1. Introducing Arguments

2. What is an argument?
Our central topic throughout this course will be arguments.
We’ll be learning how to identify them, analyze them, assess them and construct them.
So first we should get clear on what arguments are. When we say ‘argument’ in philosophy we don’t mean shouting at each other. So what do we mean?

3. Propositions
Before we give our definition of an argument, it will be useful to start with the idea of a proposition.
Propositions make claims about things being a certain way. As such, they can be true or false.
Propositions are often expressed with declarative sentences – that is, sentences that declare or state that something is the case.

4. Propositions
Propositions can usefully be distinguished from commands (‘leave the room!’), questions (‘when can I leave the room?’) and exclamations (‘eek!’).
Have a think about these other kinds of sentences. It should be clear that they cannot be straightforwardly true or false. (It doesn’t really make sense to say that ‘eek!’ is true or false.) This distinguishes them from propositions.

5. Propositions
So propositions are claims that can be true or false. In logic we often describe these qualities as ‘truth values’. If a claim is true we will say that it has a truth value of true (or sometimes just a truth value of t).
Sometimes the truth-value of a proposition could be unknown – we don’t know whether it is true or false. But if it is nevertheless the sort of thing that can be said to be true or false, it is still a proposition.

6. Proposition
One final word on propositions. It is important to note that propositions are distinct from sentences. A sentence can express a proposition. But they are not the same thing.
Note that one and the same proposition can be expressed by two different sentences. For example: - ‘I like Christmas.’ and ‘Me gusta la navidad.’ - ‘George W Bush is the son of George H W Bush.’ and ‘The 43rd President of the USA is the son of the 41st President of the USA.’

7. Propositions – some examples
Which of the following are propositions? 1) ‘It is raining.’ 2) ‘Is the cat on the mat?’ 3) ‘Callum thinks AFC Wimbledon are the greatest football team in the world.’ 4) ‘Get off me!’ 5) ‘Mary, mother of God.’ 6) ‘The king of the USA has blue hair.’ 7) ‘Great stuff!’

8. What are arguments?
Ok, so after that brief detour we can get back to our initial question: What are arguments?

9. What are arguments?
Arguments are bundles of propositions related in a particular way.
In particular, arguments are bundles of propositions where one of the propositions (the conclusion) is meant to follow from the others (the premises).
Or put differently, arguments are bundles of propositions where all but one of the propositions (the premises) are supposed to provide support or evidence for the other proposition (the conclusion).

10. What are arguments?
We might also say: in an argument we are presented with a group of propositions (the premises) which are supposed to give us reason to believe another proposition (the conclusion).
Note that this definition does not require that the propositions do in fact provide evidence for the conclusion/give us a reason to believe the conclusion etc. Only that they are supposed to do so. (Noting this we can say – bad arguments are still arguments!)

11. What are arguments?
We can usefully distinguish arguments from explanations. An argument takes something whose truth is in doubt and attempts to give reason to believe it. An explanation takes something whose truth is not in doubt (something already accepted as true) and explains why it is true.
Compare: (1) AFC Wimbledon will win the cup next year, because they are the greatest team in the world; and (2) AFC Wimbledon won the cup in 1988 because they are the greatest team in the world.

12. What are arguments? Ok, so let’s take a look at some examples.
As we go through them, let’s try to identify which propositions are the premises of the argument and which is the conclusion.

13. Some examples
All women are mortal. Diotima is a woman. Diotima is mortal.
You should get out of the kitchen. Because if you can’t handle the heat, you should get out of the kitchen. And you can’t handle the heat.
Every Frenchman I ever met was called Pierre. So, all Frenchmen must be called Pierre.

14. Recognizing arguments
Which of the following are arguments?
All dogs are mammals. Geoff is a dog. So Geoff is a mammal.
The Titanic sunk because it hit an ice berg.
No one has ever regretted taking Phil before. So you will not regret taking Phil either.

15. Recognising arguments
Clubs are good for hitting people over the head. The CCNY Computing Club is a club. So the CCNY Computing Club is good for hitting people over the head.
Ouch! My thumb hurts!
If pigs could fly, then CCNY is in the Bronx. So, Bernie Sanders will win in 2020.