Do syllogistic arguments face the problem of infinite regression? And should this weaken the argument type's precedent?

If I accept proposition "B" on the basis of premise "C", why do I accept premise "C"? Won't I need a basis for premise "C"? And that basis would have to come by another tenet, proposition "A"... Ad infinitum. The argument would either become circular, lead to a foundational belief which cannot be proven, or just regress infinitely without ever repeating.

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Jaymin Jordan-Allen
Student, United Reformed Church
Ontario, CA