Does the nature of a paradox discount our reliance on logic?

Without logic there can be no paradox.

Logic is a good servant, but a bad master! It has it's uses but isn't the whole picture. It represents one facet of a multi faceted diamond which is philosophy. Logic isn't knowledge, it's a rule book for guidance only.

It's like applying two dimensional geometry in a three dimensional world, sometimes a 1st or 3rd angle projection is required in order to gain a practical perspective.

Paradox represents a breakdown of the rules. An event horizon where conventional rules simply don't apply. The justification for knowledge can be usefully tested by logic, but logic applied with common sense.

Plausible knowledge is our best current estimate of how things are. It doesn't preclude the need for constant review, and the need to test it's validity to maintain a robust foundation for human advancement.

The 35-minute program in the video below is a compilation of rocket launches. In every case, the rocket logically should have functioned correctly and it each case it did not. It illustrates the difference between thinking in the modern world and thinking in the Middle Ages. Logic is not enough.

The word "paradox" is used for different things. A drug that has a certain effect at a low dose is said to have a paradoxical, opposite effect at a high dose. Bertrand Russel admitted that he was impressed by the paradoxes of Zeno of Elea, the philosopher who argued that the material world is an illusion with his Achilles and the Hare Paradox (source: Zeno article in Wikipedia).

Hamlet could have shown the Monty Hall Paradox to Horatio if he wanted to make him accept the idea of counter-intuitive truths.

You pick door number 1. Monty shows you the prize is NOT behind door number 2. There couldn't possibly be an advantage to picking door number 3 at that point - right?

"It goes to show, you never can tell."

- Chuck Berry

https://betterexplained.com/articles/understanding...

https://www.youtube.com/watch?v=Z9EnUQltR9A

"logic ultimately begs itself"

False.

We use logic because it is empirically reliable. For example, IF it is raining, THEN I will be happier being outside IF I am wearing a raincoat.

In other words,

RAINING ∧ RAIN COAT → HAPPIER than no raincoat

This is hopefully something that meshes with your experiences with reality.

"Is knowledge even plausible?"

Yes.

Knowledge is simply information [1].

You can have information about a system without having a complete description of that system (i.e. having "true" knowledge of the system; its "true" state).

For example, if I roll a pair of dice, and I tell you they do not sum to 5, then you have information (i.e. knowledge) regarding that system without having a complete description of it. You may not know if I rolled a 5 and a 3 or a 5 and a 4, but you know I did not roll a 2 and a 3; you have knowledge regarding that system.

"is it (logic) a useful tool for knowledge?"

Empirically, yes; using logic is a useful way to gain knowledge of the world we live in..

The scientific method is based on logic (specifically modus ponens [2]). The basic idea is that if you have a statement like "IF A THEN B", then if A is found to be true (e.g., it is raining and we have a raincoat), then we infer that B is also true (e.g., we are happier than if we did not have a raincoat). This isn't some esoteric rule that begs itself; it is a correlation we find through common experiences with everyday life.

The utility of this tool should be obvious; the machine you are using right now (along with almost any modern convenience) would not exist without it.

No; as, logic is not a 'reliable' source of knowledge. Logic is only relative to the mind of an individual and how it is perceived and deduced. The logic of a reasonable deduction can not be deemed a reliable source of knowledge without all the facts at hand.

The reliance of logic as a reliable source of knowledge is a paradox within itself.

Is that not logical?

Schrodinger's cat paradox is quite logical I guess. Don't you think? The cat will die one day anyway whether it lived through poisoning process or not. It must die.

Logic is true even in dealing with unreal things. Logic being true doesn't mean it being real. When dealing with paradoxical issues, logic can go along with the reasoner. When dealing with reality, it needs to be real.

Paradoxes are a three-alarm intellectual emergency, imo. Precisely because they do challenge logic. I compare our knowledge to the sense of mastery on a ship. Ya, for the most part, you can rely on your ship, but - things happen. It's not a foolproof system. Neither is logic, imo. Tho it works most of the time.

I don't really understand the question.

What form of logic is it that you refer to?

Intuitive logic?

And what is this "knowledge" you wonder about?

There's all this so called secret, underground or hidden knowledge available. How it is discovered, be it via the rational self, the inner self, the powers of faith, belief or what not....who knows??

Is all knowledge readily available? Is knowledge something to be sought?

Well we don't know.

So we go slightly mad, and sometimes tempt the bridge between reality and insanity and walk that bridge proudly with flowers in our hair, cardboard on our feet, while building a boat with wings.

Logic has a limited function. Like a ruler it measures that which it can be brought to bear against.

Generally any "paradox" is a childish play on words and has no relevance to reality.