Predictive Processing (PP) is an increasingly influential neurocognitive-computational framework. PP research has so far focused predominantly on lower level perceptual, motor, and various psychological phenomena. But PP seems to face a “scale-up challenge”: How can it be extended to conceptual thought, language, and other higher cognitive competencies? Compositionality, arguably a central feature of conceptual thought, cannot easily be accounted for in PP because it is not couched in terms of classical symbol processing. I argue, using the example of language, that (...) there is no strong reason to think that PP cannot be scaled up to higher cognition. I suggest that the tacitly assumed common-sense conception of language as Generative Grammar (“folk linguistics”) and its notion of composition leads to the scale-up concerns. Fodor’s Language of Thought Hypothesis (LOTH) plays the role of a cognitive computational paradigm for folk linguistics. Therefore, we do not take LOTH as facing problems with higher cognition, at least with regard to compositionality. But PP can plausibly play the role of a cognitive-computational paradigm for an alternative conception of language, namely Construction Grammar. If Construction Grammar is a plausible alternative to folk linguistics, then PP is not in a worse position than LOTH. (shrink)