Critical Thinking
Section 1 -- The Structure of Arguments

Arguments are what philosophers spend most of their time worrying about.  But what exactly is an argument?

Definition of an argument: a set of statements of which it is claimed that one of those statements (the conclusion) is supported by the others (the premises).

E.g., Sydney is in Cape Breton
Cape Breton is in Nova Scotia
Therefore Sydney is in Nova Scotia.
When we're analyzing an argument, we're going to adopt the practice of labelling the premises of an argument as P1, P2, ... and the conclusion as C.  Hence, the boring argument above becomes.
P1: Sydney is in Cape Breton
P2:  Cape Breton is in Nova Scotia
C: Therefore Sydney is in Nova Scotia.
Think about Singer's argument in "The Singer Solution to World Poverty" in these terms.  What are the premises, what's the conclusion?

Logical Strength

Of course, some arguments are better than others. Here's a very bad argument:

Argument #1  P1:  Sydney is in Cape Breton
C: Chipmunks like toast.
Intuitively, we all know the above is a bad argument, but why exactly is it a bad argument?
Argument #2  P1: Jefferson was President of the U.S.A.
P2: All of the Presidents of the USA have been men.
C:  Jefferson was a man.
Is Argument #2 a good argument?  How about:
Argument #3  P1:  Trudeau was Prime Minister of Canada.
P2:  All but one of the Prime Ministers of Canada have been men.
C:  Trudeau was a man.
Both of the previous two arguments are good arguments in some sense, but they differ in terms of logical strength.  Argument #2 is a deductively valid argument (i.e., one which is such that it is impossible to have all the premises of the argument be true while the conclusion is false).  Argument #3 is an inductively strong argument (i.e., one which is such that if all its premises are true, then its conclusion is probably true).  If an argument possesses either of these properties, we'll say the argument is logically strong.  You can think of deductive validity and inductive strength as different flavours of logical strength.  Notice that Argument #1 possesses neither of these properties, hence Argument #1 is not logically strong at all.

What about this argument?

Argument #4  P1:  Jefferson was President of the USA
P2:  Jefferson was never President of the USA.
C:  Monkeys are made of goo.
Is this argument logically strong?  Surprisingly, itís a deductively valid argument.  Why?  Because itís impossible to have the premises true and the conclusion false. (Look back at the definition of deductive validity if you don't see why this makes Argument #4 deductively valid.)

Is Argument #4 a good argument?  No, itís a terrible argument, but not because of its logical strength. Itís terrible because thereís no way for its premises to all be true.  No matter what, one of those premises is unacceptable.  This shows that we want more than mere logical strength out of an argument.


In general, there are two things we want out an argument.  We want it to be logically strong (and the stronger, the better) and we want it to have true premises.  The ideal argument is one which is deductively valid and has true premises.  Such an argument is said to be sound.

Note: logical strength and soundness are properties of arguments. Truth (or falsity) is a property of statements (or premises or conclusions). Never say 'that argument is false' or 'that premise is logically strong.' If you do, you're talking nonsense.

An Exception

To be accurate, however, it's worth noting that we don't always want our arguments to be sound.  Consider the following argument from an imaginary murder trial by an imaginary defense lawyer.

P1:  My client was in Ottawa 10 minutes before the murder was committed.
P2:  The murder was comitted in Toronto.
P3:  My client is the murderer.
C:  My client must have travelled from Ottawa to Toronto in 10 minutes.

This sort of argument is called a reductio ad absurdum. It's used to show that at least one of the premises of the argument must be false since together they lead us to an absurd conclusion (i.e., a conclusion that cannot be true).  What we have here is a deductively valid argument for an impossible conclusion, so it must be the case that one of the premises is false.  (Notice, however, that it's not obvious from the information presented above which one of the premises is false, although we can guess which one the defence lawyer will tell us it is.)

Clearly, when a person tries to give a reductio argument, he or she is not trying to present a sound argument since the whole idea is to show that one of the premises is false.  Most of the time, however, it's sound arguments we're interested in.

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