Bayesian reasoning in avalanche terrain: a theoretical investigation

In this article, I explore a Bayesian approach to avalanche decision-making. I mo- tivate this perspective by highlighting a version of the base-rate fallacy and show that a similar pattern applies to decision-making in avalanche-terrain. I then draw out three theoretical lessons from adopting a Bayesian approach and discuss these lessons critically. Lastly, I highlight a number of challenges for avalanche educators when incorporating the Bayesian perspective in their curriculum

Dummett’s Criticism of the Context Principle

This paper was written during my AHRC research leave on Frege's Platonism and Platonism today.This paper was written during my AHRC research leave on Frege's Platonism and Platonism toda

Richard G. Heck Jr. Reading Frege's Grundgesetze

Output Type: Book Revie

Know Your Own Competence

First paragraph: Backcountry skiing requires us to make decisions in an inherently uncertain environment with possibly fatal consequences. However, skills and competences to recognize and avoid the possible dangers in avalanche terrain can help to reduce these dangers and render the residual risk "acceptable." Also, there is a sense in which to be a responsible backcountry enthusiast is to be one who has acquired competences to deal with the relevant dangers. Thus, being a competent decision-maker is not only important to reduce the overall risk involved, but also plays a pivotal role in rendering an engagement in so-called "extreme sports" socially acceptable

Paolo Mancosu, Abstraction and Infinity

Output Type: Book Revie

A Bayesian Perspective on Avalanche Decision-Making and the Relevance of Stability tests

In this paper, I explore a Bayesian perspective on avalanche decision-making. I motivate this general outlook by introducing a well-known cognitive bias, the base-rate fallacy, and show how a similar pattern applies to decision-making in avalanche-terrain when assessing the relevance of stability tests. I then present three theoretical lessons that emerge from adopting a Bayesian perspective to avalanche decision- making. I conclude by raising numerous challenges for avalanche educators when incorporating the Bayesian perspective into their curriculum and point to future researc

A puzzle about ontological commitments

The aim of this paper is to scrutinise the necessary conditions for a specific mathematical principle to be ontologically committing and, as such, to identify the source of its ontological commitments. The principle in ques- tion is Hume’s Principle – a statement that embedded in second-order logic allows for a deduction of the second-order Peano axioms. This principle is at the heart of the so-called Neo-Fregean programme as defended by Bob Hale and Crispin Wright. Once it is clear what the source of the commitment to infinitely many ob jects of Hume’s Principle is, we should be able to re-evaluate the debate between the Neo-Fregeans – who defend Hume’s Principle as an analytic principle – and the so-called epistemic rejectionists – who deny its analytic status. The conclusions can then be generalised to other abstraction principles, principle that share a similar form to Hume’s Principle. In the first section, I will clarify what epistemic rejectionism is committed to and provide a theoretical basis for the position by introducing the notion of presumptuousness as the underlying criterion on the basis of which Hume’s Principle is to be rejected as an analytic principle. Then, in section 2 and 3, I will review certain formal results which prima facie put pressure on epistemic rejectionism. In section 4, I will propose a short thought-experiment to highlight the problem for epistemic rejectionism posed by the formal results and then suggest various responses on behalf of the epistemic rejectionist. The upshot will be to elicit a new and very basic disagreement between epistemic rejectionism and the Neo-Fregeans which will provide a new angle to properly assess and re-evaluate the current debate

Frege on Sense Identity, Basic Law V, and Analysis

The paper challenges a widely held interpretation of Frege's conception of logic on which the constituent clauses of basic law V have the same sense. I argue against this interpretation by first carefully looking at the development of Frege's thoughts in Grundlagen with respect to the status of abstraction principles. In doing so, I put forth a new interpretation of Grundlagen §64 and Frege's idea of ‘recarving of content’. I then argue that there is strong evidence in Grundgesetze that Frege did not hold the relevant sense-identity claim regarding basic law V

A Critical Introduction to the Philosophy of Gottlob Frege

Output Type: Book Revie

What mathematical knowledge could not be

This survey paper will critically discuss four different strategies to explain our knowledge of mathematics. In the first section I will outline Benacerraf ’s dilemma as put forth in Benacerraf ’s famous paper “Mathematical Truth”1 – a dilemma faced by any account of mathematical knowledge. The aim of this section is to clarify and discuss the semantic and epistemic constraints that Benacerraf (explicitly and implicitly) imposes, and show how they give rise to his well-known dilemma. In the second section I will review four strategies to overcome this dilemma as they occur in the philosophical literature. The first two platonistic strategies comply with the semantic constraint but, I will argue, provide insufficient answers to the epistemic constraint, while the other two, nominalistic strategies either reject the idea of mathematical knowledge altogether or fail the semantic constraint. In the last section, I will elicit, on the basis of my discussion of the four conceptions, what I label the fundamental assumption. I will argue that it is presupposed by all four strategies and suggest that a rejection of this assumption will give rise to a different type of platonistic response. A thorough discussion of this fifth alternative will, however, be postponed to another occasion