Paradoxes disebowlement (take 2)

For today I've prepared part 2 of the attack on some apparent paradoxal situations.


Statement:
All horses are the same color. (The Horse Paradox, pseudo-paradox)
Proof: Take a set of 1 horse. Obviously the statement holds. Assume it to true for n horses, using induction. So let's prove this for n+1 horses. But it's easy. Take out another horse from the set, we're left with n horses. Which, by the hypothesis, have the same color. Therefore all horses have the same color.

So where's the problem? The problem stands with the implicit assumption that two subsets of the same set have identical properties. For n=1, this obviously stands but induction is rendered useless by common sense. Tommorow however we'll see another apparent paradox (Raven's Paradox) that although defies common sense, the reasoning and conclusion still stands.



Statement:
Your mission is to not accept the mission. Do you accept?

This one fails to be tricky enough. A simple 'no' leads to actually not accepting the mission but performing the task involved. A 'yes' leads to accepting it but unable to perform the task. Assuming this would take place in a military environment, situation b would entertain severe consequences (failing to perform the mission).
This attempt puts an equal sign between mission acceptance and mission task but in fact saying no doesn't mean you accept the mission, only that you perform it.



Statement:
Let the God Almighty create a stone, which he can not pick up!

This one goes in line with those who assume perfection. However the existance of perfection (the perfect gas, the almighty being, the impenetrable armor) can be invalidated by logical induction, and this sentence can in fact help us in this. Either way, the almight being implied is NOT almighty at all. If he can't create the stone, then there's something this being can't do, therefore not almighty. If he does in fact create it and can't pick it up then he's not almighty once more. Both condition disprove the initial assumption that the being in question is almighty. Through induction we conclude there no being can be almighty.


Statement:
What would you see looking around if you could move faster than the speed of light?

This doesn't pretend to be a paradox but it might be interesting to analyze it.
The theory of light and relativity is quite shaky even today and is surrounded by many assumptions, of which too few have been proven or disproven by experiment.
One inconsistency (for example) is that both the particle and wave natures of light have support both in theory and practice. Einstein stated that information can't move faster than light. Yet both particle and wave can serve as information carriers (by the way they stimulate receptors on the eye's retina). Still particles can be accelerated and there's no reason (theoretically at least) to believe light in their particle aspect can't be accelerated still and still carry the information they do.
Given this, let's take the sentence above and put it into practice. We are a being capable of warp speed and sit by a building. Suddenly we start moving away from the building and at some point we look back. What do we see?
Obviously we are traveling faster than light so we soon outrun the light that carries that building's image. One trap here is to state that because of this we would see nothing at all (since the same reasoning applies to all objects behind us). This is of course false as light has been moving countinously away from the building and at any given point we encounter light that has been countinously moving away, carrying the image of the building at various points in the past. Seeing nothing does apply however in certain particular cases, such as if we start moving towards an area of the universe where light hasn't reached yet. Because light moves slower than us, looking anywhere around would make us feel blind.
This image is however affected by gravity. It wouldn't take long for us to be unable to see the house at all, our field of view would expand eventually to the whole planet as we pass through the atmosphere, but again seeing images from the past as we look back. Due to the way light's path curves around high gravity bodies (stars for example, or black holes) our image may be distorted at times.
But how about looking forward? From directions where light moves towards us, we get this at a speed that is light speed + our own speed. This means we are bombarded with fast moving images, as the delay between an images 'timestamp' (the moment when it was created) becomes smaller and smaller. For example, we know that the images of the stars and galaxies we see on the sky are in fact coming from various ages of the universe. Some of those stars may not even exista right now but we see them as the light coming from them eventually reaches us. If we would move towards them faster than light, we would get information that is more actual as we close in on them.
Should we pass such a star, we of course will fall to the other case, where we outrun light and information becomes less actual.
Moving faster than light may (as such) allow us to see the past of some objects, but this would need some improbable precondition (such as light moving in a straight line, when in fact light is curved under the extended theory of gravity) and definately not the future (as some SF work implies). In fact this is the reason why scientists continuosuly analyze snapshots taken by Hubble of the distant universe. As light takes a long time to reach us, these images are invaluable snapshots of moments in the evolution of the universe.
The theory of warp travel also implies some interesting effects, such as the relativity of time as lifecycles create their own way of measuring time, which would not apply to an entory that travels at warp speed.