[FOM] Permutations and Rearrangements

[Ivan Antonowitz]

As far as the Maths Department is concerned, a Permutation IS a 
Rearrangement. As the late Prof Niven exclaimed in exasperation, "Why can't 
you bloody chemists stick to one convention!"

And yes, I quite understand that you cannot perform the one operation 
without implicitly influencing the other isomorph.  The problem is that 
there are four ways of defining this bijection. It is these defined 
non_commutative relationships that are important in the laboratory.

Let me give a History. I am a chemical technician that interfaces between 
people and machines, and I carry around a Propositional_Calculus_Toolbox 
suitably modified to especially handle non_commutative operations when 
solving a variety of problems.

Philosophically this means I am biased in favour of combinatorial and 
constructive mathematics. It is simply not good enough to tell me that a 
Tool is available to do a Job, but that nobody can supply it. My Universals 
are defined in the context of Clausal Form Logic. This limited vision could 
be classed as using a microscope in logic.

Of course the question could be raised, "What has this to do with the 
Foundations of Mathematics?". The problem arise in the difference between 
Ontological_meaning [Chemists and Physicists] and Epistemological_semantics 
[Logicians and Mathematicians] when they try to communicate among each 
other. In a sense I have rephrased the question with which I began.

Ivan Antonowitz