Formal logic, as you may have inferred from the name, is just like your regular logic except it’s dressed up in a suit.

Ok I made that up. Formal logic is more like the name given to the process of logical deduction (feel free to google for a more refined definition). Let’s look at an example:

If it rains, I will bring an umbrella.

For the purpose of this example, we will assume that this statement is and always is true. (In real life I do forget to bring an umbrella).

What can we learn from this one simple sentence? Turns out, a lot of things.

First, to make things easier (or more confusing, depending on your perspective), formal logics are commonly denoted in the form A -> B, which is read as “if A then B”.

In this simplest logical relationship, we know that if A is true, then B must be true. In other words, knowing that A is true is sufficient to know that B is also true; knowing that it is raining is sufficient to know that I will bring an umbrella. Hence, we call A the sufficient term of this logical relationship.

On the other hand, if B is true, A is NOT necessarily true. If I have an umbrella, it doesn’t mean it’s raining. I may have it just in case (like a typical Vancouverite). However, as previously noted, B is necessarily true if A is true. If it’s raining, I necessarily have an umbrella. This is why we call B the necessary term.

Since B is necessarily true when A is true, what do we know if B is false? Well, we know that A cannot be true, because if it is, then B cannot be false. (You might find this part a little mind boggling. Just think about it and let it sink in for a bit.) Hence, we know that if B is false, A is necessarily false. We can denote this with the expression ~B -> ~A, which reads as “if not B then not A”, where the “~” is, you guessed it, the negation.

Note how in this new relationship, the position of A and B are reversed. We call this the “contrapositive” of the original relationship. Simply put, to form a contrapositive, negate both the sufficient and the necessary terms, and swap their spots. In our example:

If I do not bring an umbrella, it is not raining.

Which, by the way, is not at all true in real life. But within this logical relationship, it is. So one thing you should have learnt so far is that logical relationships do not always make sense. In time, you will see that such relationships mostly do make sense in the context of laws, but for now, let’s just stick to the basics.

Notice also how ~A -> ~B (if it’s not raining then I don’t have an umbrella) and B -> A (If I bring an umbrella then it’s raining) are both false. Surely, there’s nothing in the original statement that says they cannot happen, but there’s also nothing that says they must be true. For all we know, we are only certain that if it rains then I will bring an umbrella. Period. In the context of formal logic, if a logical relationship is not certain, it is NOT a logical relationship. Remembering this point may help you better understand the laws that you will encounter later on.

Actually, why don’t we apply our recently acquired knowledge to some laws right now? If you haven’t yet learnt some or all of these laws, do not worry, all you need to know for now is the logical component of it. You can always pick up the actual contents at another time.

• If a contract is valid (enforceable), then there is consideration.
  • What if a contract is not valid/enforceable? Does that mean there is no consideration? No, of course not. It could be that the contract is illegal, or that one party is an infant. Or maybe there is no acceptance to begin with.
  • How about if there is consideration? Does that mean the contract is valid/enforceable? Of course not. If, say, a contract is illegal, it cannot be enforceable regardless of whether or not there is consideration.

Here’s another one that may be a little trickier:

• If there is damage as a result of breach of the duty of care, then there is negligence.

But you might say, hang on a second. In order to prove negligence (in Tort Law), don’t you have to prove all three elements (duty, breach, and damage as a result)? This is exactly right, and in this case, the presence of damage as a result entails that the previous two elements must also be present. Here’s a closer look:

• If there is damage as a result, there is a breach of duty.
• If there is breach of duty, there is duty of care.

Because frankly, you cannot breach a duty of care that doesn’t exist, and there cannot be damage as a result of breach if there is no breach to begin with. In other words, duty of care is a necessary term if breach is true (Br -> DoC), and breach is a necessary term if damage is true (Dm -> Br).

This concludes our brief introduction to formal logic. I will draft up a few questions for you to practice. For now, this should be more than enough to help you digest the course contents.