Category Archives: logic

Searle’s Chinese Room and true understanding

Discussions of artificial intelligence often probe the mystical property of awareness and consciousness. The Turing test is an operational criterion for artificial intelligence: in the Turing test, a person converses with either another person or a computer, but they do not know which. If in a series of tests, the computer is indistinguishable from human, […]

Axiomatizability of classes of structures

Let’s talk about axiomatizability in first-order logic, with examples in ring theory. Let’s call a class $\Ccl$ of rings axiomatizable if there exists a set $T$ of first order sentences such that $C\in\Ccl$ if and only if $C$ is a model of $T$ (that is, satisfies every sentence in $T$.) What are some examples? The […]