Actual Infinities

[Neo-Scholastic]

I do not understand why you posted this under Christianity since it seems to belong in Philosophy. Nevertheless, thank you for a good topic. I was starting to get bored. Be that as it may, I do not find any of the Kalam-style demonstrations compelling and highly doubt that Kalam enthusiasts have thought very much about actual/potential infinities.

I see resolution of the apparent paradox in Aristotle’s distinction between two modes of existence: actuality and potentially. The number of actual infinities would be finite whereas the number of potential infinities is infinite (but not unlimited).

I have always maintained that God’s knowledge consists only of that which it is possible to know and that this position satisfies the definition of all-knowing, as in knowing all there is to know. From there I say that there is nothing to know about things that do not exist either in actuality or could not possibly be. For example, an oak may currently exist as an actual acorn and simultaneously be said to exist as a potential sapling. Thus God knows everything it is possible to know about what the acorn is (now) and what it could potentially become (later). However, God does not and cannot know what the acorn will actually become since that is in the future and the future does not yet exist. What potential will be actualized could be contingent upon the decisions of freely acting beings (humans). These people could prevent the acorn from being planted or start a forest fire.

One thing that continues to puzzle me is the ontological status of the past since technically the past does not exist anymore; it is a current memory or embodied history. That also strikes at the heart of Kalam-style demonstrations. Not only could there not be an actual infinite regress into the past, there cannot be any temporal regress at all! The passage of time is, as it were, a kind of illusion within an eternal present.

[Neo-Scholastic]

It's funny how people who can't imagine this infinite past find it incredibly easy to imagine a god with exactly the same properties.

Of course, they try and make him special by using such nonsense terms as "timeless".

We experience reality, so our ideas about it get constantly challenged. I agree that imagining an infinite past is difficult, because it kind of clashes with our intuition about how things seem to work. Since no one actually experiences God outside of their own head, it never falls under the same scrutiny. People can merrily use whatever words they want to describe it and it can break all the rules that apparently cause these paradoxes in the first place, because it never actually shows up to challenge those claims.

If it did show up, our natural curiosity would be asking all the same questions we ask of the universe.

"Timeless" yet was planning all sorts of things the whole time before creation. Interesting paradox.

The principle of noncontradiction is timeless. It exists independent of any space or time. Nor is it a observed property of any empiracly known being. So timeless is not a meaningless term.

[Anomalocaris]

And you're going to use this argument against people who are essentially in slippers because shoelaces are too complicated?

The Zeno bit with the arrow is solved because quantum, i.e., spacetime is quantized, discrete. Also with Planck length is Planck time, so I'm failing to see how the one cannot be extrapolated to the other. Further, it seems likely that this universe is 13.82 billion years old, making the whole excercize rather moot. To include infinite speculations to rationalize a point that should be clear with fractal geometry and evolution seems to be unnecessary construction. If your intended audience refuses to hear the ABCs and 123s why do you think it's going to listen to the Alephs?

Color me confused. 

I would think the Zeno paradox has been unparadoxed way before quantum mechanics.   I would think the thinking world had been analytically unstymied in closed form not long after the invention of calculus. Only lineal antecedents of those who could still believe in biblical creation in the 21st century would have still been quacking about it in the 19th century.

[robvalue]

I'd like to point out that I'm not at all claiming that there is an infinite past. I'm saying that dismissing the possibility that there could be, due to the difficulty imagining it, is (I think) an error.

Or rather, I should say, there was an infinite past. The fact that we're caught up in the reference points is what makes it hard to get our heads around it I think.

Again, I think we're missing pieces of the puzzle that make understanding "time" possible. Who the hell knows how it works as you push the boundaries back further and further. Not in ways we can easily imagine, I would wager.

[TheRealJoeFish]

Indeed. All these Kalam style stupid arguments follow the same pattern:

1) My simplistic attempts to understand our reality produce a rule R.

2) There appears to be a paradox P in relation to rule R being a full and consistent explanation.

3) Since rule R must be correct, there can't actually be a paradox. So there must be some exception E to rule R which solves the apparent paradox P.

4) ???

5) E is a sentient being, also a god, also the God of my religion, also my specific interpretation of the God of my religion, and I have a personal relationship with it.

[GrandizerII]

"Timeless" yet was planning all sorts of things the whole time before creation. Interesting paradox.

The principle of noncontradiction is timeless. It exists independent of any space or time. Nor is it a observed property of any empiracly known being. So timeless is not a meaningless term.

The principle is abstract.

[Angrboda]

Anyways, I was going to say something else - imagine the universe were deterministic. This could still be true in a quantum world if there are some mad hidden variables underlying it all, or in a many worlds interpretation - who knows. Anyways, imagine that it is deterministic. In that case, knowing the state of the universe exactly at one point in time gives you knowledge of the universe at all times. In fact, one could argue that philosophically, a snapshot at one point in time + the laws of physics is equivalent to the whole timeline, because the rest of it can be obtained using a uniquely determined procedure - the future and the past are more or less the same as the present, viewed through a different filter (and those who know how the Heisenberg picture in quantum mechanics works, might understand better what I mean).

So, time does not exist, and doesn't pass. All that exists is a static snapshot of the universe in what we would call the distant future, in which all that you and I call time, and events, and experience, is encoded.

Setting aside the fact that physics rather conclusively points towards an indeterminate universe, if time doesn't exist, in what sense am I experiencing it pass from one moment to the next though? Does this static block of being contain "tunnels" of consciousness in which the illusion of motion occurs? And what causes it to have this quality of a continuous, seamless flow in one direction?

One of Wittgenstein's famous examples is of a man walking on a hill. From the snapshot image of the man, it is impossible to tell if he is walking down the hill going forward, or walking up the hill going backward. I think when we imagine memory and experience, we imagine it as a static snapshot of the moment. But this presents us with a problem. How do we determine the direction of things if every moment is just a single image, a snapshot? I think the resolution to this is that we don't just experience the moment, there is also present in mind and in memory, a bit of the past, a trailing image as it were. So while we experience time as consisting of moments, the past is always with us trailing behind an image of the recent now. This is what gives time its arrow, because that arrow is constantly experienced at each moment in time as a composite of the now and the recently now. Thus, matter can exist simultaneously throughout all of time, but because each 'slice' of that existence contains a 'smear' of experience across time, it can be felt as progressing from past to present to future.

[Neo-Scholastic]

The principle of noncontradiction is timeless. It exists independent of any space or time. Nor is it a observed property of any empiracly known being. So timeless is not a meaningless term.

The principle is abstract.

Abstractions exist only in the mind. Some things, like the Principle of Non-Contradiction (PCR), exist independently of any mind.

[Alex K]

@Jörmungandr, Nestor

In Newtonian physics, a snapshot of all positions of all particles is indeed not enough to know the future. A snapshot of all positions and momenta at a single point in time however is enough to exactly determine the evolution of the system in the future and the past, and this is indeed what I meant. In deterministic quantum theory (and I take the many worlds interpretation as the easiest example), the equivalent that you would have to do is get a snapshot of the wave function at a single point in time - it includes all position and momentum distributions, and is hence enough to know the time evolution.

@Nestor,

Your experience of knowing the past and the unknown future lying ahead is mostly a statistical phenomenon connected to the increase of entropy.

[I_am_not_mafia]

The principle is abstract.

Abstractions exist only in the mind. Some things, like the Principle of Non-Contradiction (PCR), exist independently of any mind.

No it doesn't.

Logic is a man-made concept used to represent and reason about the world. The same with Maths.

If the human race was wiped out then logic and the principle of non-contradiction would not exist.

If you disagree with me, then bring me a True or a False.