Why Prove a Theorem Twice?

I have written before on the problem and solution of the problem of “Pythagorean Triples”. The problem, based on the Pythagorean theorem for right triangles, asks for all possible solutions to this equation which have all of whole numbers. Not just any right triangle works – for instance if then , which is definitely notContinue reading “Why Prove a Theorem Twice?”

Critical Thinking Toolkit: Straw Man Fallacy

Imagine the following scenario. A man walks up to an 80 year old with walking on his cane in the street, knocks him out with a single punch, then claims to be the best boxer who has ever lived. Sound silly? It should. This is an embodiment of what is known as the straw manContinue reading “Critical Thinking Toolkit: Straw Man Fallacy”

Database: Critical Thinking Toolkit

Up to this point, my database posts have been about compiling data from external sources. This database post is more organizational in nature. My goal here is to systematize the posts I’ve written in my series “Critical Thinking Toolkit”. The purpose of the series was to provide summary approaches to various areas of critical thinkingContinue reading “Database: Critical Thinking Toolkit”

Critical Thinking Toolkit: Necessity and Contingency

In moments of deeper thought, have you ever noticed that there seem to be certain features of the world that are quite arbitrary or random, while other things seem like there isn’t really any other way things could be? Have you ever wondered at why things are the way they are, instead of some otherContinue reading “Critical Thinking Toolkit: Necessity and Contingency”

Critical Thinking Toolkit: The Correlation-Causation Fallacy

Here, I’d like to discuss two interconnected tendencies we human beings have. We like looking for patterns, and we like explaining things. These are both incredibly important features of the way we think as humans. But they are not identical. It is easy to get them confused, and we often do get them confused. ThisContinue reading “Critical Thinking Toolkit: The Correlation-Causation Fallacy”

Critical Thinking Toolkit: Inference to the Best Explanation

I’ve talked about deductive reasoning and inductive reasoning before. Both of these are important mechanisms we use for arriving at conclusions. The first makes use of the rules of logic – which we can essentially view as limiting ourselves to the definitions of words like true and false and not allowing ourselves any other resources.Continue reading “Critical Thinking Toolkit: Inference to the Best Explanation”

Critical Thinking Toolkit: The Ad Hominem Fallacy

This one really should go without saying… and yet we need to say it anyways. So often, public discourse gets bogged down in personal insults of one variety or another. Whether attacks on a person’s morality, integrity, honesty, educational background, or any other aspect of life, our culture – especially the so-called “cancel culture” –Continue reading “Critical Thinking Toolkit: The Ad Hominem Fallacy”

Critical Thinking Toolkit: Clarifying Definitions

This is possibly the most important post I’ve written in my “Critical Thinking Toolkit” series so far. Ensuring we are clear on our definitions is so, so important. Every conversation we can ever have relies on definitions of certain important words, and so this tool always matters. Furthermore, when I look around in the worldContinue reading “Critical Thinking Toolkit: Clarifying Definitions”

Critical Thinking Toolkit: The Fallacy of Arguing from Ignorance

When debating important topics, whether with your friends, online with strangers, or in a public debate with spectators, there is always a high emphasis placed on proving your case. People ask why you believe what you do, ask you to show your evidence, ask you to give them your arguments. There is nothing wrong withContinue reading “Critical Thinking Toolkit: The Fallacy of Arguing from Ignorance”

Critical Thinking Toolkit: False Dilemma

Choices are important. Every day, we make lots of decisions about what to do and what to say. When decisions are especially important is when two possible paths we might take are totally opposite another or grind against one another. There is a certain tension that arises in decisions that carry a great deal ofContinue reading “Critical Thinking Toolkit: False Dilemma”