 Since \(q_1\) is necessarily intrinsic, while \(q_2\) is necessarily not intrinsic, it follows from the necessity of (14) that \(\varphi(q_1)\) is necessarily true, while \(\varphi(q_2)\) is necessarily false. In other words, if there is a broadly logical analysis of intrinsicality, then there is a formula \(\varphi\) contining only broadly logical vocabulary that necessarily applies to \(q_1\), and necessarily does not apply to \(q_2\). However, it can be proved that there is no such formula. For example, while ‘\(\exists w_1 \exists w_2 \exists x_1 \exists x_2 \exists x_3\)(p \(= \{\lt w_1, x_1\gt , \lt w_2, x_3\gt \})\)’ applies to \(q_1\), it also applies to \(q_2\). Hence, the reductio assumption is false, and there is no broadly logical analysis of intrinsicality. This argument can easily be adapted to show that there is no broadly logical analysis of intrinsicality given more realistic assumptions about what possible worlds there are.