Mark van Atten --The hypothetical judgement in the history of intuitionistic logic

Three points will be argued for:

Although Heyting and Kolmogorov both accept Ex Falso as a formal rule, Heyting’s justification of it would not be acceptable to Kolmogorov; Heyting’s claim that his interpretation and Kolmogorov’s are essentially the same is not correct; and Kolmogorov’s own justification is the more reasonable one of the two.
It has been claimed that a discussion in Brouwer’s dissertation shows that he at the time rejected the hypothetical judgement. This is not the case, and in fact that discussion contains an account of such judgements that served him all his life. On this account, hypothetical judgements may in certain cases have false antecedents, but there is no justification of the general principle Ex Falso.
Neither Heyting’s nor Kolmogorov’s justification of Ex Falso fits into Brouwer’s conception of logic. Unlike the name BHK-interpretation suggests, there never was one single understanding of logic that Brouwer, Heyting and Kolmogorov all agreed on.