οὐ γὰρ οἷόν τε διανεκεῖ λόγῳ τῆς οὐσίας κατὰ Ἱππίαν ἄλλως ἔχειν,
The Loeb translation: for it is impossible, by the continuous doctrine of reality according to Hippias, that it be otherwise.
I propose: however, to understand the dative with οἷόν τε : for it is impossible for the continuous doctrine of being, according to Hippias, to be otherwise.