Logic is a way of learning to think and communicate clearly and coherently. In daily living, clear and coherent communication is essential to efficiently accomplish anything which involves the participation of another. While one can come to basic understandings between parties without logic, the greater the lack of an understanding of logic by one party, the greater the likelihood of miss-communication and it's undesired results.
A person who can not think logically will have to be swayed emotionally or socially instead of intellectually (intellectual positions requiring an understanding of factual conditions, which are then weighed). Daily, they become, therefore, unwitting accomplices of superior orators, con artists, etc. rather than being able to assess and evaluate specific proposals on merit. Therefore, their own interests (if they fleshed them out) are less likely to be proposed on their behalf, but the interests of those who emotionally/socially compelled them.
At the minimum, I want to know my beliefs, why I believe them, and act correspondingly. Logic, I believe, is essential to being able to accomplish this in daily living.
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