We have reviewed evidence for the hypothesis that T-cell activation by antigen is an all or none process which is triggered when signal strength exceeds a certain threshold. Signal is generated by multivalent interaction between T-cell antigen receptors (TCR) and antigenic epitopes on the surface of antigen-presenting cells (APC) or target cells. Therefore total signal strength (Stot) will depend upon the concentration of TCR (and other accessory molecules that bind to cell surface ligands, e.g. CD4 and CD8) on T cells, the concentration of antigen on APC or targets and the affinity of interaction between receptors (a broad term incorporating TCR plus CD4 and CD8) and antigen. This hypothesis means that T-cell self tolerance is quantitatively determined by self-antigen concentrations on cell surfaces. Implications for a variety of immunological phenomenona are reviewed.