The Aftermath of TRM

I am derped in philosophical agony.

I have been working on a method for discovering philosophical solutions.  I call it, the Truth Relations Method.  What I have discovered is not that TRM can find philosophical solutions, but it shows that finding a solution to a philosophical disagreement is impossible.  Needless to say, this caused me some discontent.  However, proof that we cannot resolve disagreements is, I think, philosophical progress as I have claimed in another post.  Below I describe why solutions to philosophical disagreements are impossible.

In theory, the method works.  It is too bad we are not theoretical.  I attempted to apply the method to some basic questions in philosophy.  Briefly, I attempt to find the position that must be true.  There are a couple of ways to do this.  I relied on the truth relations between the various positions.  This means that I listed the various positions to compare them.  Second, I determined whether the positions were contrary.  If they are not contrary, they are not competing positions.  Third, I attempt to determine which position must be true.  To do so, I attempted to discover which position is contradictory to at least two other positions.  If a position is contradictory to at least two other positions, then it must be true.  Since all the positions are competing positions, they are contrary.  Since a contradictory relation is one where two propositions are contrary and sub-contrary to one another, this means I just needed to find the position that is sub-contrary to two other positions.  However, while it is relatively easy to determine whether positions are contrary to each other, I was having a very difficult time finding sub-contrareity.  I wondered why.

So, I turned to mathematical logic to help uncover this problem.  I decided to turn to value theory as the first problem.  It seemed to me that the major disagreement dealt with two properties and their negations: singular or plural, natural or non-natural.  To represent these philosophical relevantly properties, I used propositions.  That is, where P is a property, “Value is P.”  S and its negation for simple and plural; N and its negation for natural and non-natural.  Thus, there were four possibilities: S and N; S and not-N; not-S and N; and not-S and not-N.  In English, “Value is a singular and Natural property”; “Value is singular and non-natural” and so on.  No matter what proof I tried between derivational rules and truth tables, I was unable to show that one position is sub-contrary to another.  

Here is a proof illustrating what happened.  Let phi and psi represent relevant propositions about the properties about philosophical positions.  Thus, there are four possibilities as seen in the picture just below.  Thus, phi and psi represent a philosophical position, as does the one below, and so on.  With three properties we get eight.  With four properties we get sixteen, and so on.

Four possibilities

So, to show that one of these sub-contrary, I attempted to show that the negation of one of these philosophical positions implies one of the other philosophical positions.  Instead what I found is that the any of the given positions is sub-contrary to the disjunction of the remaining philosophical positions.

Positions are sub-contrary to the disjunction of the other positions.

A truth table shows the same result.  Since we are unable to show which position is sub-contrary to any of the other positions, we are unable to show that one of the theories must be true.  Since we are unable to show which of these theories must be true, it is impossible to solve a philosophical disagreement.  I have argued in this post that since we cannot solve them, we are not required to solve them.  Thus, what philosophers take to be a major project in philosophy cannot be fulfilled.  Further, since there will never be a convergence on theories, we have to look to other projects that can be fulfilled for philosophical progress.