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( See David Darling : The Universal Book of Mathematics, 2004 )
The NSTP Theoretical Resolution of First Two Paradoxes
Zeno's paradoxes, except last two, are not a matter of language or symbolic theories (e.g. set theory) or equations. They are deep rooted in profound concepts, whose appropriate analysis and synthesis shall resolve paradoxes.
The first two of Zeno's paradoxes are out of misbelief that space exists in ontological sense, i.e. as a reality, out there. In fact, space is a virtual reality, a form/kind of illusion. Consequently (spatial) motion is also a form of illusion ( to non - spatial observer/s ). Thus reality is not constrained by spatial infinities as whatever that is seen as happening in space is a mere illusion, with no resemblance to reality. And illusion could be of any logically possible kind. In other words, thoughts modulating / creating / responsible for spatial illusion do not have to bother whether mover has to first reach half of distance and so on, or faster has to first reach point where slower started or has infinitely many gaps to traverse, etc. The only thing is that they, thoughts, produce some dynamic spatial pattern ( actually / physically represented in form of appropriate non - spatial states of consciousness ), as if a mover moving or faster overtaking slower. That's it.
[ In analogy with today's desktop computers a software programmer / graphic designer do not at all have to worry with Zeno's first two arguments / paradoxes. All s/he has to do is to write a program in order to create / generate an appropriate dynamic / changing pattern on computer monitor screen. The same is true with whole universe, whose non - spatial mechanism is stated in NSTP ( Non - Spatial Thinking Process ) theory. ]
Resolution of Third Paradox
The first proposition / assumption in third paradox is false.
Resolution of Fourth Paradox
In fourth argument / paradox there is no consideration of speeds ( or concept of speed ). As A and C are travelling in opposite directions their speeds add up. And as time taken = distance covered / speed, double speed makes mover cover distance in half time.
And even if this solution has any flaw/s then ultimately there is NSTP theory, with its idea of spatial illusion, to resolve paradox.