As illustrated by the case of ethanol, claim H is that, for some biological endpoints, low-dose toxins and carcinogens exhibit hormesis, a beneficial or adaprive response characterized by biphasic dose responses and resulting from compensatory biological processes following an initial disruption in homeostasis. From this uncontroversial claim H, however, the paper argues that some toxicologists invalidly infer HG (that H is generalizable across biological model, endpoint measured, and chemical class) and HD (that a strong case can be made for the use of hormesis H as a default assumption in the risk-assessment/regulation process), Evaluating HG and HD, this paper argues for 5 claims. While (1) H is true, (2) HG falls victim to several logical fallacies and therefore is logically, scientifically, and ethically invalid. (3) Because it relies on logical fallacies, confuses necessary and sufficient conditions, and violates at least 5 sets of ethical norms, HD is logically, scientifically, and ethically invalid. (4) Five remedies could help address HG-HD flaws and failure to adequately assess low-dose exposures. (5) Three objections to these criticisms of HG and HD are easily answered.