Thursday, December 20, 2012

Paradoxes

Thoughts on Zeno's paradox, as I understand it:
1. An infinite geometric series can converge to a definite number, therefore an infinite number of tasks can take a finite amount of time. 
2. An infinitely small segment is not an actual thing. Limits can be used to discuss what happens as the number lengths approaches infinity (the length approaches 0), but you can not say what happens at infinity. 
In short, plurality does not lead to contradiction. 

Thoughts on the Pensioner's Dilemma:
You might be tempted by possibly: confessions minimizes risk. But remember, they will reach the same rational conclusion; their decision is not arbitrary. And, whatever way you come to your conclusion, if you both arrive at "I should confess," you would both realize this is irrational: why both confess when you can both not confess?
If you assume the other prisoner will arrive at the same conclusion as you (since the most rational decision would be the most rational no matter how many times it is repeated), you would not confess. But the other man knows this, so you should confess and take advantage of him. But he should realize this too... So the question is who will extrapolate further and who will stop at the right point. 
"Good" and "Evil"

When people use the words "good" and "evil," they do not specify whether according to their morality or common morality because they are usually similar.  (I suspect they are similar because all societies have similar moral requirements in order to function well, but that is a separate discussion).   However, a specification must always be implicit because their can be no objective standard; how can you say what a human life is worth (emotionally, not materially) except by consulting your own unique morals or by consulting the morality of others? I do see how another standard could be identified for the definition of "good," but I do not see how one could argue the standard to be more more right, when their is to way (or standard) to judge the standard itself. 
So, if the world accepts theft as morally correct while a certain individual does not, it is wrong according to the individual and right according to society. Theft may be colloquially referred to as "good" and seen that way by most in this imaginary world... And, in our world we would have no authority to say their world is "wrong" and that our morals are objectively "better."
Furthermore, as Bertrand Russell would say, our concept of "good" cannot come from God, because we ascribed the quality to Him and must therefore have had an idea of the concept to begin with. To define "good" as "God-like" then saying "God is good" would be meaningless. 
Sin therefore, as a transgression before God, must not be considered "evil," especially as the common morality shifts away from its former standards. 

What is a definition of "good" that every society would agree upon regardless of their morals?