Illogical logic

Archimedes, Alexander the Great, Jesus Christ, Socrates and Akhenaten were all famous men of their time. Other than their fame they all share one very specific trait. They have all passed on. They died.
The first toothbrushes were made of twigs with frayed ends around 3000 B.C. . Toothpaste, on the other hand, first came into popular usage around the early ninth century. Perhaps their lives could have been saved if only they had used toothpaste in brushing their teeth.

Ridiculous you say? How is that? Julia Roberts brushes her teeth. So do Oprah, Alice Cooper and Busta Rhymes. They are all famous people and are all still alive. That proves that toothpaste saves lives doesn't it?

People that brush their teeth with toothpaste are alive. Dead people are not alive. Dead people do not brush their teeth with toothpaste. Therefore not brushing your teeth with toothpaste kills you.
Or how about this one. All men are intelligent and articulate. All women are not men. Therefore all women are not intelligent and articulate.

They are both logical fallacies. They start at one logical point and from there attempt to pigeonhole you into automatically accepting some other logical point as true. Each one leaves out crucial information that could automatically disprove the statements being made.For example, there are plenty of people that have brushed their teeth with toothpaste every day of their lives from childhood onward who have still ended up dying.

The second example is even worse because it states a falsehood in the first sentence. Not all men are both intelligent and articulate. Some are one. Some are the other. Some have neither trait. It falsely states that all members of category A share specific traits. Then it gets even worse by going on to say that since the members of category B are not members of category A, none of them have have the two specific traits that all members of category A share. The problem here is that category A has been defined and category B has simply been called not A. There is no frame of reference for what traits the members of category B do actually have. So no fair comparison can really be made between the two.

We as people tend to try and generalize groups of data for faster easier sorting and storage. But quite often when we do so we  remove some key details that are necessary to keep the information accurate. We want to categorize and compartmentalize everything. But it really doesn't work. To avoid this, whenever possible, do your best to remember things exactly as they are instead of boiling things down to a least common denominator and remembering that.
 
With very few exceptions, this being one of them, all generalizations are false. It is unfair to say that all black people act in a specific undesirable way. Just as it is unfair to say that all white people act in a specific desirable way. All Muslims follow their religion to the letter is just as false as all Christians fail to follow their religion properly. It is just as wrong to say all rich people are jerks as it is to say all poor people are nice.

Also, we often accept certain things as fact or assume them to be without testing especially when the data comes from a source that we instinctively trust, like a parent, close friend, co-worker or sibling. Then we take that untested data and make decisions and choices that lead us to other decisions and choices and suddenly we wonder why nothing seems to be working properly.

Example, at one point we had a roommate that was unhappy with his living conditions and was considering moving out. Another person in the house said they thought he was planning on leaving in October which was about two weeks away, at the time. Concerned about losing the income from the first roommate we immediately set about replacing him and within a couple of days we had found a replacement and were asking him how soon he would have his things moved out.

As it turns out he had not even decided for sure that he was really go to move out. And even if he had decided that he wanted to move out the earliest he would have been comfortable going was November.

For awhile there was a little bad blood on all sides as a result. Without really intending to, we kind of forced him to move out. The whole thing could have been resolved with a lot less mess if we had just gone to him in the first place when it was mentioned that someone had heard he was thinking of moving out. We could have talked to him and cleared things up very quickly instead of ending up with the mess we did.

Take everything with a grain of salt. Accept that what other people tell you is what they believe to be true. Search for evidence to both support and destroy their claims. Then decide what to believe.