Most of them would prefer to change the classical logic that validates the sorites. Overlapping these logic reformers are metaphysicians who think that the sorites can be resolved by acknowledging that objects themselves are vague. He recalls that thirty years ago, there was a consensus that all necessity is linguistic. However, now most philosophers take the possibility of essential properties seriously. The view that vagueness is always linguistic has been attacked from other directions.
Mental imagery seems vague.
Another possible challenge comes from cardinality mis-matches. Natural languages must have finite vocabularies and finite rules to be learnable. The number of potential sentences in such a finitary language is infinite. But the order of infinity is low, just aleph-0. In contrast, the number of arithmetic truths is far greater.