The Fallacy of Affirming the Consequent, With a Common Example

Torin

Member
The following argument form is called modus ponens:

1. If p, then q.
2. p.
3. Therefore, q.

Modus ponens is deductively valid - given that both premises are true, the conclusion will always be true.

Now, consider the following argument form:

1. If p, then q.
2. q.
3. Therefore, p.

This argument form is called affirming the consequent. It is deductively invalid. Both premises can be true while the conclusion is simultaneously false. This often happens as the result of a failed attempt at modus ponens.

Here is a concrete example of affirming the consequent:

1. If a person is a Communist, then they are an atheist.
2. Bob is an atheist.
3. Therefore, Bob is a Communist.

This argument is deductively invalid, since it is possible that Bob is not a Communist even if both premises are true.

The preceding argument attempts to reason in modus ponens, as follows:

1. If a person is an atheist, then they are a Communist.
2. Bob is an atheist.
3. Therefore, Bob is a Communist.

This argument is deductively valid. However, premise 1 is false. Many atheists are not Communists. To know whether any given atheist is a Communist, particularly in the West where there are relatively few Communists, more information is needed.

The application of these lessons to CARM, and conservative Christian apologetics in general, is left as an exercise to the reader.
 

Authentic Nouveau

Well-known member
The following argument form is called modus ponens:

1. If p, then q.
2. p.
3. Therefore, q.

Modus ponens is deductively valid - given that both premises are true, the conclusion will always be true.

Now, consider the following argument form:

1. If p, then q.
2. q.
3. Therefore, p.

This argument form is called affirming the consequent. It is deductively invalid. Both premises can be true while the conclusion is simultaneously false. This often happens as the result of a failed attempt at modus ponens.

Here is a concrete example of affirming the consequent:

1. If a person is a Communist, then they are an atheist.
2. Bob is an atheist.
3. Therefore, Bob is a Communist.

This argument is deductively invalid, since it is possible that Bob is not a Communist even if both premises are true.

The preceding argument attempts to reason in modus ponens, as follows:

1. If a person is an atheist, then they are a Communist.
2. Bob is an atheist.
3. Therefore, Bob is a Communist.

This argument is deductively valid. However, premise 1 is false. Many atheists are not Communists. To know whether any given atheist is a Communist, particularly in the West where there are relatively few Communists, more information is needed.

The application of these lessons to CARM, and conservative Christian apologetics in general, is left as an exercise to the reader.
Why do you make stuff up from the fact that The Red Communist Party required it's members to be atheist.

Your uneducated trick didn't read that the statement does not say atheeists are all communists.

So you pulled a premise out of the air. Why?

Question

Why are atheists so famously known for lying killing and false accusations?
 

Nouveau

Active member
I would like to add that there is one form of inductively valid inference that is very similar to affirming the consequent, and which is often confused with it. This is abductive inference, aka inference to the best explanation (IBE). To use your same example, this takes the form:

P1. Being a communist would explain why one is an atheist (because all communists are atheists)
P2. Bob is an atheist
C. Therefore, (in the absence of any better explanation we can tentatively and defeasibly adopt the hypothesis that) Bob is a communist

I think most cases of affirming the consequent are more charitably diagnosed as failed abductive explanatory hypotheses than as failures of deductive logic, i.e. one could easily conclude that atheists are communists if they knew all communists to be atheists, and yet were wholly ignorant of the low prevalence of communism and high prevalence of atheism in the west, and of the fact that atheism correlates better with education level than it does with political ideology. So the abductive inference fails on account of it not really being the best explanation in light of readily available facts.
 

Gus Bovona

Member
I think most cases of affirming the consequent are more charitably diagnosed as failed abductive explanatory hypotheses than as failures of deductive logic. . . .

More charitably, for sure, but not more likely, at least what I’ve seen around here.

ETA: one indication is the lack of any qualifications that are essential to abduction.
 

Harry Leggs

Member
To know whether any given atheist is a Communist, particularly in the West where there are relatively few Communists, more information is needed.
This is cherry-picking (sins of omission) since communism is inherently atheistic and hostile to religion both in its origin and where ever communists rule. They may collaborate superficially with the Pope, for example, but that is for their own reasons. They burn down churches, lock up believers or murder, seize assets, etc. Theism and communism are incompatible via the communists. Communists may keep churches around but for their own purposes and the churches act as agents of the communists, outing believers to the party.

Communism and Religion Can’t Coexist - WSJ
The application of these lessons to CARM, and conservative Christian apologetics in general, is left as an exercise to the reader.
What? There are plenty of logic fallacies on the opposite side including appeals to outrage and a host of others. If it is viewed then confront the poster, not that it would do any good. This is overall too vague and really, (there is no context to your selectively applied indictment) nobody here comes for unsolicited lessons in logic from anonymous CARM posters.
 

Nouveau

Active member
This is cherry-picking (sins of omission) since communism is inherently atheistic and hostile to religion both in its origin and where ever communists rule.
It's not cherry-picking at all. Torin has accurately explained a common flaw in reasoning, and one you seem to be repeating yourself. Communism may well be inherently atheistic, but atheism is not inherently communist, so that one is an atheist does not warrant concluding that he is also a communist.

What? There are plenty of logic fallacies on the opposite side including appeals to outrage and a host of others. If it is viewed then confront the poster, not that it would do any good. This is overall too vague and really, (there is no context to your selectively applied indictment) nobody here comes for unsolicited lessons in logic from anonymous CARM posters.
There's nothing vague whatsoever about the OP, and Torin says nothing at all to indicate that all the fallacies are committed by one side. Rather, he very specifically explains the one specific logical error named. Perhaps you would benefit from reading the OP again, solicited or otherwise.
 

Harry Leggs

Member
It's not cherry-picking at all.
It is. Communists are atheists. If they are Theists they are generally drummed out.
Communism may well be inherently atheistic,
That means if communist then atheist.
but atheism is not inherently communist, so that one is an atheist does not warrant concluding that he is also a communist.
Straw man. Not in dispute.
There's nothing vague whatsoever about the OP,
Well who is he talking about? What is the name on the indictment?
and Torin says nothing at all to indicate that all the fallacies are committed by one side.
Then why does Torin restrict his post to conservative Christians and ignore everything else and how does he know they are conservative? They may be liberal Christians or simply nonChristian Theists.
Rather, he very specifically explains the one specific logical error named.
To who?
Perhaps you would benefit from reading the OP again, solicited or otherwise.

Right unsolicited and i read it thru the first time and i do not need, nor asked for your condescending and unsolicited advice.
 
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Nouveau

Active member
It is. Communists are atheists. If they are Theists they are generally drummed out.

That means if communist then atheist.

Straw man. Not in dispute.
That communists are atheists is irrelevant when trying to determine whether or not an atheist is a communist, which is what the OP is talking about. The entire point is that you cannot infer communism from atheism. That is not cherry-picking or strawmanning, or any other term you want to misuse.

Well who is he talking about? What is the name on the indictment?

Then why does Torin restrict his post to conservative Christians and ignore everything else and how does he know they are conservative? They may be liberal Christians or simply nonChristian Theists.
He is talking about anyone who commits the fallacy. There is no name on the indictment, as Torin explicitly leaves it up to the reader.
 

Harry Leggs

Member
That communists are atheists is irrelevant when trying to determine whether or not an atheist is a communist,

Who is saying all atheists are communists? Nobody. It is a phantom which is what i wrote and yours is hearsay. What are you, Mr Ed,.. Torin's talking horse?
which is what the OP is talking about.
It is a rudimentary lesson in logic fallacy which is available on google.
The entire point is that you cannot infer communism from atheism.
Why not? Certainly cannot infer Theism from communism. But we can infer atheism from communism since all communists are atheists. At least the ones who run things. Only women can get pregnamt does not mean all women are pregnant. Only atheists can be communists does not mean all atheists are communists.
That is not cherry-picking or strawmanning, or any other term you want to misuse.
Then we have a disagreement. Your assertion/indictment is not enough. Just because we have a disagreement does not mean i am misusing anything.
He is talking about anyone who commits the fallacy.
Then why does he specifically mention conservative Christians?
There is no name on the indictment, as Torin explicitly leaves it up to the reader.
Well he does mention conservative Christians and ignoring nonconsevatives and Non-Christians so that is both cherry-picking and vague. Again, nobody here is requsting rudiment lessons in logic from anonymous CARM posters anymore than we are asking for visits from JWs knocking on our doors. If there is a problem with a logic fallacy then bring it up to the poster who is alleged to be making the fallacy.,
 

Nouveau

Active member
Who is saying all atheists are communists? Nobody.
Anyone committing the specific example of the fallacy given in the OP.

Because that is to commit the fallacy given in the OP.

Then why does he specifically mention conservative Christians?
Ask him. He still explicitly leaves it up to the reader to determine applicability.

Again, nobody here is requsting rudiment lessons in logic from anonymous CARM posters anymore than we are asking for visits from JWs knocking on our doors.
If you don't think you need the lesson then you can ignore it and move on.
 
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