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Google is failing me in my search for examples of identical sets which do no have causal relationships between them. What I mean is that all and only objects which belong to set A belong to set B, but an object being in set B is not caused by its being in set A, nor is an object being in set A caused by its being in set B.

My prof said she heard of something once that went along the lines of "set A = animals that have a spleen, set B = animals that have a different organ" but she couldn't remember the exact details, and I can't seem to find what she was talking about (I don't know enough biology to say off the top of my head)...

Can anyone think of examples?

Thanks in advance :)

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    An example that is often used is that creatures with hearts are the same as creatures with kidneys.
    – E...
    Oct 12, 2019 at 19:54
  • Thank you so much!! That's exactly what I was looking for :)
    – Lily
    Oct 12, 2019 at 20:51
  • Perhaps you could describe what prompted this question.
    – Mark Andrews
    Oct 13, 2019 at 19:45
  • @MarkAndrews, sure. We were studying the Euthyphro Dilemma in class, and it seemed a little bit off to me. If I understood it correctly, Euthyphro posited that all and only actions which are pious are actions which are loved by the gods. Ie. Pious actions and god-loved actions are identical sets. From that, Socrates seemed to assume a direct causal relationship between the two sets, such that either an action is pious because it is loved by the gods or it is loved by the gods because it is pious.
    – Lily
    Oct 14, 2019 at 11:24
  • But I didn't see what justified this assumption, or eliminated the possibility of some alternative explanation for them being identical sets.
    – Lily
    Oct 14, 2019 at 11:24

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