On a personal level I highly value critical and logical thinking in all interactions, and while I may not be a grand example of this, it is my over-arching goal. In this article I wanted to ponder and discuss the qualities of logic that are often missed when people raise opinions. Most often logical errors arise during the course of criticism, as this is often a pitfall of personal bias, but with careful consideration I think great strides can be made for myself and others.

Mathematical Thinking

There are many great resources on Mathematical Thinking, and they certainly don’t require a great depth of Mathematics. One of my favorite books on Mathematical Thinking and logic, is “Introduction to Mathematical Thinking” by Keith Devlin.

One component of mathematical thinking is in the consideration of statements as variables, and prone to substitution. What I mean by this, is if a statement is based on a premise, then the objects used in the statement can be replaced by parallel premises.

For example:

A statement like, "a Mac is the best computer because it's the easiest to use," has a logic error (regardless of personal truth).  

The statement on Mac computers is really saying this:

a [X] is the best [Y] because it's the easiest to use

Since ease of use is raised as importance, it is a constant (remains the same).  This person is saying, whatever is easiest to use is therefore the best.  Therefore if we find Objects that are easier to use, they should be considered best. 

Consider these variations of the same argument:

a [Jitterbug] is the best [Smartphone] because it's the easiest to use

Certainly a Jitterbug phone, made for seniors (with limited options, making it simple to use) is hardly the best smartphone on the market.

What if we take the inverse of a logic statement to test its truth?

Reusing the above example, "a Mac is the best computer because it's the easiest to use," consider testing truth.

The logic statement boils down to:
a [X] is the best [Y] because it's the easiest to use

Now let's consider the opposite, a computer system that is often considered challenging to use:

a [Linux System] is the worst [Computer] because it's the hardest to use

Since many home users would find non-gui Linux a challenge to use, does that mean it's the worst type of computer setup?  Yet the internet runs on Linux distributions, many servers having no GUI at all.  Obviously Linux is not the "worst".  

Bias is often exposed in variable substitution. As long as we can a) break a statement into logical components b) replace the object with similar objects that break the conclusion, we can identify the bias.

All Inclusive Logic Failures

I see this quite often with article headlines:

“This is why everyone buys…”

“We don’t like ….”

“Everyone knew this to be true…”

“All people agree with…”

The problem with this type of statement is the inference that EVERYONE thinks/feels the same way on a particular topic. As though EVERYONE wants a Windows 11 PC, or NO ONE likes a particular celebrity. All it takes is some simple reasoning:

If there is only 1 challenge to the all inclusive statement, the statement fails in proof. If we find one person who prefers Mac to Windows, the argument fails. If we someone who defends the celebrity, that argument fails.

Headlines like the one’s above are designed to either trigger a click, or demand compliance to the thought. It’s all about control, and control turning into ad revenue for the content creator.

My recommendation is that if you have the ability to individually censor/silence news headlines – silence the ones with demands like the ones above. You effectively cut off one more source of revenue and keep a clean mental space.

Strawman Arguments

Another common logic failure that comes up is when a person falsely attributes a belief to a person or group. A few years back a podcaster I listened to made the Strawman Argument, “Did you hear about the climate change protestor who said we’re at a tipping point we may need to become cannibals? I’m against cannibalism, so therefore I’m against these protestors.”

His argument was considerably flawed. He took one activist who made an outrageous statement, and attributed it to ALL climate change protestors (all inclusive failure compounded with a strawman argument). In other words, he’s saying that ALL climate change protestors believe in cannibalism as a viable lifestyle.

Often, this type of fallacy, is hidden and obfuscated. But if you sense some bias, look to see if there’s a false attribution.

Tl;DR

There are many more logic fallacies, more than I want to raise here. I wanted to point out a better way to ingest and consider positions raised by other (or by ourselves). Variable substitution, all-inclusive and strawman statements can point out our own biases, as well as the biases of others.