Philosophers have recognized for some time the usefulness of semantic conceptions of truth and belief. That the third member of the knowledge triad, evidence, might also have a useful semantic version seems to have been overlooked. This paper corrects that omission by defining a semantic conception of evidence for science and mathematics and then developing a semantic conception of knowledge for these fields, arguably mankind’s most important knowledge repository. The goal is to demonstrate the advantages of having an answer to (...) the more modest question “What is necessary and sufficient for introducing a knowledge predicate into scientific and mathematical languages?” – as contrasted with the ambitious Platonic question “What is knowledge?” After presenting the theory, the paper responds to a wide range of objections stemming from traditional philosophical concerns. (shrink)