Is logic a science or an art? Of course, a logician would answer Yes, and here is why.
A science is a systematic study of some aspect of the natural world that seeks to discover laws (regularities, principles) by which God governs His creation. Whereas botany studies plants, astronomy studies the sky, and anatomy studies the body, logic studies the mind as it reasons, as it draws conclusions from other information. Logic as a science seeks to discover rules that distinguish good reasoning from poor reasoning, rules that are then simplified and systematized. These would include the rules for validity, of inference and replacement, and so on.
For example, logic as a science could study the apostle Paul’s reasoning in 1 Cor. 15, “If there is no resurrection of the dead, then Christ has not been raised… But Christ has been raised, and is therefore the first fruits from among the dead.” It then simplifies this into a standard pattern: If not R then not C, C, therefore R. This rule can be further simplified, named, and organized in relation to other rules of logic.
An art is a creative application of the principles of nature for the production of works of beauty, skill, and practical use. The visual arts apply their principles to the production of paintings, sculptures, and pottery. The literary arts produce poems and stories. The performing arts produce operas, plays, and ballets.
Logic is one of the seven liberal arts, which include the Trivium of grammar, logic, and rhetoric. These arts are the skills which are essential for a free person (liberalis, “worthy of a free person”) to take an active part in daily life, for the benefit of others. Specifically, logic as an art seeks to apply the principles of reasoning to analyze and create arguments, proofs, and other chains of reasoning.
Logic is the science and art of reasoning well. Logic as a science seeks to discover rules of reasoning; logic as an art seeks to apply those rules to rational discourse.