8/12/2019 Why is Modus Tollens a Valid Form of Argument

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Why is modus tollens a valid form of argument?sk8terasked 1 year ago

Was originally asked on Yahoo Answ ers United States

The definition of validity in philosophy is: An argument is valid if and only if (iff) the truth of the

premises guarantees the truth of the conclusion.

Modus tollens:

If P, then Q.

Not Q.

Therefore, not P.

With a valid modus tollens, the aim is to reject the consequent in order to reject the antcedent.

Here's my confusion: "If P, then Q, not Q, therefore, not P" suggests that P causes Q, and is the only

condition for Q. An example, "If I am in Chicago, then I am in the United States. I am not in the UnitedStates. Therefore, I am not in Chicago," makes sense. But consider this example, "If Sam is

competent, he will get the job. Sam did not get the job. Therefore, Sam is not competent." Is

competency the only condition for Sam to get a job? Consider another example: If Mary was born in

Canada, then she is Canadian. Mary is not Canadian. Therefore, Mary was not born in Canada. But

what if Mary was born in Canada but gave up her citizenship for the United States? So how is

rejecting the consequent in order to reject the antecedent a form of valid argument in terms of the

philosophical definition of validity? Does modus tollens rely on the soudness of an argument or does it

only involve the form of an argument regardless of its content?

Thanks!

Additional Details

A logical fallacy called denying the antecedent is as follows:

If Mary was born in Canada, then she is Canadian.

Mary was not born in Canada.

Therefore, Mary is not a Canadian.

In modus tollens, P implies Q. So why is the example above (denying the antecedent) a logical

fallacy? Since P implies Q, if it is not P, then it can't be Q. Why is this form of argument invalid?

1 year ago

Qeidx, thank you very much. I think you have cleared my confusion, but I have to read your

explanation a few more times in order to really understand and absorb it. Quick question: Doesmodus tollens have to be a sound argument? Again, thank you!

1 year ago

Best Answer Asker's Choice

http://answers.yahoo.com/question/index?qid=20120918220240AAI8vKqhttp://ca.answers.yahoo.com/activity?show=HG45W33BZJZGGNSBG4J7SCD2RQ&t=ghttp://answers.yahoo.com/question/index?qid=20120918220240AAI8vKqhttp://ca.answers.yahoo.com/activity?show=HG45W33BZJZGGNSBG4J7SCD2RQ&t=g

8/12/2019 Why is Modus Tollens a Valid Form of Argument

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HelloWorldanswered 1 year ago

Explanation:

1. If A then B

This means, that if A is the case, then B is the case, however, B could be the case from another

source.

2. ~B, therefore, ~A

This is valid because, if B is not the case, then B has not been gained from ANY source, and we

know that one way B could be the case is if A is the case. B isn't the case, so it

MUST be true that A is not the case either, since if A was the case, then B would, B isn't, so A isn't

either.

If it is raining, then the sidewalk is wet.

The sidewalk is not wet.

Therefore, it is not raining, since, if it is raining, then the sidewalk WOULD be wet. Sidewalk isn't wet,

so it certainly is not raining.

Edit: If you want more examples or a deeper explanation, I can go on further, just let me know in the

additional details. ^^

---------------------------------------...

To your additional details:

If Mary was born in Canada, then she is Canadian.

Mary was not born in Canada.

Therefore, Mary is not a Canadian.

If M then C~M

Therefore, ~C.

Simply because IF Mary was born in Canada, then she is a Canadian, this does not mean that this is

the ONLY way she could be a Canadian.

If it is raining, then the sidewalk is wet.

It is not raining.

Therefore, the sidewalk isn't wet.

Entirely invalid for the same exact reason. Just because it is not raining doesn't mean this is the

ONLY way the sidewalk could be wet. I could have just gotten done hose'n it down. There are manyways that the sidewalk could be wet, regardless of whether or not it is raining.

However, if it is raining, then certainly this means the sidewalk is wet.

Modus Tollens is a valid argument form REGARDLESS of the content of the premises. It is always

logically valid.

Denying the antecedent is an invalid argument form REGARDLESS of the content of the premises. It

is always logically invalid.

As I was away, I thought of two more examples.

http://ca.answers.yahoo.com/activity?show=7O6SJABUFH7RDSTBOHTUIBIJWQ&t=ghttp://ca.answers.yahoo.com/activity?show=7O6SJABUFH7RDSTBOHTUIBIJWQ&t=g

8/12/2019 Why is Modus Tollens a Valid Form of Argument

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Modus Tollens:

1. If I am murdered, then I am dead.

2. I am not dead.

______

3. Therefore, I am not murdered.

The necessary logical validity seems especially prominent to me in that example.

Denying the antecedent:

1. If I am murdered, then I am dead.

2. I am not murdered.

______

3. Therefore, I am not dead.

Perfectly demonstrates why that line of reasoning is invalid. You don't need to have been murdered in

order to be dead. There are many ways to be dead other than being murdered.

Again, if there is ANY confusion or any other questions, do add additional details. ^

-------------------------------

Edit for your question about Modus Tollens being sound:

Not necessarily. We can make any number of arguments that take the form of Modus Tollens but that

have false premises, and thus, are unsound.

Such as:

1. If turtles exist, then I am a human.

2. I am not a human.

____________

3. Therefore, turtles do not exist.

Completely valid, but it is also an unsound argument. ^^