I agree; infinity is not a number.
No, I think there may have been infinitely many past events.
Above your last sentence, you said you agreed that infinity is not a number. Then you contradict yourself by saying that “there may have been infinitely past events.” Do you think that by leaving the word, “number,” out of that sentence that it will somehow escape our attention, or mean something completely other than what it says?
“…infinitely many past events” = an infinite
number of past events – nothing more and nothing less.
Logically, if
infinity is
NOT a number than it cannot be said there is an infinity of past events. If what you are saying were true, event creation would now be stopped, motion would be stopped, and, time would be no longer. We would have reached an infinity (infinite number) of past events. But, as we can plainly see, time is still being measured and events are still occurring and receding into the past.
Infinite number = infinity – nothing more and nothing less.
If we have not reached infinity, i.e., if we have not reached the point of having an infinite number of past events, then more events can be added to the collection or, set, of past events, correct? Isn’t that what is occurring? Aren’t events still being added to the collection, or set, called “past events”? If so, then we have not reached an infinity of past events yet. At an infinite number (infinity) of past events, no more events can be added as no more events can possibly take place or happen. It is the same as saying that there are a dozen eggs in the egg container and all 12 places already contain an egg. No more eggs can be added.
There are only two types of infinity: actual infinity and potential infinity (except, of course, the car - I forgot about the car - darn it!). But, back to reality.
Time is not a real thing. It is merely a measurement. It is the measure of motion. No motion - no time. No time - no motion. Time, as the measure of motion, is a continuum since its beginning so long as there is motion. We measure time with a clock of some sort, mechanical, electrical, or atomic. Time is meaningful to us as it supplies us with a reference for traversing space.
Since time is a mathematical continuum, and since time has yet to reach infinity, it can be added to. Thus we are still measuring the passage of time, so to speak.
Space is the expanse, or medium, between two or more mobile objects. Space requires at least two such objects, in the universe because, like motion, it is relative.
Saying that in an infinite past all logically possible numbers have been traversed doesn’t make any sense to me. For one thing, we’re talking about time, not numbers. However, if you assign numbers to time, there is no reason that you must have traversed all possible numbers to get to the present.
Of course there is. An infinity of numbers is the set of all possible real numbers, which of course, cannot exist. Number does not exist. Number is merely predicated of that which exists. Number is predicated of Being. Number exists only as it qualifies Being, such as, there are two Beings, or things. Take away the things or, beings, and you take away number. It is a mental construct referring to quantity of being.
As number does not exist, neither does an infinite number exist. Does the potential for there to be an infinite number of things out there exist? Yes - as you will always be able to add (or subtract) one, two, three, or more from the collection of things, thus the collection is not infinite but only potentially infinite. What do we call incredibly large numbers, numbers to big to count? They are called trans-finite numbers and that’s too bad. Because, Georg Cantor and the other set-theory guys usurped the word for their purposes thus confusing everyone else.
jd