On the basis of an analysis of everyday experience and practice, criteria of legitimate assertions of existence and truth are offered. A specific object, like a newspaper, can be asserted to exist if it has some invariant characteristics and is present in actual perception. A statement, like “This newspaper is black and white,” can be accepted as true if it is well-established in some empirical domain. Each of these criteria provides a sufficient condition for acceptance of existence and truth, respectively, (...) at the empirical level. Following Herman Weyl, it is argued that these criteria can be extended to the scientific theoretical level to support a selective and moderate version of scientific realism according to which entities like the electromagnetic and gravitational fields, but not crystalline spheres or some topological manifolds, can legitimately be asserted to exist. (shrink)