## Conmathematical Resolution of Russell's Paradox

Written by Dr Kedar Joshi

Continued from page 1

Now conmathematically Russell's paradox is quite easy to resolve. The conmathematical resolution could be stated in just one sentence : As there is no barber who shaves every man who doesn't shave himself, and no one else, likewise there is no set of all sets that aren't members of themselves.

This sentence is justified or explained below.

Suppose there is a barber who shaves every man who doesn't shave himself, and no one else. Now barber himself is a man and supposition requires that barber shave himself if and only if he does not ! This contradiction straightaway implies that supposition is false. That is, there is no barber who shaves every man who doesn't shave himself, and no one else.

The justification of sentence 'there is no set of all sets that aren't members of themselves' goes on similar lines. Conmathematial foundations of mathematics, being very profound and deep, easily absorb shocks of such fuzzy paradoxes, where set theoretical foundations need to be reformulated.

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## The NSTP Theoretical Resolution of Zeno's Paradoxes

Written by Dr Kedar Joshi

Continued from page 1

( 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. ]

The first proposition / assumption in third paradox is false.