An attempt at clarity about religion

I start with a quote from "Introduction to Modern Set Theory" by Judith Roitman.

".... 'x is a unicorn in Africa' describes exactly the same set of animals as 'x is a winged horse in Europe'. Both sets are empty.  But the descriptions are quite different."

"In philosophy, descriptions are related to a notion called intensionality, which has to do with how the mind gives meaning to language.   The actual thing described is related to a notion called extensionality.  In mathematics we care only about extensionality.  We don't care about intensionality".

What does "the actual thing described" mean?

For the purposes of an atheist like Richard Dawkins, {Jehovah, Angels, Satan} and {Allah, Satan, Prophets} are equally empty sets (extensionally, per Dawkins "the actual thing described" is the empty set); and Dawkins' analysis proceeds from there.  This works for what Dawkins wants to talk about.  But when one asks the question,  can one explain the differences between Christian and Islamic societies?  the identical empty set doesn't help.

Similarly, in some context, extensionally, Hamlet and Iago are characters in Shakespeare's plays, and in that context it may be appropriate to talk about them at that level.  But to an actor seeking to portray one or other on the stage, the extensional meaning not useful.

What I want you to take away from the above that "the actual thing described" really depends on what you hope to be able to do with the description.   This applies in spades to "religion".

• Europeans came to India and some subclass of phenomena that they observed in India among the Gentoos, they mapped extensionally via analogy into Christianity.  E.g., if "the actual thing described" is "bowing before an altar", then this phenomenon maps into some Christian practice. Similarly with "god", "scripture", "temple", "idol",  "sacredness", etc.  They reified this subclass of phenomena into a religion called "Hinduism", and since they governed India per this conceptualization  (e.g., they would try not make laws interfering with practices that were "in the Gentoo scriptures") the Gentoos bought into this conceptualization over time.
  
• Empirically, it turns out this extensional definition of religion bursts at the seams.  This is well-known among the professional scholars of religion. They hope to be able to save this conceptualization; their attempts at saving the definition have been going on for decades.  
  
• Empirically it also turns out that this extensional definition of religion is useless in the same sense as in the examples above, e.g., for the actor seeking to portray Hamlet on the stage.   To borrow an example from Jakob de Roover, this definition does not help a judge in India to identify the "core religious practices" of the Jains so as to determine whether the secular Indian state has overstepped itself in making some regulation.
  
• If one retraces Balu's steps to deal with this situation, one starts over with "what makes Christianity into a religion?". Balu constructs a theory, not merely a definition.  A religion constrains its adherents "to go about in the world" in a particular way that the theory describes.  Balu's theory explains among other things, why Europeans were pretty much constrained by their worldview to construct "Hinduism" and similarly to construct religions in all the other cultures that they encountered.  It explains why "Hinduism" is not only not a religion, it is non-existent except in the sense of "some mishmash subset of traditions, practices, writings, beliefs, etc., of the people of India".   It explains how the phenomenon of secularization works, and how religion propagates under the covers, so to speak.  And so on.

PS: The above is not a final word on anything.  I reserve the right to edit the above to improve it at any time.