If you take the position that these values exist but are probabilistic (rather than simply that there are limits on measurement) then you have indeterminism. But what if you take the view that the values exist but are not measurable or even that they do not exist and the particle is "smeared" across space?
The last point of view is the only one that is consistent with observations. The idea that the values of position and momentum exist, but are not observable is one variant of what is known as hidden variables (variables that exist but cannot be observed). hidden variables have been ruled out by experiments Bell's inequality is evaluated.
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