Impossibility exists

I intend on demonstrating the existence of impossibility through examples and logic. My contentions:1. Self-referential Paradox2. Squaring the Circle3. Barber Paradox4. Time Travel Paradox5. Generic Theoretical DemonstrationContention One: Self-Referential ParadoxBy proving the all-inclusive opposite of something to be false, one proves the original proposition to be true. This logic may be applied to the concept of an impossibility; by proving false the statement that nothing is impossible, it is proven that impossibility exists. I feel this is best expressed in the form of a syllogism.Premise One: The statements that impossibility exists and that nothing is impossible are all-inclusive opposites.Premise Three: The statement that nothing is impossible is false.Conclusion: The statement that impossibility exists is true.Premise OneFor the purposes of this debate, for impossibility to exist, something must be impossible. If nothing is impossible, impossibility does not exist. If the statement "nothing is impossible" is true, the conclusion "impossibility does not exist" is always valid.Premise TwoIf nothing is impossible, it must be true that it is impossible for something to be impossible. To rephrase that, the statement "nothing is impossible" applies universally; everything is possible. But what about something being impossible? Is that possible? If Con answers yes, he agrees that it is possible for something to be impossible, that impossibility exists. If Con answers no, he states that nothing is impossible, that it is impossible for anything to be impossible. Either way, the statement is found to be false and Con is agreeing that at least one instance of impossibility exists.ConclusionWhen both premises are true, the conclusion is true.Contention Two: Squaring the CircleThe problem of squaring the circle, to quote Wikipedia, is "the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge." The article goes on to state that "[a]pproximate squaring to any given non-perfect accuracy, in contrast, is possible in a finite number of steps, since there are rational numbers arbitrarily close to pi." However, creating a square with area exactly equal to that of a circle (with just a compass and straightedge) is impossible, as proven by the Lindemann-Weierstrass theorem.[1]Con may claim that Leonardo da Vinci or another man achieved this feat, but, in the example of Leonardo da Vinci, only 99.8% accuracy was achieved.[2] Besides that, the feat is mathematically impossible.[1][2]The Lindemann-Weierstrass theorem proves that pi is transcendental, that is to state that it is not algebraic. Because pi is not algebraic, math dictates that it is impossible to create a square with exactly the same area using just these tools.Contention Three: Barber ParadoxImagine a town with just one barber, who happens to be male. Every male member of the society keeps himself shaved through one of two actions:A. Shaving himself, orB. Having the barber shave himThus, we reach the paradox, the barber. Who shaves the barber? Because each male in the town does exactly one of the two actions, the situation is paradoxical. If the barber shaves himself, then he is fulfilling both options. He is shaving himself and having the barber shave him. If he does not shave himself, then he fulfills neither option. He is neither shaving himself nor having the barber shave him. This directly contradicts the statement that every male in the society is shaved through one of the two options. Thus, the scenario is an impossibility.Contention Four: Time Travel Paradox*This contention is not stating that time travel is impossible*Once again, I ask you to consider a hypothetical scenario. Imagine that a scientist invents a time machine. The technology becomes available to a specific individual who decides to go back in time. Upon arriving in the past, said individual murders the scientist before he invents the time machine. Once again, this is an impossible scenario because if the scientist were to be murdered before inventing the time machine, it would be impossible for an individual to go back in time using a time machine designed and built by the same scientist.Contention Five: Generic Theoretical DemonstrationThis contention shall be presented in the form of a syllogism as well.Premise One: All X are instances of Y.Premise Two: Z is an example of X.Conclusion: It is impossible that Z is not an instance of YI would go into more depth with each premise and the conclusion, but I feel it would be superfluous, as this one is extremely self-explanatory. As per the definitions of this debate, impossibility does not have to have material being. Even a completely theoretical instance of it is enough to affirm the resolution.ConclusionI have shown through my contentions that the only alternative to impossibility's existence is a self-referential paradox and thus cannot be true. I have given multiple examples, material, hypothetical, and theoretical, of impossibility's existence. With these five contentions, I will stop in order to give Con enough space to respond and now open the floor to him.Sources[1] http://en.wikipedia.org...[2] http://arthistory.about.com...