The doctrine that meanings are entities with a determinate and indepen- dent 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. The philosophy of language in the twentieth-century, with a grain of salt, can be regarded as the rise and fall of semantic realism. The century began with an outline of what it would mean that meanings exist as in- dependent entities. To make this view explicit and to defend it was a major achievement of Gottlob Frege and Edmund Husserl. 1 In the second half of the century scepticism about meanings became prevalent. It was fostered importantly by two challenges, one due to W. V. Quine (1960) and well- known as the thesis of the indeterminacy of translation, the other often attributed to Hilary Putnam (1983) and discussed as the model-theoretic argument against metaphysical realism. Frege and Husserl set the rules for the game when they formulated three principles as constraints for any theory of meaning. The first one became known as the principle of com- positionality and says that the meaning of an expression is determined by the meanings of its parts. The second one is what I call context principle. It claims that two expressions fail to differ in meaning just in case a sub- stitution of one for the other has no effect on the meaning of any of their embedding contexts (Throughout the text I understand 'context' to mean linguistic rather than situational context). While the former two principles go back to Frege, the last one, the category principle, is due to Husserl.