A Quick Intro to Logic

Logic. Most people assume they understand logic and reasoning.
They don’t.
What they are good at is rationalization and fallacies, but believe themselves to be Titans of Logic, instead of the clowns of rationalization.
As a Man of the West, logic is as needed as any tool. You should be familiar with the basics and be able to spot actual logical fallacies in other’s arguments, and just as importantly, your own.
At the heart of it all, logic is how men grapple with understanding and reason. It’s the basis of math and science. It how we evaluate situations and make decisions. You may not become the next Aristotle or Antony Flew, but you can add logic to your toolbox.
Let’s start easy. Logic is a vast and wooly subject, but the basics aren’t.
At Infogalactic, logic is defined as “Logic (from the Ancient Greek: λογική, logike) originally meaning the word, or what is spoken, (but coming to mean thought or reason) is generally held to consist of the systematic study of the form of arguments. A valid argument is one where there is a specific relation of logical support between the assumptions of the argument and its conclusion. (In ordinary discourse, the conclusion of such an argument may be signified by words like ‘therefore’, ‘hence’, ‘ergo’ and so on.) The form of an argument type is a schematic way of representing what is common to all arguments of that type.”
See? It’s really not overly complicated. A few definitions are needed now before we continue.
An argument consists of premises, together with the conclusion, which the premises support.
For our basic tour of logic, we’ll consider two types of arguments, deductive and inductive, but focus on deductive.
“A deductive argument asserts that the truth of the conclusion is a logical consequence of the premises.” Infogalactic [2].
If you accept the premises, follow the chain of a deductive logic argument, and the argument is both sound and valid, then you have to accept the conclusion.
If you don’t accept the conclusion even after accepting the premises, you aren’t interested in the truth. You may not like the conclusion but the conclusion is logical and cannot be waved away because your fee-fees are hurt. If you think something is wrong, start with the premises and work through the argument. Again, if you accept the premises, you have to accept the conclusion as being logical if and only if the argument is valid and sound. I’ll get to those last two terms.
“An inductive argument, on the other hand, asserts that the truth of the conclusion is supported to some degree of probability by the premises.” (Infogalactic)
Inductive arguments are either weak or strong and they deal with probabilities. I won’t touch on them much more than that for now.
What makes a good deductive argument?
It must be valid, and it must be sound.
“If one assumes the premises to be true (ignoring their actual truth values), would the conclusion follow with certainty? If yes, the argument is valid. Otherwise, it is invalid. If a deductive argument is valid and its premises are all true, then it is also referred to as sound.” (Infogalactic).
Great, but what does it mean?
There are forms a deductive argument can take. There are forms which produce valid arguments, and forms that don’t, which are called invalid. The conclusion of an invalid argument might be true or, mostly likely, false. But it doesn’t matter; we can’t figure out the truth of the argument because it’s invalid in form.
Here’s one of the most widely used examples of a valid, sound deductive argument:
Socrates is human and all humans are mortal.
Therefore, Socrates is mortal.
A slightly different take:
All Greeks are human and all humans are mortal.
Therefore, all Greeks are mortal.
Those are both valid and sound arguments.
Here’s an invalid argument:
1. If it is raining, then I eat pears.
2. It’s not raining.
3. Therefore, I am not eating pairs.
This is a formal logical fallacy known as “Denying the Antecedent”.
Logical forms take certain shapes.
Here’s a simple valid form:
If p then q.
P so therefore q.
Here’s a simple invalid form:
If p then q.
Not q so therefore not p.
An invalid form is always some sort of fallacy.
I’m going to dive into valid and invalid forms later and not in this post.
So what makes the deductive argument so powerful?
We’re going to take a step out of logic and into something a little more meta.
Deductive reasoning rests on intuitive principles. You cannot prove these principles, but we accept their validity intuitively.
There are three principles that I see as being linchpins to logic:
a. Identity. If something is true, then it is true. If something exists, then it exists.
b. Non-contradiction. If something is true, then it cannot be false at the same time. If it exists, it cannot also NOT exist.
c. Excluded Middle. A thing cannot sorta exist and sorta not exist. A concept cannot be somewhat true and somewhat false. Either the proposition is true (our Sun is hot) or the negation is true (The sun is not cold) but they can’t be true at the same time (Our hot cold Sun). And by ‘concept’ and ‘thing,’ I mean something simple and nigh atomic.
We can’t prove these. But we understand them intuitively to be true. Anyone arguing against them is besieging a fortress beyond their powers to conquer and is an active agent for the Enemy.
Logic is big topic and deserves more than one post. I’ll be discussing valid forms and logical fallacies the next time.