In our usage, a trading system is an alogorithm to decide what, when, and with what allocation of capital needs to be bought or sold to maximize profit and minimize risk. Such decisions are made regularly and are based on a variety of input data, reflecting the changing market environment and prior history. The adequate level of complexity is high enough to require that a trading system be implemented as a computer program. The tasks of order execution may but do not need to fall into the scope of a trading system in our usage of the word.
Under conditions of complete market efficiency (when price quote time series is a martingale) there is no need for a trading system in our sense of the word — Modern Portfolio Theory will suffice. In some contexts the meaning of the term is reduced to denote an electronic or computer system that merely executes external orders, rather than generates them.
One may argue (as does Taleb) that everyday human experience which emphasizes cooperation in a more or less deterministic environment prepares us poorly for survival in the markets which are random to a very high degree. Our brain may be poorly equipped to deal with the randomness, let alone detect those traces of predictability and order which do exist in it. A response to this challenge may be to use higher faculties of our brain to build trading systems around abstract concepts (which are beyond the reach of computers) and then leave to computers the execution of routine decision making (counting odds) according to those systems.
Developing, back-testing and marketing buy-side trading systems for the forex traders is the main goal of the Forex Automaton™ project.