Part I: Terms and Definitions
• A statement is any unambiguous declarative sentence about a fact (or non-fact) about the world. It says that something is (or isn’t) the case. • An argument is a series of statements meant to establish a claim. • A claim or conclusion is the statement whose truth an argument is meant to establish. • A statement’s truth value is either true or false.
o All statements have a truth value. A statement is false when what it says about the world is not actually the case. A statement is true when what it says about the world is actually the case. • A premise is a statement that is used in an argument to establish a conclusion.
What we can say about an argument:
• An argument is valid if its premises necessarily lead to its conclusion. That is, if you accept that the premises are all true, you must accept that the conclusion is true. • An argument is sound if it is valid and you accept that all its premises are true. • A good, convincing argument is a sound argument. That is, since you accept all the premises are true, you must accept the conclusion is true (because the argument is valid). • A bad argument is any other kind of argument.
• “Every animal needs to breathe in order to live. Fish are animals. Fish cannot breathe in the air. Therefore, fish cannot live in the air.” Here, the claim is that “fish cannot live in the air.” The premises are “Every animal needs to breathe in order to live,” “Fish are animals,” and “Fish cannot breathe in the air.” The argument is valid – the premises necessarily lead to the conclusion. The argument is also sound – the premises are true. It is a good argument.
• “Oranges are green. All green things make me sick. Therefore, oranges make me sick.” The claim is “oranges make me sick.” The premises are “Oranges are green,” and “All green things make me sick.” The argument is valid – if we accept the premises, we are forced to accept the conclusion. However, the argument is not sound – oranges are not, in fact, green, so one of the premises is false. This is a bad argument.
• “Broccoli is green. Some green things make me sick. Therefore, broccoli makes me sick.” The claim is “broccoli makes me sick.” The premises are “Broccoli is green,” and “Some green things make me sick.” Here, all the premises are true. However, the argument is not valid – even if we accept the premises, we are not forced to accept the conclusion. Just because some green things are sickening does not mean that broccoli is. This is a bad or unsound argument. (Notice, it doesn’t make any difference whether or not broccoli makes me sick – whether or not the conclusion is true. Even if the conclusion is true, the premises have not given us reason to believe that it is true.)
• “Whales know how to play hockey. Therefore, Canadians like winter.” The claim is “Canadians like winter.” The premise is “Whales know how to play hockey.” The argument is neither valid nor sound. It’s a bad argument. (Again, it doesn’t make any difference whether the conclusion is true.)
Part II: Analyzing an Argument
Reconstructing the argument
The examples I’ve given are overly simplistic. Usually arguments come in complicated prose. It is therefore difficult to figure out what the argument is, let alone whether it is good. Our first step is to reconstruct the argument. That is, we must convert the argument into a series of statements, identifying the premises and the conclusion and laying them out so that the premises lead to the conclusion.
Take Socrates’s argument in the Apology:
“For Death is to be as it were nothing, and to be deprived of all sensation... And if no sensation remains, then death is like a dreamless sleep. In this case, death will be a blessing. For, if any one compares such a night as this, in which he so profoundly sleeps as not even...