The paper attempts a novel defense of the main claim of Wittgenstein's Private Language Argument, i.e. that 'inner' ostensive definition is impossible. Part 1 traces Wittgenstein's target to the idea that 'ostensive definition' is a mental act, an idea that makes it tempting to think that its objects might just as well be private as public. Part 2 discusses a recent interpretation and defence of Wittgenstein's position due to Stroud and McGinn. On their view, private ostensive definition establishes no pattern of use because it fails to specify the type of inner episode that is being ostended. But not explicitly specifying a type is harmless so long as the ostension in fact brings it about that the subject's usage is sensitive to it. Part 3 proposes a new argument. Private ostensive definition does sustain a pattern of use, but that use is semantically indeterminate: nothing in it (or in the subject's mind) settles which of two alternative schemes of reference applies. The conclusion discusses Wittgenstein's best-known remarks on the subject from the perspective of this new argument.