 TSB  follows from  Qualitative Supervenience  (see  §4.3)  together with a less controversial principle we might dub ‘Truth Supervenes on the Qualitative’, derived from  TSB  by replacing ‘perfectly natural’ with ‘qualitative’. It is thus unsurprising that putative counterexamples to  Qualitative Supervenience  extend to  TSB.  For example, if one took being left-handed to be a qualitative property that need not be preserved by bijections that preserve perfectly natural properties, one might plausibly think that worlds could agree on which objects there are and which perfectly natural properties they instantiate without agreeing on which ones are left-handed. Similarly, if one posits higher-order perfectly natural properties which do not supervene on the first-order ones, one should have doubts about  TSB,  assuming one interprets  TSB’s  talk of “objects” in a way that does not include objects. However in that case one might hold on to a variant of  TSB  that gives the same status to all propositions \(R(X_1,\ldots,X_n)\) where \(R\) is perfectly natural (of whatever type) and \(X_1,\ldots,X_n\) are of the right types to be arguments to \(R\). 