Distinguish valid from invalid arguments and sound from unsound VALID VS INVALID Distinguish valid from invalid arguments and sound from unsound All dogs have 4 legs. All tables have 4 legs. Therefore, all dogs are tables.

An argument is a group statements, called premises, offered in support of a conclusion. A deductive argument claims that its premises support its conclusion by logical necessity. Logical necessity means this: If you are holding one apple with your right hand and another apple with your left hand, then—by logical necessity—you are holding two apples. Or If all objects are things that exist in space-time, then—by logical necessity—a pizza is an object. If all triangles have three sides, and on page 12 of your geometry book there is a triangle—by logical necessity—that triangle has three sides.

What if I told you that I’m holding 3 apples or that I ate a pizza that was not an object or that in my book there is a triangle with 5 sides? That's impossible! It is logically necessary that if you have 2 apples you have 2 apples and that a pizza is an object and that triangles have 3 sides. But what if I told you that the sun will not rise tomorrow or that we are in the Matrix? Perhaps this sounds absurd. But on closer examination it is not logically necessary that the sun must rise tomorrow or that we are not in the Matrix. It is possible. So, if something could not be otherwise, it is logically necessary. 3+3 = 6. This could not be otherwise. It is logically necessary.

If the premises of an argument support the conclusion by logical necessity, the argument is DEDUCTIVELY VALID. VALIDITY is a property that applies only to deductive arguments. It means that premises support the conclusion by logical necessity. Another way to put it: The premises IMPLY the conclusion. So, if the premises of an argument IMPLY the conclusion, that argument is DEDUCTIVELY VALID.

Consider the following argument: All actors are robots. Tom Cruise is an actor. Therefore, Tom Cruise is a robot. This is a valid argument. Why? Assuming that the premises are true, it is impossible for the conclusion to be false. Just think about it: If premises 1 and 2 were true, could you deny the conclusion? No! Thus this argument is deductively valid, but UNSOUND.

Another valid argument: People from England speak English. Marc is from England. Therefore, Marc speaks English. Once again: Assuming that the premises are true, is it possible for the conclusion to be false? No! Again, this is a deductively valid argument and if there is a Marc who is from England, the argument is SOUND.

Answer: The argument is INVALID. What happens when a deductive argument is not successful? What happens when the premises do not support the conclusion by logical necessity? What happens, that is, when the premises do not imply the conclusion? Answer: The argument is INVALID.

VERY IMPORTANT: The conclusion of an INVALID argument can be a true statement or a false statement! In fact, an argument can have true premises and a true conclusion and still be INVALID! The president of the US must be born in the US. Donald Trump was born in the US. Therefore, Donald Trump is the president of the US. I know what you’re thinking: “But it is true that Trump is the president of the US!” Sure, but it is NOT premise 1 and 2 that make the statement true! VALIDITY AND TRUTH ARE 2 DIFFERENT THINGS!

If the premises of a deductive argument fail to support the conclusion, the argument is INVALID This means that the premises do not support the conclusion by logical necessity. Another way to put it: The premises do not imply the conclusion.

All actors are robots. Tom Cruise is a robot. Therefore, Tom Cruise is an actor. Now think about it: If the premises are true, do they imply the conclusion? Perhaps you want to say: “But I know that he is an actor!” Sure, but the question is not whether he in fact is an actor. The question is whether premise 1 and 2 IMPLY that Tom Cruise is an actor. And they clearly don’t. So, because the premises fail to support the conclusion, this argument is a DEDUCTIVELY INVALID argument.

British people speak English. Marc speaks English. Therefore, Marc is British. Ask yourself: If the premises are true, is it possible for the conclusion to be false? Yes, of course! Marc may have learned to speak English. The premises do not imply that Marc is British! Perhaps you say: “But Marc could well be British!” Granted, but once again, the question is NOT what could be. The question is whether premises 1 and 2 IMPLY that Marc is British. It is obvious that they don’t.

Okay! Now you’ll tell me if the following arguments are valid, invalid, sound, unsound. Remember: Ask yourself, “Assuming that the remises are true, does the conclusion follow by logical necessity or does not follow at all?

INVALID! The Pope speaks 13 languages. This man speaks 13 languages. Therefore, this man is the Pope. INVALID!

1. All female TV hosts are successful TV hosts. 2 1. All female TV hosts are successful TV hosts. 2. Oprah Winfrey is a successful TV host. 3. Therefore, Oprah Winfrey is a female TV host. INVALID!

Premise 1 says that all females who are TV hosts are successful. So, if you are a female, and you are a TV host, you are successful. However, premise 1 does not assert that ALL TV hosts are females. This implies that there are successful male TV hosts too. Now, what does premise 2 assert? It asserts that Oprah Winfrey is a successful TV host. But it does not say anything about her sex. I know what you’re thinking: “But I know Oprah! She is a female TV host.” Granted, but the question is NOT who Oprah in fact is. Once again, the question is whether the premises imply the conclusion. It is a matter of relationship between premises and conclusion, and not between reality and conclusion.

VALID! BUT UNSOUND Students who received an F pass the course. Philippa received an F. Therefore Philippa passed the course. VALID! BUT UNSOUND

INVALID If you are playing soccer, you have a soccer ball. Therefore you are playing soccer. INVALID

INVALID All trees are plants. This is a plant. Therefore, this is a tree. INVALID

INVALID All plants are green. Trees are green. Therefore, trees are plants. INVALID

INVALID All things with 3 sides are triangles. Some things with 3 angles are triangles. Therefore, some things with 3 angles are things with 3 sides. INVALID

Let’s change terms: Things with 3 sides become ants Triangles become insects Things with 3 angles become things that fly

INVALID All ants are insects. Some things that fly are insects. Therefore, some things that fly are ants. INVALID

VALID BUT UNSOUND All dogs are cats. Fluffy is a dog. Therefore, Fluffy is a cat. VALID BUT UNSOUND

? VALID But is it sound? Whatever begins to exist has a cause. The universe began to exist. Therefore, the universe has a cause. ? VALID But is it sound?

THIS IS THE END Questions?