A rational spirituality Copyright © 1998-2021 www.djv.us.  All rights reserved.
Link to https://www.djv.us/ars for original or expanded material.
Permission to reproduce this page is granted provided this copyright
appears visibly and in its entirety, and the above links remain intact.
The local Table Of Contents

Solving Paradoxes

I have found that whenever a paradox arises, it is due to one or more invalid assumptions.  Careful study of the entire system can reveal the bogus assumption and often solve the paradox.  The following definition of paradox is of use:

"An argument that apparently derives self-contradictory conclusions by valid deduction from acceptable premises"
--- Webster's Third New International Dictionary, Unabridged. Merriam-Webster, 2002. http://unabridged.merriam-webster.com (2 Jun. 2007).

"Acceptable premises" are the weak point in the system.  Indeed, build a bogus foundation and the whole structure crumbles.  Some examples follow.

1. The classic Liar Paradox

Three examples:

  1. "This statement is false."
  2. "Is the answer to this question no?"
  3. "My next sentence is false.  My previous sentence is true."

These classic liar paradoxes must be included for completeness but they essentially offer little more than amusement.  Anyone can create an invalid series of statements deliberately or accidentally.  A solution here however, to recognize the paper bag out of which we must break, was pointed out to me by Sean Bascom.  He calls these self-fulfilling paradoxes:

"[... what] matters for the statement to be a paradox is the perception of the people involved who will view it that way [... It is no longer a paradox when they realize that] the person making the statement knows the statement to be contradictory..."

Yes, the trick is to recognize the flawed system of logic before you play the game - accepting the system at face value (by trusting the speaker) gives it validation - it must be confronted from the outside.   Some of the bogus assumptions in effect here are:
  1. The speakers puzzle will be solvable
  2. Spoken languages are always logical and acurate, and thus inherently prevent cocktail party abuse
  3. I need more to drink :)

There are a number of other self-referential paradoxes that all run in the same vein.  What is helpful here however is to practice stepping outside the paradoxical system in order to see the assumptions involved.

2.   1 + 1 = 0

Yes! In a binary system 1 + 1 does indeed equal 0 (even though most of the time there is also a carry into the next digit).  This is a result of "wrap around" or a system built with a finite number of possible states less than the reality it tries to describe, and it causes quite a number of computer headaches, Y2k being the most famous.  When working in a fixed number (or a fixed logic) system make sure there are enough states to represent all possible outcomes!

The bogus assumptions:

  1. we only need 2 digits to represent the last thousand years
  2. this program will never be used for more than a decade or so
  3. memory/disk drives will never get to be that big

3. Conservation of energy/matter during time travel

"If I go back in time I can prevent myself from being born and then I shouldn't, but still do?, exist."  Variations on this one always crop up in time travel movies.  But if Hollywood payed proper attention to general relativity they would also have to wrestle with the massive energy and matter equilibrium issues that result from moving any matter backwards or forwards through time.  E=mc2 outlines the extent of the energy/matter conservation problems that would result.  Do the math, it's huge.  (hydrogen bombs only use a fist full of matter but Hollywood is always transporting entire bodies through time)  If you ignore E=mc2, you can do pretty much anything you want, but then be prepared to face at least one if not several major paradoxes.  (like "I might be my own father" and thus my father's entire side of my DNA tree cannot be traced, and then there are the objects et. al. brought through time to the past that "spontaneously update" to reflect changes made in what is now the "present"; etc.)  Also remember that it is not general relativity that creates the stumbling block - it is "Nature".  GR simply describes Nature to the best of our ability so far.

4. Transfer of knowledge during travel backward in time

"If I build a time machine I could make billions on the stock market!!  Let's fund that sucker now!" 

I see two bogus assumptions right off, one is that sure, only you and your development team will ever make a time machine, and two, that no machine will ever be built and used nefariously! i.e. you are thinking with a very limited scope.

Another assumption is that information has meaning outside of its context.  In the stock market application of such a device, the information passed back through the time machine is assumed to have the same context both in the moment when the message is sent, and in the moment when the message arrives.  But in reality the context is slightly different.  If you get a message from yourself in the future saying "buy Microsoft" this message is based on the fact that you were not going to invest in Microsoft on this date.  If you do invest in Microsoft you are about to render the source context of the message invalid.  "Big deal" you say, "I can't affect the stock market enough to change the results, so what is the problem?"  The problem is the first assumption - that time machines have limited scope - that you are the only one who will ever build or have access to a time machine!  When we remove both of these invalid assumptions, the ability to pass information back to the past has no other possible conclusion than to saturate the medium to the point of unusability, and thus completely alter the target environment.

Here is an alternate (and simpler argument).  The stock market functions correctly, therefore the ability to pass knowledge through time must be impossible.  If a communication time machine can be built, at least one person in the infinity of the future will build a machine and try to gain wealth from it by communicating with the past.  (and we know that at least one person will not exercise restraint)  If one tries it, others will follow, mistakes will be made, or deliberate sabotage will be attempted.  The result would be that the world would have already have felt the completely overwhelming impact of such a possibility.  And it hasn't, therefore passing even information back in time must be impossible.