# representation

1. <logic> Of a function.

A function f of n arguments from natural numbers to natural numbers is represented in a system iff there is a wff A with n+1 free variables such that A is a theorem when its variables are instantiated to the natural numbers k1...kn+1 when f(k1...kn) = kn+1, and not a theorem otherwise. Strong representation of a function A function f is strongly represented in a system iff it is represented in the system by wff A, and A is a theorem iff ~A is not a theorem.

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[Glossary of First-Order Logic]

2. <logic, mathematics> Of a set.

A set N is represented in a system iff there is some propositional function with exactly one free variable, Px, such that Px is a theorem whenever x is instantiated to a member of the set, and a non-theorem otherwise. Or if N is a set of natural numbers, n is a natural number, and is a numeral for n, then N is represented iff |- P/x <=> n : N.

3. <philosophy of mind, philosophy of language, epistemology> that which stands for, refers to or denotes something or the relation between a thing and that which stands for or denotes it.

Chris Eliasmith - [Dictionary of Philosophy of Mind] Homepage

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Nearby terms: reliable communication « renaissance « replacement - rules of « representation » representationalism » repression » requirements