What's more, the definitions of the religions themselves are so slippery, we can barely begin to compare religions. For example, suppose we take the author's advice and try to dereference the term "afterlife" in a comparison of Christianity and Islam.
Our first step would thus be to ask: What happens to an individual's consciousness after death, according to each of the two religions? But here our inquiry goes right to pieces, because we won't be able to agree on how to define the set of beliefs constituting each religion.
Is Christianity defined as the set of beliefs expressed in the Bible? And likewise for Islam and the Koran? But if so, then what about adherents of those religions who are not fundamentalists? Are we to ignore people who call themselves Christians and Muslims, yet believe that only some, or perhaps none, of the scripture is literally true?
But if we define Christianity and Islam so as not to exclude those people--which seems like the intellectually honest choice--how can we possibly agree on a set of beliefs that constitutes each religion?
Perhaps we could administer a scientific poll of self-identified Christians and Muslims, asking them to agree or disagree with various theological propositions. Those propositions which are supported by a majority of self-identified adherents become part of our definitions, and the rest do not.
That may allow us to continue with our project of comparing afterlife beliefs, but it still seems incorrect somehow. Now we've greatly oversimplified the actual beliefs of Christians and Muslims worldwide. By establishing an arbitrary threshold (>50% belief), we've painted over a lot of distinctions that matter to real-world adherents. Equally badly, the arbitrariness of the threshold makes our definitions suspect. Had we chosen a different threshold, we'd probably have arrived at radically different definitions, suggesting that our definition has little authority.
Thus the problem of comparing religions seems intractable.