Leopold Karl

Leopold Karl

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Should mathematicians care about applications?

Introduction Since mathematical discoveries seem to be some of the main ingredients to both beneficial and (potentially) harmful tools (e.g. in telecommunications, nuclear weapons, ...), questions of ethical responsibility for applications of a published mathematical result arise. In particular, from a mathematicians point of view the question "Should mathematicians

Wittgenstein's view on descriptive and mathematical statements

Introduction This week's reading "Conatus mathematico-philosophicus" by Roy Wagner introduced me to Wittgenstein's philosophy of mathematics. In this essay I will answer the following questions: What differs a descriptive from a mathematical statement according to Wittgenstein? What makes a proposition mathematical in Wittgenstein'

Non-Euclidean Arithmetic

Introduction This week's reading "Mathematics as Sign" by Brian Rotman introduced me to a system of numbers which is very different from what we are used to work with, so in what follows I will, firstly, introduce this notion of numbers, called the Non-Euclidean Arithmetic, and,

Monster-barring, exception-barring and the method of lemma incorporation

This essay is about to discuss some of the methods of proof analysis/adaption which occur in ”Proofs & Refutations” by Lakatos, a discussion on how to properly adjust proofs when they appear to be incomplete. Amongst these methods are monster-barring, exception-barring and the method of lemma incorporation. After discussing

A (late) Happy New Year!

Better late than never is the motto of this blog post. How comes? Well, after some relaxation days together with my family around Christmas and a visit to my friends back in Austria at Sylvester, the so-called learning phase begun for me, since I am having most of my exams

Analytic Proofs and Pluralism

Introduction In chapter 12 of her book "Pluralism in Mathematics" Michele Friend introduces the notion of axiomatic and analytic proofs and argues why every proof can and better be seen as analytic. This essay will focus on the definition of an analytic proof and the reasons for the

A sample of paradoxa arising in Pluralism

Introduction In Chapter 10 of her book "Pluralism in Mathematics" Michele Friend gives a sample of three paradoxa arising in Pluralism, a philosophy of mathematics she introduces in the same book: the external, the internal and the transcendental paradoxon. These three paradoxa shall be discussed in this essay.

On structuralism

Some words on structuralism Even though the structuralist position can be split up into different streams, the idea all of them have in common is that mathematics is about investigating structures as opposed by the realist who claims to study real objects. Thereby, the structuralist avoids committing to an ontology

Formalism and Realism - a comparison

This blog post continuous a series of posts on the philosophy of mathematics and is will therefore not go into detail on the meaning of the various technical terms used. As we already discussed formalism and realism in class, I will try to summarise what makes the difference between the

number theory - my favorite field of mathematics

Of course, my favorite field of mathematics may change over time, but until now number theory has been my favorite for as long as I remember. How comes? I guess, this is highly linked to my approach and relationship to mathematics: I've always enjoyed playing games, thouroughly understanding

the Acquisition Argument - intuitionism vs. realism

Introduction This essay is the second in a series of the sooner announced essays on the philosophy of mathematics. This time, I will elaborate on the differences in the understanding of true and false between realists and intuitionists which is a results of their disagreement on semantics. As a specific

why I cycle long-distance and what it feels like

why I cycle long-distance and what it feels like

This topic has been suggested to me by Benjamin, a friend of mine, during today's running session. It came up because I cycled from Bern to Zurich yesterday afternoon and he wondered what it felt like. Thanks for bringing up this topic and suggesting it for today'

revision makes perfect

I honestly don't know if I really agree on the "perfect" in this week's title, however, this translation of the German saying "Übung macht den Meister" expresses what has probably been the most important takeaway from my first year at university. In

philosophy of mathematics - my current position

When choosing some extra subjects for the semester of autumn 2022, I accidently came across the course "Pluralist Philosophy of Mathematics" and immediately knew, I was going to take it since this combination seemed really interesting to me for the last three years or so. Now, right at

reviewing my first academic year

Since my new academic year (2022/23) just started off a week ago, I decided to review what happened in the last one, especially because it's been my first year at university - and what a tough one! Honestly, I didn't really plan to attend university

welcome

Hi everyone and a warm welcome to my website! In this very first post, I would like to first explain the structure of my personal website, continue with my motivation on creating and maintaining it and finally, give you some insights in what made me start writing a blog. Let&