User:Silphaer/Musings

This page is, in effect, a list of my thoughts based on logic, philosophy and morality, with a dash of science.

Introduction
A "Paradoxical Situation" or simply "Paradox" is an argument that apparently derives self-contradictory conclusions by valid deduction from acceptable premises. Paradoxes are one of the most fascinating logical and philosophical questions that we humans pursue an answer to, as they appear to have simply no answer, something that infuriates my fragile brain. Logically, if something has perfectly acceptable premises, should it not then be a perfectly acceptable situation with perfectly acceptable outcomes or conclusions?

I have frequently devoted my thoughts to some of the most well-known paradoxes, attempting to come up with an answer, and, whilst I have concocted many a conjecture on the subject matter, I have never been able come up with any conclusive answer, leading me to believe that a paradox is inherently something that may appear to have acceptable premises, but when looked at more closely, does not, logically allowing its conclusion to also be self-contradictory. Here are just two examples.

The Omnipotence Paradox
The Omnipotence Paradox is probably my favourite paradox, and one which I was originally led to think about during my thoughts on the divine.The version I most commonly refer to goes something like this:"'If something is truly omnipotent, then by the definition of omnipotence, it can create anything and everything, as well as destroy anything and everything. However, if it can create anything, then it must be able to create something which it cannot destroy, which would mean that it cannot destroy everything, therefore the existence of omnipotence contradicts itself.'"My original thoughts on this were that the omnipotence would only exist until the thing created something which it was unable to destroy, and then the omnipotence would disappear, however, I came to the conclusion that by having the merest ability of creating something which it cannot destroy, its omnipotence cannot exist in the first place, and also, with the ability to destroy anything, then it cannot create something which it cannot destroy, still meaning it does not possess omnipotence.

I eventually decided that the premises of this paradox were unacceptable to begin with - true omnipotence is impossible - which would technically mean that it isn't a paradox. This, whilst possibly being an answer, raises far more questions than it answers. If the premises of the omnipotence paradox are impossible, meaning it isn't a paradox, does that mean that the very concept of paradoxical situations is, in itself, a paradox? So I looked at another paradox.

Hilbert's paradox of the Grand Hotel
Hilbert's paradox of the Grand Hotel relates to mathematics, so I love it. Here it is:"'There is a hotel with a countably infinite number of rooms, all of which are occupied. A new guest arrives, asking for accommodation. You move each guest from room n to room n+1, allowing the new guest to move into room 1. A countably infinite number of guests arrive, asking for accommodation. You move each guest from room n to room 2n, freeing all of the odd numbered rooms, of which there are a countably infinite number. There are a countably infinite number of rooms, all of them are occupied, but because there are a countably infinite number of them, you can still accommodate more guests.'"Once again, after much thought, I came to the conclusion that the definition of "logically acceptable premises resulting in a self-contradictory conclusion" is incorrect. You can't have a countably infinite number of rooms, yet still have all of them occupied. It's logically and mathematically impossible. Even if you have a countably infinite number of people, if you add one person to that, it's still a countably infinite number of people. By the very definition of infinity, you never run out of people, but you never run out of rooms either.

Conclusion
In conclusion, a paradox, by definition, is a paradoxical concept. "Logically acceptable premises resulting in a self-contradictory conclusion" simply can't happen. If the premises are logically acceptable, then by logic, the conclusion must also be logically acceptable, however in a paradox, they aren't. What people really mean when they say paradox, isn't, "logically acceptable premises resulting in a self-contradictory conclusion", it's, "logically unacceptable premises that appear logically acceptable at first glance, resulting in a self-contradictory conclusion."

The definition we give to a paradox doesn't describe the things we then refer to as paradoxes. We say that a paradox derives itself from logical premises, but when we look closer, it doesn't. It derives itself from illogical premises that are worded in a way which makes them appear logical. In the end, it's one big misconception. A definition that doesn't accurately describe what it's trying to define. Perhaps a paradox is something that the human brain is incapable of properly wrapping its head around the concept of a paradox, because it always looks for logical answers, but in truth, there are no logical answers in paradoxes.

They're still really fun to analyse though.