movement does not exist
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consider that a train travels at 100 kilometers per hour, before crossing 100 kilometers it must cross 50 kilometers before crossing 50 kilometers it must cross 25, before crossing 25 it must cross 12.5, this can go on ad infinitum, since it is impossible to complete a infinite task, it is impossible to complete the task of traveling 100 meters, this applies for any distance x that anything x tries to travel.
Let's imagine the smallest instant in which the time x that it takes for any object x to travel a distance x can be divided, at that instant the object cannot move since if it did, the time would be divisible, since the distance traveled would be divisible, given that at that instant, the object x does not move, nor can it do so at any other instant of equal magnitude, joining 2 of those instants does not produce any movement, if you join 10, neither, if you join 100, neither, the movement never occurs.
Pro's arguments are essentially variants of Zenon's paradoxes.
The first is a variation of the Achilles paradox:
the second is a variation of the arrow paradox:
Archimedes and other mathematicians have shown that as distance geometrically decreases, so does time:
when we finish adding the infinite distance divisions and the infinite time divisions, we get the total distance and the time (for the example of the pro, 100 km/h)
the definition of motion is "change of position", the position of the object at time b is different from that at time a, so object x moves even in the shortest possible time.
1.infinitesimal calculus is a part of mathematics, the impossibility of movement is a philosophical question, on the other hand, it is irrelevant if time is reduced geometrically, it is only possible to arrive at the sum total of the infinite divisions of time and distance (100 km/h) if it is possible to complete an infinite series of additions, however the definition of infinity is "something that never ends", it is not possible to travel at 100 km/h because this requires completing an infinite series of movements, which which is a logical contradiction.
2. At time b there is no change in position with respect to time a, since no distance can be traveled at any instant.
Convergent series are series of infinite sums, all of them are complete, it is possible to finish a series of infinite sums:
it is an empirical fact that objects are continuously in positions different from their other instants, the proposition of pro implies too strong a solipsism let us not forget that zenon of elea was a student of parmenides, who defended that everything that exists has always existed, that everything is cohesive and that everything we see is illusory:
1. not really, "convergent" in math means that it is
equal to the value of an infinite series, if you look at these convergent series, you will see that they are finite, they occupy a finite space, they all have a finite number of sums, the convergent series are not infinite series, but representations of infinite series, my opponent has shown that an infinite series can be represented, not that an infinite series can be terminated.
2. I am willing to accept the degree of solipsism that my position requires, logic prevails over empiricism, the senses fail, I never look at objects, I look at the light that comes out of them, I never feel the objects, I feel the signals of electricity that occur, the idea that there is a movement between each instant is contradictory.
I disagree, we observe things and then we reason, not the other way around, also, how is light and electrical signals transferred without movement?