Translation from German to English by Daniel Fidel Ferrer -/- What Does it Mean to Orient Oneself in Thinking? -/- German title: "Was heißt: sich im Denken orientieren?" -/- Published: October 1786, Königsberg in Prussia, Germany. By Immanuel Kant (Born in 1724 and died in 1804) -/- Translation into English by Daniel Fidel Ferrer (March, 17, 2014). The day of Holi in India in 2014. -/- From 1774 to about 1800, there were three intense philosophical and theological controversies underway in (...) Germany, namely: Fragments Controversy, the Pantheism Controversy, and the Atheism Controversy. Kant’s essay translated here is Kant’s respond to the Pantheism Controversy. During this period (1770-1800), there was the Sturm und Drang (Storm and Urge (stress)) movement with thinkers like Johann Hamann, Johann Herder, Friedrich Schiller, and Johann Goethe; who were against the cultural movement of the Enlightenment (Aufklärung). Kant was on the side of Enlightenment (see his Answer the Question: What is Enlightenment? 1784). -/- What Does it Mean to Orient Oneself in Thinking? / By Immanuel Kant (1724-1804). [Was heißt: sich im Denken orientieren? English]. (shrink)

There are different narratives on mathematics as part of our world, some of which are more appropriate than others. Such narratives might be of the form ‘Mathematics is useful’, ‘Mathematics is beautiful’, or ‘Mathematicians aim at theorem-credit’. These narratives play a crucial role in mathematics education and in society as they are influencing people’s willingness to engage with the subject or the way they interpret mathematical results in relation to real-world questions; the latter yielding important normative considerations. Our strategy is (...) to frame current narratives of mathematics from a virtue-theoretic perspective. We identify the practice of mathematizing, put forward by Freudenthal’s ‘Realistic mathematics education’, as virtuous and use it to evaluate different narratives. We show that this can help to render the narratives more adequately, and to provide implications for societal organization. (shrink)

English translation of Kant's Beantwortung der Frage: Was ist Aufklärung? (Königsberg in Prussia, 30 September 1784).

Penelope Maddy’s Second Philosophy is one of the most well-known ap- proaches in recent philosophy of mathematics. She applies her second-philosophical method to analyze mathematical methodology by reconstructing historical cases in a setting of means-ends relations. However, outside of Maddy’s own work, this kind of methodological analysis has not yet been extensively used and analyzed. In the present work, we will make a first step in this direction. We develop a general framework that allows us to clarify the procedure and (...) aims of the Second Philosopher’s investigation into set-theoretic methodology; pro- vides a platform to analyze the Second Philosopher’s methods themselves; and can be applied to further questions in the philosophy of set theory. (shrink)