Arakasi Takeda wrote:
To further illustrate the reason I do not hold axioms as 'undeniable truths', here's a simple example:
...
But they are not necessarily true unless one can prove that the axioms of a specific logical system are identical to the axioms of the 'real world'.
AT
This doesn't make since to me. First, just because some calls time an axiom doesn't mean I think it is. I have never thought that it was an axiom. In fact, I have always thought of time as just a measurement.
That is
exactly the point I am making Tolthar. You are claiming that one man's axiom isn't necessarily true. What constitues a proper axiom,
to you, is based solely on
your own definitions.
Just because
you only consider time to be a 'measurement' does not mean that scientists studying relativity or quantum mechanics view it the same way. You have your logical system and they have theirs. You have your definitions and boundaries, and they have theirs.
If you ignore reference to some
shared reality by which you can measure your axioms against theirs, there is
NO way to define one set of these axioms as 'True' and another 'False'. Because of this, I only agree that axioms are necessarily true within their own logical systems.
I happen to believe, however, in the existence of a 'shared' reality - the 'real world', the Universe, the big Objective Reality. Comparisons of axiomatic statements are therefore possibly by comparing them to the axioms dictating knowledge within this Objective reality. Those logical systems whose axioms match those of Objective reality can be considered 'ultimately true'; those which do not are ultimately false.
I also don't see how your example makes time 'relative'.
If I am at the sun (getting a tan or something) and am 2 light minutes away from the earth; and there is someone watching the sun from earth (Bob), time is not different for us.
If I were to travel towards Bob at the speed of light, two minutes still went by for both of us. Bob won't see me for about 2 minutes, and I won't see Bob for about two minutes.
This is really a different topic though since I don't hold time as an axiom. I only hold things that are undeniable as axioms.
The reason this doesn't make sense to you is because you obviously have a flawed sense of what Relativity is.
Suppose you and Bob are both at the sun. You both have watches which measure 'Absolute Time', and are both synchronized to keep time exactly the same. Both of your observe a solar flare occuring at exactly 12:00pm according to your watches.
Bob is then transferred instantly to Earth, which is approximately eight light-minutes away from the sun. A second solar flare occurs, and you both record the exact 'absolute time' displayed on your watchs for when you see the event.
Sitting at the sun, you record that the second solar flare occured at exactly 12:10pm. Bob, sitting on earth, using the same absolute time measurement as yourself, records the solar flare as having occured at 12:18pm.
This is why we can time 'relative'. The timing of a single event, which
both of you observed occurs at different 'relative' times, depending solely on the position of the observer. You swear the event occured at 12:10pm. Bob, who watched the exact same event as you, swears the event occured at 12:18pm. You cannot both agree on an 'Absolute Time' on which the exact same event occured. It is completely dependent on your positions.
Now, if you know something about Relativistic Mechanics, you can diagram this event on something called a Light Cone, which shows the event itself as a 'world line' spreading out from the Sun, eventually intersecting with yourself (at 12:10pm relative time) and then, later, with Bob on Earth (at 12:18pm) and, thereby, realize that you really are talking about the
same event.
This would be impossible to do if you existed in a world based solely on Newtonian Axioms. In Newtonian physics, if one event is observed to occur at 12:10pm and another at 12:18pm, it is impossible for these to be the same event. If Time is an absolute, an single event cannot occur at two different times.
AT