In the present paper, we introduce and investigate the notion of 2-local linear maps on vector spaces. A sufficient condition is obtained for the linearity of a 2-local linear map on finite-dimensional vector spaces. Based on this result, we prove that every 2-local derivation on a finite-dimensional semisimple Jordan algebra over an algebraically closed field of characteristic different from 2 is a derivation. Also, we show that every 2-local 1-automorphism (i.e. implemented by single symmetries) of mentioned Jordan algebra is an automorphism.