Is an action that causes a paradox impossible?

Question

Suppose you went back in time and tried to murder your 2 year old self. Since murdering yourself in the past erases you, then you can no longer kill anything because you don't exist. Therefore, no matter how or why you try to kill your younger self you won't succeed, because even if you succeed you no longer exist to succeed. Also, if you were to purge this post from your memory, then you still wouldn't be able to do it.

Another example is if you tried to create a condition in which there was no nothing and no things. This is a paradox because if you destroy every "thing", then you are left with nothing, and if you try to destroy that then you are left with things again. Thus, no matter how hard you try, you can't create such condition.

A final example is if you tried to do something an infinite number of times. The more you do, the closer you are to infinity, but infinity is forever out of reach (paradox of you can/can't achieve a single thing). Thus, no matter how hard you try, you will never do something ∞ number of times.

The basic idea here is that if something is paradoxical, it is not only physically impossible, but by definition even if you disregarded the notion of "impossible" and tried to do it you would never be able to do it. Am I correct?

Answer 1

Time travel paradoxes have been discussed here often, eg

• Given that we do not have the ability to time travel backwards, can we prove that there will never be backwards time travel?

• Time travel and changing the past

• Will this break the laws of physics?

Currently we don't know of anything that explicitly makes the closed time-like curves impossible, that can be constructed in General Relativity.

We don't seem to see evidence of paradoxes, which has led to the 'chronology protection conjecture'.

One possibility, is that when changes occur, a branching parallel world is created, like those of the Many Worlds interpretation of Quantum Mechanics.

In Quantum Mechanics space & time are just assumed as background with no mechanism for their origin. In General Relativity space time & gravity are all assumed to be continuous, which is at odds with the quantised picture covering everything else, & no evidence of a 'graviton' force carrying particle has been found at all. Until we have a theory that can unite time with our wider picture of forces, we simply, don't know.

Answer 2

The gist of your question seems to be 'if you disregard impossibility, would things still be impossible?' the paradoxical nature of which prevents a meaningful answer.

Answer 3

Well I'm not sure that all of your examples are of this kind, but surely if an action A is such that "x has done A" entails S and S cannot be true (say, because it is a contradiction) then by logic alone it is obvious that "x has done A" cannot possibly be true, i.e. it is impossibile to do A.

In your first example, lets assume that A is travelling back in time and killing the 2y.o. version of oneself and that doing A implies being dead before doing A and also being alive before doing A (since to do something you arguably have to be alive), then A implies a contradiction (at least with the very mild assumpion that being dead is not being alive) and therefore it is impossible.

Answer 4

If one says, "I am lying," or, "This very sentence that I am now uttering aloud, is false," one might think that by one's actions one has concretized a paradox-generating sentence-type (we might speak of "parapraxis," to be overly technical). Likewise, if one person says to another, "Don't comply with this very command that I am now issuing," or (supposing one is conversing with a djinn), "I wish that this wish would not be granted!" one might also be engaging in some parapraxis.

Or if change/motion are paraconsistent (even outright inconsistent!), then whenever one enacts a change, or moves, one would be manifesting e.g. Zenoan paradox "then and there."

I also asked a question about whether moral dilemmas might be resolvable by enacting the contradiction that they seem to encode. See CriglCragl's response for various considerations regarding that question, including references to the Indian existential tetralemma and the enigmatics of Zen Buddhism.

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Addendum: supertasks (and beyond)

Regarding the question of actions that take an infinite amount of effort to completely perform, there is an SEP article on supertasks that is pertinent (and a good introduction to the topic). (For hypertasks, and even ultratasks, see Al-Dhalimy and Geyer[16].)

Answer 5

Some theories about time travel paradoxes found in SF literature:

1. The "many universes" theory. You don't actually travel back in time. You travel into a different universe that is exactly like ours 50 years ago. You can kill the child that looks exactly like you did 50 years ago. Fifty years from now, there's nobody to time travel into the universe that looks like hours 100 years ago, so no child that looks like you gets killed. So 100 years from now, someone from that universe will travel into the universe that looks like ours 150 years ago and kill a child. No paradox.

2. Time paradox is not possible, but a time loop is. You travel into the past, make changes, but the changes will unplanned by you lead to something else happening that will cause the same effect. So there is a causal loop where even though you killed yourself, something happens that will cause the same effect.

3. The universe protects itself. You try to build a time machine, something will happen that stops you (in one SF story, they found out that many civilisations in the galaxy that should have been capable of building a time machine were wiped out for example by their sun becoming a supernova).