Lotteries and Chess Engines - Possibility and the Ability to Do Otherwise in Dennett's Free Will Intuition Pumps
Reference Material:
Intuition Pumps and Other Tools for Thinking – Daniel Dennett
I recently read Dan Dennett’s Intuition Pumps and Other Tools for Thinking and it’s got the mental gears turning. Here I want to revisit and build on (and then question) some of the ideas in Freedom’s Debt to Reason. I’ll use two of Dennett’s intuition pumps on free will to come at the issues from a slightly different angle. The central idea will be that, when it comes to freedom and free will, the kind of possibility that is relevant is epistemic possibility, which is in some sense orthogonal to determinism. Let’s dive in.
Two Lotteries
Imagine two lotteries. In lottery A, the tickets are sold, the stubs are mixed up, and then the winner is drawn and announced. By contrast, in lottery B, the stubs are detached, mixed up, and the winning stub is drawn (and ensconced in an undisclosed, secure location). Only then are the tickets sold and the winner announced. (Ignore, for present purposes, the complications in lottery B caused by the difficulty of predicting how many tickets will be sold. These are easily dealt with, and irrelevant.) Question – are the lotteries equally fair? Of course, lottery A is fair. What about B? One might have the intuition that lottery B contains some kind of unfairness because, when the tickets are sold, one has already been determined to be the winner, and the rest are worthless. What should we make of this?
The force of this intuition pump hangs on the claim that the lotteries are, in fact, equally fair. First, let’s ignore the fact that in a real-world lottery B, it might be possible to manipulate where and to whom the winning ticket gets sold. Let’s rule this possibility out for the sake of argument – say we’ve managed to ensure that this won’t happen. Second, note that the lotteries are, from a probabilistic perspective, equivalent. In a very real sense, everyone has the same, and equal, chance of winning in both lotteries. This intuition is apparently widely shared – as Dennett points out, scratch-offs are extremely popular, and they’re just versions of lottery B. The winnings for each card have already been determined at the time of sale.
If you accept that both lotteries are equally fair, and I think you should, then presumably you accept the characterization that, in both lotteries, everyone has an equal chance of winning. But this implies that in B, you have a possibility (in some sense) of winning, even though whether or not your ticket is a winner has already been determined (in some sense). This may seem contradictory, but it’s not – the winner has already been determined metaphysically, but not epistemically – you don’t know if your ticket is winning or not. It’s in this sense, the epistemic sense, that you have a chance of winning. The larger takeaway is that there is a notion of possibility, epistemic possibility, that is very relevant to human affairs and judgements, and yet completely independent of determinism.
We can drive this point home even further. The lotteries are both fair, and our judgement that “everyone has an equal chance of winning” is independent of when the winner is determined. So in principle, we could “switch on” determinism globally for both lotteries, making the winner in each determined, say, at the big bang, and our judgement about their relative fairness should not change. Everyone still has an equal chance of winning in both lotteries, and the type of possibility being invoked in that “chance” is entirely epistemic, and entirely independent of determinism.
So there is a sense of chance or possibility that is independent of determinism and that is relevant to human affairs and judgements, at least in some domains. That sense is epistemic possibility. The big question is – is this a kind of possibility relevant to the free will debate? Can it be used to cut through any of the classic disagreements? Let’s consider another of Dennett’s intuition pumps.
Three Chess Engines
Before introducing this thought experiment, it’s important to make clear a property of chess engine play. Chess engines run on computers, which we will assume here are deterministic, in the metaphysical sense. However, chess engine play is often nondeterministic, in the sense that a given position as input doesn’t always yield the same move as output, for a variety of reasons. First, the engine’s code might use pseudorandom number generators to break ties between two equally good moves, or to truncate certain branches of a tree search, for example. But even if the engine’s code is completely deterministic (no consulting of pseudorandom number generators), the play can also be nondeterministic for reasons having to do with the time control strategy of the chess engine, the CPU time available to the engine for any given move, and the interaction of multiple cores during parallel computations.
Now to Dennett’s intuition pump. Imagine we have three chess computers: A, B, and C. A is better than B in the sense that, if they play a 1000 game tournament against each other, A beats B in a solid majority of games. Another important aside – how should we explain this regularity? It doesn’t really help to note that A is causally determined to beat B in every game that it in fact does, even though this is true. To provide a useful explanation of why A beats B, we have to describe the engines at a higher level, as strategists with capacities. Something about the computational structure of A gives it the capacity to find moves and create positions that B just can’t handle. Though it’s not the focus here, this is what Dennett calls the “intentional stance”.
Continuing with the thought experiment – engine C is better than both A and B (in the same sense as above). Now imagine that, from an A vs. C tournament and a B vs. C tournament, we notice that in a particular round the same exact game was played in both tournaments up until move 12. Experts analyze the game and agree that on move 12, if either A or B had castled, they likely would have gone on to at least draw, if not win. So the designers of A and B dig into their programs to see why they didn’t castle on move 12. B was nowhere close to castling – the move wasn’t even in the top 3 candidate moves at the time B selected a move. A had 2 top moves under consideration – castling and an alternative, the move it played. It consulted a random number generator to break the tie, choosing the alternative. Dennett claims that A’s designer is licensed to claim “A could have castled” but B’s designer is not. This is because what we (should) mean by “A could have castled” is whether A had the capacity to castle. Just as above, whether A in fact castled in this exact situation (whether A was causally determined to castle in that instant) isn’t informative. What is informative is whether A castles in sufficiently similar situations – in this case, the same chess position but with a different draw from the random number generator. If A does castle in some of these situations, A has a capacity in this position, a capacity that B lacks. So we get a situation where there is a sense in which A “could have done otherwise” but B couldn’t, independent of determinism.
My point with this intuition pump here is this – note how Dennett’s explanation of the sense of “could have done otherwise” that matters actually leverages the same ideas from the lottery thought experiment. We claim that in lottery B, “everyone has an equal chance of winning”. Another way to say this is that, in the ensemble of possible worlds exactly like this one, except where the winning ticket number (the relevant fact about which we are ignorant) is varied, there is exactly one possible world where every ticket holder wins. Similarly, when we say “A could have castled”, we mean something like, in the ensemble of possible worlds exactly like this one, except where the random number generated (again, the relevant detail that’s hidden from us) is varied, A castles in some of those games. In both the lottery and the chess game, the possibility in “chance” or “could have” is epistemic, not metaphysical.
So what has the chess engine example got us? Does it answer the “big question” from before? Is the familiar morally-relevant sense of “could have done otherwise” completely independent of determinism? I don’t think it can deliver a verdict there. Chess engines have capacities that are too narrow in a “world” that is too small and simple (though the possibilities are still dazzling and complex) to make good analogies to moral agents. But the thought experiment has clarified my thinking with regard to possibility, the ability to do otherwise, and the past versus the present. I believe I erred in Freedom’s Debt to Reason in claiming that the epistemic possibility relevant to our ability to do otherwise in the present is absent in the past. Looking back at a past decision, the relevant epistemic perspective is that of the moment of the decision, not that of the present. The same epistemic possibility exists from moment to moment, past to present, and therefore so does our ability to do otherwise.
I’m starting to sound like a compatibilist…
Intuition Pumps and Other Tools for Thinking – Daniel Dennett
I recently read Dan Dennett’s Intuition Pumps and Other Tools for Thinking and it’s got the mental gears turning. Here I want to revisit and build on (and then question) some of the ideas in Freedom’s Debt to Reason. I’ll use two of Dennett’s intuition pumps on free will to come at the issues from a slightly different angle. The central idea will be that, when it comes to freedom and free will, the kind of possibility that is relevant is epistemic possibility, which is in some sense orthogonal to determinism. Let’s dive in.
Two Lotteries
Imagine two lotteries. In lottery A, the tickets are sold, the stubs are mixed up, and then the winner is drawn and announced. By contrast, in lottery B, the stubs are detached, mixed up, and the winning stub is drawn (and ensconced in an undisclosed, secure location). Only then are the tickets sold and the winner announced. (Ignore, for present purposes, the complications in lottery B caused by the difficulty of predicting how many tickets will be sold. These are easily dealt with, and irrelevant.) Question – are the lotteries equally fair? Of course, lottery A is fair. What about B? One might have the intuition that lottery B contains some kind of unfairness because, when the tickets are sold, one has already been determined to be the winner, and the rest are worthless. What should we make of this?
The force of this intuition pump hangs on the claim that the lotteries are, in fact, equally fair. First, let’s ignore the fact that in a real-world lottery B, it might be possible to manipulate where and to whom the winning ticket gets sold. Let’s rule this possibility out for the sake of argument – say we’ve managed to ensure that this won’t happen. Second, note that the lotteries are, from a probabilistic perspective, equivalent. In a very real sense, everyone has the same, and equal, chance of winning in both lotteries. This intuition is apparently widely shared – as Dennett points out, scratch-offs are extremely popular, and they’re just versions of lottery B. The winnings for each card have already been determined at the time of sale.
If you accept that both lotteries are equally fair, and I think you should, then presumably you accept the characterization that, in both lotteries, everyone has an equal chance of winning. But this implies that in B, you have a possibility (in some sense) of winning, even though whether or not your ticket is a winner has already been determined (in some sense). This may seem contradictory, but it’s not – the winner has already been determined metaphysically, but not epistemically – you don’t know if your ticket is winning or not. It’s in this sense, the epistemic sense, that you have a chance of winning. The larger takeaway is that there is a notion of possibility, epistemic possibility, that is very relevant to human affairs and judgements, and yet completely independent of determinism.
We can drive this point home even further. The lotteries are both fair, and our judgement that “everyone has an equal chance of winning” is independent of when the winner is determined. So in principle, we could “switch on” determinism globally for both lotteries, making the winner in each determined, say, at the big bang, and our judgement about their relative fairness should not change. Everyone still has an equal chance of winning in both lotteries, and the type of possibility being invoked in that “chance” is entirely epistemic, and entirely independent of determinism.
So there is a sense of chance or possibility that is independent of determinism and that is relevant to human affairs and judgements, at least in some domains. That sense is epistemic possibility. The big question is – is this a kind of possibility relevant to the free will debate? Can it be used to cut through any of the classic disagreements? Let’s consider another of Dennett’s intuition pumps.
Three Chess Engines
Before introducing this thought experiment, it’s important to make clear a property of chess engine play. Chess engines run on computers, which we will assume here are deterministic, in the metaphysical sense. However, chess engine play is often nondeterministic, in the sense that a given position as input doesn’t always yield the same move as output, for a variety of reasons. First, the engine’s code might use pseudorandom number generators to break ties between two equally good moves, or to truncate certain branches of a tree search, for example. But even if the engine’s code is completely deterministic (no consulting of pseudorandom number generators), the play can also be nondeterministic for reasons having to do with the time control strategy of the chess engine, the CPU time available to the engine for any given move, and the interaction of multiple cores during parallel computations.
Now to Dennett’s intuition pump. Imagine we have three chess computers: A, B, and C. A is better than B in the sense that, if they play a 1000 game tournament against each other, A beats B in a solid majority of games. Another important aside – how should we explain this regularity? It doesn’t really help to note that A is causally determined to beat B in every game that it in fact does, even though this is true. To provide a useful explanation of why A beats B, we have to describe the engines at a higher level, as strategists with capacities. Something about the computational structure of A gives it the capacity to find moves and create positions that B just can’t handle. Though it’s not the focus here, this is what Dennett calls the “intentional stance”.
Continuing with the thought experiment – engine C is better than both A and B (in the same sense as above). Now imagine that, from an A vs. C tournament and a B vs. C tournament, we notice that in a particular round the same exact game was played in both tournaments up until move 12. Experts analyze the game and agree that on move 12, if either A or B had castled, they likely would have gone on to at least draw, if not win. So the designers of A and B dig into their programs to see why they didn’t castle on move 12. B was nowhere close to castling – the move wasn’t even in the top 3 candidate moves at the time B selected a move. A had 2 top moves under consideration – castling and an alternative, the move it played. It consulted a random number generator to break the tie, choosing the alternative. Dennett claims that A’s designer is licensed to claim “A could have castled” but B’s designer is not. This is because what we (should) mean by “A could have castled” is whether A had the capacity to castle. Just as above, whether A in fact castled in this exact situation (whether A was causally determined to castle in that instant) isn’t informative. What is informative is whether A castles in sufficiently similar situations – in this case, the same chess position but with a different draw from the random number generator. If A does castle in some of these situations, A has a capacity in this position, a capacity that B lacks. So we get a situation where there is a sense in which A “could have done otherwise” but B couldn’t, independent of determinism.
My point with this intuition pump here is this – note how Dennett’s explanation of the sense of “could have done otherwise” that matters actually leverages the same ideas from the lottery thought experiment. We claim that in lottery B, “everyone has an equal chance of winning”. Another way to say this is that, in the ensemble of possible worlds exactly like this one, except where the winning ticket number (the relevant fact about which we are ignorant) is varied, there is exactly one possible world where every ticket holder wins. Similarly, when we say “A could have castled”, we mean something like, in the ensemble of possible worlds exactly like this one, except where the random number generated (again, the relevant detail that’s hidden from us) is varied, A castles in some of those games. In both the lottery and the chess game, the possibility in “chance” or “could have” is epistemic, not metaphysical.
So what has the chess engine example got us? Does it answer the “big question” from before? Is the familiar morally-relevant sense of “could have done otherwise” completely independent of determinism? I don’t think it can deliver a verdict there. Chess engines have capacities that are too narrow in a “world” that is too small and simple (though the possibilities are still dazzling and complex) to make good analogies to moral agents. But the thought experiment has clarified my thinking with regard to possibility, the ability to do otherwise, and the past versus the present. I believe I erred in Freedom’s Debt to Reason in claiming that the epistemic possibility relevant to our ability to do otherwise in the present is absent in the past. Looking back at a past decision, the relevant epistemic perspective is that of the moment of the decision, not that of the present. The same epistemic possibility exists from moment to moment, past to present, and therefore so does our ability to do otherwise.
I’m starting to sound like a compatibilist…