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4.2 Identity in P


Haecceities &
Individuals		 P1-P9 specify conditions that haecceities and individuals must satisfy. These conditions make haecceities identity properties,22 for embodying Y guarantees identity with y.
T30 for allxy(x emb Yequivalentx = y)
Likewise, containing y guarantees identity with y.
T31 for allxy(x cont yequivalentx = y)
So, embodying Y is necessary and sufficient for containing y.
Embodiment &
Containment		 A particular embodies a haecceity just in case there is some complex to which the haecceity and constituents of the particular belong:
T32 for allxy(x emb Yequivalentfor somewz(w.Z emb X & w.Z cont x & w.Z emb Y))
Similarly, a particular contains an individual just in case there is some complex to which the individual and constituents of the particular belong.
T33 for allxy(x cont yequivalentfor somewz(w.Z emb X & w.Z cont x & w.Z cont y))

cont.

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