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Paper on unspecific antecedents

A new paper (draft) on counterfactuals with unspecific antecedents, to appear in a festschrift for Al Hájek. The paper discusses a range of phenomena related to the "Simplification of Disjunctive Antecedents". I argue that they can't be explained by a chance-based account of counterfactuals, as Hájek has suggested. Instead, I hint at an RSA-type explanation. I also suggest that this explanation might somewhat weaken the case for counterfactual skepticism.

I regret how much time I have spent on this topic. I first noticed it in 2006, and thought I had a nice explanation. When I posted it on the blog, Kai von Fintel kindly pointed me towards some literature. A little later, Paolo Santorio suggested that my explanation resembles the one in Klinedinst (2007). This seemed right, but I had in mind a more pragmatic implementation. I eventually wrote up my proposal in Schwarz (2021). Although my original interest was sparked by conditionals, that paper focuses on possibility modals, and only briefly mentions how the account might be extended to conditionals. When I got the invitation to write something for Al's festschrift, I thought I could spell out the application to conditionals, and compare it with Al's account. But I couldn't really make it work. So I ended up defending a more orthodox derivation based on Kratzer and Shimoyama (2002).

Logic 2 notes in HTML

It would be nice if my papers and lecture notes were available in HTML, I thought. Let's start with my lecture notes on modal logic (PDF) I thought. I'll need to convert them from LaTeX to HTML, but surely there are tools for that. I thought.

I was right. But ah, LaTeX! There are, of course, multiple options. You can use pandoc. Or tex4ht. Or lwarp. Or LaTeXML. All of them sort of work, after some fiddling and consulting their thousand-page manuals. But none of them support all the packages I use. And shouldn't those gather lists have more line-spacing, etc.?

A fork time puzzle

According to a popular view about counterfactuals, a counterfactual hypothesis 'if A had happened…' shifts the world of evaluation to worlds that are much like the actual world until shortly before the time of A, at which point they start to deviate from the actual world in a minimal way that allows A to happen. 'If A had happened, C would have happened' is true iff all such worlds are C worlds. The time "shortly before A" when the worlds start to deviate is the fork time.

Now remember the case of Pollock's coat (introduced in Nute (1980)). John Pollock considered 'if my coat had been stolen last night…'. He stipulates that there were two occasions on which the coat could have been stolen. By the standards of Lewis (1979), worlds where it was stolen on the second occasion are more similar to the actual world than worlds where it was stolen on the first occasion. Lewis's similarity semantics therefore predicts that if the coat had been stolen, it would have been stolen on the second occasion. This doesn't seem right.

Reasoning about doom

I occasionally teach the doomsday argument in my philosophy classes, with the hope of raising some general questions about self-locating priors. Unfortunately, the usual formulations of the argument are problematic in so many ways that it's hard to get to these questions.

Let's look at Nick Bostrom's version of the argument, as presented for example in Bostrom (2008).

An RSA model of SDA

In this post, I'll develop an RSA model that explains why 'if A or B then C' is usually taken to imply 'if A then C' and 'if B then C', even if the conditional has a Lewis/Stalnaker ("similarity") semantics, where the inference is invalid.

I'll write 'A>C' for the conditional 'if A then C'. For the purposes of this post, we assume that 'A>C' is true at a world w iff all the closest A worlds to w are C worlds, by some contextually fixed measure of closeness.

It has often been observed that the simplification effect resembles the "Free Choice" effect, i.e., the apparent entailment of '◇A' and '◇B' by '◇(A∨B)', where the diamond is a possibility modal (permission, in the standard example). But there are also important differences.

An RSA model of free choice

Let's continue. I'm going to present a new (?) model of free choice. Free choice is the phenomenon that a disjunction embedded in a possibility modal conveys the possibility of both disjuncts. 'You may have tea or coffee', for example, conveys that you may have tea and you may have coffee. Champollion, Alsop, and Grosu (2019) present an RSA model of this effect, drawing on the "lexical uncertainty" account from Bergen, Levy, and Goodman (2016). I'll present a model that does not rely on lexical uncertainty.


In this post, I want to compare the Rational Speech Act approach with the Iterated Best Response approach of Franke (2011). I'm also going to discuss Franke's IBR model of Free Choice, turn it into an RSA model, and explain why I find both unconvincing.

Let's back up a little.

Lewis (1969) argued that linguistic conventions solve a game-theoretic coordination problem.

RSA models with partially informed speakers

Let's model a few situations in which the hearer does not assume that the speaker has full information about the topic of their utterance.

Goodman and Stuhlmüller (2013) consider a scenario in which a speaker wants to communicate how many of three apples are red. The hearer isn't sure whether the speaker has seen all the apples. Chapter 2 of problang.org gives two models of this scenario. The first makes very implausible predictions. The second is very complicated. Here's a simple model that gives the desired results.

var states = ['RRR','RRG','RGR','GRR','RGG','GRG','GGR','GGG'];
var meanings = {
  'all': function(state) { return !state.includes('G') },
  'some': function(state) { return state.includes('R') },
  'none': function(state) { return !state.includes('R') },
  '-': function(state) { return true }
var observation = function(state, access) {
    return filter(function(s) {
        return s.slice(0,access) == state.slice(0,access);
    }, states);
var hearer0 = Agent({
    credence: Indifferent(states),
    kinematics: function(utterance) {
        return function(state) {
            return evaluate(meanings[utterance], state);
var speaker1 = function(obs) {
    return Agent({
        options: keys(meanings),
        credence: update(Indifferent(states), obs),
        utility: function(u,s){
            return learn(hearer0, u).score(s);
showChoices(speaker1, [observation('RRR', 2), observation('GGG', 2)]);

Pragmatic non-equivalence despite semantic equivalence

Bergen, Levy, and Goodman (2016) assert that "the rational speech acts model, and neo-Gricean models more generally, cannot derive distinct pragmatic interpretations for semantically equivalent expressions".

In the previous post, I gave a counterexample. I presented an RSA model that explains why 'pockets' is interpreted as plural and 'a pocket' as singular, even though the two expressions are semantically equivalent.

RSA models of scalar implicature

In this post, we'll model different kinds of scalar implicature. I'll introduce several ideas and techniques that prove useful for other topics as well.

Let's begin with the textbook example, the inference from 'some' to 'not all' (for which Goodman and Stuhlmüller (2013) give an RSA-type explanation).

A speaker wants to communicate the results of an exam. The available utterances are 'all students passed', 'some students passed', and 'no students passed'; for short: 'all', 'some', and 'none'. We can represent their meaning as functions from states to truth values:

var states = ['∀', '∃¬∀', '¬∃'];
var meanings = {
    'all': function(state) { return state == '∀' },
    'some': function(state) { return state != '¬∃' },
    'none': function(state) { return state == '¬∃' }

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