Philosophy Now Forum

Logic insists that between two points lies an infinite set of divisions, making it "impossible" to traverse from start to end. Yet, in practice, the finger does move from the beginning to the end in finite time.

The Dean paradox thus reveals that empiricism rationalism etc , like all philosophical systems dependent on human reasoning (Aristotle Plato Hume Kant Hegel Schopenhauer Nietzsche Wittgenstein Russell Quine science mathematics philosophy ie everyone) is constrained by the inherent flaws of logic, and cannot guarantee a coherent or reliable account of reality

janeprasanga wrote: ↑Thu May 01, 2025 9:43 am Logic insists that between two points lies an infinite set of divisions, making it "impossible" to traverse from start to end. Yet, in practice, the finger does move from the beginning to the end in finite time.

Ben JS - 2012 wrote: From: https://www.ilovephilosophy.com/t/tenseless-time/35015
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I was thinking of Tenseless Time and an idea occurred to me.

The image in my mind was of a cartoon flip book. Every page illustrating each deviation space.
I made the assumption that each page was in order, and there’s X amount of pages which flow in a linear manner.
But if the pages were not in order, based on the contents of each page, we wouldn’t be able to distinguish that there wasn’t order. For on each page, the environment would be completely mapped out.
It’s similar to the idea of someone being implanted with false memories. All they are aware of is the present and have no tools to validate their past.
The same could be said for us in Tenseless Time.

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If space-time is a static block, what and where is the motion that gives us the illusion of change?
Is every point always true and active?
Am I a point that is forever locked?

Ben JS - 2015 wrote:I strongly believe that the universe is similar, in that is has no starts or ends - but is a cycle of all potential states in an order (the order of change being how we deduce laws of reality).

I also buy into eternalism / block universe / tenseless time. That’s how I see the universe - with time as a literal dimension.

http://en.wikipedia.org/wiki/Eternalism ... y_of_time)
http://en.wikipedia.org/wiki/B-theory_of_time

The universe is like a film reel of 4D states, constantly flicking by. Each slide (state) is separated by another by the smallest increment of change possible. That that is the speed of time. But the film reel exists in it’s entirety as the film plays. The reel is one long loop, feeds back on itself and is constantly a smooth transition between slides - no abrupt change of state: like in a 3D reel if you’re watching an ocean scene, then it immediately cuts to a scene in a city without any logical transition of states.

There is no rest of it. I define the universe as the encapsulation of all that exists - if it exists somewhere, then it part of the composition of the universe.

Ben JS wrote: If we could slice existence along the dimension of time,
between the smallest / fastest interactions that ever transpire,
then compare slices:
If the interactions of existence,
are only ever influences by itself,
and always react the same way given the same conditions / environment,
then:
If any slice, matches another slice,
we’ll call these slices C1 & C2,
logically,
the slice after C1 and the slice after C2,
should also match -
and the slice before C1 and before C2,
should also match.
This pattern would continue until you fully connect C1 & C2.
Cycle 1, cycle 2, cycle 3 etc.
But why count or differentiate these cycles at all?
For all intents and purposes, they’re identical to each other.
We can just call it the one cycle - time’s a loop.

Ben JS wrote: ↑Fri May 02, 2025 9:58 am No idea who Dean is,
but they're describing Zeno's paradoxes from 5th century BCE.

godelian wrote: ↑Fri May 02, 2025 3:10 am

janeprasanga wrote: ↑Thu May 01, 2025 9:43 am Logic insists that between two points lies an infinite set of divisions, making it "impossible" to traverse from start to end. Yet, in practice, the finger does move from the beginning to the end in finite time.

It is not first-order logic (FOL) that insists on such a thing. FOL does not insist or axiomatize in any shape or fashion the axiom of infinity.

The axiom of infinity is indeed assumed in (ZF) set theory. It is, however, not supported at all in, for example, (PA) arithmetic theory.

Furthermore, the axiom of infinity is a Platonic abstraction that in and of itself has nothing to do with the physical universe.

Mathematics is about Platonic abstractions -- if mathematics is uberhaupt about anything at all. Physics ("science"), on the other hand, is about the physical universe. Hence, these two disciplines are not even about the same universe.

If his statement is about mathematics, then sorry, there are no abstract Platonic fingers in the abstract universe that mathematics seeks to describe.

If his statement is about physics, then he must support his claim with an experimental test report that others can reproduce. In physics, there simply are no experimental tests available that will detect an infinite set of divisions between two points.

Conclusion. You cannot use the axiom of infinity in the physical universe. You cannot even use it in arithmetic. It is typically only used in set theory. Furthermore, all of this has nothing to do with (first-order) logic.