Dr.Waterland has given a comprehensive division of "necessity" into _four_ kinds, denominated respectively, the Logical, the Moral, the Physical, and the Metaphysical.
"Logical necessity" exists wherever the contrary of what is affirmed would imply a contradiction; and in this sense we call it _a necessary truth_ that two and two make four, that a whole is greater than any of its parts, and that a circle neither is nor can be a square.

It amounts to nothing more than the affirmation, that the same idea or thing _is what it is_; and it relates solely to the connection between one idea and another, or between one proposition and another, or between subject and predicate.

This is "logical necessity;" we cannot, with our present laws of thought, conceive the thing to be otherwise without implying a contradiction.
"Moral necessity," again, denotes a connection, not between one idea and another, or between the subject and predicate of a proposition, but between _means_ and _ends_.

It is not necessary absolutely that any man should continue to live; but it is necessary _morally_ that, if he would continue to live, he should eat and sleep, food and rest being, according to the established constitution of Nature, a _necessary condition_ or indispensable means for the support of life.

There is in like manner a "moral necessity" that we should be virtuous and obedient, if we would be truly happy, virtue and obedience being, according to the established constitution of Nature, an indispensable means of true and permanent happiness.