What are the 3 main components of Arguments?
Arguments are usually described as good/bad, strong/weak
1. Validity
2. Soundness
3. Inductive Force
Discuss the Argument: P1) The Taoiseach’s dog is
infested with fleas, P2) All fleas are bacteria, C) The Taoiseach’s dog is
infested with bacteria.
In Argument A, the conclusion follows from the premises.
- Even though (at least one of) the premises are in fact false.
- (If the premises were true, the conclusion would be true as well).
- The argument is “truth preserving”
Discuss the Argument: P1) Dan owns a dog, P2) All Labradoodles are dogs, C) Dan owns a Labradoodle.
In Argument B, the conclusion does not follow from the premises.
- Even though the premises are in fact true.
- (Even though the premises are true, the conclusion could be false).
- The argument is not “truth preserving”
What is Validity?
- This “following from” relationship is the concept of validity.
- It relates to the connection between premises and conclusion, not their actual truth values.
- i.e., an argument is valid when the conclusion follows from the premises.
- So, a single proposition can be true or false, but not valid or invalid. An argument can be valid or invalid, but not true or false
What is the definition of Validity?
1) To say that an argument is valid is to say: If the premises were true, then the conclusion would also have to be true.
2) To say that an argument is valid is to say: It would be impossible for all the premises of the argument to be true, but the conclusion
false at the same time.
Are arguments A & B valid?
- An argument (such as Argument A) can still be valid, even if one or
more of its premises is false. Because if the premises were true, then the conclusion would also have to be true. - An argument (such as Argument B) can be invalid, even if it has a true conclusion (… even if everything it says is true). Because it would be possible for the argument to have all true premises and a false conclusion at the same time
What is Indirect Proof?
- If you have an argument that you know is valid, but you also know the conclusion is (in fact) false, then you know that you must have at least one false premise.
- Why? Because it’s a valid argument: if the premises were true, the
conclusion would have to be true as well
How would an argument be sound?
- To say that an argument is sound is to say: The argument is valid, and all its premises are actually true.
- and thus, from the definition of validity, we know that the conclusion of a deductively sound argument must be true. (Hooray!)
How can you judge Validity?
- Ignore the actual truth values of the premises and conclusion, and
- Pretend the premises are all true. Then ask: - “Given these premises, could the conclusion conceivably/possibly be false?”
- If “no,” then the argument is valid.
- If “yes” then the argument is invalid
What are Conditional Sentences?
A compound proposition, made up of two parts (each of which is also a proposition), joined by a “connective”
e.g. It is Thursday, We’re having burgers for Dinner
- If, then
If it is Thursday, then we’re having burgers for dinner
“Antecedent” “Consequent”
Some arguments can be viewed as valid or invalid, independently of their content. Name the four examples?
- Affirming the Antecedent(Valid),
- P1) if P, then Q P2) P C) Q - Denying the Consequent(Valid)
- P1) if P, then Q P2) Not -Q C) Not -P - Denying the Antecedent(Invalid)
- P1) if P, then Q P2) Not -P C) Not -Q - Affirming the Consequent(Invalid)
- P1) if P, then Q P2) Q C) P
What are Forceful Arguments?
- Some arguments are still forceful even though the truth of the premises does not guarantee the conclusion:
P1) Socrates was Greek.
P2) Most Greeks around 400BCE ate fish.
C) Therefore, Socrates ate fish - We say that such an argument is “inductively forceful” (or that it has “inductive strength”)
- The truth of the premises, though not guaranteeing the conclusion, certainly makes the conclusion more likely or more reasonable.
