So stated we already know it's false; Nicaraguan Sign Language emerged ex nihilo and has no ancestors. For something slightly less clear-cut than that, but also spoken, there are various creole languages around the world that show little to no grammatical relationship to their ancestors (though they are strongly related in terms of vocabulary).
I did not intend to endorse the assumption that all languages have a common origin; I intended to impugn the claim that we can discern a relationship of any kind between Indo-European and Afro-Asiatic. We can't; the only relationship we can perceive between them is the one we begin by postulating.
That said, we also can't disprove that all "traditional" languages go back to a common root. It's just a meaningless claim the evidence for or against which can't exist.
I did not intend to endorse the assumption that all languages have a common origin; I intended to impugn the claim that we can discern a relationship of any kind between Indo-European and Afro-Asiatic. We can't; the only relationship we can perceive between them is the one we begin by postulating.
That said, we also can't disprove that all "traditional" languages go back to a common root. It's just a meaningless claim the evidence for or against which can't exist.