Interests In Everything

Another Lewis Carroll puzzle solution.

I cover the next operation after addition: Subtraction. Subtraction is the inverse, the "opposite" of addition. It is also (though lesser known) a slow version of division.

In this video, I go over how mathematics leads to counting, which directly leads into addition.

I recently covered the converse, inverse, and contrapositive. Now I show you why the converse and inverse are errors, and how they tie in with "one-to-one" errors in mathematics.

I go through a few examples of how you would find the logical symbols in regular reading/sentences.

I cover the logic symbols "and", "or", "if...then...", "if and only if..." and "not".

I go through the truth values and truth tables for the following symbols: ~ "not" & "and" v "or" ⊃ "if, then" ≡ "if and only if"

Continuing the breakdown of deductive logic, the next subsection is Propositional Logic as compared to Categorical Logic.

These are the three (3) laws of deduction (deductive logic). 1. The Law of Identity 2. The Law of Excluded Middle 3. The Law of Non-Contradiction.

The difference between induction and deduction raises some questions about our universe. I know I pretty much oversimplified the Continuum Hypothesis (which is actually about induction between infinities), but I think that oversimplification is somewhat necessary for understanding the basics of the question. Even though the Continuum Hypothesis is about measuring infinite sets, I think this breakdown of a simple "1 and 0" is a better way of understanding induction, deduction, and their importance to the questions of our universe.

This is an overview of Logic, most importantly in its role as a language. The rigor of Logic is an attribute of its DEDUCTION - not induction.

Some examples of induction versus deduction, using sentences/arguments.

This is an introduction to formal logic. I cover induction and deduction.

Some examples of mathematics as the LANGUAGE that it is. It's a strong, powerful vocabulary. It is an infinite vocabulary.

Abstraction is crucial to having fun with ideas and learning. It's fundamental to mathematics. Note: When speaking of the George Boolos (logician) quote (1:34), my explicit point is that the Law of Excluded Middle is fundamental to Logic, hence math. Since you can't even reason about something when you get rid of that fundamental law, then the ability to abstract (which is reasoning) also gets thrown out the window. Your ability to abstract is tied to your ability to fundamentally think logically and mathematically.

Is mathematics PRACTICAL? Yes. But there's more to that question.

"How can math HELP me?" It's a common question from students. The answer is, it literally helps you all the time, everywhere.

Will you use math? Yes. You will. How?

The direct connection between logic and mathematics

I try to concisely give an overview of what "mathematics" actually is.

You may want to watch the video about the truth tables for the implication (the "if then"). I cover the converse, inverse, and contrapositive.

I run through the logic of a really simple Lewis Carroll puzzle.

Some comparisons of validity, sound arguments, and truth values.