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\title{SIMPLE DETERMINISTIC FREE WILL}
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\author{
    John McCarthy
}
\date{from May 16, 2002 until \today}

\maketitle

\begin{abstract}
  A central feature of free will is that a person has choices among
  alternative actions and chooses the action with the apparently most
  preferred consequences.  In a determinist theory, the mechanism that
  makes the choice among the alternatives is determinist.  The
  sense of free will comes from the fact that the mechanism that
  generates the choices uses a non-determinist theory as a
  computational device and that the stage in which the choices have
  been identified is introspectable.  This treatment is based
  on work in artificial intelligence (AI).
  
  We present a theory of \emph{simple deterministic free will}
  (\textbf{SDFW}) in a deterministic world.  The theory splits the
  mechanism that determines action into two parts.  The first part
  computes possible actions and their consequences.  Then the second
  part decides which action is most preferred and does it.
  
  We formalize SDFW by two sentences in \emph{situation calculus}, a
  mathematical logical theory often used in AI.  The situation
  calculus formalization makes the notion of free will technical.
  According to this notion, almost no animal behavior exhibits free
  will, because exercising free will involves \emph{considering the
  consequences of alternative actions}.  A major advantage of our
  notion of free will is that whether an animal does have free will
  may be determinable by experiment.  Some computer programs, e.g.
  chess programs, exhibit SDFW.  Almost all do not.  At least SDFW
  seems to be required for effective chess performance and also for
  human-level AI.
  
  Many features usually considered as properties of free will are
  omitted in SDFW.  That's what makes it simple.  The criterion for
  whether an entity uses SDFW is not behavioristic but is expressed in
  terms of the internal structure of the entity.
\end{abstract}

\section{The Informal theory}

% /u/ftp/jmc/freewill.tex The older paper.

Let the course of events, including events in my brain (or yours or
his or its) be deterministic.  It seems to many people that there is
no place for free will.  Even our thoughts are determined.

However, if we examine closely how a human brain (or chess program)
deterministically makes decisions, free will (or imitation free will
if your philosophy forbids calling it real free will) must come back
in.  Some deterministic processes consider alternative actions and
their consequences and choose the actions they think have the most
preferred consequences.  This deterministic decision process uses a
nondeterministic theory to present the set of available actions and
the consequences of each of them.

When a person, animal, or machine reacts directly to a situation
rather than comparing the consequences of alternative actions, free
will is not involved.  So far as I can see, no animals consider the
consequences of alternative actions; hence they don't have free will.
Others think that apes sometimes do compare consequences.  A relevant
experiment is suggested in section \ref{sec:apes}.  Using free will is
too slow in many situations, and training and practice often have the
purpose of replacing comparison of consequences by automatic reaction
to a situation.

We believe this simple theory covers the most basic phenomenon of human
free will.  We'll call it \emph{simple deterministic free will} and
abbreviate it SDFW.  Robots with human-level intelligence will also
require at least this much free will in order to be useful.

Beyond having free will, some systems are conscious of having free
will and communicate about it.  If asked to tell what it is doing,
humans or some machine will tell about their choices for action and
say that they intend to determine which action leads to the best
consequence.  Such a report, whether given externally or contemplated
internally, constitutes the human sense and the human report of
free will.  SDFW does not require consciousness of having free will or
the ability to communicate about it.  That's what's simple about SDFW.
Thinking about one's free will requires theoretical structure beyond
or above SDFW.  So will considering actions as praiseworthy or
blameworthy.  SDFW also doesn't treat game theoretic situations in
which probabilistic mixed strategies are appropriate.

In AI research one must treat simple cases of phenomena, e.g.
intentional behavior, because full generality is beyond the state of
the art.  Many philosophers are inclined to only consider the general
phenomenon, but this limits what can be accomplished.  I recommend to
them the AI approach of doing the simplest cases first.
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Situation calculus formulas for SDFW}

Artificial intelligence requires expressing this phenomenon formally,
and we'll do it here in the mathematical logical language of situation
calculus.  Situation calculus is described in \cite{McCHayes69},
\cite{Shanahan97}, \cite{Reiter01}, and in the extended form used
here, in \cite{McC02}.  Richmond Thomason in \cite{Thomason03b}
compares situation calculus to theories of action in the philosophical
literature.  As usually presented, situation calculus is a
non-deterministic theory.  The equation

\begin{displaymath}
    s' = Result(e,s)
\end{displaymath}
%
asserts that $s'$ is the situation that results when event $e$ occurs
in the situation $s$.  Since there may be many different events that
can occur in $s$, and the theory of the function $Result$ does not say
which occurs, the theory is non-deterministic.  Some AI jargon refers
to it as a theory with branching time rather than linear time.
Actions are a special case of events, but most AI work discusses only
actions.

Usually, there are some preconditions for the event to occur, and
then we have the formula

\begin{displaymath}
    Precond(e,s) \rightarrow s' = Result(e,s).
\end{displaymath}
%

\cite{McC02} proposes adding a formula $Occurs(e,s)$ to the language
that can be used to assert that the event $e$ occurs in situation $s$.
We have

\begin{displaymath}
    Occurs(e,s) \rightarrow (Next(s) = Result(e,s)).
\end{displaymath}

Adding occurrence axioms, which assert that certain actions occur,
makes a theory more deterministic by specifying that certain events
occur in situations satisfying specified conditions.  In general the
theory will remain partly non-deterministic, but if there are
occurrence axioms specifying what events occur in all situations, then
the theory becomes deterministic, i.e. has linear time.

We can now give a situation calculus theory for SDFW illustrating the
role of a non-deterministic theory in determining what will
deterministically happen, i.e. by saying what choice a person or
machine will make.

In these formulas, lower case terms denote variables and capitalized
terms denote constants.
Suppose that $actor$ has a choice of just two actions $a1$ and $a2$
that he may perform in situation $s$.  We want to say that the event
$Does($actor$,a1)$ or $Does($actor$,a2)$ occurs in $s$ according to
which of $Result(Does($actor$,a1),s)$ or
$Result(Does($actor$,a2),s)$ $actor$ prefers.

The formulas that assert that a person (actor) will do the action that 
he, she or it thinks results in the better situation for him are


\begin{equation}
  \label{eq:a1}
  \begin{array}[l]{l}
Occurs(Does(actor,Choose(actor,a1,a2,s),s),s),
  \end{array}
\end{equation}
(\ref{eq:a1})

\noindent
and

\begin{equation}
  \label{eq:a2}
  \begin{array}[l]{l}
Choose(actor,a1,a2,s) = \\ \textbf{if}\
Prefers(actor,Result(a1,s),Result(a2,s))\\
\textbf{then}\ a1\ \textbf{else}\ a2.
  \end{array}
\end{equation}
% nonmonotonic reasoning

Adding (\ref{eq:a2}) makes the theory deterministic by specifying which
choice $actor$ makes.\footnote{(\ref{eq:a2}) uses a conditional expression.
  $\textbf{if}\ p\ \textbf{then}\ a\ \textbf{else}\ b$ has the value
  $a$ if the proposition $p$ is true and otherwise has the value $b$.
  The theory of conditional expressions is discussed in \cite{McC63}.
  Conditional expressions are used in the Lisp, Algol 60, Algol 68,
  and Scheme programming languages.}

 Here $\mbox{Prefers}(actor, s1,s2)$ is to be understood as 
 asserting that $actor$ prefers $s1$ to $s2$.

Here's a non-deterministic theory of greedy John.

%
\begin{equation}
  \label{eq:a3}
  \begin{array}[l]{l}
Result(A1,S0) = S1, \\
Result(A2,S0) = S2, \\
Wealth(John,S1) = \$2.0\times 10^6, \\
Wealth(John,S2) = \$1.0\times 10^6, \\
(\forall s\ s')(Wealth(John,s) > Wealth(John,s')\\
\quad\quad\quad  \rightarrow \mbox{Prefers}(John,s,s').
  \end{array}
\end{equation}
As we see, greedy John has a choice of at least two actions in
situation $S0$ and prefers a situation in which he has greater wealth
to one in which he has lesser wealth.

From equations 1-3 we can infer
\begin{equation}
  \label{eq:a4}
  \begin{array}[l]{l}
Occurs(Does(John,A1,S0)).
  \end{array}
\end{equation}
 
 For simplicity, we have omitted the axioms asserting that $A1$ and
 $A2$ are exactly the actions available and the nonmonotonic reasoning 
 used to derive the conclusion.

 Here $\mbox{Prefers}(actor, s1,s2)$ is to be understood as
 asserting that $actor$ prefers $s1$ to $s2$.  I
 used just two actions to keep the formula for $Choose$ short.  Having
 more actions or even making $Result$ probabilistic or quantum would
 not change the nature of SDFW.  A substantial theory of
 $\mbox{Prefers}$ is beyond the scope of this article.
 
 This illustrates the role of the non-deterministic theory of $Result$
 within a deterministic theory of what occurs.  (\ref{eq:a1}) includes
 the non-deterministic notion of $Result$ used to compute which action
 leads to the better situation. (\ref{eq:a2}) is the deterministic
 part that tells which action occurs.
 
 We make four claims.
 
 1. Effective AI systems, e.g. robots, will require identifying and
 reasoning about their choices once they get beyond what can be
 achieved with situation-action rules.  For example, chess programs
 have always computed their choices and compared their consequences.
 
 2. The above theory captures the most basic feature of human 
 free will.
 
 3. $Result(a1,s)$ and $Result(a2,s)$, as they are computed by the
 agent, are not full states of the world but elements of some
 theoretical space of approximate situations the agent uses in making
 its decisions.  \cite{McC00a} has a discussion of approximate
 entities.  Part of the problem of building human-level AI lies in
 inventing what kind of entity $Result(a,s)$ shall be taken to be.

 4. Whether a human or an animal uses simple free will in a type of
 situation is subject to experimental investigation---as discussed in
 section \ref{sec:apes}.
  
 Formulas (\ref{eq:a1}) and (\ref{eq:a2}) illustrate
 $person$ making a choice.  They don't say anything about $person$
 knowing it has choices or preferring situations in which it has more
 choices.  SDFW is therefore a partial theory that requires extension
 when we need to account for these phenomena.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\section{A generalization of SDFW}
\label{sec:gen}

We can generalize SDFW by applying preferences to actions rather than
to the situations resulting from actions.  The formulas then become


\begin{equation}
  \label{eq:a7}
  \begin{array}[l]{l}
Occurs(Does(actor,Choose\mbox{-}action(actor,a1,a2,s),s),s)
  \end{array}
\end{equation}
(\ref{eq:a1})
%
\noindent
and



\begin{equation}
  \label{eq:a8}
  \begin{array}[l]{l}
Choose\mbox{-}action(actor,a1,a2,s) = \\ \textbf{if}\
Prefers\mbox{-}action(actor,a1,a2,s)\\
\textbf{then}\ a1\ \textbf{else}\ a2.
  \end{array}
\end{equation}

(\ref{eq:a7}) and (\ref{eq:a8}) obviously generalize (\ref{eq:a1}) and
(\ref{eq:a2}), because the earlier case is obtained by writing

\begin{equation}
  \label{eq:a9}
  \begin{array}[l]{l}
Prefers\mbox{-}action(a1,a2,s) \equiv Prefers(Result(a,s),Result(a2,s)).
  \end{array}
\end{equation}

I am doubtful about the generalization, because I don't see how to
represent commonsense preferences between actions except in terms of
preferring one resulting situation to another.

%A possibility is that the ability to compare actions, without
%necessarily comparing their consequences, may have evolved.  Thus
%evolution would have compared the consequences.



\section{Knowledge of one's free will and wanting more or fewer choices}
\label{sec:know}

This section is less worked out than basic SDFW and not axiomatized.
That's why it was best to start simple.

Here are some examples of it being good to have more choices.

``I'll take my car to work today rather than bicycling so I can shop
on the way home if I want to.''

``If you learn mathematics, you will have more choices of scientific
occupations''.

``The more money I have, the more models of car I can choose from.''

``If I escape from Cuba, I will have more choice of what to
read, what I can say or write, and where to travel.''  

%[formulas to come---maybe]

We want to say that situation $s1$ is at least as free as situation
$s2$, written $s1 \geq_{freedom} s2$, if every fluent (AI jargon for
what holds in a situation) achievable by a
single action from $s2$ is achievable from $s1$.  Just as with
equation (\ref{eq:a1}), we can say that $person$ chooses an
action that leads to more freedom at the next situation.

\begin{equation}
  \label{eq:morefree}
  \begin{array}[l]{l}
  s1 \geq_{freedom} s2 \\ 
\equiv \\
 (\forall f) ((\exists a)(Holds(f,
  Result(Does($person$,a),s2))) \\ 
\quad\quad\quad\quad \rightarrow \\ (\exists a)(Holds(f,
  Result(Does($person$,a),s1)))).
  \end{array}
\end{equation}

Here $f$ ranges over fluents.  Having more choices is usually
preferred.  However, one sometimes wants fewer choices.  Burning
one's bridges, nailing the flag to the mast, and promising to love
until death do us part are examples of actions that reduce choices.
The conditions under which this occurs are too difficult for me to
formalize at present.  They can involve fearing that one's preferences
in the future might be different from one's present preferences for
future actions or that making a commitment about one's future actions
confers a present benefit.

%Perhaps we can regard making restrictions on future choices as a
%metachoice and can suitably formalize metachoices.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\section{Philosophical issues}
\label{sec:phil}

The formalism of this paper takes sides in several philosophical
controversies. 

\begin{enumerate}

\item It considers determinism and free will, as experienced and
  observed by humans, as compatible.  This is in accordance with the
  views of Locke and Hume.%, as John Perry told me. % /u/jmc/RMAIL.S02==974
  
\item It takes a third person point of view, i.e. considers the free
  will of others and not just the free will of the observer.
  
\item It breaks the phenomenon of free will into parts and considers
  the simplest systems first---in contrast to approaches that demand
  that all complications be understood before anything can be said.
  In this it resembles the approaches to belief and other intentional
  states discussed in \cite{Dennett71}, \cite{Dennett78}, and
  \cite{McC79a}.  Starting with simple systems is the
  practice in AI, because only what is understood can be implemented
  in computer programs.
\end{enumerate}

It seems to me that formulas (\ref{eq:a1}) and (\ref{eq:a2})
expressing the use of the branching time $Result(e,s)$ function in
determining what events occur make the philosophical ideas definite.
Thus we can see which modifications of the notions are compatible with
(\ref{eq:a1}) and (\ref{eq:a2}), and which require different axioms.

%Simple deterministic free will won't satisfy many philosophical,
%theological, and other advocates of free will.  However, it is enough
%to account for behavior involving making choices and for the feeling
%that one has choices.

The process of deciding what to do often involves considering a pruned
set of actions which eliminate those that have obviously bad
consequences.  The remaining actions are those that one \emph{can}
do.  When someone refers to a pruned action, one sometimes gets the
reply, ``Oh, I could do that, but I really can't, because \ldots .''

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\section{Praise and blame}
\label{sec:praise}

We have maintained that the basic notion of free will is the same for
humans, animals and robots.  Praising or blaming agents for their
actions is an advanced notion requiring more structure, e.g. including
good or bad actions or outcomes.  Blaming or praising humans requires
taking human peculiarities, not shared with agents in general, e.g.
robots, into account.

Consider the verdict: \emph{``Not guilty by reason of insanity''} as
applied to a person with schizophrenia.  Schizophrenia is basically a
disease of the chemistry of the blood and nervous system.  At a higher
level of abstraction, it is regarded as a disease in which certain
kinds of thoughts enter and dominate consciousness.  A patient's
belief that the CIA has planted a radio in his brain is relieved by
medicines that change blood chemistry.  If the patient's belief caused
him to kill someone whom he imagined to be a CIA agent, he would be
found not guilty by reason of insanity.  If we wanted robots
susceptible to schizophrenia, we would have to program in something
like schizophrenia, and it would be a complicated and unmotivated
undertaking---unmotivated by anything but the goal of imitating human
schizophrenia.  The older M'Naghten criterion, ``unable to understand
the nature and consequences of his acts'', uses essentially the
criteria of the present article for assessing the presence or absence
of free will.

I don't know if all praise or blame for robots is artificial; the
matter requires more thought.  Verbally one might praise a robot as
way of getting it to do more of the same.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\section{A possible experiment with apes}
\label{sec:apes}

Here's a \emph{gedanken} experiment aimed at determining whether apes
(or other animals) have free will in the sense of this article.  The
criterion is whether they consider the consequences of alternate
actions.

The ape can move a lever either to the left or the right.  The lever
causes a prize to be pushed off a shelf, either to the left or the
right.  The goody then hits a baffle and is deflected either to the
ape in control of the lever or to a rival ape.  On each trial, the
baffle is set by the experimenter.  The whole apparatus is visible to
the ape, so it can see the consequences of each choice.

The free will involves the ape having two choices and being able to
determine the consequences of each choice.

There is a possibility that the ape can win without determining the
consequences of the possible actions.  It may just learn a rule
relating the position of the baffle and the action that will get the
prize.  Maybe we wouldn't be able to tell whether the ape predicted
the consequences or not.

We can elaborate the experiment to obviate this difficulty.  Let there
be a sequence of (say) six baffles that are put in a randomly selected
configuration by the experimenter or his program at each trial.  Each
baffle deflects the prize one way or the other according to how it is
set.  If the ape can mentally follow the prize as it would bounce from
baffle to baffle, it will succeed.  However, there are 64
combinations of baffle positions.  If a training set of (say) 32
combinations permits the ape to do the remaining 32 without further
trial and error, it would be reasonable to conclude that the ape can
predict the effects of the successive bounces.

I hope someone who works with apes will try this or a similar
experiment.

Frogs are simpler than apes.  Suppose a frog sees two flies and can
stick out its tongue to capture one or the other.  My prejudice is
that the frog doesn't consider the consequences of capturing each of
the two flies but reacts directly to its sensory inputs.  My
prejudice might be refuted by a physiological experiment.

Suppose first that frogs can taste flies, i.e. when a frog has a fly
in its mouth, an area of the frog's brain becomes active in a way that
depends on the kind of fly.  Suppose further that when a frog sees a
fly, this area becomes active, perhaps weakly, in the same way as when
the frog has the fly in its mouth.  We can interpret this as the frog
imagining the taste of the fly that it sees.  Now further suppose that
when the frog sees two flies, it successively imagines their tastes
and chooses one or the other in a consistent way depending on the
taste.  If all this were demonstrated, I would give up my prejudice
that frogs don't have SDFW.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Dennet on complexity

\section{Comparison with Dennett's ideas}
\label{sec:dennett}
% Drescher too /u/jmc/e05/drescher

Daniel Dennett \cite{Dennett03} writes about \emph{The evolution of
  freedom}.  I agree with him that free will is a result of evolution.
It may be based on a more basic ability to predict something about
what future will result from the occurrence of certain events
including actions.  He compares \emph{determinism} and
\emph{inevitability}, and makes definitions so that in a deterministic
world, not all events that occur are inevitable.  He considers that
freedom evolves in such a way as to make more and more events
\emph{evitable}, especially events that are bad for the organism.

Dennett's ideas and those of this paper are in the same direction and
somewhat overlap.  I think SDFW is  simpler, catches the intuitive
concepts of freedom and free will better, and are of more potential
utility in AI.

Consider a species of animal with eyes but without a blink reflex.
Every so often the animal will be hit in the eye and suffer an injured
cornea.  Now suppose the species evolves a blink reflex.  Getting hit
in the eye is now often evitable in Dennett's sense.  However, it is
not an exercise of free will in my sense.\footnote{Dennett (email
of 2003 Feb 27) tells me that the blink reflex involves no
significant free will in his sense}  On the other hand, deciding 
whether or not to go through some bushes where there was a danger of
getting hit in the eye on the basis of weighing the advantages against 
the dangers would be an exercise of free will in my sense.  It would
also be an evitability in Dennett's sense.

Evitability assumes that there is a normal course of events some of
which may be avoided, e.g. that getting hit in they eye is normal and
is avoided by the blink reflex.  My notion of free will does not
involve this, because the choice between actions $a1$ and $a2$ is
symmetric.  It is interesting to ask when there are normal events that 
can sometimes be avoided.  %This should be rather common, but we may
%need some axioms involving $Normally\mbox{-}occurs(e,s)$.

The converse of an evitability is an opportunity.  Both depend on a
distinction between an action and non-action.  In the case of
non-action, nature takes its course.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Summary and remarks}
\label{sec:remarks}

A system operating only with situation-action rules in which an action
in a situation is determined directly from the characteristics of the
situation does not involve free will.  Much human action and almost
all animal action reacts directly to the present situation and does
not involve anticipating the consequences of alternative actions.

 One of the effects of practicing an action is to remove deliberate
 choice from the computation and to respond immediately to the
 stimulus.  This is often, but not always, appropriate.
 
 Human free will, i.e. considering the consequences of action, is
 surely the product of evolution.
 
 Do animals, even apes, ever make decisions based on comparing
 anticipated consequences?  Almost always no.  Thus when a frog sees a
 fly and flicks out its tongue to catch it, the frog is not comparing
 the consequences of catching the fly with the consequences of
 not catching the fly.  %Even if there are two flies and it catches one
% after a hesitation, it still isn't comparing consequences of catching
% one fly or the other. %Ranaism.
 
 One computer scientist claims that dogs (at least his dog) consider
 the consequences of alternate actions.  I'll bet the proposition can
 be tested, but I don't yet see how.
 
 According to Dennett (phone conversation), some recent experiments
 suggest that apes sometimes consider the consequences of alternate
 actions.  If so, they have free will in the sense of this article.
 
 Even if even apes do not ordinarily compare consequences, perhaps
 they can be trained to do so.

 Chess programs do compare the consequences of various moves, and so
 have free will in the sense of this article.  Present programs are
 not conscious of their free will, however.  \cite{McC96} discusses
 what consciousness computer programs need.
 
 People and chess programs carry thinking about choice beyond the
 first level.  Thus ``If I make this move, my opponent (or nature
 regarded as an opponent) will have the following choices, each of
 which will give me further choices.''  Examining such trees of
 possibilities is an aspect of free will in the world, but the
 simplest form of free will in a deterministic world does not involve
 branching more than once.
 
 Daniel Dennett \cite{Dennett78} and \cite{Dennett03} argue that a
 system having free will depends on it being complex.  I don't agree,
 and it would be interesting to design the simplest possible system
 exhibiting deterministic free will.  A program for tic-tac-toe is
 simpler than a chess program, but the usual program does consider
 choices.
 
 However, the number of possible tic-tac-toe positions is small enough
 so that one could make a program with the same external behavior that
 just looked up each position in a table to determine its move.  Such
 a program would not have SDFW.  Likewise, Ken Thompson has built
 chess programs for end games with five or fewer pieces on the board
 that use table lookup rather than look-ahead.  See \cite{Thompson86}.
 Thus whether a system has SDFW depends on its structure and not just
 on its behavior.  Beyond 5 pieces, direct lookup in chess is
 infeasible, and all present chess programs for the full game use
 look-ahead, i.e.  they consider alternatives for themselves and their
 opponents.  I'll conjecture that successful chess programs must have
 at least SDFW.  This is not the only matter in which quantitative
 considerations make a philosophical difference.  Thus whether the
 translation of a text is indeterminate depends on the length of the
 text.
 
 Simpler systems than tic-tac-toe programs with SDFW are readily
 constructed.  The theory of greedy John formalized by (\ref{eq:a3})
 may be about as simple as possible and still involves free will.
 
 Essential to having any kind of free will is knowledge of the
 consequences of one's possible actions and choosing among them.  In
 many environments, animals with at least SDFW are more likely to
 survive than those without it.  This seems to be why human free will
 evolved.  When and how it evolved, as with other questions about
 evolution, won't be easy to answer.

 Gary Drescher \cite{Drescher91} contrasts situation-action laws with 
 what he calls the \emph{prediction-value paradigm}.  His
 prediction-value paradigm  corresponds approximately to the
 deterministic free will discussed in this article.

 I thank Drescher for showing me his forthcoming \cite{Drescher06}.
 His notion of \emph{choice system} corresponds pretty well to SDFW,
 although it is imbedded in a more elaborate context.
 
 This article benefited from discussions with Johan van Benthem,
 Daniel Dennett, Gary Drescher, and John Perry.  The work was partly
 supported by the Defense Advanced Research Projects Agency (DARPA).

\bibliography{/u/jmc/1/biblio}
% Its full name is /u/jmc/1/biblio.bib
%\bibliography{biblio} % Tom worked some magic.
% for use with Alpha on Powerbook 3400
\vfill
\begin{latexonly}
{\tiny\rm\noindent /@steam.stanford.edu:/u/ftp/jmc/freewill2.tex: begun Thu May  16, 2002, latexed
\today}
\end{latexonly}
 
 \end{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

hide-and-seek

Metachoices:  I chose to have no choice in this matter.

@Article{ObhiHaggard04,
  author =       {Sukhvinder S. Obhi and Patrick Haggard},
  title =        {Free Will and Free Won't},
  journal =      {American Scientist},
  year =         {2004},
  volume =       {92},
  pages =        {358--365},
  month =        {July-August},
  note =         {},
}
sobhi@uwo.ca

Check Drescher

Emphasize utility of fw

discuss formalization of evitability in Dennett section

What good is free will?  Just so story.

Whether a system has free will depends on where you cut.

Much choice among alternatives is done in advance and compiled into
situation-action rules, e.g. the route to drive to the store.

regrets about past choices, desire to change Prefers

The multi-worlds interpretation of quantum mechanics doesn't change
matters.  The worlds don't especially branch on human decisions; the
branch all the time.  A human's or computer's deterministic choice
mechanism is just as reliable as any other deterministic mechanism.

%%% John Perry suggestion
I think a bit of reorganization would help this paper.  I would start
with something like

Locke, Hume and other philosophers develop an account of freewill (or
at least freedom) that is compatible with determinism about human
actions.  Call this Basic Free Will.  Basic free will requires that
an agent's action is caused by the agent's preferences between
alternative results of alternative actions.  The causation involve may 
be, but need not be, deterministic.  My view is that humans have basic 
free will, that their having it can be explained evolutionarily, that
it is a good thing that we have it, and that our sense of being free
is based on our experience of contemplating the results of different
actions and making such preference guided choices.

In this paper I show how to formalize basic free will with formalisms
developed in AI, and argue that ... (Then incorporate some of the
material from secttion 5 into this introduction)  (And material from
the abstract and the present section 1.


%\subsection{What kind of an entity is $Result(a,s)$?}
%\label{sec:whatis}

%According to (\ref{eq:a1}) and (\ref{eq:a2}) $person$
%computes $Result(a1,s)$ and $Result(a2,s)$ and computes which is
%better.  If (\ref{eq:a1}) is to describe human or robotic choice,
%the computation must be feasible.

%In the original proposals \cite{McCHay69} for situation calculus, a
%situation was a complete snapshot of the world at an instant.  One
%could not know situations---one could only know facts (fluents) of
%situations.  For present purposes we don't want snapshots of the
%world, because it is indefinite what event an action like
%$Move(Block1,Top(Block2))$ corresponds to in a given state of the
%world.  Is $Block1$ moved slowly or rapidly?

%Therefore, the situations of our theory must be approximate
%entities.  Thus $Occurs(Move(Block1,Top(Block2)),s)$ should result
%in a definite approximate situation
%$Result(Move(Block1,Top(Block2)),s)$.

%However, we don't always want to take our approximate situations as
%elements of a fixed set of finitely describable objects.  That's okay
%for a game like chess, but human-level AI often requires something
%more general.  We would like to allow for the possibility that
%unexpected events may occur, e.g. $Block1$ falling off $Block2$.

%%[more to come]

%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%

%A human (and maybe a dog) has a notion of what he ought to do.  This
%has both social and individual aspects and general and specific
%aspects.  In general I ought not to drink so much coffee, and if I do
%drink coffee, I ought not put so much sugar in it.  Perhaps I
%ought to pour out the cup of sugared coffee sitting on my desk.  These
%oughts are individual rather than social.

%I ought to read my student's paper so I can talk to him about it this
%afternoon.  This is a specific ought, but in general I should try to
%understand better my students' states of mind.

%Humans develop this notion of ought from a very early age, maybe 2
%years old or maybe 4.  One's idea of what one ought to do or ought not 
%to do affects one's actions, but does not determine it.  Sometimes it
%is mere weakness of will that prevents us from doing what we ought,
%but sometimes it is a rejection of a criterion seen as imposed from
%without.

%We need to distinguish what an agent ought to accomplish from the
%actions it intends to achieve that result.

%%%%%%%%%%%%%%%%%%%%%%

% Contrariwise, the anthropologist John F. Hoffecker \cite{Hoffecker02} 
% holds that only modern humans could consider the consequences of
% alternative actions.  The Neanderthals couldn't and neither could the 
% first humans, modern in body form.  Only when modern humans settled
% ice age Eastern Europe did what Hoffecker calls \emph{symbol-based
%   technology} develop.
 

%%%%%%%%%%%%%%%%%%
 
%\section{No free will after all?}
%\label{sec:nofree}

%We can make a formalism in which even the comparison of alternatives
%is regarded as just an immediate reaction to the situation.  We do it
%by \emph{externalizing} the facts about the choices available.

%Compare the following to cases in which the actor chooses a hotel
%room.  In one case, he goes into both rooms, comes out and then
%decides.  In the other case he decides on the basis of the
%descriptions of the rooms.  We can reduce the second case to the first 
%by \emph{externalizing} the facts about the room, i.e. regarding that
%aspect of the brain or the computer memory as external to the decision 
%process.  In either case, however, their is a need to compare
%alternatives which isn't simply a reaction to a situation.

%Maybe Brooksians or telereactors would accept writing a program to
%choose a hotel room as a challenge.
