I think that the uncertainty is linked whit probability concept. With neural nets, we do not want to construct an exact formulation for the biological neurons, but simply to simulate their basic fuctionality. The problem is not whether the NN can learn to act as a logic unit, but rather how AI can help that this unit has the congitive knowledge of what it does. The vector space of a NN can actually contain many thousands of dimensions, this does not mean that we should try and translate them all into multi-dimensional logic. I can not agree with that.
Probability has nothing to do with fuzziness.
Propability applies to mutually exclusive states, while fuzziness applies when things belong to more than one state at the same time.