE), can lead to confusion about what is being asserted.

2. What’s the difference between a sentence being VAGUE and a sentence being AMBIGUOUS?

If I ask my daughter when she’ll be back from visiting friends and she says “Later”, that’s a VAGUE answer. It's not specific enough to be useful.

On the other hand, if I ask her which friend she’ll be visiting, and she says “Kelly”, and she has three friends named Kelly, then that’s an AMBIGUOUS answer, since I don’t know which Kelly she’s talking about. The problem isn’t one of specificity, it’s about identifying which of a set of well-specified meanings is the one that was intended.

Note that all natural language suffers from vagueness to some degree. If I say that the grass is looking very green after last week’s rain, one could always ask which shade of green I’m referring to. But it would be silly to think that you don’t understand what I’m saying just because I haven’t specified the shade of green.

For purposes of identifying claims in arguments, the question to ask isn’t “Is this sentence vague?”, but rather, “Is this sentence TOO vague, given the context?”.

If all I’m doing is trying to determine whether the grass needs watering or not, the specific shade of green probably doesn’t matter. But if I’m trying to pick a green to paint a room in my house, specifying the shade will be more important.