One of my most favorite responses to questions from students is: “It depends on how you see it.” To many of my students this response can be quite frustrating at times. “Why can he not give us a clear, clean, yes/no answer to a simple question? Why does he always want to explore the ‘grey zone’? I want to have some certainty!”, they say. Continue reading »

 

Originally I wanted to call this episode “Does Math Reflect Reality?” or “The Limits of Math” but then I decided on the title “How Math can be Right and Wrong at the Same Time” – it sounds more, how shall I say… captivating.

And yes, I’m going to start off with a little mathematical task to illustrate that mathematical solutions do not always correspond to reality. Let’s start off simple. Certainly you remember the Pythagorean Theorem. If the length of two sides of a right triangle are known, then it’s easy to calculate the third side: a²+b²=c². I’m going to show you now an example using this formula.

Lets use some simple values to make calculation easy. If the lengths of the two legs of the right triangle a and b have the values 3 and 4 (a=3 and b=4), what is the length of the hypotenuse c? Continue reading »

Have you ever heard of the strange looking group of mammals, the Rhinogradentia? If you don’t know what they are, then maybe the name Snouter rings a bell? No? Don’t worry, I’m going to explain what they are. In this episode I’m going to use the names Rhinogradentia and Snouters interchangeably, they refer to the same animals. And, yes, I’m also not forgetting about some Theory of Knowledge aspects. In particular I’m going to address the concept of “justified true belief” as a definition of knowledge. So in that sense this episode is somewhat introductory in nature. But first, let’s talk about the Rhinogradentia, the Snouters.

The Rhinogradentia are a group of mammals and were first discovered by the Swedish explorer Einar Pettersson-Skämtkvist in the year 1941. They are a fairly recent discovery, even if this was over 60 years ago. He discovered them on the Polynesian Hi-yi-yi islands in the Pacific ocean, while escaping captivity as a prisoner of war. This was during the second world war. Unfortunately only a few years later, in 1945, the island was destroyed by an earthquake. Continue reading »

 

A student recently wrote me an email and asked me about the similarities and differences between relativism and constructivism. I already started to write an email to answer this question when I reconsidered and decided to take this opportunity to make another podcast episode out of it.

Now before I start off, I just want to say that we have to be a bit careful that we are not getting too theoretical about this. And if a “real” expert on this topic discovers some inaccuracies in my explanation, I kindly request some forgiveness….. I have not studied this particular aspect in much detail myself.
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A few years ago I had the opportunity to visit a cultural exhibition. There were all sorts of interesting exhibits, ranging from art work to the local food… and of course there were also rooms filled with religious objects, handicrafts, clothing etc. I also remember the nice photographs of the landscape that were on display. For the purpose of this episode, the country is of no importance. We were a small group of approximately 10 visitors and we had one tour guide for the museum.
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What is truth? This is an interesting but also difficult question to answer. It is possible to distinguish several different definitions or approaches of truth. Here are three of them.

• Correspondence Theory of Truth: This theory states that a statement (a “proposition”) is true if it corresponds to (or reflects) reality. If somebody states “It is raining” (the proposition) then it is true only if it is really raining outside (reality). The interesting question is now: “What is reality”? We know that senses can deceive us. So how is reality really like? And of course we have to assume that something like reality really does exist and is not simply a product of our mind.

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The tree criteria needed for a person to know something are:

• Lack of justification: “I know that aliens exist” – there is no way that you can provide a justification for this claim. Therefore you can not know it.
• Lack of belief: “I know that the world is round but I don’t believe it.” – this is a contradictory statement. For you to know something you have to believe in it. But not every belief is knowledge!
• Lack of truth: I know that a circle has 3 corners. – You can not know things that are evidently not true.

Four possible ways to justify one’s belief are:

• Memory
• Authority
• Logics
• Empirical evidence