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).

This paper analyses the hidden use of new axioms in set-theoretic practice with a focus on large cardinal axioms and presents a general overview of set-theoretic practices using large cardinal axioms. The hidden use of a new axiom provides extrinsic reasons in support of this axiom via the idea of verifiable consequences, which is especially relevant for set-theoretic practitioners with an absolutist view. Besides that, the hidden use has pragmatic significance for further important sub-groups of the set-theoretic community---set-theoretic practitioners with (...) a pluralist view and set-theoretic practitioners who aim for ZFC-proofs. By describing this, the paper gives a more complete picture of new axioms in set-theoretic practice. These observations, for instance, show that set-theoretic practitioners interested in ZFC-proofs use tools that go beyond ZFC. The analysis is based on empirical data that was collected in an extensive interview study with set-theoretic practitioners. (shrink)

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)

There can sometimes be weariness surrounding coordinated efforts to induce inclusion. Detractors of certain such efforts may cite coercion or a loss of autonomy as a concern. In their book Nudge, Thaler and Sunstein presented the idea of the “nudge.” Nudges change the context in which a decision is made to increase the likelihood that a certain choice is made by the decision maker. However, nudges are designed to be easy to avoid. Thaler and Sunstein laid out criteria such that (...) nudges can remain ethical. In this paper, I show that certain nudges that greatly increased inclusion in their respective communities do follow these criteria. In fact, subjected even to the relatively tighter constraints imposed by a prominent critic of Thaler and Sunstein’s philosophy, Wilkinson, these nudges remain unscathed. Thus, inclusion-promoting nudges are not necessarily unethical from the standpoint of manipulation or autonomy. (shrink)