Sidgwick famously claimed that an argument in favour of utilitarianism might be provided by demonstrating that a set of defensible philosophical intuitions undergird it. This paper focuses on those philosophical intuitions. It aims to show which specific intuitions Sidgwick endorsed, and to shed light on their mutual connections. It argues against many rival interpretations that Sidgwick maintained that six philosophical intuitions constitute the self-evident grounds for utilitarianism, and that those intuitions appear to be specifications of a negative principle of universalization (according to which differential treatments must be based on reasonable grounds alone). In addition, this paper attempts to show how the intuitions function in the overall argument for utilitarianism. The suggestion is that the intuitions are the main positive part of the argument for the view, which includes Sidgwick's rejection of common-sense morality and its philosophical counterpart, dogmatic intuitionism. The paper concludes by arguing that some of Sidgwick's intuitions fail to meet the conditions for self-evidence which Sidgwick himself established and applied to the rules of common-sense morality.