An interval based approach to the concept of linguistic truth is presented. First ’truth’ and ’false’ are associated with two subintervals \(I_ T\), \(I_ F\) of [0,1], and the algebra \((I_ T,I_ F,\neg,\vee,\wedge)\) appears then to be an extension of classical logic. Second, more generally, linguistic qualifiers such as ’very true’ are associated with subintervals of [0,1]. It is studied when a family of such subintervals is closed under the operations \(\neg\), \(\vee\), \(\wedge\). Author’s approach represents an alternative to Zadeh’s representation of linguistic truth by fuzzy subsets of [0,1].