The doctrine that meanings are entities with a determinate and independent reality is often believed to have been undermined by Quine's thought experiment of radical translation, which results in an argument for the indeterminacy of translation. This paper argues to the contrary. Starting from Quine's assumption that the meanings of observation sentences are stimulus meanings, i.e., set-theoretical constructions of neuronal states uniquely determined by inter-subjectively observable facts,the paper shows that this meaning assignment, up to isomorphism,is uniquely extendable to all expressions that occur in observation sentences. To do so, a theorem recently proven by Hodges is used. To derive the conclusion, one only has to assume that languages are compositional, abide by a generalized context principle and by what I call the category principle. These assumptions originating in Frege and Husserl are coherent with Quine's overall position. It is concluded that Quine's naturalistic approach does not justify scepticism with regard to meaning, but should rather result in a view that affiliates semantics with neuroscience.