We analyse the decision of an agent with time-inconsistent preferences to c
onsume a good that exerts an externality on future welfare. The extent of t
he externality is initially unknown, but may be learned via a costless samp
ling procedure. We show that when the agent cannot commit to future consump
tion and learning decisions, incomplete learning may occur on a Markov perf
ect equilibrium path of the resulting intra-personal game. Tn such a case,
each agent's incarnation stops learning for some values of the posterior di
stribution of beliefs and acts under self-restricted information. This cond
uct is interpreted as strategic ignorance. All equilibria featuring this pr
operty strictly Pareto dominate the complete learning equilibrium for ally
posterior distribution of beliefs.