Three fundamental rules of logic must be followed for any rational discussion to take place. They are most basic; other rules of logic necessarily follow from these three. Furthermore, if any of these three fundamental rules are broken, the statements or arguments associated with this violation must be false.


1.) Law of Non-contradiction:


A statement and its negation cannot both be true at the same time and in the same sense. Examples of statements and their negation are below.
Original: "I am typing on a computer."
Negation: "I am not typing on a computer."
I may be typing on a typewriter, or I may not be typing at all.
Original: "It is raining outside (where I live)."
Negation: "It is not raining outside (where I live)."
The parenthetical statement is not necessary. Common sense shows that it is most certainly raining somewhere.
Common sense also lets us know that the original statement applies only at the time the statement is made; we would not assume the original statement is to be considered true at all times.
Light rain, drizzle, downpour? I don't care about the details in this article. Let's not be picky.
Original: "2 + 3 = 5"
Negation: "Two plus three does not equal 5."
The original statement implies normal base-10 arithmetic.
There's no need to try to be clever and talk about the possibility of other bases, modular arithmetic, or anything else not clearly indicated.


2.) Law of Excluded Middle:


Either a statement or its negation must be true; there is no third option.
Either "2 + 3 equals 5" or "2 + 3 does not equal 5."
There is no other possibility.
Notice I did not say "Either 2 + 3 equals 5 or 2 + 3 equals 6."


3.) Law of Identity:


Statement X is statement X. Huh? The Law of Identity sounds redundant and useless at first. However, it is important. Moreover, it is necessary. If I make a statement about something (e.g. There is a calculator on my desk), then I am stating something about my calculator's identity. I could make many other statements about this specific calculator's identity, but why bother? Think of it this way, if no statements could be made about some thing's or some idea's identity, if it has no identity, then it would not exist, right?


Reality has specific things true about it. If it is not true, then it is not real. Right?


The Law of Identity necessarily follows from reality.


Granted, what you or I are stating may be false, but then the first law (i.e. Law of Non-contradiction) would come to our rescue; it cannot be true that there is a calculator on my desk and no calculators on my desk (at the same time and in the same sense.) The second law (i.e. Law of Excluded Middle) also comes into play; either there is a calculator on my desk or there is not a calculator on my desk. There is no third option.


I could find examples from today's headlines to further discuss these three laws, but that would take away from further blog posts. This article is small and quick. There are many places on the Internet to research these topics further.