&gt; because computation is not (classical) math<p>Of course, computation is more foundational. It&#x27;s mathematics that&#x27;s just applied computation.<p>&gt; as it does not preserve equality under substitution<p>You just need to stop using broken models.<p>&gt; but the recognition that their entire justification is not mathematical but pragmatic<p>I don&#x27;t see a distinction. To me, nothing is more pragmatic to use than a reliable mathematical model.<p>&gt; the (leaky) abstraction of those models<p>Other than the finiteness of real computers, what else is leaky? Mind you, abstracting over the finiteness of the computer is an idea that even... uh... “less mathematically gifted” languages (such as Java) acknowledge as good.<p>&gt; such as empirical results showing a certain &quot;affinity&quot; to human cognition<p>Experience shows that humans are incapable of understanding computation at all. But computation is here to stay, so the best we can do is rise to the challenge. Denying the nature of computation is denying reality itself.