What is reasonable is not necessarily logical. One can believe two things and realize that they imply a third thing. Instead of coming to believe the third thing, that person might find they should stop believing one of the first two if they have a good reason to believe the third is false. Similarly, a person with those beliefs, except without a good reason to believe the third is false, might still not infer that the third is true: they might be utterly uninterested in whether it is true or not. There are many things one believes, and though it would be logical to follow those beliefs to their logical conclusions, this would result in one’s mind being filled with trivialities; a consequence that makes the action unreasonable.

In order to understand the difference between reason and logic, I think it is important to first understand reason more deeply.

Reason is traditionally split into two types. Theoretical reasoning is a type of thought to come to a certain belief, whereas practical reasoning is a type of thought to change plans or intentions. What is reasonable in one type, is not necessarily reasonable in the other. For example, in practical reasoning one might be presented with multiple, equally satisfactory options. It would be rational to choose an arbitrary option; otherwise one would be stalled through inaction. The same does not hold for theoretical reasoning: when presented with multiple, equally satisfactory beliefs it would not be rational to arbitrarily choose one to believe. However, it is possible to rationally choose which beliefs or questions one evaluates with theoretical reason. The conclusions remain unaffected.

Ordinarily, reasoning is applied in a conservative manner. One’s current beliefs and intentions are changed if there is a special reason to do so, and conserved otherwise. This is in contrast with foundational reasoning, where a belief should only be continued to be held if there is a justification to do so. In such a reasoning system, there are some foundational beliefs that require no further justification, such as current perceptions and logical axioms. In general, humans reason conservatively.

Logical processes can be divided into three modes. One such mode is deduction, where logical conclusions are reached from premises. A proof that some conclusion is true through deduction starts with the premises, then consists of a series of steps where each step follows logically from the prior steps or the premises, and finally leads to the conclusion. This proof is sometimes called “deductive reasoning”.

In reality, it is not actually a type of reasoning. In constructing such a proof, one can have many different considerations. One first determines what they are setting out to prove, upon which they might consider which intermediate steps could be useful. They then aim to prove these intermediate steps, and only then prove the conclusion is true using those intermediate results. The reasoning behind constructing a logical proof does not necessarily follow the same structure as the proof itself: the deductive rules must be satisfied for the proof, but are not necessarily followed in the proof’s construction.

As such, something that is reasonable is not necessarily logical, and something that is logical is not necessarily reasonable. One can reason about deductions, but deduction is not a kind of reasoning. Logic, at least its deductive mode, is not a theory of reasoning and does not tell us how we govern our beliefs and intentions.

If you would like to explore logic and reasoning in more detail, I highly recommend reading the article Internal critique: A logic is not a theory of reasoning and a theory of reasoning is not a logic, by G. Harman (2002).