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In addition, the finite standpoint allows operations on finitary objects.
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In order to carry out the task of providing a secure foundation for infinitistic mathematics, access to finitary objects must be immediate and certain.
Focus on one particular object.
Concentrate on one of these objects.
The Volume object lives on NotRest objects and subclasses.
Some objects are, in a way, founded on other objects.
to execute on those objects.
The platform is based on widget objects.
Lean on nearby objects.
Object accessors act on specific ChIPS objects.
Extensions of the original finitist standpoint have been proposed and defended on broadly finitary grounds, e.g., Gentzen (1936) defended the use of transfinite induction up to ε0 in his consistency proof for PA as "indisputable," Takeuti (1987) gave another defense.
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