PHI 202: Symbolic Logic

This is a 2-credit course containing all the material on formal logic from PHI 100. For a general description of logic and its importance to mathematics, see the description of PHI 220.

PHI 202 is good preparation for mathematics courses. Do you need it? Here is a way to find out: in analysis, the rigorous definition of limit is ``the limit of $f$, as $x$ approaches $a$ is $L$ if and only if for any $\epsilon > 0$, there is a $\delta > 0$ such that for all $x$, if $0<\vert x - a\vert < \delta$, then $\vert f(x) - L\vert < \epsilon$''. Now suppose we wished to prove that the limit of $f$, as $x$ approaches a is not $L$. What would we have to show?

One fluent in logic is able to answer quite easily: ``We must show that there is an $\epsilon > 0$ such that for all $\delta > 0$ there is an $x$ such that $0<\vert x - a\vert < \delta$, but $\vert f(x) - L\vert \geq \epsilon$.''