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For example, "You are rich because you are blessed (God blessed you with riches). If you are not rich then you must not be blessed (God chose not to bless you oh ye of little faith)."

Second example, "By the super secret law of attraction you can manifest riches in your life. If you don't have riches it is because you did not attract it into your life you stupid idiot. It's so easy. Do you hate money?"

Does this make sense?

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Problem

Your two examples have different logical structures. So I will treat them separately.

First example

Negating Antecedent and Consequent (also known as improper transposition)

The logical structure simply is:

A → B, therefore ¬A → ¬B

The fallacy lies in not switching antecedent and consequent. Therefore, it is the inverse rather than the contrapositive. It is only the contrapositive that is logically equivalent to the original proposition and therefore already implied in it. You can read more helpful links and thoughts explaining these terms and their differences in this related answer.

Second example and header

The header and the second example have another logical form. They correctly state the implication (NOT syllogism!)

A → B, therefore ¬B → ¬A

But the validity (or truth value) of this depends on the truth value of 'A → B'. Therefore, arguing along these lines without further support is begging the question or petitio principii, as another answer correctly stated. It is a type of circular reasoning.

Explanation

Your second example basically argues that by attracting money, you become rich, and as you are not rich, you did not attract money. Here, you presuppose that it is only by attracting money you become rich, and from that, you gather the implication, the contrapositive. As both sides (before and after "therefore") are logically equivalent, it can be transformed into

A → B, therefore A → B

Or, if you like: X → X

It is like saying "There IS God, therefore there is God.", while thumping on the table. This is begging the question.

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I'll look at the second example: "By the super secret law of attraction you can manifest riches in your life. If you don't have riches it is because you did not attract it into your life you stupid idiot. It's so easy. Do you hate money?"

The first part is a completely unproven conjecture. The conjecture is: "There is a super secret law of attraction which could be used by anybody to manifest riches in their lives". It's just that - a conjecture. Why would anybody believe that it is true?

The middle part is a conclusion: "If you don't have riches it is because you did not attract it into your life." Actually, that's not a fallacy. If part 1 were true, which it isn't, then the conclusion would be correct. Since part 1 is not true, this conclusion is worthless.

Then we have an insult, "you stupid idiot". Seems like a rather pathetic attempt to preemptively insult anyone who is going to contradict the conclusion. "It's so easy". Come on. If it was possible to attract riches into your life, and if it was easy, everyone would do it. So we have good evidence that it is not easy. "Do you hate money?" That's another insult, intented to enable an ad hominem attack to anyone daring to contradict the speaker. The speaker tries to display the person as an irrational human being.

So there is no logical fallacy here really. But there is plenty wrong: Making bold unproven assumptions, and telling us to believe them without any reason. Insulting the careful listener to weaken their arguments.

  • -1 Because you did not answer the question: 1.) The question was whether there occurs a fallacy or not. Assuming a super secret law is logically correct; hence the discussion whether one should believe this is superfluous and leads you (and the ones that upvoted you erroneously) to miss the forest for the trees: You say "there is no logical fallacy here really", not seeing the 'poisoning of the well' or the 'argumentum ad hominem' though you speak about them phenomenologically -- and, strangely, they are right under your nose. – user26880 Jul 27 '17 at 21:33
  • You don't address the first example, which does not fit into this analysis. – jobermark Jul 28 '17 at 2:56
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There is no fallacy here. The primary pitfall here is not one of logic, but one of semantics.

In abstract terms, your title describes a correct deduction. If A only occurs because B always causes it, then when A does not occur, B must not have happened. In an indicative mood, if we are being perfectly careful, this is what we mean, because we have "open quantification". Unfortunately, English does not make that a rule, because the subjunctive markers in English have evolved into a useless mess, and can therefore be omitted at any time.

You can make the statement without implying the always. If B only sometimes causes A, then obviously in those cases when it fails to do this causing, you have B and not A. But in that case, you should say B may cause it, not that it does cause it.

You can also make the statement without implying the only. But in that case you should say A may be caused by B, not that it is caused by B. It might occur for other reasons. But that omission still allows you to deduce that if you don't have A, B wasn't there.

So this English statement can have three different meanings with very different logical implications. You can only tell if you know your speaker is an absolute pedant, or by context. And deduction in your title is only true for two of them.

This ambiguity is one way of seeing what is wrong with your first example.

For example, "You are rich because you are blessed (God blessed you with riches). If you are not rich then you must not be blessed (God chose not to bless you oh ye of little faith)."

'You are rich because you are blessed' only means that riches is one possible effect of being blessed, not that they are always an effect. Any blessing may cause riches, it is not true that every blessing does cause riches. It can happen that one person is rich because he was blessed, but that another person would be blessed in a different way.

Second example, "By the super secret law of attraction you can manifest riches in your life. If you don't have riches it is because you did not attract it into your life you stupid idiot. It's so easy. Do you hate money?"

This does not have either problem, the the modal is there to clarify. So the claim really is that doing B will always cause A for you, and the deduction is valid. But a valid deduction from a false premise is still no good. Not really a problem of logic or semantics, just a problem of having the wrong facts.

  • -1// jobermark 1.) I do not see the sense of your only and always. This is really strange, but this is your style... what you write is (for me) often nearly illegible, and I think it is because you do not really focus on the questions. — I am sure that the OP just means an ordinary implication B --> A. // 2.) The problem in the first example does not come from equivocation, since in the “law” it would be possible to write “one” instead of “you”. With that the second third of your answer also begins to disappear in a flash. … – user26880 Jul 28 '17 at 21:45
  • I don't care. I do not need your criticism, because a large number of people do not share your opinion of my posts. They understand them. It may be possible that we two can only write for different audiences, but the people who do understand what I have written, often find it to be true. – jobermark Jul 28 '17 at 21:47
  • … Instead the ideological/religious mania slumbering within these religious/esoteric laws are the problem, not equivocation. // 3.) Now to the liquidation of the last third: For the second example you say: wrong facts. Which wrong facts? Have ideologies ever consisted of facts? It has been presumed as “law”, with the tacit assumption that it must and cannot be proved because it is a transcendent law. This is the game of theology/religion/sectarians. They work with these laws; how can you say they are “wrong”? – user26880 Jul 28 '17 at 21:48
  • … If we discuss it as law, as indicated in the title, then we must change in the modus that this is the valid law. BTW example 1 and 2 are exactly identical cases. Just considering that Job had to wait long until Jehovah had tried him sufficiently, helps to see that these (transcendental) laws thereby rightly expounded make sense in the theological/religious/sectarian world view, without using fallacies (arg. ad hominem like “idiot” etc.), as occurring in the examples. Patience is the clue! Hence, nothing is wrong with these laws as you claim. – user26880 Jul 28 '17 at 21:49
  • the answer has also changed since you read it. And you didn't bother to check. So what you are saying in 2 is corrected. This kind of consistent inattention is just as bothersome to me as my style is to you, but I do not pick it out. I only bring it up now because you feel entitle to declare my way of doing things wrong, and you have your own faults. – jobermark Jul 28 '17 at 21:49
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Lawrence suggested in an early version of his answer that your examples involve the logical fallacy of "affirming the consequent". However, that's incorrect.

"Affirming the consequent" would be a fallacy like this :

  1. If you're born into money, you're rich
  2. You're rich
  3. Therefore, you must be born into money

The reason that's a logical fallacy, is because there can be many reasons for being rich :

  • You were born into money
  • You invested in a company that became very profitable overnight
  • You won the lottery
  • You had just the right connections to team up with for your business
  • You were lucky to start the right business at the right time
  • ...

What happens here, is that you assume a cause because that cause happens to lead to a certain consequence. However, by doing so, you ignore all other possible causes!

That argument is not equivalent to your argument; however. Your argument kinda goes like this :

  1. If you're born into money, you're rich
  2. You're not rich
  3. Therefore, you must not be born into money

This would actually be a correct assumption of being born into money automatically results to being rich. However, it doesn't. You can be born into money and not being rich.

Suppose that you are not rich. Does that mean that you were not born into money? Well, no. Maybe you were born into money, but you lost it all with bad investments or gambling.

Or does that mean that you don't have the right connections? Well, no. Maybe you have the right connections, but you prefer to be an employee rather than starting your own business.

etc. etc.

So if B is caused by A, the lack of B does not imply a lack of A per se, because there might actually be a C that prevents A from leading to B... or a C + D + E...

Real life is far, far, far more complex than every single event being directly caused by an individual previous event or prevented by the lack of an individual previous event. Real life is multi-dimensional, and everything that happens is literally the consequence of an intricate convergence trillions upon trillions of other events that happened before it and that are all entangled and entwined with each other!

I don't think the issue here is a logical fallacy, but merely an oversimplification on how causality works!

  • The problem in the first case is not about multiple reasons for being rich, it is about ways other than being rich to have been blessed. If being rich is the only way to be blessed, even if there are other ways of being rich, not being rich means you were not blessed. – jobermark Jul 28 '17 at 2:01
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    @Lawrence : I don't think "begging the question" applies either. Anyway, I modified my answer. – John Slegers Jul 28 '17 at 8:30
  • @jobermark : Are there other ways to have been blessed? Are you sure? What is a "blessing" anyway? It seems to me to be something religious people made up a long time ago as a religious equivalent of "luck", but it kinda has no real meaning to me... which is why I avoided to use that particular example ;-) – John Slegers Jul 28 '17 at 8:55
  • The nonsesical nature of the premises do not affect the logic involved. What you are saying here does not apply to the stated case. It applies to the opposite direction of implication. If you do not intend to read what is written before objecting, don't bother responding. – jobermark Jul 28 '17 at 20:59
  • @jobermark : The logic applied, is "if (1) A -> B and (2) !B then (3) !A". I gave a real life use case of that argument as close as possible to the imaginary use case in the original question (I'm sorry, but the concept of "being blessed" is just something primitive people made up) and tried to explain what' the problem with that real life use case. The same logic I applied to that real life use case can be applied to the imaginary one : in both cases, the problem is an oversimplification of how causality works since the assumption that A always implies B is wrong! – John Slegers Jul 29 '17 at 11:54
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The title of the question is not a fallacy, but the two examples are fallacious versions of argumentum ad hominem or of poisoning the well.

If these laws (blessing by God as condition // the super secret law) are premised, the conclusion is correct according to modus tollens.

However, both examples mentioned by the OP, additionally to modus tollens, concern sectarian, denatured bookkeeping laws or ideologies. Ideologies intend to colonize men, trying to morally or intellectually (--> part 1, § 3) manipulate them by ‘poisoning the well’ or by fallacious variants of ‘argumentum ad hominem’. This is the reason why the overall argumentations in the two examples become fallacies and confusing.

The occurring fallacious variants of argumentum ad hominem are the following:

  • Little faith leads to not being blessed (--> fallacious argumentum ad hominem, insinuating “little faith” as personal character defect).

  • If one does (for any reason) not (want to?) apply (or believe in) the super secret law, one is an “idiot” (--> fallacious argumentum ad hominem, insinuating a mental defect).

In both cases the well is poisoned, too, because the position of these persons has been shocked in advance.

0

It's called begging the question.

To beg a question means to assume the conclusion of an argument—a type of circular reasoning. This is an informal fallacy, in which an arguer includes the conclusion to be proven within a premise of the argument, often in an indirect way such that its presence within the premise is hidden or at least not easily apparent. - wikipedia

It's not always the case that the natural-language pattern B causes A translates fully to the logic statement B -> A. But if we accept the mapping for sake of discussion, then the deductive step itself is simply taking the contrapositive and therefore sound: B -> A, therefore !A -> !B.

The problem with the two natural-language examples in your question is that in each case, "A occurs because B causes it" hasn't been established. It is simply assumed, and a conclusion is derived from that assumption.

Let X = "B causes A" and Y = "!A -> !B".

Then the argument is "X, therefore Y". But since X and Y are logically equivalent, if someone doesn't already accept Y then it makes for a weak argument to prove Y by simply assuming X. In your examples, if the statements of causation aren't already accepted as axiomatically true, then they don't help establish the respective deductions.

  • -1, The OP's question is a (though paradox) example of modus tollens (= contraposition), which is logically sound as you rightly say. Hence it cannot be "affirming the consequent" as you claim. – user26880 Jul 27 '17 at 18:58
  • @Zeus I've changed my answer to match the question. – Lawrence Jul 27 '17 at 23:38
  • @Zeus, it is only logically sound if it is appropriately strengthened by the assumption that open quantification is fully universal. But this is optional in English. "Diabetes happens because insulin resistance causes it" is true as an ordinary English statement, but it can mean three different things -- that insulin resistance is the only cause, that diabetes is always its effect, or both. Only the second one is actually true. – jobermark Jul 28 '17 at 20:55
  • @jobermark This all is not so important. I think that you focus too much on detail questions and in consequence lose the overall context, which is much more important than tiny details and special cases. This is the antagonism synthetic/analytic. I had just finished a long comment to “liquidate” your answer when I received your above comment. So, please read the new comment below your answer that I will post in a few minutes. – user26880 Jul 28 '17 at 21:39
  • @Zeus It is not your place to determine where I should focus. Facts are facts whether they are picayune or grand. There is no need to diagnose me. – jobermark Jul 28 '17 at 21:43

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