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This paper compares the nascent theory of the ‘semiotic symbol’ in cognitive science with its computational relative. It finds that the semiotic symbol as it is understood in recent practical and theoretical work does not have the resources to explain the role of symbols in cognition. In light of this argument, an alternative model of symbol internalisation, based on Vygotsky, is put forward which goes further in showing how symbols can go from playing intersubjective communicative roles to intrasubjective cognitive ones. Such a formalisation restores the symbol’s cognitive and communicative dimensions to their proper roles.