Paper presented during the Annual Conference of the Philosophical Society of Southern Africa, 16 - 18 January 2008. Hosted by the Department of Philosophy, University of Pretoria. ABSTRACT: It is a foundational premise of classical logic that the Principle of Bivalence obtains. This paper will see an exposition of how it can come to be that the truth value of some statements is indeterminate, in other words, that it cannot always be presumed that the truth value of a statement will be either true or false. The paper will investigate two premises for an argument for indeterminacy (counter the Principle of Bivalence): (1) If the metaphysical state of affairs is such that no evidence is available to serve as truth conditions for a claim, that claim is indeterminate and not merely false. (2) If truth is regarded an epistemic notion (evidentially constrained) then many of our statements remain indeterminate in truth value. The conclusion forwarded will be that premise (1) is more problematic than premise (2) but can still serve, if adequately defended, an argument for indeterminacy. If, however, both premises are accepted they would labour interdependently for such a conclusion. Accepting that certain statements remain indeterminate will mean that the unconditional acceptance of the Principle of Bivalence is wrong.