Heidegger and the later Wittgenstein agree that the basis of intelligibility, the groundless ground of our conceptual edifice, is the everyday shared reality in which we already find ourselves.That can't be right, can it? The basis of intelligibility, if there is such a thing, must be independent of intelligibility, hence unintelligible. But how could we find ourselves in an unintelligible "everyday shared reality"? There's also this:
Both Heidegger and Wittgenstein intended to lay bare the background experiences, the forms of life, the worldhood of the world, that first make language meaningful.How can language be made meaningful? If it isn't already meaningful then it isn't language.
A little charity might be in order. There isn't a background that makes language meaningful or a ground that is the basis of intelligibility. At least not if the words 'basis,' 'ground', etc. are being used in the normal way. Rather, when we look for a basis or background all we find is everyday reality, forms of life, etc. But these are not the foundation of language, however important they might be in or to language. Language is not the kind of thing that could have a foundation. Asking for its basis is like asking what matter (or whatever we call the fundamental stuff of material reality) is made out of, as if matter were a cake whose ingredients we could discover. We can ask what goes in the cake, and what baking powder, etc. are made of, and what atoms are made of, but at some point it's a mistake to think you can ask "And what's that made of?" The fundamental constituent of material things is not itself made of anything else. Similarly, language is what stories, arguments, etc. are made of. It is not itself made of anything else. (It isn't made of words, for instance, because a word is not a word unless/until it is part of a language. So we can say that language is made of words, but not in any foundational sense. The words don't come first even if sounds and marks that later become words do.)