Aristotle's two concerns are both based on his belief that there must be first, unprovable principles for any science. The first concern is that if there are no first, unprovable principles, then any science will be circular. The second concern is that if there are no first, unprovable principles, then demonstrations will not be explanatory.
source https://plato.stanford.edu/entries/aristotle-mathematics/
Dear Panagiotis Michael Mougoyannis
With respect to the first question, a circular argument or explanation is characterized by the fact that one of the premises supposes the conclusion, so that, if one wants to find a justification for that premise, one must appeal to the conclusion that -in turn- it presupposes the premise, and thus a semantic circle is produced from which it is not possible to get out, and which is not useful.
This is valid for reasoning, explanations (or explanatory reasoning) and for definitions.
For example, if you want to define "life" and you use "vital signs" in the definition, it happens that to understand the meaning of "vital sign" you have to understand what "life" means, so the argument becomes circular.
On the other hand, a infinite regress occurs when an unquestionable or definitive justification or foundation of something is sought, and a premise is provided that, in turn, requires to be justified by another, and so on. For example, Karl Popper denies that scientific observation statements are the unquestionable basis of scientific knowledge from which conclusions are formulated, because an apparently true statement such as "this is a glass of water" actually assumes previous theories, since "water" means an element with a certain molecular structure, etc. So, from the argumentative or logical point of view, it is always possible to ask for a further justification of any statement taken as a premise in science; that is, the search for indubitable knowledge leads to a infinite regress.
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