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CDT for reflective agents (EDC, ch.3)

Chapter 3 of Evidence, Decision and Causality is called "Causalist objections to CDT". It addresses arguments suggesting that while there is an important connection between causation and rational choice, that connection is not adequately spelled out by CDT.

Arif discusses two such arguments. One is due to Hugh Mellor, who rejects the very idea of evaluating choices by the lights of the agent's beliefs and desires. I'll skip over this part because I agree with Arif's response.

The other argument is more important, because it touches on an easily overlooked connection between rational choice and rational credence.

Consider the "Psycho Button" case from Egan (2007).

Reading Evidence, Decision and Causality

How odd. I'm in the office. I'm not terribly exhausted. I have some time to read and think and write. Where do I start?

Here's a book that I've long wanted to read carefully, but never got around to: Arif Ahmed's Evidence, Decision and Causality (Ahmed (2014)). I'll work my way through it, and post my reactions. This first post covers the preface, the introduction, and the first two chapters.

The book is an extended defence of Evidential Decision Theory. When I read a text with whose conclusion I disagree, I often find that the discussion already starts off on the wrong foot, with dubious presuppositions about the topic and how to approach it. Not so here. I'm largely on board with how Arif frames the disagreement between Evidential Decision Theory (EDT) and Causal Decision Theory (CDT). I like his broader philosophical outlook – his positivism, his distrust of metaphysics, his conviction that decision-makers should see themselves as part of the natural world. It should to be interesting to see where we'll end up disagreeing.

Two Puzzles About Truthfulness

1. Suppose you have strong evidence that L are the true laws of nature, where L is a system of deterministic laws. You also have strong evidence that the universe started in the exact microstate P. Your have a choice of either affirming or denying the conjunction of L and P. You want to speak truly. What should you do?

Intuitively, you should affirm. But what would happen if you denied?

Since L is deterministic, L & P either logically entails that you affirm, or it logically entails that you don't affirm. Let's consider both possibilities.

Counterpart theory in the SEP

Until recently, the Stanford Encyclopedia of Philosophy didn't have anything on counterpart theory. The editors thought the topic isn't worth an entry of its own, but at least it now has a section in the entry on "David Lewis's Metaphysics". This isn't ideal, since counterpart-theoretic approaches to intensional constructions are best seen as metaphysically non-committal. But it's better than nothing.

I also wrote an "appendix" to the entry with an overview over counterpart-theoretic interpretations of quantified modal logic. It explains some unusual features of counterpart-theoretic logics, how they arise, and how they could be avoided.

A difficult tableau proof

By the way, here's another problem my prover can't solve (in reasonable time):

Show: ∀y∃z∀x(Fxz ↔ x=y) → ¬∃w∀x(Fxw ↔ ∀u(Fxu → ∃y(Fyu ∧ ¬∃z(Fzu ∧ Fzy))))

This is problem 54 in Pelletier 1986. It is a pure first-order adaptation of a little theorem proved in Montague 1955. Montague gives a fairly simple proof. His proof uses the Cut rule, which the tableau method doesn't have. I've tried to construct a tableau proof by hand, but failed.

This might be a nice example of a relatively straightforward fact that can be proved easily with Cut, but not without.

Identity (equality) in automated semantic tableaux

It's been quiet here. I haven't had much time or energy for philosophy since the pandemic turned me into a stay-at-home dad on top of the regular job(s). At least teaching has finally come to an end a few weeks ago. I've used my newly found free time to build support for identity into the tree prover.

This is something I've wanted to do for a long time. Every five years or so I look into it, but give up because it's too hard. Here I'll explain the challenges, and the approach I chose.

The metaphysics of quantities

I've long been puzzled by the nature of quantities, but I've never really followed the literature. Now I've read Jo Wolff's splendid monograph on the topic. I'm still puzzled, but at least my puzzlement is a little better informed.

The basic puzzle is simple and probably familiar. On the one hand, being 2m high or having a mass of 2kg appear to be paradigm examples of simple, intrinsic properties. On the other hand, these properties seem to stand in mysterious relationships to other properties of the same kind. First, there's an exclusion relationship: nothing can have a mass of both 2kg and 3kg. Second, there are non-arbitrary orderings and numerical comparisons: one thing may be four times as massive as another; the mass difference between x and y may be twice that between z and w. If 2kg and 8kg are primitive properties, why couldn't an object have both, and where does their quasi-numerical order and structure come from?

Ability, control, and chance

In my paper "Ability and Possibility", I argued that ability statements should be analysed as simple possibility modals: 'S can phi' is true iff S phis at some world compatible with relevant circumstances.

This view is widely considered inadequate because it seems to violate two (related) intuitions about ability.

One is that ability requires a kind of robustness: if you have the ability to phi, then you reliably phi whenever the need arises, under a variety of circumstances.

Epistemic luck

I've been teaching a course on classical epistemology this term, so I've thought a little about knowledge.

A common judgement in the literature seems to be that knowledge is incompatible with a certain kind of luck -- the kind of luck we find in Gettier cases. This is then cashed out in terms of safety: for a belief to constitute knowledge it must be true in all nearby possible worlds.

While I share the initial judgement, the development in terms of safety doesn't look plausible to me. It has the wrong kind of structure.

Reversible Sobel Sequences

A Sobel sequence is a sequence of conditionals with increasingly strong antecedent. Lewis used Sobel sequences to motivate his "variably strict" analysis of counterfactuals.

For example, intuitively (1) and (2) might both be true, which seems to contradict a simple strict analysis:

(1) If the US had destroyed its nuclear weapons in 1965, there would have been war.
(2) If every country destroyed its nuclear weapons in 1965, there would have been peace.

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