Please enable JavaScript.
Coggle requires JavaScript to display documents.
Common Invalid Forms of Formal Falicies, Denying the Antecedent - Coggle…
Common Invalid Forms of Formal Falicies
Take a look at the following argument:
If you give lots of money to charity, then you are nice.
You do not give lots of money to charity.
Therefore, you must not be nice.
This might initially seem like a valid argument. However, it is actually invalid in its form. To see that this argument is logically invalid, take a look at the following argument with the same form:
If my cat is a dog, then it is a mammal.
My cat is not a dog.
Therefore, my cat is not a mammal.
This second example is clearly invalid since the premises are true and the conclusion is false. Therefore, there must be something wrong with the form. Here is the form of the argument:
P → Q
~P
∴ ~Q
Because this argument form’s second premise rejects the antecedent, P, of the conditional in the first premise, this argument form is referred to as denying the antecedent. We can conclusively demonstrate that the form is invalid using the truth table method
Affirming the Consequent
Another famous formal logical fallacy also begins with a conditional. However, the other two lines are slightly different. Here is the form:
Q
∴ P
Because the second premise states the consequent of the conditional, this form is called affirming the consequent. Here is an example:
If you get mono, you will be very tired.
You are very tired.
Therefore, you have mono.
The invalidity of this argument can be seen in the following argument of the same form:
If my cat is a dog, then it is a mammal.
My cat is a mammal.
Therefore, my cat is a dog.
Clearly, this argument is invalid because it has true premises and a false conclusion.
P → Q
Formal Fallacies
Denying the Antecedent