skippy

I am totally unfamiliar with Poppers. Just what do we do with theories that are proven wrong??? Put them to a vote??? What do we do with new theories which predict things the old theories can't? Put our heads in the sand? Aristotle gave us earth, air, fire and water = PHYSICS. Plasmatic thinks Aristotle was a really smart guy. Therefore everything can be explained in terms of earth, air, fire and water. Are you living in a parallel universe, or what. Cheers, Skippy

Precisely. Formal set theory (ZF or ZFC) was an attempt to codify all of mathematics into a few comprehensible axioms. There is no possible proof of the consistency of these axioms although a century of searching (by a lot of really clever people) has yet to display an inconsistency. The existence of the empty set is proven using the Axiom of Separation and the Axiom of Infinity (see, for example, chapter 1 of "Set Theory" by Thomas Jech). The purpose or use of the empty set is to be able to actually construct mathematical objects like numbers and functions and everything else. Mathematics does not concern itself with sets of apples or oranges; only sets that it can construct in a precise way. Real proofs in formal set theory can contain thousands of steps for quite simple theorems. As a simple example, the natural numbers can be defined in terms of the empty set by identifying Zero with the empty set {}, One with {{}}, the set containing the empty set, Two with { {}, {{}} }. In general each natural number is the set containing all natural numbers less that it. Now, you don't have to accept set theory at all. Some professional mathematicians do not "believe" in sets. The natural numbers can be constructed in a very intuitive way with the Peano axioms, or in very unintuitive way using the methods of Principia Mathematica (Russel & Whitehead). None of these methods can be proven consistent. While 99.9% of all mathematicians ignore these issues the few that concern themselves with the foundations of mathematics fall into roughly three groups: Formalists. Mathematics is a game played by clever manipulation of axioms (set theory or otherwise). Platonists. Mathematical truths, in particular the natural numbers, EXIST independently of any intelligent creatures which might use or study them. Ultrafinitists. Something like Platonists except that they only believe in the existence of a FINITE quantity of natural numbers. They probably number about 0.01% of the 0.1% that actually care about these things. So, pick your poison. If you don't want to accept set theory, don't talk about the continuum or things like differentiable functions, they don't exist. Cheers, Skippy

There are, right now, hundreds of theoretical physicists who have spent their entire adult lives trying to answer this question. There are three or four directions that they are following (Loop Quantum Gravity, String Theory (AKA M-Theory), Causal Dynamical Triangulations, Graphity &ct.). Some of them (e.g. String Theory) assume a preexisting void or "container space", others hypothesize an underlying structure (spin-foam, loops or graphs) which, WHEN VIEWED ON LARGE SCALES, give an intuition of a continuous spacetime. In any event, it is well to remember that physics and science in general CANNOT PROVE ANYTHING. Theories which have explanatory power are put forward and they stand until proven false. The General Relativity and the "Big Bang" currently have a lot of explanatory power and have yet to be proven wrong. If you accept it as an explanation, then it is the event which created all the physical space and time of our universe. To ask where it occurred or what came before or what is outside our (probably finite) space is as meaningless as asking "What is South of the South Pole?" Skippy

Please read more carefully. I said "MY dog" not "a dog". Skippy

I can hardly believe that our country has deteriorated so far that the "Free Choice Act" is even a topic of serious discussion. It is something the dirt-bags in Atlas Shrugged could have dreamed up. Even GEORGE MCGOVERN is opposed to it. Skippy

I would really like to come back as MY dog. That is one creature that has it made. Skippy

I am a product of (what was then known as) a mixed marriage. Mother was Roman Catholic, father a free thinking agnostic. She put me through 16 years of Dominicans and Jesuits. He kept his copies of Playboy under Spinoza, Kant, Voltaire, Aristotle and Thomas Aquinas. Whatever faith I had was gone by age 11; not sure if it was Spinoza or Miss September. Later in life, After reading everything written by Ian Stevenson, I came to believe in the real possibility of reincarnation. So currently I believe in a spirit or soul but no Cosmic Dictator or Creator. It works for me but probably few others. Skippy

My first post here. I started rereading Atlas Shrugged last week. It seems I read it about every 20 years or so. (Hope to get 2 or 3 more in.) Guess what? I don't have to watch or read the news any more. Its all there, every disgusting detail: every lying corrupt power hungry weasel, every mindless victim, the ignorant herd mentality. Although I am an atheist, I came to believe in reincarnation a number of years ago through the scientific studies of Ian Stevenson. Not sure if I have the moral courage to want to come back. Please say hello, it might cheer me up. Skippy