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. Nowrepparttar barber himself is a man andrepparttar 127623 supposition requires thatrepparttar 127624 barber shave himself if and only if he does not ! This contradiction straightaway implies thatrepparttar 127625 supposition is false. That is, there is no barber who shaves every man who doesn't shave himself, and no one else.

The justification ofrepparttar 127626 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, whererepparttar 127627 set theoretical foundations need to be reformulated.

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 ofrepparttar First Two Paradoxes

Zeno's paradoxes, exceptrepparttar 127622 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 resolverepparttar 127623 paradoxes.

The first two of Zeno's paradoxes are out ofrepparttar 127624 misbelief that space exists inrepparttar 127625 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,repparttar 127626 thoughts modulating / creating / responsible forrepparttar 127627 spatial illusion do not have to bother whetherrepparttar 127628 mover has to first reach half ofrepparttar 127629 distance and so on, orrepparttar 127630 faster has to first reachrepparttar 127631 point whererepparttar 127632 slower started or has infinitely many gaps to traverse, etc. The only thing is that they,repparttar 127633 thoughts, produce some dynamic spatial pattern ( actually / physically represented inrepparttar 127634 form of appropriate non - spatial states of consciousness ), as if a mover moving orrepparttar 127635 faster overtakingrepparttar 127636 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 onrepparttar 127637 computer monitor screen. The same is true withrepparttar 127638 whole universe, whose non - spatial mechanism is stated inrepparttar 127639 NSTP ( Non - Spatial Thinking Process ) theory. ]

Resolution ofrepparttar 127640 Third Paradox

The first proposition / assumption inrepparttar 127641 third paradox is false.

Resolution ofrepparttar 127642 Fourth Paradox

Inrepparttar 127643 fourth argument / paradox there is no consideration of speeds ( orrepparttar 127644 concept of speed ). As A and C are travelling inrepparttar 127645 opposite directions their speeds add up. And as time taken = distance covered / speed, double speed makesrepparttar 127646 mover coverrepparttar 127647 distance in half time.

And even if this solution has any flaw/s then ultimately there isrepparttar 127648 NSTP theory, with its idea of spatial illusion, to resolverepparttar 127649 paradox.

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