Achinstein is the son of Betty (née Comras) and economist Asher Achinstein. He received his B.A. and Ph.D. from Harvard with a dissertation on Carnap's theory of probability. It was the German philosopher Carl G. Hempel, in a visit to Harvard in 1953–4 (replacing W.V. Quine who was on leave), who motivated him to pursue Philosophy of Science. Upon getting a Harvard Traveling Fellowship, Achinstein spent a year in Oxford in 1959 working under the guidance of P. F. Strawson. In Oxford he attended seminars and lectures delivered by Gilbert Ryle, A.J. Ayer, and J.L. Austin. Achinstein specializes in philosophy of science with strong interests in the history of science.