Haecceities and Individuals: Identity and Ontology

2.3 Identity and Ontology

The reciprocal connections of individuals and haecceities scaffold properties of identity which, perhaps because they resist analysis in classical terms, have generally been taken to be self-evident--and ontology-free. Nevertheless, that identity is weakly reflexive, identicals indiscernible, and indiscernibles identical if self-identical are propositions which rest in HI upon more basic ontological principles. Upon analysis the notoriously "self-evident" dictum that everything is self-identical thus divulges ontological conditions whose satisfaction depends not on a logician's fiat but on the way the world is. In HI+, where every haecceity is exemplified and every individual exemplifies, these conditions hold, making identity strongly reflexive and indiscernibles identical. In contrast, HI- posits a world populated by unexemplified haecceities and non-exemplifying individuals, where identity is not strongly reflexive and not all indiscernibles are identical. Which of these worlds is ours? Ask not Logic, for Logic will not decide.

Tableau of Theorems
But I promised an account of the properties of the identity relation as this applies to particulars. So far we have seen nought but individuals and haecceities. The road to particulars is from individuals and haecceities by way of complexes. I now turn to C, the theory of complexes.

Complexes

	The reciprocal connections of individuals and haecceities scaffold properties of identity which, perhaps because they resist analysis in classical terms, have generally been taken to be self-evident--and ontology-free. Nevertheless, that identity is weakly reflexive, identicals indiscernible, and indiscernibles identical if self-identical are propositions which rest in HI upon more basic ontological principles. Upon analysis the notoriously "self-evident" dictum that everything is self-identical thus divulges ontological conditions whose satisfaction depends not on a logician's fiat but on the way the world is. In HI+, where every haecceity is exemplified and every individual exemplifies, these conditions hold, making identity strongly reflexive and indiscernibles identical. In contrast, HI- posits a world populated by unexemplified haecceities and non-exemplifying individuals, where identity is not strongly reflexive and not all indiscernibles are identical. Which of these worlds is ours? Ask not Logic, for Logic will not decide.
	Tableau of Theorems But I promised an account of the properties of the identity relation as this applies to particulars. So far we have seen nought but individuals and haecceities. The road to particulars is from individuals and haecceities by way of complexes. I now turn to C, the theory of complexes.
	Complexes