A Brief Guide to Logic - The 3 Laws
By Andrew Dart, author of 'Building Your Skeptical Toolkit'.
As well as a good understanding of the scientific method, by which evidence can be evaluated and sound conclusions reached, a good skeptic should be well acquainted with the three founding principles of informal logic, the form of logic generally used in debates and arguments.
Whenever you find yourself in discussion with a believer or proponent of some pseudoscientific or paranormal claim an understanding of basic logic is important for you to effectively be able to get across your reasons for being skeptical, as well as being able to identify flaws and fallacies in your opponent’s arguments. Over the following pages we will take a look at some of the more common logical fallacies you are likely to come across, but before we do that it is a good idea to quickly go over the three “laws” of informal logic, how they work and why they are important.
Before we do, I have a confession to make. Though I have always thought of myself as someone with a scientific outlook on life it wasn’t until recently, when I first became aware of skepticism, that I learnt about the laws of logic. Almost as soon as I did I found myself thinking back over conversations that I’d had and I was fairly quickly able to identify where the arguments that I had presented, and at times had even won the debate with, failed in their logic and as such were in fact poor and flawed arguments. By understanding the laws of logic and making sure that any arguments you present adheres to them you can only strengthen your side of the discussion.
The Law of Identity
As Popeye the Sailor Man was fond of pointing out, “I yam what I yam,” and this simple idea is pretty much all there is to the law of identity. This principle of informal logic states that something has an identify, meaning it is what it is and conversely it is not what it is not. For example, a dog is a dog and it is also, if you will excuse the double negative, not not a dog. This is one of those things that people tend to take for granted, but it is in fact a fundamental component of any debate, or any conversation for that matter. If you and your opponent are unable to agree that a dog, or whatever it is you are discussing, is indeed a dog then you will never get anywhere. Generally, we have no problem with the idea that a dog is a dog, a book is a book and a car is not not a car. This is actually a pretty good thing, or we would all have a lot more difficulty getting anything done that involved more than one person.
The Law of Non-Contradiction
This principle holds that something can’t hold two contradictory properties at the same time and still be valid. A fire cannot be both hot and not hot at the same time. This is what is known as a conjunctive proposition, that being a proposition that uses the word "and", as in "this and that." In the example above we have the proposition that “the fire is hot AND the fire is not hot.” As these things are contradictions then the proposition itself must be false.
It is worth noting that in the above example it is simply taken as read that I am saying that the fire is hot and the fire is not hot at the same time and in the same place. In everyday use we don’t tend to explicitly state these details and assume people will simply fill in the gaps. This is worth remembering, as something does not violate the law of non-contradiction when what you are describing takes place at different times and places. Let’s swap from fire to water to better explain this. Now if I say the water is hot and the water is not hot at the same time and in the same place, well then I have fallen foul to the law of non-contradiction. However, it is completely possible for the water to be hot and the water to not be hot if we are talking about different places and/or times for the two variations. It is also possible for the water to be partly hot and partly cold as the same time, though we would probably just call it warm. These points should be kept in mind during a debate when addressing something that appears to violate this law. Always make sure that your opponent is indeed talking about two contradictory properties existing at the same time and place before pointing out the flaw in their logic.
The Law of Excluded Middle
The final law of informal logic applies to propositions that make a related disjunctive claim, or in other words sentences that have the word OR in the middle. This applies when you have two statements and one of them is true or the other one is. A good example of this is one that Brits like me are very familiar with, it is raining OR it is not raining. One or other of these two statements must be true. Now we already know from the law of non-contradiction that they both can’t be true at the same time and place so why have this law at all? Well the law of excluded middle refers to the non-existence of a third option. It is either raining or it is not; there is no third choice, or to put it another way we have excluded the middle option. A very good way of remembering this one is the saying “you can’t be a little bit pregnant.” Being pregnant is a situation where you either are pregnant or you are not, there is no middle ground.
In order to make an argument that is logically valid it must adhere to these three laws. However, it is worth noting that just because an argument is logically valid that does not necessarily mean that it accurately reflects reality or that it is true. For example, a sound logical argument could be made for a flat earth and yet the evidence would still show that the earth is a sphere. Logic is important and is a powerful tool for use in verbal arguments, but all good science should always come back to the evidence. And if something is supported by good evidence then the logic should flow naturally from there.