What is an argument with a necessarily true conclusion?

An argument typically has premises and a conclusion. An argument which is such that once you assume the premises true then the conclusion can only be true is said to be logically "valid".

For example:

Ex. 1 - Aristotle is not here but he could have given you the answer you want; therefore, Aristotle could have given you the answer you want.

Ex. 2 - It rains and the sun is shining, therefore it rains.

"*Necessarily true*" just means that given the truth of the premises, it is not possible that the conclusion be false.

The fact that the premises may in fact be false themselves is irrelevant. "*Assuming the premises true*" means that you choose to accept they are true irrespective of whether they are actually true.

For example:

Aristotle was Russian and all Russians ate caviar for breakfast; therefore, Aristotle ate caviar for breakfast.

The conclusion is presumably false. And so are the premises. However, once you choose to assume the premises true, then the conclusion can only be true as well. Said differently, if the premises were true, the conclusion would have to be true as well.

The fact that the conclusion is sometimes necessarily true given the truth of the premises comes from the form of the argument. It is the form of the argument that makes the truth of the conclusion "follow from" the truth of the premises.

The notion of "necessity" here is crucial. It conveys the idea that once someone has accepted that the premises are true, they are compelled to accept the truth of the conclusion, and this merely by virtue of the form of the argument that makes the truth of conclusion follow from he truth of the premises.

This is crucial also because this is what ensures that we can agree on some conclusions. If we both accept the truth of the premises and if we can both understand that the truth of the conclusion follows necessarily from the truth of the premises, then we will agree that the conclusion is true.

3“Necessarily” is not defined in classical logic, one needs modal logic to really make sense of it. However, when examples are considered people entertain possibilities of various statements being true or false, which is a naive way of engaging in modal logic. Then "necessarily true" is used for statements that can never be false. For example, "1+1=2" would be true necessarily, while "Sally loves Tommy" just for the sake of the argument. – Conifold – 2019-06-25T11:01:41.973

Please do not change questions in a way that the emphasis or core of the question changes if there already are valid answers. If you have an interest in other points, simply ask a new question instead of in invalidating existing answers by such edits. – Philip Klöcking – 2019-10-18T17:42:10.747