We've been talking for a while in the meta threads about doing a primer series on logic, so here goes. Note that this is not a normal debate post, so the normal rules don't apply - feel free to just reply to this with your answers.

A deductive argument is one that reasons from premises (usually 2 or more) to a conclusion.

For example:

Premise 1: All dogs are mammals.

Premise 2: All puppies are dogs.

Conclusion: All puppies are mammals.

When evaluating an argument such as the above, there are three possibilities:

1. The argument is invalid. This happens when the logic in an argument does not work. It doesn't matter if the premises are true or not - if the conclusion does not follow from the premises, the argument is invalid and must be discarded.

2. The argument is valid but not sound. This happens when the logic is correct, but one (or more) of the premises is not true. Valid arguments are not as bad as invalid arguments, but are not as good as sound ones.

3. The argument is valid and sound. (Sound for short.) This happens when the logic is correct (i.e. the conclusion follows from the premises) AND the premises are also true. If someone presents you a sound argument, if you are a rational individual you must accept the conclusion as true (unless you can find a reason why it is not sound).

Consider our example above involving puppies.

The first question we have to ask is if the form of the argument is valid. And, yes, it is. "All A are B. All B are C. Therefore, all A are C" is a valid form of argument. Ok, so, check. If the logic didn't work, we would stop here and reject the argument as invalid. But since the logic works, we know it is at least valid, so we have to move on to the second question.

The second question is if the premises are true. This can get a little tricky, as people can engage in hair splitting ad infinitum. So I suggest just using a plain reading to these things and not being like all, "But what about puppy robots??" and all that. So, is it true that dogs are mammals? Yes. Is it true that puppies are dogs? Yes. Ok, so both of the premises are true, so this argument is both valid and sound, or just "sound" for short. If either of the premises were false, then it would be valid but not sound.

So let's run through some examples and you can test yourself to see how you do.

Are these arguments invalid, valid but not sound (written as "valid" for short), or valid and sound (written as "sound" for short)?

Argument 1

Premise 1: All humans have hair

Premise 2: Mark Zuckerberg has hair

Conclusion: Mark Zuckerberg is a human

Invalid/Valid/Sound? Respond with your answers in the comments.

Argument 2

Premise 1: All plants have flowers

Premise 2: Yucca is a plant.

Conclusion: Yucca has flowers.

Invalid/Valid/Sound? Write your answer below!

Argument 3

Premise 1: Rule 3 of r/debatereligion requires posts to have a thesis statement in either the title or in the first sentence of the post. If it does not, it needs to be deleted by the moderators.

Premise 2: This post (https://old.reddit.com/r/DebateReligion/comments/nz04wl/atheists_cannot_shoulder_their_burden_of_proof/) has a thesis statement.

Conclusion: That post does not need to be deleted for a Rule 3 violation.

Valid? Invalid? Sound?

Argument 4

Premise 1: All triangles have a sum of their internal angles equal to 180 degrees.

Premise 2: A square has a sum of its internal angles not equal to 180 degrees.

Conclusion: A square is not a triangle

Valid / Invalid / Sound?

Argument 5

Premise 1: God, in Christianity, is usually defined as the omnipotent, omniscient, omnipresent creator of all reality in the universe.

Premise 2: Brahman, in Hinduism, is defined as the ultimate reality of the universe.

Conclusion: God created Brahman

Valid / Invalid / Sound?

EDIT: Answers:

Argument 1 - Invalid argument. Dogs have hair as well, but dogs are not humans (despite many of them wanting to eat human food). Note that we don't need to worry about the soundness of this argument, which some people were arguing about here - if it's invalid, it's invalid and we don't need to consider soundness.

Argument 2 - Valid but not sound. While the logic works (it is of the form "All X have Y, Yucca is an X, therefore X has Y" which is valid), it is not the case that all plants have flowers. For example, ferns do not have flowers, but are plants.

Argument 3 - Valid but not sound. The actual rule is Rule 4, not Rule 3.

Argument 4 - Valid and sound. All triangles (under a plain reading - one poster tried hair splitting) do have an interior sum of 180 degrees, and so a square (with a sum of 360 degrees) is not a triangle.

Argument 5 - Invalid. The existence of the two are plausibly mutually contradictory.