A blog dedicated to mathematical philosophy.
Nicholas Shackel (Cardiff) has a new book out that might be of interest to readers, and there is a discount code available that Nick has asked me to pass on. Details below. Bertrand’s Paradox and the Principle of Indifference Nicholas Shackel This book casts a new light on Bertrand's Paradox, giving original analyses of the paradox, its possible solutions, the source of the paradox, the…
Different policies introduced by a social planner, whether the government of a country or the head of an institution, lead to situations in which different peoples' lives go better or worse. That is, in the jargon of this area, they lead to different distributions of welfare across the individuals they affect. If we allow the unfettered accumulation of private wealth, that will lead to one…
Before you is a range of options: perhaps they are different laws you might implement in the country you govern, or institutions you might inaugurate; perhaps they are public health measures you might implement, or strategies for combating the climate crisis. Whatever they are, there is a population they will affect, and there is some uncertainty about how well-off each option will leave each…
As a dear departed friend used to tell me, only a fool never changes their mind. So, endeavouring not to be fool, I have changed my mind about something. In fact, I've changed it back, having changed it once before. The matter is a certain argument that Hannes Leitgeb and I proposed for the Bayesian norm of Conditionalization, which says that you should update your credences in response to…
More preparation for the formal (or fine-grained) epistemology meets mainstream (or coarse-grained) epistemology conference! In my previous post , I asked what a certain Bayesian approach might say about certain questions from the recent mainstream epistemology literature on inquiry. Now I want to ask what that same approach might say about what Mona Simion calls 'epistemic duties to believe', and…
In August, I'll speak at a conference that aims to bring together what we might call 'mainstream epistemology' and 'formal epistemology'. I always find it hard to draw the line between these, since what people usually call mainstream epistemology often uses formal tools, such as those developed in epistemic logic or in modal semantics, and formal epistemology quite frequently uses none. But they…
Like Lara Buchak , I think rationality permits many different attitudes to risk: without ever falling into irrationality, you might be extremely risk-averse, quite risk-averse, just a little risk-averse, risk-neutral, a teeny bit risk-inclined, very risk-inclined, exorbitantly risk-inclined, and many points in between. To illustrate, suppose you are offered a choice between two units of utility…
There is a PDF version of the blogpost here . There are some things whose value for us we can't know until we have them. Love might be one of them, becoming a parent another. In many such cases, we can't know how much we value that thing until we have it because only by having it can we know what it's like. The nature of the experience of having it---how it feels, its phenomenal character---plays…
A PDF of this blogpost is available here . [This blogpost is closely related to the one from last week . In this one, I ask how someone should choose on behalf of a group of people when she doesn't know their attitudes to risk; in the previous one, I asked how someone should choose for themselves when one of their decisions might cause them to change their attitudes to risk. Many of the same…
A PDF of this blogpost is available here . A transformative experience is one that changes something significant about you. In her book , Laurie Paul distinguishes two sorts of transformative experience, one epistemic and one personal. An epistemically transformative experience changes you by providing knowledge that you couldn't have acquired other than by having the experience: you eat a durian…
There is a PDF of this post here . Take a quantity whose value you wish to estimate---the basic reproduction number for a virus; the number of jelly beans in a jar at the school fête; the global temperature rise caused by doubling the concentration of CO2 in the atmosphere; the number of years before humanity goes extinct. Ask a group of people to provide their estimate of that value, and take the…
There is a PDF version of this post here. Pick a question to which the answer is a number. What is the population of Weston-super-Mare? How many ants are there in the world? Then go out into the street and ask the first ten people you meet for their answers. Look how far those answers lie from the truth. Now take the average of the answers---their mean. And look how far it lies from the truth. If…
I'm cross-posting this from the Effective Altruism Forum. It's the latest version of my critique of longtermism that uses Lara Buchak's risk-weighted expected utility theory. Here's the abstract: Longtermism is the view that the most urgent global priorities, and those to which we should devote the largest portion of our current resources, are those that focus on ensuring a long future for…
A PDF version of this post is available here . The question of this blogpost is this: Take the various decision theories that have been proposed for individuals with imprecise probabilities---do they recommend themselves? It is the final post in a trilogy on the topic of self-recommending decision theories (the others are here and here ). One precise kitten and one imprecise kitten Let's begin by…
A PDF of this blogpost can be found here . Last week, I wrote about how we might judge a decision theory by its own lights. I suggested that we might ask the decision theory whether it would choose to adopt itself as a decision procedure if it were uncertain about which decisions it would face. And I noted that many instances of Lara Buchak's risk-weighted expected utility theory ( REU ) do not…
A PDF of this blogpost is available here . Once again, I find myself stumbling upon a philosophical thought that seems so natural that I feel reasonably confident it must have been explored before, but I can't find where. So, in this blogpost, I'll set it out in the hope that a kind reader will know where to find a proper version already written up fully.* I'd like to develop a type of objection…
A PDF of this blogpost is available here . I don't have an estimate for how long it will be before the Greenland ice sheet collapses, and I don't have an estimate for how long it will be before the average temperature at Earth's surface rises more than 3C above pre-industrial levels. But I know a bunch of people who do have such estimates, and I might hope that learning theirs might help me set…
In the previous two posts in this series ( here and here ), I described two arguments for the conclusion that the members of a group should agree. One was an epistemic argument and one a pragmatic argument. Suppose you have a group of individuals. Given an individual, we call the set of propositions to which they assign a credence their agenda. The group's agenda is the union of its member's…
There is a PDF version of this blogpost available here . In the previous post , I introduced the norm of Consensus. This is a claim about the rationality of groups. Suppose you've got a group of individuals. For each individual, call the set of propositions to which they assign a credence their agenda. They might all have quite different agendas, some of them might overlap, others might not. We…
You can find a PDF of this blogpost here . Should everyone agree with everyone else? Whenever two members of a group have an opinion about the same claim, should they both be equally confident in it? If this is sometimes required of groups, of which ones is it required and when? Whole societies at any time in their existence? Smaller collectives when they're engaged in some joint project? Of…
For a PDF version of this post, see here . Many years ago, I was climbing Sgùrr na Banachdich with my friend Alex. It's a mountain in the Black Cuillin, a horseshoe of summits that surround Loch Coruisk at the southern end of the Isle of Skye. It's a Munro---that is, it stands over 3,000 feet above sea level---but only just---it measures 3,166 feet. About halfway through our ascent, the mist…
For a PDF version of this post, see here . In defence of pluralism Recently, after a couple of hours discussing a problem in the philosophy of mathematics, a colleague mentioned that he wanted to propose a sort of pluralism as a solution. We were debating the foundations of mathematics, and he wanted to consider the claim that there might be no single unique foundation, but rather many different…
In a recent paper discussing Lara Buchak's risk-weighted expected utility theory, Simon Blessenohl notes that the objection he raises there to Buchak's theory might also tell against permissivism about rational credence. I offer a response to the objection here. In his objection, Blessenohl suggests that credal permissivism gives rise to an unacceptable tension between the individual preferences…
In their 2018 paper, 'Living on the Edge' , Ginger Schultheis issues a powerful challenge to epistemic permissivism about credences, the view that there are bodies of evidence in response to which there are a number of different credence functions it would be rational to adopt. The heart of the argument is the claim that a certain sort of situation is impossible. Schultheis thinks that all…
Over the summer, I got interested in the problem of the priors again. Which credence functions is it rational to adopt at the beginning of your epistemic life? Which credence functions is it rational to have before you gather any evidence? Which credence functions provide rationally permissible responses to the empty body of evidence? As is my wont, I sought to answer this in the framework of…
