Parmenides

Parmenides is one of the hardest Plato texts that I have read up to this date. In the beginning of the dialogue, Socrates challenges Zeno/Parmenides view on "the one"; Zeno/Parmenides believes that it is absurd for anyone to believe in the view of plurality of beings. That is, it is impossible for things to be both like and unlike (along with many other terms that are contrary by nature). While discussing what "the one" would be, Parmenides goes through many contradictory statements to discuss what "the one" isn't; by doing this, he is providing a reductio ad absurdum argument for what the "one" is by discussing what it couldn't possibly be. The Reductio ad absurdum argument is used in Aristotle's Metaphysics book to account for logical forms that don't appear valid at first glance.

Yet, the reductio ad absurdum does not necessarily provide new information about the concept at hand; instead, this line of argument to me is only able to express what the item isn't.
It seems that this tool of reductio ad absurdum works well when it isn't fully examined by a keen philosophical mind; that is, as a tool for persuasion, it works very well. It compares two concepts, one particular concept in a negative light and the other idea in a more positive light; it attempts to prove that the idea in the positive is the only logical conclusion left after the validity of the other concept has been proven false.

I look back on Parmenides' argument of oneness and it seems that his line of reasoning still leaves other possibilities; I do not feel satisfied with the results that arise out of the argument simply because they conclude out necessity with few alternatives that might still be possible.

I believe that we (collectively as a society), still use this type of reasoning (even though it can be fallacious) to a certain degree. We still forget to look for more alternatives to the conclusion we quickly arise to; that is, in any given situation, I believe that although there is only one possible conclusion that is valid, it is still possible for a conclusion to arise out of premises that is invalid; not because of a flaw in the argument, but by not introducing enough facts to arise to the correct conclusion. In the case of describing how things relate to one another, I believe that we are simply unable to capture even one quality or concept of all the possible things in this world (universe, space outside that universe, etc. to infinite).

Still, I must commend Plato's attempt to reconcile all the things of this earth in his theories of forms so that philosophers might know all instances of a form by knowing the form itself.