This paper seeks to enhance understanding of the philosophical underpinnings of our discipline and the resulting practical implications. Radiology reports exist in order to convey new knowledge about a patient's condition based on empiric observations from anatomic or functional images of the body. The route to explanation and prediction from empiric evidence is mostly through inference based on inductive (and sometimes abductive) arguments. The conclusions of inductive arguments are, by definition, contingent and provisional. Therefore, it is necessary to deal in some way with the uncertainty of inferential conclusions (i.e. interpretations) made in radiology reports. Two paradigms for managing uncertainty in natural sciences exist in dialectic tension with each other. These are the frequentist and Bayesian theories of probability. Tension between them is mirrored during routine interactions among radiologists and clinicians. I will describe these core issues and argue that they are quite relevant to routine image interpretation and reporting.