The complexity of the environment demands a well-constructed composite environmental index (CEI) to provide a useful tool to draw attention to environmental conditions and trends for policy purposes. Among the common difficulties in constructing a proper CEI are uncertainties due to the selection of the most representative underlying variables or indicators. A degree of uncertainty accompanies experts' judgments, and to deal with vague, subjective or inconsistent information, logic other than classic is required. This study analyzes a procedure that uses different experts' opinions in constructing a CEI, with the use of paraconsistent annotated logic. For this, a sensitivity analysis of the Environmental Sustainability Index (ESI 2005) was used as an example to assess the reliability of experts' opinions. The uncertainty due to the disagreement in experts' opinions clearly indicates that the forms we presently use to measure and monitor the actual environment are insufficient, that is, there is a lack of a "science of sustainability".