Show, using your own examples, how affirming the consequent and denying the antecedent are deductively invalid argument forms. What makes these examples of forms of fallacious reasoning?
I answered half of the question already but i'm stuck on these two key points related to the question .can you please help me..
1.Explain invalidity with reference to deduction.
2. Explain how the argument forms are fallacious
1. In logic, an argument is considered deductively valid if the conclusion necessarily follows from the premises. This means that if the premises are true, the conclusion must also be true. Conversely, an invalid argument is one where the conclusion does not necessarily follow from the premises, even if the premises are true. Invalidity in deductive reasoning indicates a flaw in the logical structure of the argument.
2. Affirming the consequent and denying the antecedent are fallacious argument forms because they violate the basic principles of deductive reasoning.
- Affirming the Consequent: This argument form assumes that if the consequent of a conditional statement is true, then the antecedent must also be true. However, this is not always the case. Here is an example:
Conditional Statement: If it is raining (A), then the ground is wet (B).
Affirming the Consequent: The ground is wet (B), therefore it is raining (A).
This argument is invalid because there could be other causes for the ground being wet, such as someone watering the lawn. Just because the consequent (B) is true, it does not necessarily mean that the antecedent (A) is true. Therefore, affirming the consequent is a fallacious argument form.
- Denying the Antecedent: This argument form assumes that if the antecedent of a conditional statement is false, then the consequent must also be false. However, this is also not always the case. Here is an example:
Conditional Statement: If it is raining (A), then the ground is wet (B).
Denying the Antecedent: It is not raining (not A), therefore the ground is not wet (not B).
This argument is invalid because there could be other causes for the ground being wet, such as a recent spill or a leaking pipe. Just because the antecedent (A) is false, it does not necessarily mean that the consequent (B) is false. Therefore, denying the antecedent is also a fallacious argument form.
In both cases, the invalidity of the argument forms stems from drawing unwarranted conclusions based on the truth or falsity of the consequent or antecedent in conditional statements.