  In considering a certain mathematical practice (or a theory used to codify it) from a philosophical perspective, we need to clarify with the greatest possible precision the assumptions which are made within it as well as the consequences which arise from those assumptions. This is particularly true when working with theories which are based on a weaker logic than the classical one, for which a deeper, more precise insight is mandatory. Many technical tools are available which can help us clarify those aspects. Among the available instruments, there are proof-theoretic techniques, such as proof-theoretic interpretations, as well as semantic techniques, such as realisability, Kripke models, Heyting-valued semantics. In fact, in the literature one often witnesses the interplay of proof-theoretic and semantic techniques. We here give a cursory look into some of these topics and suggest further reading.