# What's wrong with this?

I had a nice argument with someone who said roughly the following:

- Fact: All succesful companies pay high salaries.
- Fact: My company is not succesful.
- Therefore: the company should increase salaries.

To me this is obvious nonsense. However, I found it difficult to logically point out the error in this. What's wrong with this (yes, it's probably simple but I just don't see it... )

MathematicalPhysicist
Gold Member
it's simple (or so i think) you deduct from a->b the opposite that if b therefore a.

in this case, paying high salaries wont make the company succesful.

This basically uses the same idea as the "Affirmation of the consequent" argument flaw, i.e. that if A implies B, the erroneous assumption is if B is true it would imply A.

i.e. If a persons head is not attached to his body he is/will soon be dead,
but if George is dead doesn't imply that his head isn't attached.

Look at the pre great depression era, they'd pay little boys next to nothing to work in coal mines and the companys were doing pretty well.

This basically uses the same idea as the "Affirmation of the consequent" argument flaw, i.e. that if A implies B, the erroneous assumption is if B is true it would imply A.

i.e. If a persons head is not attached to his body he is/will soon be dead,
but if George is dead doesn't imply that his head isn't attached.
Yes! That makes perfect sense to me. Thank you for explaining it so clearly.

@wasteofo2: LOL!

MathematicalPhysicist
Gold Member
This basically uses the same idea as the "Affirmation of the consequent" argument flaw, i.e. that if A implies B, the erroneous assumption is if B is true it would imply A.

i.e. If a persons head is not attached to his body he is/will soon be dead,
but if George is dead doesn't imply that his head isn't attached.
how is what you said any different than what i said?

Hurkyl
Staff Emeritus
Gold Member
It comes with a vivid picture.

and also with cool terminology ("Affirmation of the consequent").

Originally posted by loop quantum gravity
how is what you said any different than what i said?

Just a different wording to get the same idea across.

suyver

- Fact: All succesful companies pay high salaries.
- Fact: My company is not succesful.
- Therefore: the company should increase salaries.

As you constructed the argument it would be invalid even if the minor premise were:'My company is successful' [assuming 'must' instead of 'should' and that unsuccessful companies must pay low wages].From the first premise (the major premise) and the new minor premise I wrote above does not follow that 'the company must increase salaries' but only that 'the company must pay high salaries'!Indeed one of the golden rules of the logic of syllogisms is to keep the subject (here the company,my company),the predicate (pay high salaries) and the middle term (successful companies) the same over the whole argument.

But your argument,as you wrote it,does not seem to be a deductive or an inductive argument since an unsuccessful firm can still pay a high salary irrespective of the premises...But by making explicit the (probably implied) extra premise that 'rationally managed unsuccessful firms do not pay high salaries' we obtain a valid inductive argument with the conclusion 'the company should not pay high salaries' (assuming also-not in the initial premises-that the managers of your company manage it rationally usually).

Assuming that you meant 'the company must pay high salaries' and that unsuccessful companies must pay low salaries it is simple to see that the [deductive] argument 'the firm must pay a high salary' is invalid using the Venn diagrams.Another way is to apply the reductio ad absurdum (Aristotle's method to prove the validity or invalidity of syllogistic consequnces) by considering that 'the company must pay high salaries' is TRUE.In this case by combining it with the major premise 'all succesful companies pay high salaries' results the new conclusion that your company is successful which,of course,is contradictory with the other premise (considered TRUE) that your company is not successful.Therefore 'the company must pay high salaries' is FALSE and in the virtue of excluded middle principle 'the company must pay low salaries' is TRUE.

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similar:
all four-legged cats are four-legged animals.

if x is a cat with four legs, then x is an animal with four legs.

however, not all four-legged animals are cats.

given a conditional if A then B, A->B, the converse is B->A. the converse is not equivalent to A->B, as others have written.

what is equivalent is the contrapositve:
notB->notA.
for example: if x is not an animal with four legs then x is not a cat with four legs is equivalent to the original statement.

(equivalent means equally true or equally false)

Kerrie
Staff Emeritus
Gold Member
i can tell you what's wrong with this:

you have to define "successful"...that terms is very subjective...

Thanks for all the great answers, guys!

- Fact: All succesful companies pay high salaries.
- Fact: My company is not succesful.
- Therefore: the company should increase salaries.

The problem is that there is no causal relation defined in the first bit, about successful companies and high salaries. The person did not bother to include the necessary relation, such as "The personnel in successful companies recieve high wages because the company is successful and can afford to give high wages."

whoops

High salaries are the result, not the cause, of a company's success.

A successful result cannot be produced without satisfying the (unstated)conditions which cause success.

I'm editing this to say ...I see a major flaw. It could be that high salaries do lead to a company's success. Ex: Let's say you have a billionare starting up a company and can afford to pay high salaries from the get go. The high pay may be a perfect incentive for ever-increasing job performance and high productivity. Which may lead to great company success and consequent high/er salaries.

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High salaries can contribute very significantly to the success of a company. However they can also bankrupt it. The context is everything.

- Fact: All succesful companies pay high salaries.
- Fact: My company is not succesful.
- Therefore: the company should increase salaries.

There's nothing wrong with that argument because it doesn't necessarily affirm the consequent.
S > H

~S > ~H

of course it's possible that

~S > H

but isn't possible that

S & ~H

So it's perfectly reasonable that the company should increase salaries (presumeably to a high salary assuming the goal is to be successful and they don't already have high salaries). affirming the consequent would be to say that the company will be successful if high salary is paid, or H > S, but that's not what the argument suggests. There's plenty of room in the argument for H to be a limiting factor without needing to be the antecedent.
In other words you can read the sentence, "If we are to be successful then we will need high salaries" without needing to read it, "If we have high salaries then we will be successful."

Evo
Mentor
suyver said:
I had a nice argument with someone who said roughly the following:

- Fact: All succesful companies pay high salaries.
- Fact: My company is not succesful.
- Therefore: the company should increase salaries.

To me this is obvious nonsense. However, I found it difficult to logically point out the error in this. What's wrong with this (yes, it's probably simple but I just don't see it... )
Here is what is wrong with this, if we go just by what is written and don't start throwing in "what if's".

- Fact: All succesful companies pay high salaries. - They pay high salaries to highly qualified proven performers that deserve high pay because they consistently bring in more money for the company. The company makes much more than they are paying in salaries

- Fact: My company is not succesful.
- Therefore: the company should increase salaries. - Wrong. If the current employees are not being profitable, it is likely they aren't as qualified and don't have the skills necessary to make the company successful. Paying incompetant unskilled labor more money will not change the fact that the workers aren't highly skilled or productive and will not result in more money being brought into the company. The company would probably end up going out of business because they will be paying more and receiving nothing more in return.

The better logical answer would be to spend the money to hire "new, qualified employees" and get rid of the deadbeats, or spend money to train the current employees to make them more profitable, of course that could just be a waste of time & money if they aren't capable of learning new skills.