<aside> 💡 TL;DR An argument is an attempted proof and a proof is a successful argument.

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In the following sections, a distinction between proof systems and argument systems will be made. The distinction between the two is quite technical and requires extensive formal definitions, and rather than getting lost in the small details here, let’s quickly go through the basic differences. Arguments have belief as their goal, while proofs have knowledge as their goal. Arguments are meant to persuade to accept an idea as true and cal applied more easily to a broad set of topics, whereas a proof establishes that an idea is objectively true and is much more rigorous and objective (and does not necessarily exist for all situations). More simply, an argument is an attempted proof and a proof is a successful argument.