Paradox Powered

Some might have missed the point of the previous post, because it's a subtle one. The initial statements we made were based on the assumption that there is an underlying physical world which is fundamental and true. Then we added that all observers are phenomena within this physical world and whose relative reality is necessarily bounded, even though the underlying reality remains true.

The main point is that values such as truth are not universal but relative. We may take them for intrinsic qualities of reality but that only works within a limited scope. Truth is itself an outcome of the interaction of phenomena and we would like in this post to develop this idea a bit further, by bringing out its dynamical qualities.

Let's dive right in. If the truth is the state of a system then a proposition is the external stimulus. The system reacts to the stimulus by going either to the state 'true' or 'false'. If we wish to make a statement about everything then we must also include the state of the system itself in the statement. Such is an example of a complete set:

This statement is true.

albeit not a very enlightening one. The statement connects the outcome of the truth system and of the statement, which in this case are the same entity. It's a complete statement, the same as an equation that describes the dynamics of the system as a whole, like the equations that governed the motion of our magnet-and-detector system. As an equation, it can be solved by finding the true/false trajectory that satisfies it. So if we start by assuming the statement "This statement is true." to be true then the statement tells us the statement is true, which corresponds to a trajectory

where each square represents the truth value of the statement at a given time (flowing from left to right, black means 'true', white means 'false'). If we start by assuming the statement is false then the opposite of being true is false, so the statement is consistently false

Try however, this equation instead:

This statement is false.

If we start with the assumption that the statement is true, then it is false. If however it is true then it must be false. This equation has no stationary solutions. They are:

Both equations can be described in the following way:

Once we realize that paradoxes can be treated as equations with non-stationary solutions then we're pretty much ready to analyse just about anything. A scientific view is a collection of logical statements which are connected somehow, of which some of them are the theory and some of them are the observational evidence. They must form a complete set, so that the equations can be solved. We usually expect the scientific view to be like

which is a stable view. However, it looks more often like

where some problems remain unsolvable. Nevertheless, even a stationary view can be challenged by the results of an experiment

In this case, the system undergoes some turmoil but then returns to a stable configuration with the conclusion that the experiment is wrong. However, this behaviour is also possible

which is called a scientific revolution. The very complex linkage between statements makes the system prone to radical changes, a very common feature of complex systems. Here, the system is pushed out of balance by the new evidence and undergoes a transition phase as it's caught in the basin of attraction of another stable configuration which eventually becomes the next accepted paradigm.

Stationary solutions are common but have a huge lack of adaptability and are therefore selected away by the constant inflow of knowledge. Real theories, like real organisms, include mostly stable statements but also some oscillating ones, persistent loops of logic.

When we include ourselves in the theory we quickly run into such loops. That's why it's so difficult to think about the consciousness as our reasoning inevitably starts to chase after its own tail. But we should not be discouraged by this event: it actually reveals the phenomenological and dynamical nature of reality. It means that, instead of worshipping it like a precious stone, we have to treat our theory like a living organism, with its evolving traits but also its cyclic ones, its beating heart and breathing lungs. We started from the assumption that subjective experience stems from physical phenomena and we found that physical phenomena stem from subjective experience. None is more fundamental, they revolve around each other in a logical gravitation.

On the other hand, string theory and other religious movements perpetually seek additional statements which preserve the stable structure of certain dogmatic ones. This ends up being a neurotic behaviour eventually leading to a messy, energy-consuming organism of very little use, like a fat untouchable king cloistered amongst his own devout guard. Sane views abandon the pretence of universalness.