**Abstract** : We argue that the double-slit experiment can be understood much better by considering it as an experiment whereby
one uses electrons to study the set-up rather than an experiment whereby we use a set-up to study the behaviour of electrons.
We also show that Heisenberg's uncertainty principle is related to Gödel's concept of undecidability and how the latter can be used in an intuitive way to make sense of the double-slit experiment and the quantum rules for calculating coherent and incoherent probabilities. We meet here a situation where the electrons always behave in a fully deterministic way, while the detailed design of the set-up may render the question about the way they move through the set-up experimentally undecidable.
Heisenberg's uncertainty relation is a rule of thumb to predict such undecidability (but only one among others). It is very important to make a distinction in quantum mechanics between the determinism of nature (Einstein) and the decidability of a question within an experimental set-up (Bohr). The former is about the absolute truth of an answer to a yes or no question, and follows binary logic
(true or false), the latter about what an experimental set-up can decide and tell about the truth of that answer, and follows ternary logic (true, false or undecidable). Binary and ternary logic are incompatible.
The viewpoints of Bohr and Einstein are thus operating on different levels and it is only by confusing these two levels that these two viewpoints seem to be irreconcilable. A very important element in the analysis is the problem of the existence of common probability distributions. And this is a recurrent theme in other situations that are felt as paradoxical. The CHSH inequality used in the experiments of Aspect et al. clashes with quantum mechanics because it is based on the assumption that there would exist a common probability distribution for the hidden variables in the different experiments that intervene in the inequality. That such a common probability distribution does not exist is well known from quantum mechanics (because the operators that come into play do not commute and therefore do not have common eigenstates, i.e. common probability amplitudes). But this fact is not a prerogative of quantum mechanics and can also be explained by purely classical reasoning.