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### Course: Wireless Philosophy > Unit 1

Lesson 2: Fallacies- Fallacies: Formal and Informal Fallacies
- Formal and Informal Fallacies
- Fallacies: Fallacy of Composition
- Fallacies: Fallacy of Division
- Division and Composition
- Fallacies: Introduction to Ad Hominem
- Fallacies: Ad Hominem
- Ad Hominem, Part 1
- Ad Hominem, Part 2
- Fallacies: Affirming the Consequent
- Fallacies: Denying the Antecedent
- Denying the Antecedent and Affirming the Consequent
- Fallacies: Post Hoc Ergo Propter Hoc
- Post Hoc Ergo Propter Hoc
- Fallacies: Appeal to the People
- Fallacies: Begging the Question
- Begging the Question
- Fallacies: Equivocation
- Fallacies: Straw Man Fallacy
- Fallacies: Slippery Slope
- Fallacies: Red Herring

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# Fallacies: Denying the Antecedent

In this video, Matthew C. Harris explains the fallacy of denying the antecedent, the formal fallacy that arises from inferring the inverse of a conditional statement. He also explains why graduate students might also be humans.

Speaker: Matthew C. Harris, Duke University. Created by Gaurav Vazirani.

Speaker: Matthew C. Harris, Duke University. Created by Gaurav Vazirani.

## Want to join the conversation?

- What are
**modus ponens**and**modus tollens**?(8 votes)- Expanding slightly on what was said at2:19:
*Modus ponens*is a**valid**argument which looks like this:

**P1**: If P is true, then Q is also true.**P2**: P is true.**C1**: Therefore, Q is also true.

Hopefully that one's simple enough to understand.*Modus tollens*or*denying the consequent*is a**valid**argument which looks like this:**P1**: If P is true, Q is also true.**P2**: Q is false.**C1**: Therefore, P is also false.

Since Q is always true if P is true, it follows that P cannot be true if Q is false. Therefore P must be false (as if P was true Q would be true).(8 votes)

- The following argument has the logical form of denying the antecedent, but is it deductively invalid?

P1: If either Mitt Romney is the president of the U.S. or Mitt Romney is the commander in chief of the U.S., then both Mitt Romney is the president of the U.S. and Mitt Romney is the commander in chief of the U.S.

P2: It is not the case that either Mitt Romney is the president of the U.S. or Mitt Romney is the commander in chief of the U.S.

C: It is not the case that both Mitt Romney is the president of the U.S. and Mitt Romney is the commander in chief of the U.S.(8 votes)- I don't quite agree with elm.parkinson's argument form:

P1: If (p or q), then (p and q).

( IC1: If p, then (p and q). [From P1] )

( IC2: If q, then (p and q). [From P1] )

( IC3: If p, then q. [From IC1] )

( IC4: If q, then p. [From IC2] )

( IC5: If p, then q and if q, then p. [From IC3 and IC4] )

( All of the above intermediate conclusions are unnecessary because P1 itself is unnecessary, but it explains how elm.parkinson interpreted P1. )

P2: Not (p or q)

C: Not (p and q) [From P2]

For all propositions p and q:

If (p and q), then (p or q).

This follows from the definition of the logical conjunction and disjunction operators.

All conditionals have a contrapositive as so:

Conditional: If p, then q.

Contrapositive: If (Not q), then (Not p).

The contrapositive is true if and only if the conditional is true and can always be replaced with the conditional.

Thus, we can take the contrapositive of this conditional to find that for all propositions p and q:

If [Not (p or q)], then [Not (p and q)].

Thus, your argument above is valid as it follows from this conditional.

Although this has the form of denying the antecedent, the fallacy is only present if we reason so. If we do reason that C is true from P1 and P2 by denying the antecedent, then we are making a logical fallacy and our argument would be fallacious, but that doesn't mean that the premises don't imply the conclusion. Reasoning that premises don't imply a conclusion because a certain reasoning that says so is fallacious is a fallacy itself:

http://en.wikipedia.org/wiki/Argument_from_fallacy

I hope this helps someone!(2 votes)

- I'm a bit confused. What's the difference between denying the antecedent and affirming the consequent?(3 votes)
- If
**John loves Mary**, then**John will want to marry Mary.***is the

The above statement is called a conditional.

*John loves Mary*antecedent***John will want to marry Mary**is the*consequent*.*Denying the antecedent*means denying**John loves Mary**. In other words**John does not love Mary**.*Affirming the consequent*means asserting**John will want to marry Mary**.

In symbolic form, let**John loves Mary**= J and**John will want to marry Mary**= M

So, the above conditional now becomes J --> M which is read as "If J, then M"

J is the sufficient condition. That is, if J is true, then M is also true.

So we have the valid argument below:

J --> M

J

Therefore, M

Denying the antecedent fallacy occurs if we reason in the following way:

Note that ~J means NOT J and ~M means NOT M

J --> M

~J

Therefore, ~M

John may not love Mary but he may still want to marry her, for money, etc.

Affirming the consequent fallacy occurs if you reason in the following way:

J --> M

M

Therefore, J

John may want to marry Mary but he may not love her.(3 votes)

- At2:15are both Modus Ponens and Modus Tollens valid or invalid? I think they're both valid, just not 100% sure.(1 vote)
- They are both valid.

For Modus Ponens:`P1) If A, then B`

P2) A

C) B

This is a simple conditional. It should be obvious that A causes B because it is in the first premise, so if A is true, then B has to be true also. Here's an example:`P1) All cats are animals.`

P2) Tom is a cat

C) Tom is an animal

For Modus Tollens:`P1) If A, then B`

P2) not B

C) not A

This is the inverse of Modus Ponens. Since A causes B, if B is not true, then A cannot be either. Here's an example:`P1) All cats are animals.`

P2) Mark is not an animal.

C) Mark is not a cat.(3 votes)

- P1: If P, Then Q

P2: Not Q

C: Not P

This form of argument is always valid? Right?(2 votes) - help here:

If life involve quantity,its physical.

life does not involve quantity.

ergo,they are not ultimate.(1 vote) - This is still confusing. I don't find Khan helpful at all. You are explaining it the way my professor does and I need it to be changed into something like "if you go shopping and do thus and such." ....(1 vote)
- Hello,

can a modus Tollens have a false conclusion? If yes is it still a valid argument or not?

Thank you(1 vote) - What if the argument is stated like this?

P1: If I have a job next year, it's gonna be a ski instructor

P2: I will not have a job next year.

C1: Therefore I'm not gonna be a ski instructor.(0 votes)

## Video transcript

(intro music) Hello, I'm Matthew Harris. I'm a philosophy graduate[br]student at Duke University, and today I'll be discussing the formal fallacy of[br]denying the antecedent. Denying the antecedent[br]is a formal fallacy, meaning that the argument has a flaw contained in its logical form. This is important because whenever this pattern of argument occurs, regardless of topic or content, the argument will always be invalid. So how can we tell when the fallacy of denying[br]the antecedent occurs? Well, it happens when we mistake the direction of a conditional, or confuse it for a biconditional. And it starts with the denial of the conditional statement's antecedent, then concludes the[br]denial of its consequent. The logical form of arguments that commit the fallacy of denying the[br]antecedent look like this: "If P, then Q. "Not P. Therefore, not Q." Now, let's take a look[br]at this conditional: "If you are a ski instructor,[br]then you have a job." The antecedent statement[br]of this conditional is "you are a ski instructor," and the consequent is "you have a job." But suppose someone made an argument with this conditional[br]as its first premise. Premise (1): If you are a ski[br]instructor, then you have a job. Premise (2): But you are[br]not a ski instructor. Conclusion: Therefore,[br]you do not have a job. Here, the second premise is[br]a denial of the antecedent. This premise does not tell us that only ski instructors have jobs. So, even if the conditional[br]statement is true (that ski instructors have jobs), it cannot be inferred that if[br]you are not a ski instructor, then you are unemployed. A conditional could validly be used to argue for the[br]truth of this consequent by affirming the antecedent. We find this in the arguments of a form called "modus ponens." It is also valid to argue from[br]the denial of a consequent to a denial of the antecedent. But it is never, ever valid[br]to deny the antecedent to reject its consequent. Let's try another example: "If you are a property[br]owner, then you are a human. "But you are not a property owner. "Therefore, you are not a human." The antecedent, that you are a property owner, is being denied. Even though you need to be[br]a human to own property, this has no bearing on humans who do not own property at all. For example, graduate students. Let's consider one last example: "If anyone is watching this video, "then they are on the internet. "Some people are not watching this video. "Therefore, they are not on the internet." Again, denying the antecedent by pointing out that not everyone is currently watching this video does not validly demonstrate[br]the denial of the consequent, that they're not on the internet at all. These have been a few cases[br]that I hope will come in handy in avoiding this formal[br]fallacy in your own arguments. For more related to the fallacy[br]of denying the antecedent, I recommend that you take a[br]look at the other related videos on informal and formal fallacies, the fallacy of affirming the[br]consequent, and conditionals. Subtitles by the Amara.org community