## When can we be absolutely certain that something is true?

Are there any statements that are absolutely and certainly true? Yes! Analytic statements are true by their own nature. In this post I’ll outline some of them.

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 »

## Of Science, Math and Beauty

In this post I’m pondering on the relationship between math and beauty. Can math be beautiful as well? And what is beauty in the first place?

I recently read an article about the mathematics of beauty. Researchers found out that beauty is not in the eye of the beholder, and that beauty can indeed be quantified. If you want to read the article, here is a link.

Now, if it is possible to describe what beauty is using mathematical formulas, maybe it is also possible to look at the issue the other way around. Can math itself be considered beautiful or ugly? I did find an answer to this question by the English mathematician G. H. Hardy (1877-1947):
Continue reading »

## How can Math be Right and Wrong at the Same Time?

To what extent does math reflect the real world? Some mathematical equations deliver results that have no connection to reality. This episode applies the correspondence and coherence theory of truth to the area of mathematics.

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 »

## Of Justified True Belief and the Snouters

In this episode, I’m going to apply Plato’s definition of knowledge (justified true belief) to the recently discovered mammals, the Rhinogradentia. Can you know that they existed?

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 »

## On Relativism and Constructivism

In this episode I’m going to explain the differences between the philosophical concepts of relativism and constructivism.

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.
Continue reading »

## Three Different Types of Truth

Here I will explain the differences between the Correspondence Theory of truth, the Coherence Theory and the Pragmatic Theory.

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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