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Resolution Machinery

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Document pages: 15 pages

Abstract: The value of syntax is controversial:some see syntax as defining us as species,while for others it just facilitates communication.To assess syntaxwe investigate its relation to problem resolving.First we define a problem theory from first principles,and then we translate the theory concepts to mathematics,obtaining the requirementsthat every resolution machine has to implement.Such a resolution machine will be able toexecute any possible resolution, that is,any possible way of taking a problem expressionand computing the problem solutions.Two main requirements are found:1) syntax is needed to express problems, that is, separate words are not enough, and2) the resolution machine has to be as powerful as lambda calculus is, that is, it has to be Turing complete.Noting that every device that can generateany possible syntax, that is,any possible syntactically correct sentenceof any possible, natural or artificial, language,has to be Turing complete,we conclude that syntax and problem resolvingcan use the same components, as, for example,sentences, functions, and conditionals.The implication to human evolution is thatsyntax and problem resolving should haveco-evolved in humans towards Turing completeness.

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