Semantic determinacy and indeterminacy

There are arguments that our language is paradoxically indeterminate. For instance, Wittgenstein-Kripke arguments for underdetermination of rules by cases, Quine’s indeterminacy of translation arguments, or Putnam’s model-theoretic arguments.

There are also arguments that our language is paradoxically determinate. First order logic shows that there is a smallest number of grains of sand that’s still a heap.

In other words, there are cases where we want determinacy, and we find indeterminacy threatening, and cases where we want indeterminacy, and we find determinacy puzzling. I wonder if there is any relevant difference between these cases other than the fact that we have different intuitions about them.

If we are to go with our intuitions, we need to bite the bullet on, or refute, both sets of arguments, in their respective cases. But if we embrace determinacy everywhere or embrace indeterminacy everywhere, then it’s neater: we only need to bite the bullet on, or refute, one family of arguments.

I find embracing determinacy everywhere rather attractive.