1. Arguments in Natural Language

2. Natural and formal languages
Later in this course we will start looking at formal languages – artificial languages designed for doing logic.
But before that we’ll be doing some more work on what logicians call natural languages – like English, Spanish, Mandarin, Hindi etc etc.
In particular we’re going to do some work on how to recognize (and begin to formalize) arguments in natural language.

3. Arguments in natural language
Take a look at the following sentences of English.
It’s just ridiculous to think that real socio-political change is going to come from the ruling elite. After all, they have all the money and power, and history tells us that if people have all the money and power in society, then they won’t give it up freely.

4. Arguments in natural language
These sentences constitute an argument. That is, they express a series of propositions such that one of those propositions is supposed to be evidenced or supported by the others. They attempt to give us a reason to believe the conclusion.
One of our main objectives in this class is to understand such arguments. Formal logic will give us extensive tools for assessing arguments. But before we can assess them we first need to identify them. So let’s look at how we do that identification.

5. Arguments in natural language
Integral to the idea of arguments that we are working with here is the claim that they consist of premises and a conclusion. So a great place to start is to identify which parts of the natural language sentences contain the premises of the argument and which contains the conclusion.
Let’s go back to the example we just saw.

6. Arguments in natural language
It’s just ridiculous to think that real socio-political change is going to come from the ruling elite. After all, they have all the money and power, and history tells us that if people have all the money and power in society, then they won’t give it up freely.
The blue sentence expresses the conclusion, and the green sentence expresses the premises.

7. Finding the conclusion
Conclusions often come at the end of arguments. But they can also come at the beginning (as in the example we just looked at) – and even in the middle of them.
What you’re really looking for when you’re trying to find the conclusion is the sentence that expresses the thing that the other sentences are providing evidence or support for.

8. Indicator words
Fortunately, natural language arguments often offer a number of clues as to what’s going on in terms of premises and conclusions. In particular, there are some tell-tale indicator words that are usually (but not always) good indicators of what’s what.
Let’s go back to our example.

9. Indicator words
Think about that green premise sentence: After all, they have all the money and power, and history tells us that if people have all the money and power in society, then they won’t give it up freely.
The words ‘after all’ are a dead give away that what is being introduced is a premise. ‘After all’ is usually used to introduce something that is a reason believe the thing that has just been said – i.e. a premise. So ‘After all’ is a premise indicator.

10. Indicator words
Natural language is full of such indicator words and phrases. Here are some more premise indicators: since given that because seeing that for for the reason that as is shown by the fact that
And there are many more!

11. Indicator words
And here are some conclusion indicator words and phrases: therefore implies that so consequently hence it follows that thus we may conclude that
And here too there are many more such terms.

12. Examples
Jen is an American. Most Americans say ‘sidewalk’ instead of ‘pavement’. So Jen probably says ‘sidewalk’ instead of ‘pavement’.
If you like dark beer, you should take the stout or the porter. You do like the dark beer, and the stout is bad so you shouldn’t take that. So you should take the porter.
Some card must be red, because some cards are diamonds and all diamonds are red.

13. Beginning to formalize
So, indicator words can help us to tell the conclusion apart from the premises. But what next?
A first step comes from noticing that natural languages (particularly verbal communication, but also written) is often full of extra details and complexities. In logic, we try to trim as much of this away as we can whilst preserving as much of the basic underlying meaning as we can. This simplification process will make the task of analyzing the argument much easier.

14. Beginning to formalize
So let’s return once again to our original example: It’s just ridiculous to think that real socio-political change is going to come from the ruling elite. After all, they have all the money and power, and history tells us that if people have all the money and power in society, then they won’t give it up freely.
We have already noted that the first sentence contains the argument’s conclusion and the second contains the premises. But can we now simplify it a little too?

15. Beginning to formalize
‘It’s ridiculous to think that’ seems like a more rhetorically exciting way of saying that ‘it’s false that’ or ‘it’s not the case that’.
And ‘history tells us that’ is a way of introducing one of the premises that it seems like we could do without.
So let’s simplify along those lines.

16. Beginning to formalize
Now we get: It’s not the case that real socio-political change is going to come from the ruling elite. After all, they have all the money and power, and if people have all the money and power in society, then they won’t give it up freely.

17. Standard argument form
The next step is to put the argument into what is called standard argument form.
Standard argument form extracts and isolates each individual premise, and presents them in simplified terms in a list. The conclusion of the argument is then added at the bottom, usually underneath a line to indicate that it is the conclusion. Often the distinct claims get numbered too, just to make referring to them easier. So let’s do that.

18. Standard argument form
(1) The ruling elite have all the money and power in society. (2) If people have all the money and power in society, then they won’t give it up freely. (3) It’s not the case that real socio-political change is going to come from the ruling elite

19. Enthymemes
Often in natural language we skip important parts of our arguments – because it’s obvious what the missing step is, and it would be cumbersome to spell everything out in every little detail. Arguments with unstated premises are known as enthymemes.
When we’re putting natural language arguments in standard argument form we need to tease out all the missing steps. So sometimes we have to add the unstated premises in ourselves.

20. Enthymemes We can do this with our original example.
The argument is trying to provide reasons for the claim that it’s not the case that real socio-political change is going to come from the ruling elite. But the premises only seem to establish that the ruling elite is not going to give up their money and power freely.

21. Enthymemes
So we need to add the (obviously implied) premise that if the ruling elite is not going to give up their money and power freely, then we won’t see real socio-political change coming from them.
So we end up with…

22. Standard argument form
(1) The ruling elite have all the money and power in society. (2) If people have all the money and power in society, then they won’t give it up freely. (3) If the ruling elite won’t give up their money and power freely, then real socio-political change is not going to come from them. (4) It’s not the case that real socio-political change is going to come from the ruling elite

23. Re-phrasing sentences in the declarative mode
As well as simplifying and filling in the gaps in enthymemes, when we try to put natural language arguments in standard argument form sometimes we need to re-phrase sentences which strictly speaking are not declarative (and therefore do not express propositions) to get them into the declarative mode.
This is because in natural language non-declarative sentences are often used to suggest or imply propositions that can be more clearly using the declarative.

24. Re-phrasing sentences in the declarative mode
Take this amended form of our example: Does anyone truly believe that real socio-political change is going to come from the ruling elite? After all, they have all the money and power, and history tells us that if people have all the money and power in society, then they won’t give it up freely.

25. Re-phrasing sentences in the declarative mode
In this argument the first sentence is a question rather than a declarative sentence.
But it is nevertheless being used to imply a proposition – the same proposition that was expressed in the declarative sentence we considered in our original example: namely, that it is not the case that real socio-political change is going to come from the ruling elite.

26. Re-phrasing sentences in the declarative mode
The moral of the story is: sometimes when we are putting arguments into standard argument form we have to rephrase sentences to get them into the declarative form.
As ever, when we do this we are aiming to strike the right balance between simplifying and preserving the original meaning of the natural language locution.

27. Indexicals
Indexicals are words whose meaning changes depending on the context. Words like ‘me’, ‘he’, ‘this’ etc refer to different things when uttered in different contexts.
When putting things in standard argument form, we try to replace these indexicals with less context-dependent terms. E.g. ‘I’ when uttered by me becomes ‘Callum MacRae’, and so on.

28. Indexicals
Take for example: If John is late, George will be angry. And he will be late, so he will be angry.
The two instances of ‘he’ here need specifying. So in standard argument form this becomes: If John misses the train, George will be angry. And John will be late, so George will be angry.

29. Indexicals
Sometimes you need to be quite imaginative to iron out these indexicals.
Consider: Paul told George that Ringo forgot to say that John lost his drumsticks.
How should we paraphrase this?

30. Examples: Put these arguments into standard argument form
It’s Monday today. So there must be class, because there is a class every Monday.

31. Examples: Put these arguments into standard argument form
(1) Today is Monday. (2) There is class every Monday. (3) There is class today.

32. Examples: Put these arguments into standard argument form
Can’t you see that we’re all doomed? If we don’t change our society and economy in profound ways, we face a major environmental catastrophe. And there’s no way that’s going to happen.

33. Examples: Put these arguments into standard argument form
(1) If we don’t change our ways we face major environmental catastrophe. (2) We won’t change our ways. (3) If we face major environmental catastrophe then we’re all doomed. (4) We’re all doomed.

34. Examples: Put these arguments into standard argument form
If Frodo is late and Aragorn is on time, then Legolas will have to tell Gimli that he needs to return his bow. So long as Sam doesn’t hassle him, Frodo is bound to be behind schedule. And is Aragorn ever late? So Legolas will have to tell Gimli that he needs to return his bow.

35. Examples: Put these arguments into standard argument form
(1) If Frodo is late and Aragorn is on time, then Legolas will have to tell Gimli that Gimli needs to return Legolas’s bow. (2) If it is not the case that Sam hassles Frodo, then Frodo will be late. (3) Aragorn will be on time. (4) Legolas will have to tell Gimli that Gimli needs to return Legolas’s bow.