St Thomas; Forma substantialis totius non superadditur partibus, sed est totum complectans materiam et formam cum praecisione aliorum”:  “Nothing is added to the whole of the substantial form by the parts that constitute it, but it is the whole that embraces both content and form while maintaining the precision of the different parts that constitute the whole.”

Identity of indiscernibles

  1. The indiscernibility of identicals
    • For any x and y, if x is identical to y, then x and y have all the same properties.
      {\displaystyle \forall x\,\forall y\,[x=y\rightarrow \forall P(Px\leftrightarrow Py)]}{\displaystyle \forall x\,\forall y\,[x=y\rightarrow \forall P(Px\leftrightarrow Py)]}
  2. The identity of indiscernibles
    • For any x and y, if x and y have all the same properties, then x is identical to y.
      {\displaystyle \forall x\,\forall y\,[\forall P(Px\leftrightarrow Py)\rightarrow x=y]}{\displaystyle \forall x\,\forall y\,[\forall P(Px\leftrightarrow Py)\rightarrow x=y]}