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For some arguments on each side, see Section 4.5.
Hence classical logic prohibits primitive function symbols whose extensions are partial functions functions whose value is for some arguments undefined.
Notice that with the introduction of the μ operator for the first time we encounter a recursive function that might fail to be defined for some arguments.
It might not be possible to do this in an informative way, however; for some arguments to this effect, see Pagin (1987, 88 139).
This pair of entries correspond to a*b and b*a for some arguments a and b.
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Church's hope was that contradictions could be avoided by ensuring the possibility that a propositional function be undefined for some argument.
Nevertheless, the case for no recession has some arguments going for it.
Some arguments for and against: 1.
Plato's actually going to give us some arguments for pretty much that same claim.
There are some arguments for a referendum going beyond simply the new treaty.
We state some arguments for the stability of the resulting scheme, and perform simulations in two dimensions.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com