RE: Actual Infinity in Reality?
February 15, 2018 at 3:27 pm
(This post was last modified: February 15, 2018 at 3:29 pm by The Grand Nudger.)
Further elaboration on the above..specifically in reference to the PNC. This is an assumption of logic. It's necessary to do logic, but that doesn't mean that the universe must necessarily work that way. It's only necessary to do logic in that were it not assumed as an absolute semantics would be unworkable..and so the cheif difficulty of propositional logic - natural language- would be insurmountable.
There are, ofc, paradoxes arrived at by the pnc. These are unresolvable by insistence upon the axiom no matter how well expressed or derived we find it to be in the world around us. Every system has strengths and weaknesses..sometimes the weaknesses are brought about as a direct consequence of what gives them strength.
In the case of propositional logic..it's strength is derived from it's ability to describe a universe like ours..but because of the assumptions required it's utterly uninformative with regards to any universe unlike our own. It;s not that no such universe could exist, or the the principles of propositional logic are in some sense absolute...it;s simply that logic as a system is unable to comment upon anything like that.
There are, ofc, paradoxes arrived at by the pnc. These are unresolvable by insistence upon the axiom no matter how well expressed or derived we find it to be in the world around us. Every system has strengths and weaknesses..sometimes the weaknesses are brought about as a direct consequence of what gives them strength.
In the case of propositional logic..it's strength is derived from it's ability to describe a universe like ours..but because of the assumptions required it's utterly uninformative with regards to any universe unlike our own. It;s not that no such universe could exist, or the the principles of propositional logic are in some sense absolute...it;s simply that logic as a system is unable to comment upon anything like that.
I am the Infantry. I am my country’s strength in war, her deterrent in peace. I am the heart of the fight… wherever, whenever. I carry America’s faith and honor against her enemies. I am the Queen of Battle. I am what my country expects me to be, the best trained Soldier in the world. In the race for victory, I am swift, determined, and courageous, armed with a fierce will to win. Never will I fail my country’s trust. Always I fight on…through the foe, to the objective, to triumph overall. If necessary, I will fight to my death. By my steadfast courage, I have won more than 200 years of freedom. I yield not to weakness, to hunger, to cowardice, to fatigue, to superior odds, For I am mentally tough, physically strong, and morally straight. I forsake not, my country, my mission, my comrades, my sacred duty. I am relentless. I am always there, now and forever. I AM THE INFANTRY! FOLLOW ME!
