Logical Arguments

The structure of a philosophical argument

A good philosophy paper contains an argument: “a series of claims in which one of the claims (i.e., the conclusion) is said to follow from, or be supported by, one or more of the other claims (i.e., the premises)” (The Philosophy Skills Book). There are two kinds of arguments that come up often in philosophy: deductively valid arguments (in which the truth of the conclusion follows automatically from that of the premises; i.e., if the premises are true, then the conclusion is necessarily also true), and inductive arguments (in which the truth of the premises only makes the conclusion probable). Here’s an example of each, taken from The Philosophy Skills Book:

  1. Female soldiers have the skills and talent required for combat.
  2. Any soldiers with the skills and talent required for combat should be allowed to join a combat unit.
  3. Thus, female soldiers should be allowed to join a combat unit.

In this argument, 1 and 2 are premises, and 3 is the conclusion. Assuming 1 and 2 are both true, 3 will automatically be true as well. So, this is a deductively valid argument. Compare this to another example:

  1. Most female soldiers have the skills and talent required for combat.
  2. Major Susan Smith is a female soldier.
  3. Major Susan Smith has the skills and talent required for combat.

Here, 1 and 2 again are premises, and 3 is the conclusion. However, assuming 1 and 2 is not enough to warrant the truth of 3. It may still be the case that the Major is unfit for combat, without this contradicting 1 or 2.

Validity and soundness

In what follows, we will focus on deductively valid arguments. Interestingly, the following is also an example of a deductively valid argument:

P1. All pink elephants on Mars vote Labour.

P2. Socrates is a pink elephant on Mars.

C. Therefore, Socrates votes Labour.

Though this argument is deductively valid, it is highly unsatisfying. To say that an argument is deductively valid does not automatically mean it is also a good argument! To determine whether it is a good argument, we must also ask whether the premises are true. In the pink elephant example, P2 is false. And therefore, the argument is unsound. Because 2. is false, we cannot conclude from this argument that the conclusion is true. Now, what about the following classic, do you think?

P1. All men are mortal.

P2. Socrates is a man.

C. Therefore, Socrates is mortal.

Formalizing an argument

In most papers you will read for your degree, the author will not spell out the premises and conclusion of her argument in this structured way. Moreover, key premises will often be implicit, rather than explicitly stated. It is therefore useful to train yourself in formalizing someone else’s argument, so you can more easily check whether it is both valid and sound. (This also works in pub debates, though people will most likely avoid talking to you if you do it too often.)

Consider, for instance, the following argument:

“It seems that the existence of God cannot be demonstrated. For if His existence could be demonstrated, then that would be scientific knowledge. But our knowledge of God is through faith.” (paraphrased from St Thomas Aquinas ‘Five Ways to Prove the Existence of God’ by John Worrall)

When you come across an argument like this, you should ask yourself: what are the premises here, and what is the conclusion? Are there any hidden premises that St Thomas tacitly relies on, in order for the argument to be deductively valid? You will find that St Thomas’ argument can be formalized as follows:

P1. If God’s existence could be demonstrated, then that would be scientific knowledge.

P2. Our knowledge of God is through faith.

C. So, the existence of God cannot be demonstrated.

However, there is still a premise missing, which we need to make the argument deductively valid. Consider this longer version:

P1. If God’s existence could be demonstrated, then that would be scientific knowledge.

P2. Our knowledge of God is through faith.

P3. If we know something through faith, then we don’t know it in a scientific way.

C. So, the existence of God cannot be demonstrated.

Knowing the full form of the argument now allows us to evaluate it.

So, to sum up: when you read a philosophy paper, ask yourself what the argument in the text is: what are the premises, and what is the conclusion? Then classify the argument: is it meant to be deductive, or only inductive? If it is meant to be deductive, is it actually deductively valid (i.e., if the premises were true, would the conclusion automatically be true as well)? And is the argument sound (i.e. are the premises true)?


 

Exercises

1. Is St Thomas’ argument, as expanded above, sound?

2. Here are two more arguments you can analyse:

  1. “If the civil population cannot be defended in the event of a nuclear war, we do not need a civil defence policy. But we do need a civil defence policy if ‘deterrence’ is to be a convincing strategy. Therefore deterrence is not a convincing strategy.” (paraphrased by John Worrall from a CND pamphlet)
  2. “Those who deny global warming are right just in case they have taken a balanced view of the scientific evidence. But in fact those who deny global warming have vested interests in making money by polluting the planet.” (common environmentalist argument, paraphrased by John Worrall)

Again, ask yourself for each of these: what are the premises here, and what is the conclusion? Are there any hidden premises that are tacitly relied on, and that are needed for the argument to be deductively valid?

3. Determine, for the sections below, whether the argument is deductively valid and sound (taken from The Philosophy Skills Book, p. 87).

  1. “If smoking cigarettes is more dangerous than smoking marijuana, then smoking marijuana should be legally permitted. Smoking cigarettes is more dangerous than smoking marijuana. Thus, smoking marijuana should be legally permitted.”
  2. “The mind is indivisible. The body is divisible. Something cannot both be divisible and indivisible at the same time. It follows, then, that the mind and body are not the same thing.”