It can show any time ... The clock never started. — god must be atheist
The clock never started keeping time so it can show no time currently - so an eternal clock is impossible - not only did it never start keeping time, it never started existing so cannot exist currently.
Every system that exists within time, be it a clock, a particle, or a whole universe, requires an initial state else there are no subsequent states - the initial state is the ultimate determinant of all subsequent states. That initial state can only be given by the start of time. Without that initial state, poof, the system does not exist.
Let me ask you: Let's suppose you are right, and time does have a beginning, at which the clock was started. Then what was the time five minutes before that? Because every time you pick a specific time, there are five minutes before that, and five minutes after that. — god must be atheist
Time is UNDEFINED before the start of time and the clock does not exist. There is no time before the start of time. 'Before' is a temporal concept, it does not apply to timelessness.
Another way of showing that time is infinite is the method of mathematical induction. Mathemathical induction is a type of proof in which if you can establish that in the first instance ... The same process of induction can be applied to time. — god must be atheist
Induction cannot be used to prove past time is infinite because there is no first moment of time from which to start the induction reasoning from. The example you give is not induction, it is reverse induction - you are working backwards from today to justify infinite past time. That's not how time works; each moment defines and determines the next moment so it is only valid to use forward rather than reverse induction.
As you have found with the clock example, forward induction is impossible with infinite past time as there is no start of time from which to start the induction process.
This may strike you as unbelievable, but just because it strikes you so, you have not proven that they are impossible. They are bizarre, for which a synonym is absurd, but it has no relation to the reductio ad absurdum logic state. — god must be atheist
So you are at least admitting infinite past time is bizarre. Reductio ad absurdum is when you have an argument that leads to an absurd conclusion. You say my argument leads to a bizarre but not absurd conclusion. I think you are splitting hairs.
Consider also the measure problem:
- Assume time is eternal.
- Probability of event X happening is 1% per calendar year
- Probability of event Y happening is 0.00001% per calendar year
- Over infinite time X happens 1% * ∞ = ∞ times
- Over infinite time Y happens 0.00001% * ∞ = ∞ times
- That is the same 'kind' of infinity for both the number of occurrences of X and Y
- So X and Y are both equally likely over infinite time
- Reductio ad absurdum.
The math of probability works just fine for finite time periods, as shown above probability results in absurdities when used with infinite time. So either probability is absurd or infinity is absurd. My money is on the 2nd.
This is a false argument. You might as well challenge the infinity of the three dimensional space with a similar mental experiment.
"Infinite directions are impossibilities. To see this, you can for example imagine an infinite series of yardsticks that have been lain in one direction coming toward you, and reaches the point at which you exist. How many inches (fractions are allowed) does the yardstick show at the point on which you stand?" — god must be atheist
I do challenge the infinity of infinite space. Infinity is plain impossible - the whole idea is a pipe dream. Only in our minds can things continue ‘forever’; in reality this would surely be akin to magic. In your infinite yardsticks example, how did the infinite yard sticks come about? Someone would have to lay the infinite yard sticks out - but that's impossible - they would never finish laying them out - there is no greatest number - numbers go on forever but at no point do we ever encounter a number ∞ - so an infinite number of yardsticks is impossibility.
We can also imagine the infinite yardsticks as represented by the series of negative integers:
{ ..., -5, -4, -3, -2, -1 }
So I would be standing at the point represented by -1 and the next yardstick out would be -2 etc... The person laying out the yardsticks would have to start at the point '...' but that's impossible, that point is UNDEFINED - so they can never have started laying out the infinite yardsticks - there are no infinite yardsticks.