What is Logic?

  I want to talk about the topic of logic in discrete mathematics and programming in general. Take these words as vaguely and loosely as possible.

What is logic?

I think that whenever the answers to these questions are present...

"What is happening?"

"Why is it happening?" and

"How is it happening?"

then we can say that logic is established.

Logic is the core of computer programming. The bit logic that tells a computer what to choose (1) and what to ignore (0) marks the beginning of any journey in advanced computer subjects.

"Logic in discrete mathematics is the study of valid reasoning and inference, focusing on the principles that govern the truth of statements. It includes concepts such as propositional logic, predicates, and the rules of inference, which are essential for mathematical proofs and computer science applications." (GeeksforGeeks, Wikipedia)

to me, logic is like postulates when forming an idea. "Logical Axioms" seem more appropriate to say. But if I want to hit the meaning behind logic itself, I would look at games of logic genre. Ever played games like "Monument Valley"? 

(or, Mekorama/Hocus/...)

- https://www.youtube.com/watch?v=IdDaexqqXfQ

- https://www.youtube.com/watch?v=HnLd1dM8_SM

- https://www.youtube.com/watch?v=vaSJyEDmgWA

We know it's not real but somehow, we know that it works, and it should work; once we know the logic behind the world inside the game; the logic of "what is happening". When we play more and find out more through interactions, we know exactly "why" it seems "logical". And then we easily deduce a "how" behind this fictional reality.

Logical reasoning is just doing maths. You have a hypothesis or a given problem to solve, and you find your way to the end, which we name "conclusion" or "logical conclusion". The vague idea that separates "Logical Axioms" and "Logical Reasoning" is the part that we "don't care". Really. 

But generally, I think, by asking about logic, we look for answers to those 3 golden questions. Just like when we talk about computers and dumb them down to logic gates, we talk about how 1s and 0s represent true and false. That's "what is happening," apparently. 

But we must have also learned at some point that the reason as to "how it does that" runs even deeper. 1 represents the "presence" of voltages and 0 represents the "absence" of it. This part is not covered by the Logical Axioms; when we learn about boolean formulas and bit operations. This is exactly the part where you "relate" or "feel" the topic you are studying. This is where you feel "logic" itself.

Just like in Geometry, whenever we blindly accept the postulates to be true, and then find out that the 3 angles at each corner of a triangle sum up to 180, each and every one of us experiences a "Eureka" moment at the faintest corner of our heart. Then we look back in reminiscence and smile at the postulate that we choked on at the beginning, struggling to get how or why it even "should" work. But we now know that,

Level 1 is to accept it as is

Level 2 is to observe it's applications

Level 3 is to accept it again, but knowing it is true when applied

Level 4 is to be happy knowing that you learned something useful for your exams

"An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments." (Wikipedia)

"The starting point" means that you need to move a few steps further to know what you started doing in the first place. It's like planting a seed and waiting for the tree to grow and bear fruit to know exactly what seed you planted at the beginning.

Logic is like the node between two branches of a circuit. and when current passes through those branches through the nodes, we crown it "logical". 

Because it is only logical to do so ¯⁠\⁠_⁠(⁠ツ⁠)⁠_⁠/⁠¯

Corrections / PS:

- “Logic is better understood in the context it is established in.”

- “Once you feel the logic in the game or in code, you can then extract the general principles that apply everywhere.”