mtbturtle wrote:This has come up in a recent discussion in which it was maintained that infinite regress was a form of circular reasoning.
Natural ChemE wrote:mtbturtle,
Another way of seeing it would be where Infinite Regress is a straight line of propositions,
,
while Circular Reasoning is a loop
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The Circular Reasoning loop can be written in linear form as
,
which is the same thing as
so long as you assert the periodic equalitiesThis demonstrates that any instance of Circular Reasoning is necessarily an instance of Infinite Regress.
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Since Circular Reasoning can be expressed as an Infinite Regress plus additional constraints, i.e. periodic proposition equalities, then Circular Reasoning is a special case (subset) of Infinite Regress.
Here, one has a mere choice between:
1. an infinite regression, which appears because of the necessity to go ever further back, but isn't practically feasible and doesn't, therefore, provide a certain foundation;
2. a logical circle in the deduction, which is caused by the fact that one, in the need to found, falls back on statements which had already appeared before as requiring a foundation, and which circle does not lead to any certain foundation either; and finally:
3. a break of searching at a certain point, which indeed appears principally feasible, but would mean a random suspension of the principle of sufficient reason.
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