So far we have said that there are two different sorts of argument. We said that some arguments can make their conclusion highly probable while others can actually prove their conclusion. And for a second, we’re going to look in more depth at these deductive arguments.

It will probably come as no surprise that arguments need two things to make us believe the conclusion. Arguments are a bit like bridges. There are certain designs of bridges that are good and can hold the weight of the cars, or people, or whatever, that goes across the bridge. Philosophers call the ‘design’ of an argument its structure. And like a bridge an argument can have a good or a bad structure. If it is a bad structure, the argument can’t hold up the conclusion, but if the design/structure is good then everything works like it should. Philosophers call an argument that is well-designed, or has a good structure ‘valid’, and one with a bad design ‘invalid’.

1 Jack is a boy.

2 All boys have a ‘y’ chromosome.

C Jack has a y chromosome.

In this example, the argument is valid because the conclusion has to be true. Both the premises work together (like in a bridge) to hold up the conclusion like this:

There is one more thing that can make a bridge rubbish though. If the guys that had built the Forth Road Bridge had followed the plans exactly, but used random bits of wire in place of the odd weight-bearing beam, we wouldn’t expect it to hold the weight it was meant to! We could even expect that if they weren’t quite this crazy but they bought their girders from a dodgy salesperson, so that one in every 5 was faulty and weak, that the bridge would still fail.

Obviously the premises that are found in the deductive argument need to be true or we will be a bit like a engineer using these dodgy beams. In the picture above, if one of the towers is dodgy then the bridge itself is going to be in trouble. Again, philosophers have more posh word for these things when they are thinking about arguments. They say that an argument with good (valid) structure AND true premises is a sound argument. And they call an argument that doesn’t have true premises an unsound one.

One last thing to say is that there is one thing that makes arguments very different from bridges. Generally speaking in a bridge all the supports that ‘do something’ are fairly visible. The might be hidden by some fancy design, but even if they are the supports certainly won’t in invisible. Invisible materials just haven’t been invented yet (apart from in Indiana Jones).

With arguments it’s slightly different. Sometimes people make an argument that relies on something that they haven’t said out loud, so it’s kind of invisible. Now the difference is, that this doesn’t necessarily make an argument invalid, or even unsound. Because if this ‘hidden premise‘ is true and if the structure is still reliable, when you include the invisible bit, then it might very well be both valid and sound. Quite often these hidden premises are so obviously true that the person hasn’t bothered to say them out loud. Here are a couple of examples:

Homosexuality is obviously wrong. Why? It’s completely unnatural!

Although the conclusion itself is enough to make us question the argument, if we are going to be philosophers, we are going to look more carefully. In standard form we could put this as:

1. Homosexuality is ‘unnatural’

C. Homosexuality is completely wrong.

But this doesn’t lead to the conclusion. The reason is that the person speaking is clearly taking for granted that ‘unnatural = wrong’ this is a hidden premise. So:

1. Homosexuality is ‘unnatural’

2. (HP) what is ‘unnatural is wrong’

C. Homosexuality is completely wrong.

In terms of logic, we now seem to have a deductive argument that can stand up to some scrutiny. What if in maths you were told x=y, y=z and then someone asked you if x=z? You would know it was and that is what is going on here. So the argument’s structure is good. Both premises are untrue*, however, so we don’t need to feel we should agree with the conclusion – the argument is valid but unsound. Try it for this:

So. For an argument to convince you of anything you need to think about making two sorts of checks. The first needs to look at the structure of the argument and see if the structure is able to support the conclusion. To do this it helps to set out the premises and conclusion into a logical order (like in the examples). And the second test is to examine the premises, thinking about whether they are true. Sometimes this can get complicated if a premise is not obviously true and is a conclusion of a previous argument.

Once you have finished this page, and feel reasonably happy with all the philosophy word used so far you are ready to look more at some common mistakes in argument making ( Bad Arguments ).

* clearly depending on definitions, one could define premise 1 into being true but this would cause problems for the argument’s structure, see ‘equivocation’. premise 2 is notorious in the history of ethics and is rejected by most philosophers for a vast number of individually compelling reasons…