Kreisel's squeezing argument shows that provability in formal systems and truth in intended models can come apart, so model existence from consistency does not vindicate the claim about actual computational totality.

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Come apart(as used in logic and philosophy): To be different or separate from each other; in this case, it means mereological structure and spatial structure could be organized differently.
Computational totality(the claim that the argument challenges): The idea that everything we might want to know or prove can ultimately be calculated or figured out through computation or formal logical rules.
Kreisel(as a historical figure in logic and philosophy of mathematics): Georg Kreisel (1923–2015), a mathematical logician who studied how mathematical reasoning works and whether we can be certain about mathematical truths.
Model existence from consistency(the assumption being questioned): The principle that if a set of logical rules don't contradict each other, then there must exist some interpretation or 'world' where all those rules are actually true.

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