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Rules
The first spell of each element cast by the bearer each turn costs ① less.
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FAQ (2)
If I have two (e.g. via Replication), do the effects stack?
Yes.
How does the Philosopher's Stone work with multi-element cards, such as King Arthur and Queen Guienevere? Would King Arthur, who requires 4 mana, cost 3 or 0 Mana to cast using the Stone
Cards that have different element symbols count as a spell of each of those affinities. So Arthur and Guinevere are each an Air spell, an Earth spell, a Fire spell, and a Water spell, all at the same time. But you are still casting them together as a single spell. So, assuming Arthur is your spellcaster's first spell of the turn, the Stone will offer a discount of 1 mana for Arthur, making him cost 3 mana.
This also means that when Arthur is played he uses up the Stone for that spellcaster's turn because he's simultaneously the first Air, Earth, Fire, and Water spell played this turn. So the Spellcaster cannot continue to use the stone that turn.