A truth predicate in the object language

In Gerhard Preyer (ed.), Donald Davidson on Truth, Meaning, and the Mental. Oxford University Press (2012)
Abstract
The semantic paradoxes arise when the range of the quantifiers in the object language is too generous in certain ways. But it is not really clear how unfair to Urdu or to Hindi it would be to view the range of their quantifiers as insufficient to yield an explicit definition of ‗true-in-Urdu‘ or ‗true-in- Hindi‘. Or, to put the matter in another, if not more serious, way, there may in the nature of the case always be something we grasp in understanding the language of another (the concept of truth) that we cannot communicate to him. In any case, most of the problems of general philosophical interest arise within a fragment of the relevant natural language that may be conceived as containing very little set theory. Of course these comments do not meet the claim that natural languages are universal. But it seems to me this claim, now that we know such universality leads to paradox, is suspect. –―Truth and Meaning‖.
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