Class 8 - Inferences

Welcome back

Welcome back. In this session, we are continuing our discussion of argumentation,

Evaluating arguments

Today we’re talking about how to evaluate arguments. We’re going to talk about three kinds of arguments, and how they work. And we’re going to be thinking about how a analyse arguments more closely, so that we can be sure that they really hang together.

This is useful when thinking about other people’s arguments. But perhaps it is more useful when thinking about our own. Is what we’re arguing or saying really something that makes sense? Or does it not hold water? The art of evaluating arguments is the art of becoming a little more suspicious of ourselves.

Reading:

The reading today comes from chapter 2 of the online textbook we have been studying. This chapter is written by Nathan Smith, and in it, the author talks about evaluating arguments. Here he talks about three kinds of arguments: deductive, inductive and abductive. As a reminder, here is the chapter: https://press.rebus.community/intro-to-phil-logic/chapter/chapter-2-evaluating-arguments/

Discussion

First, let’s get this distinction clear in our minds. In groups, I want you to discuss:

1. What is a deductive argument?
2. What is an inductive argument?
3. What is an abductive argument?

In your groups, come up with one example of each for us to talk about. Write it down, so you can post it in the chat.

Deductive arguments

Let’s now look more closely at deductive arguments. How do we know deductive arguments are good ones? This is a matter of validity and soundness. I’ll talk you through this, then we’ll have another task.

Argument 1 (valid and sound):

1. All cats are mammals.
2. Aslan is a cat.
3. Therefore Aslan is a mammal.

This is a valid argument because 3 necessarily follows from 1 and 2. And is a sound argument because both 1 and 2 are true. So it is both valid and sound. It’s a winning argument!

We can represent the form of the argument like this.

1. All As are B
2. X is A
3. Therefore X is B

You can see this argument works whatever values you have for A, B and X, as long as your premises are correct. This kind of valid argument is like a little machine. If you feed true statements into it, you get a true statement out. Every time!

Argument 2 (valid, but not sound)

Let’s look at the following argument.

1. All cats are mammals.
2. My microphone is a cat.
3. Therefore my microphone is a mammal.

This has the same form as the previous argument. It is valid. But it is not sound, because the second premise is clearly nonsense.

1. All As are B
2. X is A
3. Therefore X is B

So validity is not enough. Your premises need to be true if you want to get true conclusions out of a valid argument.

Argument 3 (Neither valid nor sound)

Let’s look at a final argument.

1. All cats are mammals
2. Aslan is a mammal
3. Therefore Aslan is a cat.

This might look superficially convincing. After all, Aslan *is * a cat. But let’s look more closely. What’s wrong with this argument?

We can make this simpler by looking at the form of the argument.

So what’s wrong with argument 2? It goes like this:

1. All As are B
2. X is B
3. Therefore A is B

This is not a valid argument. We can see why if we put different values into the argument.

1. All humans are mammals
2. Aslan is a mammal
3. Therefore Aslan is a human

Suddenly, we see that form of the argument doesn’t work at all.

Exploring Deductive Arguments

I’m going to divide you into three groups:

a. Valid and sound (i.e. successful) b. Valid but not sound (i.e. not successful) c. Neither valid nor sound (i.e really not successful)

Now I want you in your groups to come up with up to three examples of deductive arguments that reflect that name of your group!

Discussion

After this, we’ll talk through your arguments!

Break!

We’ll now take a break!

Inductive Arguments

In the second half, we’ll explore inductive and abductive arguments. In everyday life, not all arguments are deductive — in fact, surprisingly few of them are! Philosophers like deductive arguments, because they are tidy and rigorous. But induction and abduction are not quite so tidy, and are much harder to formalise.

Instead of validity and soundness, inductive and abductive arguments can be evaluated in terms of strength (they have good inferences, meaning that the conclusion is more probable, given the premises) and cogency (meaning that they are strong, and that their premises are true).

Discussion

Look at the cases of the two arguments in the text. Argument 1 is this:

• The Sun rose today.
• The Sun rose yesterday.
• The Sun has risen every day of human history.
• ∴ The Sun will rise tomorrow.

And argument 2 is this:

• When the farmer came to the coop yesterday, he brought us food.
• When the farmer came to the coop the day before, he brought us food.
• Every day that I can remember, the farmer has come to the coop to bring us food.
• ∴ When the farmer comes today, he will bring food.

Now try and think of two cogent inductive arguments, and two weak inductive arguments.

Abduction

Abduction is about finding the best possible fit for a set of data. It is sometimes called “inference to the best explanation”. Think about how a detective puts together bits and pieces of information to see that on balance the most compelling explanation for a crime is such-and-such.

If we have time, we’ll talk about this, and come up with some examples of abductive arguments.

Homework

This has given you a taste, I hope, for how arguments work. What we are going to do for next time is look at an Indian tradition of philosophy that explores the question of what evidence we rely on in making arguments.

I want you to you can read the extract on knowledge sources or pramāṇas from the Nyāya sutras here. This is a tricky passage so don’t worry too much about how much you understand. Just get a feel for it. Try reading from the introduction of chapter 1 (“Epistemology, the theory of knowledge, is launched from the recognition that cognition is not always veridical or true”) up to the end of section 1.1.3. — you can read the rest if you like!

I also want you to listen to this podcast for context: Peter Adamson and J. Ganeri (2017), ‘ Where There’s Smoke There’s Fire: Gautama’s Nyāya-Sūtra’, The history of philosophy without any Gaps Podcast: https://historyofphilosophy.net/nyaya-sutra

We’ll start talking about this next time!