This is a summary of a workshop on argument reconstruction that I gave to some fellow PhD students at the MRC/CSO Social and Public Health Sciences Unit at the University of Glasgow in 2021. This is an only slightly expanded version of the slides, and is mostly here for the benefit of the people who attended at the time.

I can deliver this as a 90- or 120-minute remote workshop, including some practical exercises and group discussions – email me if you’re interested!

What is an argument?

In everyday language we use the word “argument” in a lot of different ways, but to a philosopher it means something very specific. Let’s go through some dictionary definitions (from Dictionary.com) just to be clear about what it doesn’t mean.

• an oral disagreement; verbal opposition; contention; altercation: a violent argument. ❌
• a discussion involving differing points of view; debate: They were deeply involved in an argument about inflation. ❌
• an address or composition intended to convince or persuade; persuasive discourse. ✅
• a process of reasoning; series of reasons: I couldn’t follow his argument. ✅
• a statement, reason, or fact for or against a point: This is a strong argument in favor of her theory. 🤔

What we’re talking about is a combination of the two with ticks: something that’s intended to persuade the reader or listener of something, by using a process of reasoning.

(The last one is kind of semi-right. But actually a lot of the time when we use the word like this, we really mean more like what philosophers call a “premise”.)

What is an argument?

An example:

• “Helping someone to commit suicide is the same as murder. Murder is wrong. Therefore, helping someone to commit suicide is wrong.”

Statement by statement:

• Helping someone to commit suicide is the same as murder. (premise)
• Murder is wrong. (premise)
• Therefore, helping someone to commit suicide is wrong. (conclusion)

Formal definition of an argument (Bowell et al):

• “A set of propositions of which one is a conclusion and the remainder are premises, intended as support for the conclusion.”

The “standard form”

• “I’m anti-hunting because I believe that hunting animals is wrong. After all, it’s wrong to kill simply for pleasure and hunting involves the killing of innocent animals for pleasure.” (Bowell et al)

In standard form:

• P1: Killing for pleasure is wrong.
• P2: Hunting involves the killing of innocent animals for pleasure.

• C: Hunting is wrong.

“Reconstructing an argument” means identifying the premises and conclusion in an argument, and rewriting it in the standard form.

Why bother with reconstructing arguments?

• To help figure out whether an argument is good or bad (and why)
• To help see past the “frills” and focus on the structure
• To help us talk and write more clearly about arguments

Good and bad arguments

Here are two pretty unconvincing arguments:

• P1: Erik is a cat.
• P2: Cats are good hunters.

• C: Erik is a good hunter.

• P1: Erik is a cat.
• P2: The main characters in the film Aristocats are cats.

• C: Erik is one of the main characters in the film Aristocats.

These are both unconvincing, but they seem unconvincing in very different ways.

Validity and soundness

We use the terms validity and soundness to distinguish between two different characteristics that can make an argument persuasive or unpersuasive.

Saying that an argument is valid means that:

• “If the premises are (or were) true, the conclusion would also have to be true.” (Bowell et al)

Or equivalently:

• “It would be impossible for all the premises of the argument to be true, but the conclusion false.” (Ibid.)

Saying that an argument is sound means that:

• “The argument is valid, and all its premises are (actually) true.” (Ibid.)

Implicit premises

Sometimes people don’t explicitly spell out every single premise in an argument. In that case we need to figure out what’s been left unsaid, and state it explicitly in our reconstruction.

• P1: Reducing the suffering of others is valuable.
• P2: Donating a kidney to a stranger would reduce the suffering of others.

• C: I should donate a kidney to a stranger.

This is not a valid argument. But if someone were to say something like this, they probably have something like the following P3 in the back of their minds:

• P1: Reducing the suffering of others is valuable.
• P2: Donating a kidney to a stranger would reduce the suffering of others.
• P3: I should do anything I can that reduces the suffering of others.

• C: I should donate a kidney to a stranger.

Adding in implicit premises like this is helpful, because it makes it clear what assumptions you need to make for the argument to work. Often the premise that’s left unsaid is the most controversial or questionable one. This reconstruction makes it clear that it’s a pretty extreme position, and it would take some effort to justify, because P3 is a very strong claim.

The principle of charity

From Bowell et al: “Argument-reconstruction is essentially a task of interpretation. What we are trying to reconstruct, to represent as clearly as we can, is a certain train of thought, of reasoning – however well or badly the arguer may have succeeded in expressing it.”

Even if your ultimate aim is to show that an argument is wrong, your reconstruction should give it the best possible chance of succeeding.

If you reconstruct your opponent’s argument to make it look weak, it’s easy for them to say “oh, but that’s clearly not what I meant” (plus you’ll seem like a bit of a jerk).

Intermediate conclusions

One of the premises in an argument could itself be the conclusion of another argument.

• P1: If it rained last night, then the grass would be wet.
• P2: The grass isn’t wet.

• C1: It didn’t rain last night.
• P3: If it didn’t rain last night, then the Rev Mr Green was lying in his eyewitness testimony.

• C2: The Rev Mr Green was lying in his eyewitness testimony.

Argument reconstruction step by step

1. Identify the conclusion
2. Identify any explicitly stated premises
3. Try to write them down in the standard form (P1, P2, …, C), and assess whether the result is valid
4. Identify any implicit (unstated) premises needed to make the argument valid, and add them in (if at all possible)

Some additional questions to think about:

• Is the argument sound (i.e. are the premises true)?
• How might you (or someone else) object to the argument? Which premises are most vulnerable?
• How could you (or someone else) respond to one of these objections?

An aside: inductive arguments

An example:

• P1: Erik is a Swede.
• P2: Most Swedes are proud of ABBA’s contribution to the pop music canon.

• C: Erik is (probably) proud of ABBA’s contribution to the pop music canon.

This isn’t valid, strictly speaking, but it does seem to tell us something useful about whether we should believe the conclusion. How can we make sense of this?

• Throw in words like “probably” a lot
• Develop formal rules to explain how an argument can be invalid, but still “inductively forceful” (Bowell et al)
• Just kind of don’t worry about it (👈 this is what we’ll do today for reasons of time! 🌈🌞)

Examples!

We’re now ready for some practical exercises.

The photo below is of Ronald Fisher, probably one of the most famous statisticians in the history of statistics. The examples I picked out are all from the literature about smoking and lung cancer from the 1950s, and one of them is from Fisher. He was an avid smoker, and extremely critical – often in pretty arrogant terms – about the idea that smoking might cause lung cancer for his entire life. In retrospect, his articles can be kind of entertaining to read, now that we know that he was completely wrong.

Why does this matter?

Write more clearly

• Summarising existing debates in the literature
• Writing chapter introductions
• Writing persuasive discussion and conclusion sections

Think more clearly

• …about why people might be right or wrong about things
• …about what sort of evidence would be needed to support an idea
• …or what sort of evidence would be sufficient to reject an idea

Be the change you want to see in the world

• Modern academic writing is often unclear, but it used to be better
• Philosophy is no longer a required subject at most universities (just saying)
• The universe is full of undiscovered arguments

Recommended reading

• Bowell T, Cowan R, and Kemp G. Critical thinking: a concise guide. Routledge, 5th ed. 2019.
• Blackburn S. Think: a compelling introduction to philosophy. Oxford University Press, 2001.
• Driver J. Ethics: the fundamentals. Wiley-Blackwell, 2006.
• Ask me for topic-specific recommendations!