Free Will and God's Providence Part III. The Problem of God's Grace

"Do not say 'It is the Lord's doing that I fell away',
for he does not do what he hates.   
Do not say 'It was he who led me astray',
       for he has no need of the sinful........
It was he who created mankind in the beginning,
       and he left them in the power of their own free choice."
Sirach 15:11-15

The objections to Free Will stated in Part II of this series were

1. Physics gives only one future for the Universe;
2. Our brains are pre-wired, so moral choices are not possible;
3. Our environment determines what our moral choices will be;
4. God's grace determines our actions.

I countered the first three objections in Part II, and  in Part III (here) will examine the most difficult, #4, using in part propositions set forth by Fr. Luis de Molina, a  16th century Jesuit theologian and philosopher.   Before giving these arguments, I should summarize the Church's position on free will and God's foreknowledge.   Please note that as a theological novice, I would be grateful for corrections and emendations where I err or am wanting.    The term "grace" in what follows is used without definition or exegesis (that would need a book), but my meaning is that of "Actual Grace" (God's gift undeserved by us), the push the Holy Spirit gives us to do moral deeds and salvific acts.

THE CATHOLIC CHURCH ON FREE WILL AND GOD'S GRACE

"To God, all moments of time are present in their immediacy. When therefore he establishes his eternal plan of "predestination", he includes in it each person's free response to his grace..."For the sake of accomplishing his plan of salvation, God permitted the acts (The Passion of Jesus Christ) that flowed from their blindness." - CCC, 600

A brief account of the history of the teaching of Catholic theologians on free will and God's grace is given below.   For a more extended explanation  see the references below.*  In the Old and New Testaments are many references to the tension between God's Will and man's free will (including the most excellent one from Sirach, given above).    See  On Grace and Free Will for a compendium of these.

 ST. AUGUSTINE ON GRACE AND FREE WILL

St. Augustine of Hippo laid the foundations for the Church's teaching on God's grace and man's free will in his treatise against the Pelagian heresy, "On Grace and Free Will".     His arguments, based on Scripture, can be summed up in the following quote:

".. not only men's good wills, which God Himself converts from bad ones, and, when converted by Him, directs to good actions and to eternal life, but also those which follow the world are so entirely at the disposal of God, that He turns them wherever He wills, and whenever He wills [emphasis added]— to bestow kindness on some, and to heap punishment on others, as He Himself judges right by a counsel most secret to Himself, indeed, but beyond all doubt most righteous." St. Augustine, On Grace and Free Will, Ch. 41

THEOLOGIC ARGUMENTS ON GRACE AND FREE WILL

If it is by grace given by the Holy Spirit that God affects men's will, and if, as St. Augustine says, this is done "wherever He wills, and whenever He wills", where is man's free moral choice? In order to unravel this theological knot, we have to think about how God bestows grace, given His omnipotence, His omniscience, and His will to create good.  

To give in detail the theological arguments on this question would require a chapter, not a blog post, so I'll summarize the extreme points of view by an example.   (For fuller accounts refer to the references below, particularly Controversies on Grace.)      Consider St. Maximilian Kolbe, who took the place of another prisoner at the Nazi concentration camp, Auschwitz, to die by starvation and carbolic acid injection.   We can think about  this salvific act in two ways:

• Scenario 1--God wills that St. Maximilian Kolbe acts as he does and knows by His "Free Knowledge" that St. Kolbe will perform this salvific act.  He knows that because he wills to give him grace ("efficacious" grace) to perform the act.  
• Scenario 2--God knows by his "Middle Knowledge" that St. Maximilian Kolbe, given God's grace, would perform this salvific act, but the performance of the act is dependent on St. Kolbe's free will assent to that grace.    This grace is "neutral", that is to say it is neither "efficacious" nor "sufficient".   ("Sufficient grace" is that which would be given by God even though He knows it will not be used.)

Scenario 1 reflects the Thomistic interpretation of Grace and Free Will, emphasizing the supreme sovereignty of God, His omnipotence and omniscience.    The Thomists add an extra impetus, Divine Premotion or Predetermination such that good moral actions will "infallibly result", but since these actions are not necessarily invoked, free moral choice is still available to the agent.  Both Boedder and I are puzzled by this:

"If we object to this that it is exceedingly difficult to understand how a creature thus predetermined can possibly have the actual use of its freedom, our opponents do not deny that there is some mystery in this. But they refer us to the incomprehensibility of Divine causation at once most sweet and most efficacious." Physical Premotion and Predetermination, Bernard Boedder, SJ.

The philosopher Robert Koons has attempted to explain this apparent "incomprehensibility"  by symbolic logic, legerdemain that establishes the identity of the propositions below,  such that free will is still operative:

• The character of X is such that he freely wills to do the morally correct action in circumstance C;
• God predetermines the moral choices of X by efficacious grace.

(I have to confess I don't understand the symbolic logic manipulations or the final conclusion.)

Scenario 2 gives a Molinist interpretation, emphasizing the importance of man's  free will.    There are variations of this position--Congruism, Syncretism--that vary the importance of God's sovereignty in relation to man's free will.     Thomists object to the Molinist position because it apparently sets limits to God's authority.   I don't agree with this objection.    God gave Adam and Eve freedom to commit Original Sin, as a necessary consequence of free will.      If He did not, if all we do--sinful and good--is by His will, not ours, then we are puppets on a stage;  the whole notion of moral responsibility fails.

THOUGHTS ON PRAYER AND FORGIVENESS. 

As a Catholic I pray privately and in public for the Holy Spirit to give me the grace to do the right thing and for those I love to do also.   If our actions are pre-ordained by God then these prayers are futile, and that I cannot believe.   Thomists object that active praying, absent God's pre-ordained outcome for the desired event, smacks of the Pelagian heresy that man can save himself without the grace of God.    The theologian Thomas Flint counters this argument:   praying for the Holy Spirit to make you better, for example to rid yourself of an addiction, is praying for God to do something TO you, not FOR you and is certainly dependent on God's grace.

Now we come to what the initial thrust of this series of posts was all about:  can we hold those who commit sins morally responsible for their actions and can we forgive them for their sinful deeds.   Given the Thomist view,  that God predetermines our moral behavior, I don't see how one can hold sinners responsible for their actions and so forgiveness is automatic.    Given the Molinist view, that we are freely responsible for our actions, then we can be held responsible for sins.   But as Christians, we can forgive the sinner, but not the sin.

Finally I'll say that I'm not entirely satisfied with the Molinist interpretation.   It seem to me that if God knows what we will do--even if he does not determine that we do it--we are not totally free in our moral choices.    There need to be options, different possibilities for what we can do, in order that freedom of choice--free will--be exercised.     In the fourth post of this series I'll explore what quantum theory might offer to give this freedom, with God's complete knowledge of the future and will for what occurs to hold.



 *REFERENCES
Controversies on Grace, The Catholic Encyclopedia
Divine Providence, the Molinist Account, Thomas Flint.
Dual Agency: A Thomistic Account of Providence and Human Freedom, Robert Koons.
Molina / Molinism, Alfred Freddoso.
On Grace and Free Will, St. Augustine of Hippo.
Physical Premotion and Predetermination, Bernard Boedder, S.J.

Free Will and God's Providence Part II: The Moral Responsibility of Evil-Doers

British woman who joined ISIS calls for beheading of Christians

   Headline, Christian Today, September 1st, 2014

New York man charged with hate crimes for seven 'knockout' assaults

         Headline, CNN Justice, January 6, 2014

Homegrown jihadist shoots N.J. teen

8 times, calling it a ‘just kill’: report                Headline, Washington Times, September 18th, 2014 

Scandal of the 1,400 lost girls in Rotherham      

Headline, Times of London, August 27th 2014

Fort Hood shooter sentenced to death for 2009 killings

Headline, Reuters Edition

"God created things which had free will. That means creatures which can go wrong or right. Some people think they can imagine a creature which was free but had no possibility of going wrong, but I can't. If a thing is free to be good it's also free to be bad. And free will is what has made evil possible. Why, then, did God give them free will? Because free will, though it makes evil possible, is also the only thing that makes possible any love or goodness or joy worth having. "             C.S. Lewis, The Case for Christianity 

Those are disturbing headlines (and meant to be)!   Why does God allow such evil?    The answer is given by C.S. Lewis above, and with his quote I might end this post.    But there are those who object "there is no such thing as free will" and consequently,  moral responsibility for one's deeds is a non-issue.   So we should answer their attempt to reject God's troublesome gift, freedom of choice.

FREE WILL OBJECTION 1:  THERE IS ONLY ONE FUTURE FOR THE UNIVERSE

I'll repeat what I said in the first post: "If the universe is deterministic, plays out according to set physical laws, there can be only one future and there can be no free choices.   If, as special relativity suggests, there is a particular past, present and future for each  particular reference frame, so that all is encompassed in a block universe, then everything is laid out before us, independent of our actions."

Or, as the philosopher Michael Lockwood would have it:

"To take the space-time view seriously is indeed to regard everything that ever exists, or ever happens, at any time or place, as being just as real as the contents of the here and now. And this rules out any conception of free will that pictures human agents, through their choices, as selectively conferring actuality on what are initially only potentialities." Michael Lockwood, The Labyrinth of Time

The scientific arguments against Lockwood's claim will be given at greater length in another post, but there is one common-sense refutation--if I were to believe it, why should I write this post?    To put it another way

"People may sincerely think they believe in determinism, but they act otherwise, and must act otherwise, every time they deliberate.  The great American philosopher Charles Pierce argued that a belief that cannot be consistently acted on cannot be true. If he’s right about this – and I believe he is – then determinism must be false." Greg Boyd, Three Arguments against Determinism. 

FREE WILL OBJECTION 2: MY NEURONS (GENES) MADE ME DO IT

If then universe is determined, as in objection 1, it would follow that whatever we did and thought was purely a function of our brain states, and since these brain states are physically set, there is no way to make free moral choices, no such thing as an immaterial soul to oversee our actions.   On the other hand, even in a indeterministic universe the claim of most cognitive scientists would be that the assembly of neurons, the concatenation of biochemical and electrical events in the brain, determined our acts.   Neuroscientists cite much research, ranging from the 19th century case of Phineas Gage, whose character changed radically after a railroad spike was driven through his frontal lobe, to that of the neuroscientist Michael Gazzaniga, who argues that split brain phenomena show free will does not exist.  

Neuro-materialistic arguments against free will can be summarized thus:

• Material damage to the brain causes change in behavior and moral attitudes.
• Psychoactive drugs change behavior and moral attitudes.
• Therefore behavior is determined only by the physical nature of the brain and the biochemical/electrical events occurring therein, and there is no such thing as free will.

In his book, My Brain Made Me Do It, Eliezer Sternberg has argued by analogy against this neuro-materialistic proposition.   Consider a jet fighter;  it can crash because of damage to the wings, the jet engines, faulty fuel, etc.   But even when it is fully functional, it needs a pilot to fly it.    Similarly the brain can crash due to damage or harm to its parts or to bad biochemistry, but there is still something else--which I choose to call a soul--a pilot, needed to make it function.

There is another, stronger argument against neuro-materialism. Consider identical twins (same DNA). If moral behavior is determined only by the physical and chemical natures of the brain, one would expect these genetically identical twins to behave alike--if one is a criminal, so would the other be, with 100% concordance. However, a Danish study has shown only a 52% rate for concordance between identical twins (compared to 22% for fraternal twins). Moreover, this study has been criticized as neglecting linked environmental behavioral factors by Carey: "The results suggest that the genetic influence on registered criminality may be more modest than previously thought."

Nevertheless, neuroscientists conclude that free will is an illusion, on the basis of experiments involving simple, inconsequential choices.   The most cited of these is the Libet experiment, which shows a brain potential exists before a subject is consciously aware of making a choice.  On the other hand  Timothy Bayne and Eliezer Sternberg say that the Libet experiments do not justify free will skepticism.   The most significant  objection, which Sternberg supports by several detailed examples of moral/ethical decision problems, is that the Libet experiment (and others) involve inconsequential choices, choices which do not require reflection, consideration of an unlimited set of moral and situational factors.   Sternberg classifies these kinds of decisions as "boundless", that is to say decisions that cannot be determined algorithmically, as might be done in a computer, unlike those processes that proceed almost without conscious deliberation (like riding a bicycle).   Since ethical decision making is "boundless", it cannot proceed solely from algorithmic brain processes, but requires another agency.  

I am not foolish enough to argue that ethical behavior does not involve physical and chemical characteristics of the brain, or that heredity might not have some influence on the capacity for making good moral choices.   I suggest that the brain is, like the jet fighter in Sternberg's analogy, a necessary vehicle for something else--the soul, the will, conscience--that which is endowed in each person by the Holy Spirit at conception.    How this matures as the human matures, how it acts for each of us is still and may remain a mystery.

FREE WILL OBJECTION 3:  "IT'S OUR BRINGING-UP THAT GETS US OUT OF HAND"

The best (and most entertaining) case for nurture as the prime element determining moral behavior is the "Gee Officer Krupke" routine in West Side story.   It encompasses all the factors--parental neglect, economic deprivation, bad moral influences--that sociologists claim as causal for criminality.  

However, there are two objections to nurture as the sole determinant.    First, there are many examples of people who have escaped poor economic circumstances, racial prejudice, bad parenting to become models of moral behavior.    Second, there are many examples of people in good economic circumstances, with good parents who do evil deeds.     Thus economic circumstances and parental care are neither neccessary nor sufficient conditions for evil behavior.    If we look at the headlines above, many of those involved--the rap singer who converted to Islam, the Fort Hood shooter, the 9/11 terrorists--were comfortably situated economically or even well-to-do.    For every "knock-out" criminal who comes from a single-parent environment, there is another that gets to be a judge or politician.

Again, the influence of a poor environment--economic or parental--can not be overlooked.   But it is not the only or the sole factor in moral behavior.    There is that small, still voice within us that tells us what is right or wrong, implanted at birth, the " ius naturale est quo natura omnia animalia docuit", the natural law which underlies the behavior of a rational being.

NOTE (added later):   a recent study at St. Mary's College, University of London has shown that terrorists are more likely to be well-off and educated.

FREE WILL OBJECTION 4: GOD'S GRACE DETERMINES OUR ACTIONS

In his arguments against the Pelagian Heresy, On Grace and Free Will, St. Augustine said

"There are some persons who suppose that the freedom of the will is denied whenever God's grace is maintained, and who on their side defend their liberty of will so peremptorily as to deny the grace of God. This grace, as they assert, is bestowed according to our own merits. It is in consequence of their opinions that I wrote the book entitled On Grace and Free Will." 

Whether God's arbitrary (?) bestowal of Grace negates Free Will will be dealt with at length in the next post on this topic, as will how we should deal with forgiveness, given that free will and moral responsibility exists.

Free Will and God's Providence. Part I: An Introduction to the Problem

 Then came Peter to him, and said, Lord, how oft shall my brother sin against me, and I forgive him? till seven times?  Matthew 18:21 (KJV)

"I have set before you life and death, blessing and cursing: therefore choose life, that both thou and thy seed may live." Deuteronomy, 30:

“To be a Christian means to forgive the inexcusable because God has forgiven the inexcusable in you.”  C.S. Lewis.

"Of course I believe in free will. I have no choice."  Isaac Balshevis Singer, The Salon Interview 1987.

INTRODUCTION

In the past decades we have seen outrage after outrage committed by religious terrorists, gangs, members of drug cartels--the murder of Christian, Jewish and Arab children, the rape of Christian nuns, the trafficking of women and girls, "knockout" beatings of whites, the teaching of hate.   In this post I'll not discuss how these villains attempt to justify their acts on the basis of religion or deprived socio-economic status.   Rather, I want to address the following questions.

• Do the terrorists commit these deeds freely, as we understand Free Will?
• If they do act freely, how is it possible, for us as Christians, to forgive them?
• Whether or not their actions be free, is there a way to see this evil  as compatible with or proceeding from God's Foreknowledge?

There will be three posts which attempt to study these acts as a case study in terms of the general subject of Free Will and God's Providence.    The first (this one) will attempt to define the problem.   The second will rebut  physicalist assertions that there is no such thing as free will and will therefore support the contention that we are morally responsible for our actions.     The third  will discuss how free will is compatible with God's Foreknowledge and Divine Will,  in a context provided by the Middle Knowledge of Luis de Molina (Molinism) and how this might enable us to "forgive" those who commit evil.

THE PROBLEM OF FREE WILL

" 'Free Will' is a philosophical term of art for a particular sort of capacity of rational agents to choose a course of action from among various alternatives." Timothy O'Connor, Stanford Encyclopedia of Philosophy

Timothy O'Connor's definition above of Free Will sets the stage for stating the problem, although one important adverb has been omitted from his definition: rather than "agents to choose" I would write "agents to choose freely".    One might also add "after due deliberation and reflection".  

What are the objections to Free Will as thus defined?  

• First, if the universe is deterministic, plays out according to set physical laws, there can be only one future and there can be no free choices.   If, as special relativity suggests, that there is a particular past, present and future for each  particular reference frame, so that all is encompassed in a block universe  and everything is laid out before us, independent of our actions.
• Second, if our genes determine our personality, character and intelligence, how can there be different ways for us to choose, and thus to be free?
• Third, if, on the other hand, we are formed by economic and social circumstances that mold our morals and attitudes, what ethical options are then open?

Or, if as some would have it, the randomness of quantum mechanics governs our decisions, how can this randomness be reconciled with conscious deliberation and free choice?
Where is the entity within us, the soul, that can act freely?

THE PROBLEM OF DIVINE PROVIDENCE

"By His providence God protects and governs all things which he has made... even those things which are yet to come into existence through the free action of creatures"  First Vatican Council, Dei Filius

As a Catholic, I believe in a transcendent, omnipotent and omniscient God.   "Omnipotent" means God can do what He wills, all that does not contradict the laws of logic or of necessary truths--God  can't and wouldn't make 2+2=5 or a four-sided triangle.    "Omniscient" means God knows what has happened, is happening, and will happen.    God is eternal, so that past, present and future (in any frame of reference) are in His ken.  (Not all theologists agree with this last dictum.)    Such is Divine Providence, God's omnipotence and His omniscience, including His Foreknowledge, the knowledge of the future.

Thus God knows whether I will do my daily prayer, sleep late and miss Mass tomorrow, get angry at the slow driver in front of me next week,...But if God does know all my actions, past and future, where is my freedom to do differently?   Supposedly God has given me free will to choose, but if he knows what I will choose, am I truly free, even if I think I am?  That is the problem of reconciling Free Will and God's Foreknowledge.

THE PROBLEM OF MORAL RESPONSIBILITY.

If we do not have free will can we be held to be morally responsible for evil acts?  Insanity--lack of knowledge of the moral implication of our acts--is a defense against murder and claims of "irresistible impulse" have been used to deny guilt.
The Catholic Catechism gives

"Mortal sin is sin whose object is grave matter and which is also committed with full knowledge and deliberate consent."1857

The phrase "deliberate consent" implies a free will consent, so we might ask whether  addiction, genetic predisposition, socio/psychological factors  could be considered mitigating factors.   The theologians are not in total agreement, but some do propose that addiction and other conditions negating free will mitigate the gravity of sin.    Or, as the Jets proclaim to Officer Krupke in West Side story, "It's just our upbringing that gets us out of hand".

THE PROBLEM OF FORGIVENESS

So, what we have to examine in the next posts are

•  Do those committing these acts have free will, i.e. do they commit them with "full knowledge and deliberate consent"?
• Does God know beforehand that these acts of terror will be committed?   And, if so what does this say about God permitting evil and allowing free choice?
• And, given the answers to those two questions, what does "forgiveness" mean, and how do we effect it?

REFERENCES

(I've been on a steep learning curve in this set of posts--there's a vast literature  both on the web and in texts, and I'm only going to cite a very few of these that I've found particularly useful.)
Robert Kane, Reflections on Free Will and Determinism

John Martin Fischer, Robert Kane, Derk Pereboom, Manuel Vargas, Four Views on Free Will.
Timothy O'Connor, Free Will (Stanford Encyclopedia of Philosophy)
Eliezer J. Sternberg, My Brain Made Me Do It: The Rise of Neuroscience and the Threat to Moral Responsibility
Alfred Freddoso, Molinism
St. Augustine, On Grace and Free Will
The Block Universe of Special Relativity
Other references will be added in subsequent posts.

Do Quantum Entities Have Free Will? (And Do We?); Or, "Does it Matter if God Plays Dice?"

"Of course I believe in free will. I have no choice."  The Salon Interview, 1987, Isaac Balshevis Singer,   "There is no evidence for determinism." Princeton Lectures, John H. Conway "Philosophy is too important to be left to philosophers" Unification beyond the Core , Frank Wilczek (also attributed to John Wheeler) "Does it even matter if God plays dice?"  Rachel Thomas' Plus-math Interview of John Conway "...dearly beloved...be not disturbed by the obscurity of this question; I counsel you first to thank God for such things as you do understand; but for all which is beyond the reach of your mind, pray for understanding from the Lord, observing at the same time peace and love among yourselves... "On Free Will and Grace , St. Augustine of Hippo

The Proof of the Kochen-Specker Theorem
(from plus-maths discussion, by Rachel Thomas)

In one of the later Foundation novels, Isaac Asimov envisages a world, Gaia, in which a super conscious mind pervades the world, from the smallest virus or rock to the humans (and robots) in it.   In such a world it would be natural that quantum entities have free will, and there would be nothing remarkable in the  Conway-Kochen Free Will Theorem :

"It asserts, roughly, that if indeed we humans have free will, then elementary particles already have their own small share of this valuable commodity. More precisely, if the experimenter can freely choose the directions in which to orient his apparatus in a certain measurement, then the particle’s response (to be pedantic – the universe’s response near the particle) is not determined by the entire previous history of the universe." The Strong Free Will Theorem, John Conway and Simon Kochen. 

I won't give an extended discussion of the proof (see the link in the caption for a very clear and detailed presentation by Rachel Thomas or the link for the quote for the rigorous mathematical proof).   Nor will I give an extended discussion of what free will might be (a topic about which philosophers have contended over the past millennia).   Halfway through writing this post, I discovered John Conway's six Princeton lectures on his Free Will Theorem online.   So really, rather than writing, I should just direct the reader to those lectures to see what the Free Will Theorem is all about.   I should also note that Conway does not claim his Free Will Theorem disproves determinism;  indeed, he says there is no way to disprove determinism, despite the fact that there is no evidence for it.

Nevertheless, I would like to use the Free Will Theorem (abbreviated as FWT) as a springboard to discuss several issues in interpreting quantum mechanics, namely how randomness and consciousness might enter into interpretations of quantum mechanics.  (Fear not, gentle reader--this will not be a "What the Bleep" presentation, or a jump into Eastern mysticism.)

From "The Spin Family"
5 sculptures by Adrian
Voss-Andreae

First, let's see how the three axioms are empirically justified by contemporary physics;  I'll phrase the axioms to make the physics clear (I hope).
1.  SPIN.   There exist particles with intrinsic angular momentum (spin) with spin quantum number, S= 1, such that components of angular momentum along a preferred axis (as defined by, say, an electric/magnetic field or a polarizer) are 1,  0,  and -1 (for angular momentum, I'm using units of hbar, where hbar = Planck's constant/(2pi)).   The three components are shown in the illustration, "The Spin Family".   The total angular momentum vector precesses about the defined direction.   The upper cone shows the component with 1; the flat disc, the component with 0; the downward pointing cone, the component with -1.     Then quantum mechanics shows that the squared components of spin in some arbitrary choice of three perpendicular directions  must be either 0,1,1;   1,0,1; or 1,1,0 .   Note that photons have S=1, which is handy, because laser experiments can be done with photons.
2.  TWIN.   It is possible to produce a pair of particles with combined total spin angular momentum  0, in what is called a "singlet" state.    Thus, if particles a and b are so produced in a singlet state, then if particle a has angular momentum component (in units of hbar)  +1 along the defined direction, particle b must have component -1; if particle a has component 0, so must particle b;  if particle a has component -1, then particle b must have component +1.   If the two particles should be separated after being created in a singlet state, their spin components will still be correlated:  if a value of 1 or 0 for the squared component is measured in a certain direction for particle a, the same value must be measured in that direction for particle b.    This "entanglement" of spin components for separated particles was used by David Bohm in his version of the EPR (Einstein-Podolsky-Rosen) paradox and entered into Bell's Theorem, to confirm (or disprove) hidden-variable theories for quantum mechanics.   Such entanglement has been verified by many experiments (done to test Bell's  Theorem) over separated distances of many miles.
3. MIN (the original third axiom was FIN, having to do with limitations of speeds of transmission because of special relativity). We'll take two investigators A and B who are separated in space. The spin system A studies is labeled a, and the spin system B studies is labeled b; a and b are separated parts of a singlet, and each has spin quantum number S=1. Then Conway/Kochen state in axiom 3 that the choices by A and B for studying direction of spin components are independent:
"Assume that the experiments performed by two investigators A and B are space-like separated. Then experimenter B can freely choose any one of the 33 particular directions w, and a’s response is independent of this choice. Similarly and independently, A can freely choose any one of the 40 triples x, y, z, and b’s response is independent of that choice."
This axiom was chosen to make the FWT stronger, and to overcome objections made to the use of the FIN axiom.

We can proceed now with a short summary of the Conway-Kochen theorem proof.   First, it rests on the Kochen-Specker theorem (KST), which itself is quite important.   KST shows that hidden-variable theories for quantum mechanics having functional relations amongst the variables, independent of measurement procedures, are not valid.    Or, as Conway puts it, "the spin chooses its value on the fly." Accordingly, the  measured value does not depend on the previous history of the world.   Conway/Kochen's proof   assumes that separated investigators (A-Alice and B-Bob) have free will in choosing the direction for measuring spin.   Then by use of the Twin, Spin and Fin axioms, and the Kochen-Specker theorem, they show, in a proof by contradiction, that there is no functional relation for spin measurements by Bob, and therefore that the spin response is independent of the previous history of its worldline, i.e. the spin system's response is "free".

What do Conway/Kochen mean by "free will"?    Both for the investigator and for particle system they mean that the choice--what is done--does not depend on previous history.   A more conventional interpretation might be that free will is the ability to freely choose amongst several options.   The term "freely" is understood, but susceptible to a number of definitions. (As with Justice Potter Stewart's definition of pornography, "I know it when I see it").   In his Princeton lectures and interviews for Rachel Thomas,  Conway is quite emphatic that this freedom is not just "randomness".    To show how randomness might enter, he sets a backgammon tournament as an example.    The tournament director casts all the throws of the dice the night before the tournament, and then calls them out sequentially as each game is played, so that there is a level playing field for each contestant.  An example more familiar to me is that of a duplicate bridge  tournament.    At each table the four hands are dealt out randomly to begin with

Duplicate Bridge: Declarer's Hand  (Wikipedia article)

and the teams rotate from table to table, so that each team has played at each table with the same dealt hands.   There is a predetermined initial lay of the cards, but the players are free to deal with the sets of hands as they will.  (Is this an example of what philosophers call "compatibilism" in free will?)   Conway strongly argues that the FWT forbids randomness as an agency, whether occurring at the event or predetermined:

"That’s why it doesn’t matter if God plays dice with the Universe, or not. Even if we allowed random numbers into the Universe, which I’ll think of as God’s dice, that’s not sufficient to explain the lack of pre-determinism in quantum physics." quoted in Rachel Thomas's article.

I have a problem understanding this assertion.    Granted that the FWT  shows that the particle response cannot be predicted by a function involving past history, how exactly does that dispense with pseudo-randomness, predetermined before the world began?    What can we learn from physics, in general, and quantum mechanics, in particular, to understand Conway's argument?

Let's consider first "random noise" in electronic devices, my old friend from nmr spectroscopy and MRI.   Such noise can be characterized by mean square amplitude and correlation times, which in turn can be related to physical parameters.  Molecular motion candidates for randomness also obey functional relationships.  I've cited these as examples that don't contradict Conroy's argument about predetermined randomness.   Can the reader cite others that might?  I can't.

Schrodinger's Cat (U. Toronto, Physics)

If we turn to quantum mechanics, the state function, which most generally can be put as a superposition of basis states ("Schrodinger's Cat"), evolves deterministically.   The randomness comes at measurement, when the state function collapses, except for that basis state which gives the measured result.    Chance/randomness for the measured result comes from the component nature of basis states, and should be distinguished from weighting in a mixture of states.  (For links to basic web material on quantum mechanics, please refer to another post of mine, Quantum divine intervention.. )  Quantum Mechanics does not include this state function collapse on measurement as part of the general theory, and thus results the so-called Measurement Problem .

Amongst the various interpretations and alternative theories which attempt to resolve the measurement problem, I'd like to focus on two:  1) the relation between the observer, consciousness and measurement in quantum mechanics;  2)  many worlds/many minds (relative state theory).   From the earliest days of quantum mechanics, the great thinkers--Von Neumann, Wigner, Schrodinger--have posited that the final step in the measurement process was observation by a mind, a consciousness, and thus the mind and quantum mechanics were entwined.   The delayed choice experiment adds weight to this belief, I believe. There are many physicists (not abashed by the popularization of this notion in quantum leap science fiction) who subscribe to the Many Worlds interpretation of quantum mechanics that at each measurement one option is made apparent and the rest branch (into alternative universes, alternative minds?).

Here finally is my take:  as with John Wheeler, I believe there is a participatory universe created by the observer, conscious minds (ours? God's? both?).  The free will of the quantum entity is our own free will.    There is an infinitude of possible universes and our ego, our consciousness traverses these as it makes choices.   If there is a universe where we measure the particle going through one slit, there is another (with other conscious minds) where it goes through both. Such a view resolves a conflict between free will and God's omniscience and omnipotence--if God knows what our future actions will be, how can our will be free?  And the answer would be a type of Molinism, God is aware of all possible counterfactuals, but they are only counterfactuals for our mind, our ego, not for God.