This paper is devoted to the topic of indexicality in relation to the problem of cognitive significance. I undertake a critical examination of what I call the Millian Notational Variance Claim; this is the claim that those versions of a neo-Fregean semantics for demonstratives and other indexicals which rest upon the notion of a de re sense are eventually notational variants of a directly referential or Millian semantics for indexicals. I try to show that several lines of reasoning that might (...) be pursued by Millian theorists with a view to establishing the Millian Notational Variance Claim are inconclusive, and hence that the claim is in general unsound. The problem of cognitive significance is tackled in connection with those categories of indexicals concerning which neo-Fregeanism and Millianism are alleged to yield similar results, viz. temporal indexicals, spatial indexicals, and perceptual demonstratives. I argue towards the conclusion that the notions the Millian theorist might invoke to accommodate the phenomena of cognitive significance in this area of indexicality are hardly adequate to the effect, and hence that senses are indispensable also here. (shrink)