  This paper provides a critical overview of Georg Kreisel's method of informal
rigour, most famously presented in his 1967 paper `Informal rigour and
completeness proofs'. After first considering Kreisel's own characterization in
historical context, we then present two schemas under which we claim his
various examples of informal rigour can be subsumed. We then present detailed
reconstructions of his three original examples: his squeezing argument in favor
of the adequacy of the model theoretic analysis of logical validity, his
argument for the determinacy of the Continuum Hypothesis, and his refutation of
Markov's principle in intuitionistic analysis. We conclude by offering a
comparison of Kreisel's understanding of informal rigour with Carnap's method
of explication. In an appendix, we also offer briefer reconstructions of
Kreisel's attempts to apply informal rigour to the discovery of set theoretic
axioms, the distinction between standard and nonstandard models of arithmetic,
and the concepts of finitist proof, predicative definability, and
intuitionistic validity.
