Logic is essentially the study of argument form. When I say argument though I don’t mean the kind of infuriating argument I might have with my wife when I see her watching soap operas and in my opinion wasting away her life; rather logical arguments are ones where we make a series of carefully reasoned steps to show that something is true or false.

Now I said that logic is essentially the study of argument form, here is an example of logical form;

If A then B

A

Therefore B

So argument form is a separate thing from an actual specific topic of argument such as:

If Alice studies physics then she does not study art.

Alice does study physics.

Therefore Alice does not study art.

If you are in Utah then you are in America.

You are in Utah.

Therefore you are in America.

The moon is green.

If the moon is green then it is made of cheese.

Therefore the moon is made of cheese.

These three example arguments have the same logical form, but they are clearly not the same as each other.

The first argument is certainly questionable even if you believe that it is likely that a student who studies physics would not study art. Saying that something is likely to be true would be a rational argument, notice the word “ratio”. The words rational and ratio are cognates (related words). In a rational argument you weigh up the evidence. I hope to write sometime about rationality, but for now I want to focus on logic.

Moving on, the third argument is clearly wrong. So logic doesn’t ensure us that our conclusions will be correct. You’ll also notice the order of the premises doesn’t matter, though certain orderings may be easier to follow.

What are premises? Pre- defines the part of an argument that come before the conclusion, hence premise, like other words that denote something that comes before; prewar, pre-Socratic, and pre-Copernican.

A conclusion comes at the end and in spoken argument is usually made clear by the use of words such as: therefore, so, it must follow that, etc.

To help make it more clear, let’s break down the logical form of previous examples.

##########

If ########## then **********

So **********

########## denotes the premise, where as ********** denotes the conclusion.

If we look back at the argument about the moon being made of cheese we can see that the premises are wrong, the moon is not in fact made of cheese. The logic though is valid but the problem is that the premises are false.

The second argument about Utah being in America has true premises. Using valid logic with true premises gives us what is called a sound argument.

Using invalid logic with either true or false premises cannot tell us whether the conclusion is true or not though. This is important to remember! Just because an argument’s logic is invalid does not mean that the conclusion is false! Let me give an example to make this clear.

The moon is rainbow coloured.

If the moon is rainbow coloured then vampires are real.

Therefore Neil Armstrong walked on the moon.

The premises are false, yet the conclusion is, as a matter of fact, true. The logical form is invalid. Can you work out what the logical form of this argument is?

I think I’ll leave this first post here. In the second post I will talk about some of the basic logical operations (negation, conjuction, disjunction, etc) and also provide a few exercises for those who want to test themselves to double check that they’ve understood things.

If you find any mistakes or have trouble understanding something that I’ve written, please point it out to me, I’ll try to make it clearer.