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”

Computing Derivatives: Part 2 (Explaining Calculus #8)

Most recently in the series on calculus, we did some overview on some “precalculus” topics that we’d need for later calculus discussions. Having now done this, we move on to several examples of more ‘complicated’ rules that derivatives follow. We will then investigate some more difficult specific functions and their derivatives. Finally, at the end,Continue reading “Computing Derivatives: Part 2 (Explaining Calculus #8)”

Critical Thinking Toolkit: Self-Defeating Statements

Have you ever heard someone say something you find completely unbelievable? I’m sure we all have. Often, we think this because we know things that make the opposing claim unbelievable. There are many examples I could give, but I think your thoughts have probably already filled in some examples for me, so I won’t. AbsurdContinue reading “Critical Thinking Toolkit: Self-Defeating Statements”

Critical Thinking Toolkit: Non Sequiturs

Whenever we are presenting reasons for a position we believe or are involved in dialogue with a person we disagree with, one of the most important things for us to do is to to clearly lay out our reasons for what we believe. Built into this important criteria of conversation is the idea that ourContinue reading “Critical Thinking Toolkit: Non Sequiturs”

Topics From “Precalculus”: Part 2 (Explaining Calculus #7)

Because of the directions I’d like to be able to go later on in this series, we need to make an aside about more topics that aren’t specifically calculus related. If you’ve made it this far, great for you! You’re now getting into the realm of calculus. This is a fun ride, and it isContinue reading “Topics From “Precalculus”: Part 2 (Explaining Calculus #7)”

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”

Computing Derivatives: Part 1 (Explaining Calculus #6)

In the previous post in this series, we set up a definition of the derivative of a function, which is a new function that tells us how the original function changes over time. Now that we have set up this idea of derivatives, we are going to enter into a period of showing how toContinue reading “Computing Derivatives: Part 1 (Explaining Calculus #6)”

Derivatives, Tangent Lines, and Change (Explaining Calculus #5)

We’ve spent a few posts now developing the ideas of limits and continuity, two of the foundational ideas of calculus. We are now going to introduce the third foundational idea, the derivative. The derivative can be thought of as a way to capture the way that things change over time into one single formula. InContinue reading “Derivatives, Tangent Lines, and Change (Explaining Calculus #5)”