Avestan pairidaeza combines pairi, around, and diz, to build a wall: an enclosed park. Persian kings maintained these walled royal gardens and hunting preserves; Xenophon borrowed the word as paradeisos to describe them, and the Septuagint used paradeisos for the Garden of Eden, welding the Persian park to the Hebrew garden. English inherited it through Latin and French by around 1200; the sense of Muslim heaven follows by 1400.
Before the Persians walled their gardens, heaven had no fixed real estate. After the loan, paradise became the default address for the blessed in Judaism, Christianity, and Islam alike, three religions sharing one Iranian landscaping term. The wall traveled with the meaning: paradise is always somewhere others are kept out of.
The claim: pairidaeza encodes the logic of all paradises, value defined by exclusion, a garden is only royal if the wall holds, and every utopia since has inherited the architecture: the bliss inside is proportional to the barrier outside. Verdict: the etymology literally states it, and Eden's own sequel, guarded by cherubim and a spinning sword, confirms the wall survives expulsion. The Persians did not invent exclusion. They just gave heaven its building permit.
Why did the afterlife need a fence?