This paper analyzes the concept of truth in terms of an account of Fregean sense as cognitive value. The account highlights the importance of understanding-based knowledge of co-reference for the individuation of senses. Explicit truth attributions, like ‘that I smell the scent of violets is true’ involve an inter-level version of understanding-based knowledge of co-reference in the that-clause concepts of thoughts that they employ: one cannot understand the that-clause concept of the thought in the truth attribution without understanding the thought the that-clause concept is a concept of. This is not a redundancy that eliminates or deflates cognitive value, but an exploitation, by the concept of truth, of the inter-level version of understanding-based knowledge of co-reference in critical reflective thinking. The cognitive value of the concept of truth is to combine semantically with explicit ways of thinking of thoughts to make critical reflective thinking possible. This account of the cognitive value of the concept of truth assigns cognitive value not by construing the concept of truth as a way of thinking about some thing, but by articulating its broader cognitive role.