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What Is Logic?

Many people do not know the answer to this question. Logic is the study of arguments. But if I ask someone what logic is, the answer I am looking for is something that shows they understand what an argument is, not a precise definition.

Logic is the systematic study of the forms of inference, the relations that lead to the acceptance of one proposition, the conclusion, on the basis of a set of other propositions, the premises. More broadly, logic is the analysis and appraisal of arguments. The premises may or may not support the conclusion; when they do not, the relation is characterized as a fallacy.

In ordinary discourse, inferences may be signified by words such as therefore, thus, hence, ergo, and so on.

Wikipedia - Logic

An argument is composed of propositions/statements and an inference. A proposition or statement is a sentence which is either true or false. There are two kinds of propositions in an argument: premise and conclusion. The premises support or infer the conclusion. Unlike a proposition, an inference is not said to be true of false. In a deductive argument, it's said to be valid or invalid. In a non-deductive argument, it's said to be strong or weak.

A deductive argument is composed of statements that can be true/false and an inference than can be valid/invalid. This leads to some interesting scenarios. In the argument above, the premises are true and the inference is valid, therefore the conclusion is true and the argument is said to be sound, rather than unsound. This structure allows you to have premises that are false, but a conclusion that is true. Or an inference that is valid but a conclusion that is false.

In this argument the premises are false, but the inference is valid and the conclusion is true. This means that even if the premises are wrong, the inference can still be valid and the conclusion can still be true. This is important to understand. For a deductive argument to be sound, the premises must be true and the inference must be valid.

In this argument, the premises are true, but the infrence is invalid and the conclusion is false.

Here, the premises are true and the conclusion is true, the only thing wrong is that the inference is invalid. Understanding how arguments work is at the heart of logic. While these examples may sound silly, these types of arguments do appear and it's helpful to be able to recognize them.

You can't assume that just because a conclusion is true, than the argument is sound. This is a big issue. Once a human being decides (x) conclusion is true, they often assume that their arguments must be sound, but that is not always the case. Being correct about a conclusion, does not make your argument sound.

When debating, people often focus on and attack each others conclusion. But it's not the conclusions you should be focusing on. When you are dealing with an argument, you can only demonstrate that it is unsound by attacking the premises or inference, not the conclusion. An argument is sound if the premises are true and the inference is valid.

Does God Exist?

The debate on the existence of god(s) is a great way to better understand logic. It is heavily debated and most people focus on the conclusion, rather than the soundness of the argument.

The inference in this argument is valid. That's right, it is valid. However, at least the first premise is false. This argument is unsound. However, that does not mean the conclusion is false. That does not mean that God does not exist. All it means is that the argument is unsound. When dealing with deductive arguments, the only thing you can do is show that the argument is either sound or unsound. And even if you demonstrate that the argument is unsound, you still cannot determine if the conclusion is false based on that.

This may be considered an annoyance. But it also makes things easier. When debating, you don't have to prove that the conclusion is true or false, you only have to demonstrate that the argument is sound or unsound. This makes debate easier in some ways.

Deductive vs Inductive

In a deductive argument, the conclusion must be true, if the premises are true. But in an inductive argument, even if the premises are true, there is still a chance that the conclusion is false.

The premises in these types of argument don't deduce the conclusion. Instead, they support the conclusion. For example, if all the swans you have ever seen are white, then you may infer that all swans are white. The premise, that every swan you and everyone you know has ever seen are white, supports the conclusion that all swans are white. However, black swans have been observed, and so this contigent truth has been falsified.

In an inductive argument an inference is not valid/invalid, it is strong/weak. And an argument is not sound/unsound, it is cogent/uncogent. Deduction and induction are how we make inferences from premises.

Necessary Truth vs Contingent Truth

Yes, there are different kinds of truths and this is important to know the difference. A necessary truth is also known as a logical truth. Something that is necessarily true, must be true. While something that is a contigent truth, could have been false.

necessary truth
A truth is necessary if denying it would entail a contradiction.
A statement that is true in all possible worlds.
contingent truth
A truth that happnes to be true, but could have been false.

The statement "1 + 1 = 2" is necessarily true. It is true in all possible worlds. Also, the negation of this statement is a contradiction "1 + 1 ≠ 2". A contingent truth could have been false, such as the statement "Harry met Sally". It's not true in all possible worlds. Harry may not have met Sally. But... it's not possible for "1 + 1 = 2" to have been false. By definition, it is true. It's a logical truth.