Podcast – Page 2 – Todd Decker

Systematic Theology: Ethics

The statutes and judgments given to Israel were a mark of their special wisdom and understanding: “Surely this great nation is a wise and understanding people.” (Deuteronomy 4:6) Such wisdom and understanding are valuable to us not only for understanding the way things are but also for knowing how to live. The laws and statutes given by God are worth continual study and bring great reward: “O how I love thy law! It is my meditation all the day.” (Psalm 119:97)

The history of the world is punctuated with certain transformative events that have fundamentally altered its course. The most significant of such events was the mortal life of Jesus of Nazareth. At the completion of that event, with the Resurrection of Christ, everything changed. The most salient fact of human existence, our finite temporal horizon ending with death, was abolished. Another transformative event took place about one thousand years before that in the wilderness of Sinai, when Moses received the torah (תּוֹרָה) “instruction”, at the hand of the Lord. This too was a foundational event in the history of the world on which the legal, moral, and philosophical developments of the nations have turned in the centuries since. Moses himself witnessed to the people that this would be the case and called their attention to it in his great recitation in Deuteronomy:

“Surely I have taught you statutes and judgments, just as the Lord my God commanded me, that you should act according to them in the land which you go to possess. Therefore be careful to observe them; for this is your wisdom and your understanding in the sight of the peoples who will hear all these statutes, and say, ‘Surely this great nation is a wise and understanding people.’ For what great nation is there that has God so near to it, as the Lord our God is to us, for whatever reason we may call upon Him? And what great nation is there that has such statutes and righteous judgments as are in all this law which I set before you this day? (Deuteronomy 4:5-8, NKJV)

The statutes and judgments distinguish Israel and make it noteworthy among the nations. “Surely this great nation is a wise and understanding people.” Considering how many nations and peoples look to the Bible, to the statutes and judgments that the Lord gave to Israel, it seems to me that this has been dramatically fulfilled in the centuries following Sinai.

I find the torah a joy to read: a rich source of inspiration for the mind and for the practical aspects of life, both theory and wisdom. I recently read a Psalm that seemed like a perfect response to the Lord’s divine instruction.

“O how I love thy law! it is my meditation all the day.
Thou through thy commandments hast made me wiser than mine enemies: for they are ever with me.
I have more understanding than all my teachers: for thy testimonies are my meditation.
I understand more than the ancients, because I keep thy precepts.
I have refrained my feet from every evil way, that I might keep thy word.
I have not departed from thy judgments: for thou hast taught me.
How sweet are thy words unto my taste! yea, sweeter than honey to my mouth!
Through thy precepts I get understanding: therefore I hate every false way.”
(Psalm 119:97-104, KJV)

What kind of person do you want to be? You could do a lot worse than aspire to wisdom and understanding. The Lord was pleased when Solomon asked to be blessed with “an understanding heart to judge” and to “discern between good and evil.” (1 Kings 3:9, NKJV) And the Lord said: “Because you have asked this thing, and have not asked long life for yourself, nor have asked riches for yourself, nor have asked the life of your enemies, but have asked for yourself understanding to discern justice, behold, I have done according to your words; see, I have given you a wise and understanding heart.” (1 Kings 3:11-12, NKJV) These are aspirations of the highest good. No wonder then that law, torah, which gives wisdom and understanding, is sweet to the taste, “sweeter than honey”.

Not all studying we do in life is a delight, even if it’s necessary or useful. Sometimes we have to study subjects that aren’t all that interesting to us and that can be quite a slog. But when you’re studying something that you really find interesting, that is delightful. I really enjoy studying the sciences, which I’m fortunate enough to be able to do in my professional and academic life, as well as for pleasure. And other people have other interests. But I happen think that torah, the instruction, laws and statutes given by God in the Bible has the potential to bring universal delight to everyone, if approached receptively. It can be the kind of thing that you can’t stop thinking about, such that, like the Psalmist, you meditate on it all day.

I believe that this delight for the torah originates in our very natures. I like the way it’s put in the Catholic Catechism:

“Endowed with ‘a spiritual and immortal’ soul, The human person is ‘the only creature on earth that God has willed for its own sake.’ From his conception, he is destined for eternal beatitude. The human person participates in the light and power of the divine Spirit. By his reason, he is capable of understanding the order of things established by the Creator. By free will, he is capable of directing himself toward his true good. He finds his perfection ‘in seeking and loving what is true and good.’ By virtue of his soul and his spiritual powers of intellect and will, man is endowed with freedom, an ‘outstanding manifestation of the divine image.’ By his reason, man recognizes the voice of God which urges him ‘to do what is good and avoid what is evil.’ Everyone is obliged to follow this law, which makes itself heard in conscience and is fulfilled in the love of God and of neighbor. Living a moral life bears witness to the dignity of the person.” (Catechism of the Catholic Church, 1703-1706)

I think that’s right. Our natural attraction to the good is integral to who we are. That attraction is often clouded by immoral practice but it can be purified and cultivated. As we learn and act according to the good we are developing to become the kinds of creatures that we are meant to be. The understanding and wisdom that comes from meditation on the laws and statutes given by God are the ends to which our reasoning capacities are directed.

The Lord’s torah, instructions, statutes, and judgments include more than ethics but I will focus presently on the ethics given in scripture and tradition. The scriptural foundation for ethics is in the Ten Commandments given by God on Mount Sinai, written on tablets of stone. In what follows I’ll go through the Ten Commandments, out of order, starting with topics like murder and theft, and eventually circling in toward the core source of moral goodness in God. Some of the topics will be auxiliary to the ten commandments themselves, but are also important moral topics in Christian teaching. With many of the auxiliary topics I’ll take my lead from the 1994 Catechism of the Catholic Church, which has an excellent section on Christian moral teaching in its Part Three, “Life in Christ”. That particular text is Catholic but most of the teachings in that section agree with general Christian moral teachings.

Thou shalt kill

Murder is probably the most obvious moral evil. No one wants to be murdered. None of us wants the people we love to be murdered. And pragmatically we can’t have a stable society without prohibiting murder. The theological basis for condemning murder is the divine image in which human beings are created: “For in the image of God He made man.” (Genesis 9:6, NKJV)

Human beings are made in the image of God and, because of that, are intrinsically inviolable. This is more than just a pragmatic matter. Because this inviolability is intrinsic it goes beyond just the interest of social stability. There are many instances in history where social stability was actually the justification for the murder of minority populations. But that kind of justification is absolutely impermissible. Most such justifications would probably be mistaken anyway, but even if murder had, in a perverse way, some kind social benefit it would still be inexcusable. Human beings, all human beings, are intrinsically inviolable.

This commandment also touches on related issues like warfare, suicide, euthanasia, abortion, and bodily integrity.

Suicide, euthanasia, and abortion are all considered forms of murder in Christian moral teaching and are all wrong. The immorality of each relates to the inviolability of human beings and the premise that the person being murdered under suicide, euthanasia, or abortion is a full human person with an inviolable right to life that no one has the right to abrogate. Absolute inviolability means that people do not even have the right to murder themselves, as with suicide. In the case of abortion, although most people agree that a human fetus in its early stages of development is a human being, not everyone agrees that the fetus is a person with an inviolable right to life. The concept “person” here being a moral category.

Are all human beings persons? Yes. That’s what it comes down to. And there can be no other criteria for moral inviolability, i.e. the right to life. Differences in intelligence, strength, physical appearance, ability, stage of development, contribution to society, whatever, don’t make a difference to this right. Similarly people who have been injured, incapacitated, or simply aged, are no less persons with inviolability than anyone else. People are not more or less worthy of life because of their contribution to the Gross Domestic Product. There are no mere “drains on society” who are dispensable.

It is true that there are people who are wholly dependent on others for their survival and who do not “contribute” in tangible ways. But they are no less entitled to life than anyone else. It is perhaps instructive that the first murderer defiantly challenged God with the question, “Am I my brother’s keeper?” (Genesis 4:9) Yes, absolutely. I think the Jewish philosopher Emmanuel Levinas got it right when he said that each person is infinitely responsible for everyone else. A similar idea is the line from Fyodor Dostoyevsky that, “We are all responsible for everyone else—but I am more responsible than all the others.”

Thou shalt not steal

Theft is another moral evil that is rather obvious. We value our possessions and we don’t want people to steal from us. We don’t want to live in conditions in which we are constantly worried that we will lose everything we own the minute we leave our homes. We also want to be able to make agreements with people with confidence that people will honor their agreements. These are basic and fairly obvious conditions for a functioning and ordered society.

Along with stealing, the Catholic Catechism also lists the following as morally illicit:

“Speculation in which one contrives to manipulate the price of goods artificially in order to gain an advantage to the detriment of others; corruption in which one influences the judgment of those who must make decisions according to law; appropriation and use for private purposes of the common goods of an enterprise; work poorly done; tax evasion; forgery of checks and invoices; excessive expenses and waste, willfully damaging private or public property” (Catechism of the Catholic Church, 2409).

A related topic to the ownership of goods is the moral concern for the physical needs of the poor and vulnerable. The poor are not justified in stealing from the wealthy, but neither are the wealthy absolved of responsibility to look after the needs of the poor. This is abundantly clear in torah.

“If there is among you a poor man of your brethren, within any of the gates in your land which the Lord your God is giving you, you shall not harden your heart nor shut your hand from your poor brother, but you shall open your hand wide to him and willingly lend him sufficient for his need, whatever he needs. Beware lest there be a wicked thought in your heart, saying, ‘The seventh year, the year of release, is at hand,’ and your eye be evil against your poor brother and you give him nothing, and he cry out to the Lord against you, and it become sin among you. You shall surely give to him, and your heart should not be grieved when you give to him, because for this thing the Lord your God will bless you in all your works and in all to which you put your hand. For the poor will never cease from the land; therefore I command you, saying, ‘You shall open your hand wide to your brother, to your poor and your needy, in your land.’” (Deuteronomy 15:7-11, NKJV)

This is more than a suggestion. This is an obligation commanded in the Law. When giving these kinds of commands the Lord often reminds Israel of her former enslavement, for example: “You shall neither mistreat a stranger nor oppress him, for you were strangers in the land of Egypt.” (Exodus 22:21, NKJV) The Bible has a strong sense of what we might today call social justice. It’s not only a perversion of justice to actively steal from someone but it’s also a perversion of justice to treat someone unreasonably or with excessive harshness, even if it doesn’t technically violate a contract. For example:

“When you lend your brother anything, you shall not go into his house to get his pledge. You shall stand outside, and the man to whom you lend shall bring the pledge out to you. And if the man is poor, you shall not keep his pledge overnight. You shall in any case return the pledge to him again when the sun goes down, that he may sleep in his own garment and bless you; and it shall be righteousness to you before the Lord your God. You shall not oppress a hired servant who is poor and needy, whether one of your brethren or one of the aliens who is in your land within your gates. Each day you shall give him his wages, and not let the sun go down on it, for he is poor and has set his heart on it; lest he cry out against you to the Lord, and it be sin to you.” (Deuteronomy 24:10-15)

When someone is in a position of power they should still respect the person in the position of less power. A person’s home is a personal space, even if you’re lending them money, or even own the home. Even in the case of collateral, where it’s part of a contract, don’t be unreasonable. Don’t deprive a person of their means to live in comfort and dignity. Continuing:

“You shall not pervert justice due the stranger or the fatherless, nor take a widow’s garment as a pledge. But you shall remember that you were a slave in Egypt, and the Lord your God redeemed you from there; therefore I command you to do this thing.” (Deuteronomy 24:17-18)

Interesting that it calls this a perversion of justice. But what if everyone had agreed to the arrangement beforehand? Isn’t everyone getting exactly what was agreed to? Isn’t that just? The Lord’s notion here of justice would seem to be more than “giving everyone their due”. This kind of justice calls on the wealthier to be more generous. Continuing:

“When you reap your harvest in your field, and forget a sheaf in the field, you shall not go back to get it; it shall be for the stranger, the fatherless, and the widow, that the Lord your God may bless you in all the work of your hands. When you beat your olive trees, you shall not go over the boughs again; it shall be for the stranger, the fatherless, and the widow. When you gather the grapes of your vineyard, you shall not glean it afterward; it shall be for the stranger, the fatherless, and the widow. And you shall remember that you were a slave in the land of Egypt; therefore I command you to do this thing.” (Deuteronomy 24:19-22, NKJV)

This is really interesting. It’s your field. Don’t all the sheaves, olives, and grapes rightfully belong to you? Actually, no. It’s a fascinating concept of justice at work here.

Thou shalt not bear false witness against thy neighbor

Lying takes many forms. Bearing false witness against a person has to be one of the worst forms. Slander, libel, defamation – these are ugly and inexcusable actions. We ought not underestimate how important our reputations are to us. Unfortunately we cannot expect that we will always have the reputations we deserve. In fact we’ve been warned about the opposite, that disciples of Christ will have all manner of evil spoken against them falsely (Matthew 5:11). That will happen. But wo to the person who perpetrates these kinds of falsehoods. Bearing false witness can cause financial damage but I think the social damage is even worse.

To love God is to love the truth. Jesus said, “I am the way, the truth, and the life” (John 14:6) and Psalmist said, “Your law is truth” (Psalm 119:142). The Catechism says: “Man tends by nature toward the truth. He is obliged to honor and bear witness to it: ‘It is in accordance with their dignity that all men, because they are persons . . . are both impelled by their nature and bound by a moral obligation to seek the truth, especially religious truth. They are also bound to adhere to the truth once they come to know it and direct their whole lives in accordance with the demands of truth.” (Catechism of the Catholic Church, 2467) Why again, when studying torah, this delight, “O how love I thy law! it is my meditation all the day”? Because it’s in our nature. We are impelled toward truth, we are bound, morally, to seek and adhere to truth.

Truth isn’t merely propositional but also morally inflected. Aristotle said, “To say that that which is, is not, and that which is not, is, is a falsehood; therefore, to say that which is, is, and that which is not, is not, is true” (Aristotle, Metaphysics, 1011b26). Yes, for sure. But it’s also a moral principle. To say that that which is, is not, and that which is not, is, is wrong. It’s an offense against reality and against justice.

Thou shalt not commit adultery

Sex is either something we think too much about or not enough about. I’m reminded of Alain de Botton’s playful book title How to Think More About Sex. The title is playful because by “think” he doesn’t mean mere sexual fantasy but rather critical thinking. What part does sexuality play in the overall scheme of things?

The Catechism states: “Chastity means the successful integration of sexuality within the person and thus the inner unity of man in his bodily and spiritual being. Sexuality, in which man’s belonging to the bodily and biological world is expressed, becomes personal and truly human when it is integrated into the relationship of one person to another, in the complete and lifelong mutual gift of a man and a woman. The virtue of chastity therefore involves the integrity of the person and the integrality of the gift.” (Catechism of the Catholic Church, 2337)

Something interesting to observe in this statement is that chastity and sexuality are not opposites. Rather chastity is sexuality directed toward its proper ends. What kind of beings are we? We are certainly members of the bodily and biological world. We are mortal. And we only persist as a species through sexual reproduction. Sexuality is the way in which belonging to the bodily and biological world is expressed. In a certain sense all of ethics concerns the successful integration of the multiple aspects of our being toward those ends for which we are created. And that’s what chastity is for sexuality.

An important concept pertaining to chastity is “integrity”. The primary definition of “integrity” is general moral uprightness. But another definition of particular relevance here is of a state of being whole and undivided, having all parts integrated into a coherent unity. The Catechism states: “The chaste person maintains the integrity of the powers of life and love placed in him. This integrity ensures the unity of the person; it is opposed to any behavior that would impair it. It tolerates neither a double life nor duplicity in speech.” (Catechism of the Catholic Church, 2338) This is an interesting concept that can certainly apply to other aspects of personhood in addition to sexuality. Continuing on: “Chastity includes an apprenticeship in self-mastery which is a training in human freedom. The alternative is clear: either man governs his passions and finds peace, or he lets himself be dominated by them and becomes unhappy.” (Catechism of the Catholic Church, 2339)

Underlying all of this is the sanctity of marriage. Jesus said: “Have you not read that He who made them at the beginning ‘made them male and female,’ and said, ‘For this reason a man shall leave his father and mother and be joined to his wife, and the two shall become one flesh’? So then, they are no longer two but one flesh. Therefore what God has joined together, let not man separate.” (Matthew 19:4-6) This union is a very serious matter. And hence the gravity of adultery. The union is designed by God for the unitive and procreative purpose.

Marriage of male and female persons is what sexuality is for and is normative for it. Violations of chastity include adultery, rape, fornication, prostitution, lust, pornography, masturbation, and homosexuality.

Rape especially is an extremely serious offense. It is not only a perversion of the divinely ordained purposes of sexuality but is also violent. It is also a uniquely horrific act of violence because it is sexual, and thus much more horrific even than a regular assault. Sexual assault is a more accutely personal and existential attack. And our appropriately intense and visceral response to it indicates how deeply sexuality is situated at the core of our being and identity.

Thou shalt not covet

The forbidding of covetousness is interesting because it pertains to thoughts rather than physical actions. Our moral character and virtue is defined by our mental actions. A succinct expression of this outlook is the proverb: “For as he thinks in his heart, so is he.” (Proverbs 23:7, NKJV)

For example, the commandment says, “thou shalt not covet thy neighbor’s wife” (Exodus 20:17, KJV). This goes beyond but also extends from the commandment against adultery. To be sure, it is wrong to commit adultery. But it is also wrong to desire another man’s wife. Chastity is not only physical but is also mental. A clear example of this is Jesus’s teaching:

“You have heard that it was said to those of old, ‘You shall not commit adultery.’ But I say to you that whoever looks at a woman to lust for her has already committed adultery with her in his heart. If your right eye causes you to sin, pluck it out and cast it from you; for it is more profitable for you that one of your members perish, than for your whole body to be cast into hell. And if your right hand causes you to sin, cut it off and cast it from you; for it is more profitable for you that one of your members perish, than for your whole body to be cast into hell.” (Matthew 5:27-30, NKJV)

The most extreme example of an offense of this kind is pornography where a person is actively seeking and leering at people lustfully. This is extremely destructive to a person’s soul. Modern communications enables us to access an unlimited number of images on a scale previously unimaginable. The commandment and teaching of Jesus condemns leering and lusting after even just one person as a very serious sin.

This kind of statute relating to mental actions is in tension with more modern moral ideas like the “harm principle” as promoted by the philosopher John Stuart Mill, where actions are only immoral if they cause harm to others. We find anything beyond this invasive. What goes on inside my head is no one else’s business. But the Lord’s torah is much more extensive than this and goes deeper into the state of one’s soul.

Beyond sexuality we are also commanded to cultivate our thoughts in all our relations to others. “You shall not covet your neighbor’s house… nor his ox, nor his donkey, nor anything that is your neighbor’s.” (Exodus 20:17, NKJV) Today we might say that we must not covet our neighbor’s job, our neighbor’s car, our neighbor’s investment portfolio, our neighbor’s social prestige, etc. Thinking like that is not a proper way to live. And if you think about it, it’s certainly a way to be miserable. There’s wisdom in the idea that comparison is the thief of joy. It’s no way to live with yourself or with others in fellowship.

Honour thy father and thy mother

The family plays a central part in God’s creation, starting with husband and wife, father and mother. God has joined husband and wife together (Matthew 19:4-6) and commanded them to “Be fruitful and multiply” (Genesis 1:28, NKJV). Father and mother are the divinely appointed leaders and teachers of their children.

The Catechism states: “In creating man and woman, God instituted the human family and endowed it with its fundamental constitution. Its members are persons equal in dignity. For the common good of its members and of society, the family necessarily has manifold responsibilities, rights, and duties.” (Catechism of the Catholic Church, 2203)

The philosopher Roger Scruton distinguished between the kinds of rights and responsibilities created by agreement, as with a contract, and the kinds of rights and responsibilities that we have for reasons beyond anything we chose; what he calls “sacred obligations” (Scruton, On Human Nature, 113-117). Family responsibilities, rights, and duties are of this second type. Children do not choose to be born, nor to be born to the parents they’re born to. Nevertheless they have responsibilities of filial piety. And parents do not choose the character and personality of their children. We take then as they come. Another philosopher, Michael Sandel, has called this “openness to the unbidden” (Sandel, The Case Against Perfection). Parents are obligated to care for them and teach them, regardless of the unique and unforeseen challenges that come with each individual child. As Scruton puts it: “The field of obligation is wider than the field of choice. We are bound by ties that we never chose, and our world contains values and challenges that intrude from beyond the comfortable arena of our agreements.” (Scruton, 116) Nowhere is this more relevant than in family responsibilities.

What do parents owe to their children? The Catechism states that parents must respect their children as human persons, educate their children, create a home “where tenderness, forgiveness, respect, fidelity, and disinterested service are the rule”, teach them “self-denial, sound judgment, and self-mastery”, initiate them into “solidarity and communal responsibilities”, teach them to “avoid the compromising and degrading influences which threaten human societies”, and teach them the gospel of Jesus Christ (Catechism of the Catholic Church, 2221-2226).

What do we owe to our parents? When we are children we owe them obedience and respect. The Catechism states, “Obedience toward parents ceases with the emancipation of the children; not so respect, which is always owed to them.” As adults we must, as much as we are able, “give them material and moral support in old age and in times of illness, loneliness, or distress.”

Remember the sabbath day, to keep it holy

Labor is part of the human condition, something illustrated in Genesis with God’s words to Adam:

“Cursed is the ground for your sake;
In toil you shall eat of it
All the days of your life.
Both thorns and thistles it shall bring forth for you,
And you shall eat the herb of the field.
In the sweat of your face you shall eat bread
Till you return to the ground,
For out of it you were taken;
For dust you are,
And to dust you shall return.”
(Genesis 3:17-19, NKJV)

Nevertheless, we are ordained to more than endless toil. God has ordained that we should have periodic and regular rest. Rest is not just for a privileged elite. Everyone must have rest from labor on the Sabbath:

“In it thou shalt not do any work, thou, nor thy son, nor thy daughter, thy manservant, nor thy maidservant, nor thy cattle, nor thy stranger that is within thy gates.” (Exodus 20:10)

This includes laborers, service workers, migrants; everyone. This reprieve even extends to the animals that labor for us. As important as it is to rest from our own labors on the Sabbath it is just as important, maybe even more important to enable others to rest. As stated in the Catechism:

“Those Christians who have leisure should be mindful of their brethren who have the same needs and the same rights, yet cannot rest from work because of poverty and misery… Sanctifying Sundays and holy days requires a common effort. Every Christian should avoid making unnecessary demands on others that would hinder them from observing the Lord’s Day.”

This is a Sabbath perspective that ought to affect the way we view ourselves and others generally. Who am I beyond my labor and career? Who are other people to me beyond the benefit that I can get from them in the goods and services they provide me?

Thou shalt not take the name of the Lord thy God in vain

One of the important concepts in the Law given by God through Moses is that of holiness. Certain things are marked out as qadosh, radically separate and other from the ordinary. God is loving but his holiness also requires singular reverence. But his holiness doesn’t diminish his love and goodness. These attributes all cohere together as one in a way unique to God. An apt illustration of this is C.S Lewis’s description of Aslan, a type for Christ, in The Lion, the Witch and the Wardrobe:

“‘Aslan is a lion- the Lion, the great Lion.’ ‘Ooh’ said Susan. ‘I’d thought he was a man. Is he-quite safe? I shall feel rather nervous about meeting a lion’…’Safe?’ said Mr Beaver …’Who said anything about safe? ‘Course he isn’t safe. But he’s good.’”

I think the most powerful example of this principle in scripture comes in the episode after the people of Israel had fallen into idolatry and worshiped before the golden calf, an unimaginably grave offense before God. The Lord told Moses that he could not stay with them but would instead send an angel, a messenger, in his place.

“Then the Lord said to Moses, ‘Depart and go up from here, you and the people whom you have brought out of the land of Egypt, to the land of which I swore to Abraham, Isaac, and Jacob, saying, ‘To your descendants I will give it.’ And I will send My Angel before you… for I will not go up in your midst, lest I consume you on the way, for you are a stiff-necked people.’” (Exodus 33:1-3)

The Lord is good but he is not safe. That’s why he was hesitant to journey with the people. He knew that his holiness was hazardous to the people in their wickedness. Still he did go up with them. And he did not desire that they be distant from him. Rather he instituted laws and statutes for them to be holy like him.

“Now therefore, if you will indeed obey My voice and keep My covenant, then you shall be a special treasure to Me above all people; for all the earth is Mine. And you shall be to Me a kingdom of priests and a holy nation.” (Exodus 19:6)

We should keep these things in mind when we speak of God and approach God with the proper reverence.

The Catechism states: “Respect for his name is an expression of the respect owed to the mystery of God himself and to the whole sacred reality it evokes. the sense of the sacred is part of the virtue of religion” (Catechism of the Catholic Church, 2144).

I am the LORD thy God

We end now with the first commandment. I wanted to save this one for last because I think of this as the foundation for all of ethics. What is it that gives the laws and statutes their authority? “I am the LORD thy God” (Exodus 20:2). What follows that statement is absolutely authoritative, coming directly from the source of truth, goodness, beauty, and all that is. Nachmanides (1194 – 1270), also known as Ramban, said in his commentary on this verse:

“He said, I am the Eternal, thus teaching and commanding them that they should know and believe that the Eternal exists and that He is G-d to them. That is to say, there exists an Eternal Being through Whom everything has come into existence by His will and power, and He is G-d to them, who are obligated to worship Him.” (Ramban on Exodus 20:2)

The Lord also says, “Thou shalt have no other gods before me.” (Exodus 20:3) Which we can interpret either as having other gods in priority over the Lord or even simply in the presence of the Lord, even if in equal position. I think one possible way to summarize the whole of the Hebrew Scripture would be as Israel’s continual temptation with idolatry.

The Catechism states: “Idolatry consists in divinizing what is not God. Man commits idolatry whenever he honors and reveres a creature in place of God, whether this be gods or demons (for example, satanism), power, pleasure, race, ancestors, the state, money, etc.” (Catechism of the Catholic Church, 2113).

This first commandment is foundational. It addresses the matter of where goodness itself comes from in the first place and it also precludes the possibility that there could be any other source. What else could be the source for goodness and ethical principles? Power? Pleasure? The state? Economic output? There are ethical systems with each of these as a philosophical or ideological foundation. And each has a compelling case that is, to a limited extent, intellectually satisfying. But I don’t think that any of them is ultimately intellectually satisfying, nor ultimately emotionally or spiritually satisfying.

What should we expect and hope to receive from the law? In the end we want answers to the question, “how should I live?” Does it ultimately matter how I live? If it does matter how I live, why does it matter? On what basis? I think these questions are naturally related to the question of what kind of beings we are. What are we and why do we exist? What do we exist for? It all goes back to this first commandment: I am the LORD thy God. How we should act and what we should do ties back to our origin in God.

Human beings are the tzelem elohim, the image of God. So to understand what kind of beings we are and how we can fulfill our nature we should look to God. What attributes are constitutive of our divine nature? Holiness, justice, loving-kindness, mercy, faithfulness, honor. We are also embodied, spiritual, mental, mortal, dependent, sexual, emotional, social, familial, and rational. All of these attributes have moral implications that are addressed in God’s laws and statutes. Our fulfillment requires spiritual practice, reverence for God, filial piety, responsibilities to family members, sexual discipline, concern for the physical needs of others, respect for the physical body and for life, and discipline of the mind. God’s laws and statutes set forth the foundational ethical principles for how to fulfill our nature as human beings and as image bearers of God’s nature.

The Trinity

The doctrine of the Trinity is very important in Christianity. But people who are not Trinitarians, even non-Trinitarians who believe in the Bible and in Jesus, might wonder, what’s the reason for believing in the Trinity? Is the idea of the Trinity motivated from Biblical texts or was it something that came out of Greek philosophy or Greek culture in early Christianity? How did Christians come to understand things in this way? And why has this understanding persisted in Christian history?

With this episode I’d like to get into some more systematic theology. In a previous episode I went over the nature of God as it has been formulated in the theological and philosophical tradition of classical theism. The topic of this episode, the Trinity, is also about the nature of God but more especially about the uniquely Christian understanding of the nature of God as the triune God, God as Trinity: Father, Son, and Holy Spirit.

The doctrine of the Trinity is very important in Christianity. But people who are not Trinitarians, even non-Trinitarians who believe in the Bible and in Jesus, might wonder, what’s the reason for believing in the Trinity? How did Christians come to understand things in this way? And why has this understanding persisted in Christian history? Is the idea of the Trinity motivated from Biblical texts or was it something that came out of Greek philosophy or Greek culture in early Christianity? Or even more basic, what is the doctrine of the Trinity, really? I think these are good questions and quite common questions. So it’s a topic worth looking at.

I’ll go through this topic in seven sections: (1) a definition of the Trinity, (2) some misinterpretations of the Trinity, (3) the scriptural motivation for the doctrine of the Trinity, (4) some of the cultural and philosophical background, (5) some useful theological terms, (6) some history of the development of the doctrine, and (7) the significance of the doctrine of the Trinity to the whole Christian faith.

Definition

One definition of the Trinity I think is quite good is one with the following seven parts.

The Father is God.
The Son is God.
The Holy Spirit is God.
The Father is not the Son.
The Son is not the Holy Spirit.
The Holy Spirit is not the Father.
There is only one God.

I picked up this definition from Phillip Cary in his Teaching Company course The History of Christian Theology. And he adapted this from Augustine of Hippo (354 – 430). This definition is quite straightforward, I think. And we’ll see later how there are scriptural motivations for each of these statements. Each of the statements, taken individually, isn’t hard to understand. It’s trying to understand how they can all fit together that gets challenging. And that’s where a lot of the additional terms and concepts come in; like substance, persons, generation, and procession. But the most basic content of the definition, which all these other concepts are based on, consists of these very basic ideas. God is Father, Son, and Holy Spirit. Each of them is God. They are not the same person. And there is only one God.

Misinterpretations

That’s what the Trinity is. It’s also good to understand what the Trinity is not. There are two major misunderstandings of the Trinity, that make the mistake of either confounding the persons or dividing the essence. These two misinterpretations are modalism and tritheism.

Modalism is the view that the Father, Son, and Holy Spirit are all the same person. That each is merely a mode that God can take on. One proponent of this view in history was a man named Sabellius in the third century A.D. So this idea is also sometimes called Sabellianism. I think this is a pretty common misunderstanding of the Trinity, for both non-Trinitarians and even many Trinitarians. It’s easy to see where this comes from. If there’s only one God and the Father, Son, and Holy Spirit are God, then just say they’re all the same person. But this is quite clearly scripturally untenable, as we’ll see in the next section. We shouldn’t try to imagine that Jesus prayed to himself or spoke of himself in the third-person as if he were his own Father.

Tritheism is the view that there are three Gods: the Father, Son, and Holy Spirit. It’s also easy enough to see where this comes from. If the Father, Son, and Holy Spirit are God, then just say there are three Gods. But this is also quite clearly scripturally untenable. Monotheism is one of the most emphatic teachings of both the Old and New Testaments. Granted, the Ancient Israelites were not very good at following this and were almost irrepressible relapsing polytheists. But the prophets of the Lord were uncompromising and zealous monotheists, continually reproving the people and calling them to repent and to forsake polytheism. While there are other divine beings like angels in the Bible, they are subordinate to the one creator God. There’s no room for three such capital G Gods in the scriptures.

Scriptural Motivation

More than any other source, more than tradition, reason, or culture, the most important and authoritative source of doctrine in Christianity is in scripture. The doctrine of the Trinity is not explicitly taught in the Bible. But the doctrine is scripturally motivated. If we ask, “what is it that motivates Christians to formulate the doctrine of the Trinity?” we can find those motivations in scripture. It doesn’t come from nowhere.

There are two main groups of scriptures that motivate the doctrine of the Trinity. First, scriptures that affirm that there is only one God. And second, scriptures that affirm that Jesus is God. Other kinds of scriptures include those that affirm that the Father is God, that the Holy Spirit of God, and that they are not all the same person.

The most significant of the monotheistic passages is the Shema in Deuteronomy 6:4.

“Hear, O Israel: The Lord our God, the Lord is one!”

This is a kind of first article of faith for the religion of Israel. It’s the one Jesus called the first and greatest commandment (Matthew 22:38). The first of the Ten Commandments are similar.

“I am the Lord your God, who brought you out of the land of Egypt, out of the house of bondage. You shall have no other gods before Me.” (Exodus 20:2-3)

Among the Old Testament prophets Second Isaiah is especially emphatic in his monotheism:

Isaiah 43:12
“You are My witnesses,” says the Lord,
“And My servant whom I have chosen,
That you may know and believe Me,
And understand that I am He.
Before Me there was no God formed,
Nor shall there be after Me.”

Isaiah 44:6
“Thus says the Lord, the King of Israel,
And his Redeemer, the Lord of hosts:
‘I am the First and I am the Last;
Besides Me there is no God.’”

That’s the monotheistic foundation. One God, the Lord God of Israel. As we come to the New Testament we find passages of scriptures that indicate that this same God is actually three persons. After his Resurrection, at the moment of his Ascension, Jesus commissioned his apostles in Matthew 28:19.

“Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit”

Interesting that it’s the name, singular, ὄνομα (onoma), of the Father, Son, and Holy Spirit, rather than the names. This baptismal formula calls for baptism in the name of the three persons of the Trinity. We see elsewhere that the three persons are invoked in blessing, as with Paul in 2 Corinthians 13:14.

The grace of the Lord Jesus Christ, and the love of God, and the communion of the Holy Spirit be with you all. Amen.

In the scriptures Jesus doesn’t ever say explicitly, “I am God”. Some conclude from this is that the early Christians actually didn’t believe that he was God and that this idea developed later. I don’t think that theory works, but that’s another topic. Even without that kind of direct statement there are many reasons to conclude from the scriptures that Jesus is God.

The Gospel of John opens placing Christ at the Creation of all things in the prologue of John 1:1-5.

In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things were made through Him, and without Him nothing was made that was made. In Him was life, and the life was the light of men. And the light shines in the darkness, and the darkness did not comprehend it.

Paul also taught of an exalted origin when he quoted what appears to have been a very, very early Christian hymn about Jesus, in Philippians 2:5-11.

Let this mind be in you which was also in Christ Jesus, who, being in the form of God, did not consider it robbery to be equal with God, but made Himself of no reputation, taking the form of a bondservant, and coming in the likeness of men. And being found in appearance as a man, He humbled Himself and became obedient to the point of death, even the death of the cross. Therefore God also has highly exalted Him and given Him the name which is above every name, that at the name of Jesus every knee should bow, of those in heaven, and of those on earth, and of those under the earth, and that every tongue should confess that Jesus Christ is Lord, to the glory of God the Father.

That’s quite exalted language. The name which is abovery name. Jesus Christ is Lord. Lord is the word traditionally substituted for the name of God, YHWH. “Jesus is Lord” is probably the earliest Christian confession. Essentially another version of “YHWH is Lord”.

Paul has similarly exalted language for Jesus when he says in Colossians 2:9.

For in Him dwells all the fullness of the Godhead bodily.

In the Gospel of John Jesus makes a number of conspicuous “I am” statements, basically invoking the name of God as revealed to Moses in Exodus 3:14, “I AM THAT I AM”. For example in John 8:58.

Jesus said to them, “Most assuredly, I say to you, before Abraham was, I AM.”

And Jesus’ disciple Thomas actually calls him God in John 20:27-28.

Then He said to Thomas, “Reach your finger here, and look at My hands; and reach your hand here, and put it into My side. Do not be unbelieving, but believing.” And Thomas answered and said to Him, “My Lord and my God!”

In John Jesus also teaches about his oneness with the Father. In John 10:30.

“I and My Father are one.”

And in John John 14:9-11.

He who has seen Me has seen the Father; so how can you say, ‘Show us the Father’? Do you not believe that I am in the Father, and the Father in Me? The words that I speak to you I do not speak on My own authority; but the Father who dwells in Me does the works. Believe Me that I am in the Father and the Father in Me, or else believe Me for the sake of the works themselves.

This unity notwithstanding, it is clear from multiple instances in the scriptures that the Father and the Son are not the same person. For example at Jesus’ baptism in Matthew 3:16-17.

When He had been baptized, Jesus came up immediately from the water; and behold, the heavens were opened to Him, and He saw the Spirit of God descending like a dove and alighting upon Him. And suddenly a voice came from heaven, saying, “This is My beloved Son, in whom I am well pleased.”

The Father, Son, and Holy Spirit are all spoken of distinctly here. Jesus is also always praying to the Father, with no indication that he is in any way praying to himself. Even in their intimate unity there is distinction, as shown wonderfully in John 17:20-23.

“I do not pray for these alone, but also for those who will believe in Me through their word; that they all may be one, as You, Father, are in Me, and I in You; that they also may be one in Us, that the world may believe that You sent Me. And the glory which You gave Me I have given them, that they may be one just as We are one: I in them, and You in Me; that they may be made perfect in one, and that the world may know that You have sent Me, and have loved them as You have loved Me.”

These and other scriptures indicate that: there is only one God, that the Father, Son, and Holy Spirit are God, and that they are not all the same person.

Cultural and Philosophical Background

Christianity developed in a highly Hellenized, Greek-speaking environment. Even important Jewish leaders of early Christianity, like Paul of Tarsus, spoke and wrote in Greek and were immersed in Greek culture. The Jewish scripture for many outside of Judea was the Septuagint, a Greek translation of the Hebrew scriptures. An important Jewish theologian and philosopher of the time period, Philo of Alexandria (20 B.C. – 50 A.D.) wrote all his works in Greek and he was well-versed in Platonic philosophy.

There is a line of thought that Greek culture and philosophy was the real source of many Christian theological developments, rather than scripture. One prominent proponent of this view was Adolf Von Harnack (1851 – 1930). I happen to think this position is overstated and agree with Robert Louis Wilken that “the time has come to bid a fond farewell to the ideas of Adolf von Harnack” and that rather than positing the Hellenization of Christianity “a more apt expression would be the Christianization of Hellenism” (The Spirit of Early Christian Thought, xvi). Greek culture and philosophy are sometimes thought to have invaded and supplanted the original Hebrew foundation. But this world was already immersed in Greek influence, even the Jewish part of it. Certainly Jews and Christians drew from the ideas available to them in the surrounding culture, but in a way that was subordinate to and in the service of scripture. Robert Louis Wilkin made this observation of the writings of the Early Church Fathers:

“To be sure, many of the best minds in the early church were philosophically astute and moved comfortably within the intellectual tradition of the ancient world… But if one picks up a treatise of Origen or Basil of Caesarea and compares it with the writings of the philosopher Alcinous or the neo-Platonist Plotinus, it is apparent at once that something else is at work. For one thing… they turn always to the Bible as the source of their ideas. No matter how rigorous or abstruse their thinking–for example, in dealing with a complex and subtle topic like the distinctive identity of each person of the Trinity–Christian thinkers always began with specific Biblical texts. I have found that it is not possible to read the church fathers without the Bible open before me. The words of the Scriptures crowd the pages of their books and essays, and their arguments often turn on specific terms or phrases from the Bible. But one can detect something else in their writings, at once closer to experience yet more elusive. On page after page the reader senses that what they believe is anchored in regular, indeed habitual, participation in the church’s worship, and what they teach is confirmed by how they pray.”

This has also been my experience in reading the Early Church Fathers.

Something interesting that we get from Greeks are philosophical ideas that are quite amenable to monotheism, converging on a similar idea that we get through revelation in the Old Testament. Greek pagans, among the regular folk, were polytheists. But the more educated, intellectual, and philosophical Greek pagans tended to trace everything back to some single ultimate source. For Plato (c. 428 – c. 348 BC) this was The Good, for Aristotle (384 – 322 BC) this was the Unmoved Mover, for Plotinus (c. 204 – 270 AD) this was The One. Both reason and revelation pointed to the reality of a single first principle or God over all things. Early Church Fathers well-versed in both scripture and philosophy, like Justin Martyr (100 – 165), Origen of Alexandria (185 – 253), and Clement of Alexandria (150 – 215), could find both sources quite harmonious. Both reason and revelation were important sources in support of the foundational idea of the doctrine of the Trinity: that there is only one God.

Terms

It’s possible to define the Trinity in very simple terms, like the seven listed earlier. Those simple terms are sufficient for many purposes. They certainly were for the earliest Christians. Still, as Christians have thought more deeply about the Trinity they have found it helpful to expand their vocabulary to cover more sophisticated concepts and to distinguish them from heretical views. Before people had these terms available to them they might ask questions about the Trinity like “one what?” and “three whos?” What kinds of things are we talking about here? There weren’t terms available to tag these sorts of concepts to get a hold of them. There aren’t terms in scripture to use for these sorts of philosophical questions. But they are interesting questions. They’re terms that we can use if we want to take things to the “next level”. Let’s look at five such terms.

Substance, Homoousion, Essence

This is a term for the “one what?” question. The Greek term οὐσία (ousia) is essence or substance. The Council of Nicea used this term to describe what it is in their essence as God, that the Father, Son, and Holy Spirit share. They are the same in essence, ὁμοούσιον (homoousion), one ousia.

Persons, Hypostases

Hypostasis (ὑπόστασις) is a term for the “three whos?” question. This is an especially good example of a term that was appropriated and repurposed to make a fine distinction that wasn’t conceptualized previously. (It’s quite interesting how language can extend our thinking in this way). Hypostasis had meant something very similar to ousia. But it was later made distinct to refer to that in the Trinity which should not be confounded, the persons of the Father, Son, and Holy Spirit. Using the terms ousia and hypostasis the Trinity can be described as three hypostases, one ousia; three persons, one essence.

Perichoresis

Perichoresis (περιχώρησις) is a term to used to refer to the relations between the three persons of the Trinity. It means “going around” and when used to describe the Trinity it refers to their particular interrelation or interpenetration. As used historically in the writings of theologians like Maximus Confessor (c. 580 – 662), Gregory of Nazianzus (329–389), and John of Damascus (c. 675 – 749) it conveys a sense of motion, dynamism, even a kind of eternal dance between the Father, Son, and Holy Spirit. This idea has special currency for the mystical side of Christianity, in pursuit of direct, experiential, and personal relationship with the Triune God.

Eternal Generation, Eternal Begetting

The Nicene Creed states that Christ is “begotten, not made”, γεννηθέντα, οὐ ποιηθέντα (gennethenta, ou poiethenta). The point being that the Son is not a creature, not created by the Father. But he is begotten, or put another way, generated by the Father. Is this a distinction without a difference? No. Unlike any created being, the Son exists necessarily and eternally, just like the Father. Each has life in himself. “For as the Father has life in Himself, so He has granted the Son to have life in Himself”. (John 5:26) There’s a relation of begetter and begotten. But this is something more akin to a logical process than a process in time.

A geometrical analogy of generation that comes to mind is the relation of the center point of a circle to all the points on its circumference. By definition all points on a circle are equidistant from the center of the circle. In a sense the center point generates all the points on the circle. But which part comes first? Well neither really comes first. The relation doesn’t even come to be in any kind of temporal process. There’s a relation there but it’s just there, without needing to have ever started, much less one part before another.

One philosophy contemporary with the Council of Nicea, Neoplatonism, certainly provided intellectual tools to come up with this kind of idea. In the metaphysics of Plotinus (204 – 270) all things are understood to derive from a single great source, an absolute One. The first level of emanation from this One is the Divine Mind. The One eternally generates the Divine Mind in a way very similar to the way Christian theologians understood the Father to generate the Son.

Procession

In the Nicene Creed it is said that the Holy Spirit “proceeds from the Father”, τὸ ἐκ τοῦ Πατρὸς ἐκπορευόμενον (to ek tou Patros ekporeuomenon). Catholics and Protestants also say that the Holy Spirit proceeds from the Father and from the Son. Filioque in Latin. One example from scripture for this idea is John 14:23,

But the Helper, the Holy Spirit, whom the Father will send in My name, He will teach you all things, and bring to your remembrance all things that I said to you.

History

A key historical moment for the development of the doctrine of the Trinity was the Council of Nicea in 325. The Council was a response to the teachings of Arius (265 – 336). Arius taught that the Son, Jesus Christ, was a creature, a creation of the Father, the first and greatest of God’s created beings, but still a created being. The key idea of this doctrine was that “there was a time when he was not”.

Arius’ teachings were very influential, not just among clergy and theologians but even among regular folks. Gregory of Nyssa (335 – 395) described the controversy in this way:

“The whole city is full of it, the squares, the marketplaces, the crossroads, the alleyways; rag dealers, money-changers, food-sellers, they are all busy arguing. If you ask someone to give you change, he philosophizes about the Begotten and the Unbegotten; if you inquire about the price of a loaf, you are told by way of reply that the Father is greater and the Son inferior; if you ask, “Is my bath ready?” the attendant answers that the Son was made out of nothing.” (“On the Deity of the Son” PG xlvi, 557b)

Πάντα γὰρ τὰ κατὰ τὴν πόλιν τῶν τοιούτων πεπλήρωται͵ οἱ στενωποὶ͵ αἱ ἀγοραὶ͵ αἱ πλατεῖαι͵ τὰ ἄμφοδα· οἱ τῶν ἱματίων κάπηλοι͵ οἱ ταῖς τραπέζαις ἐφεστη κότες͵ οἱ τὰ ἐδώδιμα ἡμῖν ἀπεμπολοῦντες. Ἐὰν περὶ τῶν ὀβολῶν ἐρωτήσῃς͵ ὁ δέ σοι περὶ γεννητοῦ καὶ ἀγεννήτου ἐφιλοσόφησε· κἂν περὶ τιμήματος ἄρτου πύθοιο͵ Μείζων ὁ Πατὴρ͵ ἀποκρίνεται͵ καὶ ὁ Υἱὸς ὑποχείριος. Εἰ δὲ͵ Τὸ λουτρὸν ἐπιτήδειόν ἐστιν͵ εἴποις͵ ὁ δὲ ἐξ οὐκ ὄντων τὸν Υἱὸν εἶναι διωρίσατο. Οὐκ οἶδα τί χρὴ τὸ κακὸν τοῦτο ὀνομάσαι͵ φρενῖτιν ἢ μανίαν͵ ἤ τι τοιοῦτον κακὸν ἐπιδήμιον͵ ὃ τῶν λογι σμῶν τὴν παραφορὰν ἐξεργάζεται.

So the Church had to ask, what do we say about this? Is this right? The First Council of Nicea (325) and the Nicene Creed were the result. The Nicene Creed was later adjusted further in the First Council of Constantinople (381) to the version in use today. In response to Arius the Nicene Creed affirmed that Jesus Christ is:

“Begotten of the Father; Light of Light, very God of very God, begotten, not made, consubstantial with the Father”

The key being that Jesus is God. That was the line drawn.

There were also some very significant theologians and texts written following the council that have been important in the history of Christian theology, especially theology of the Trinity. Some theologians of special note are

Athanasius of Alexandria (296 – 373)
Basil the Great (330 – 379)
Gregory of Nyssa (c. 335 – c. 395)
Gregory of Nazianzus (329–389)
Augustine of Hippo (354 – 430)
Hilary of Poitiers (310 – 367)

Arianism continued to be a prominent view, sometimes supported by the Roman Empire. And many of the Barbarian kingdoms in the West were Arians. These theologians worked diligently to teach the orthodox view against Arianism.

One of the most significant texts of this period was Augustine of Hippo’s On the Trinity (De Trinitate). It’s not only an impressive theological defense and explanation of the Trinity but it also ends up being a fascinating work on the philosophy of the mind and personal identity. This was because Augustine pursued the idea that human beings, being created in the image of God, must be created in the image of the Trinity and therefore bear features of the Trinity in themselves and in their minds.

Significance

In his Intercessory Prayer in John 17:3 Jesus said to the Father:

And this is eternal life, that they may know You, the only true God, and Jesus Christ whom You have sent.

Knowing God is foundational to Christian life. This means knowing both the Father and his son Jesus Christ. And also the Holy Spirit, who testifies of both. This brings home the importance of Jesus Christ to Christian faith.

This is what makes Christianity unique. There are other monotheistic religions and even monotheistic philosophies. But the unique and special revelation of Christianity is the one we find in Jesus Christ.

How to Use Entropy

Entropy is an important property in science but it can be somewhat challenging. It is commonly understood as “disorder”, which is fine as an analogy but there are better ways to think about it. As with many concepts, especially complex ones, better understanding comes with repeated use and application. Here we look at how to use and quantify entropy in applications with steam and chemical reactions.

Entropy is rather intimidating. It’s important to the sciences of physics and chemistry but it’s also highly abstract. There are, no doubt, more than a couple of students who graduate with college degrees in the physical sciences or in engineering who don’t have much of an understanding of what it is or what to do with it. We know it’s there and that it’s a thing but we’re glad not to have to think about it any more after we’ve crammed for that final exam in thermodynamics. I think one reason for that is because entropy isn’t something that we often use. And using things is how we come to understand them, or at least get used to them.

Ludwig Wittgenstein argued in his later philosophy that the way we learn words is not with definitions or representations but by using them, over and over again. We start to learn “language games” as we play them, whether as babies or as graduate students. I was telling my daughters the other day that we never really learn all the words in a language. There are lots of words we’ll never learn and that, if we happen to hear them, mean nothing to us. To use a metaphor from Wittgenstein again, when we hear these words they’re like wheels that turn without anything else turning with them. I think entropy is sometimes like this. We know it’s a thing but nothing else turns with it. I want to plug it into the mechanism. I think we can understand entropy better by using it to solve physical problems, to see how it interacts (and “turns”) with things like heat, temperature, pressure, and chemical reactions. My theory is that using entropy in this way will help us get used to it and be more comfortable with it. So that maybe it’s a little less intimidating. That’s the object of this episode.

I’ll proceed in three parts.

1. Define what entropy is

2. Apply it to problems using steam

3. Apply it to problems with chemical reactions

What is Entropy?

I’ll start with a technical definition that might be a little jarring but I promise I’ll explain it.

Entropy is a measure of the number of accessible microstates in a system that are macroscopically indistinguishable. The equation for it is:

S = k ln W

Here S is entropy, k is the Boltzmann constant, and W is the number of accessible microstates in a system that are macroscopically indistinguishable.

Most people, if they’ve heard of entropy at all, haven’t heard it described in this way, which is understandable because it’s not especially intuitive. Entropy is often described informally as “disorder”. Like how your bedroom will get progressively messier if you don’t actively keep it clean. That’s probably fine as an analogy but it is only an analogy. I prefer to dispense with the idea of disorder altogether as it relates to entropy. I think it’s generally more confusing than helpful.

But the technical, quantifiable definition of entropy is a measure of the number of accessible microstates in a system that are macroscopically indistinguishable.

S = k ln W

Entropy S has units of energy divided by temperature, I’ll use units of J/K. The Boltzmann constant k is the constant 1.38 x 10^-23 J/K. The Boltzmann constant has the same units as entropy so those will cancel, leaving W as just a number with no dimensions.

W is the number of accessible microstates in a system that are macroscopically indistinguishable. So we need to talk about macrostates and microstates. An example of a macrostate is the temperature and pressure of a system. The macrostate is something we can measure with our instruments: temperature with a thermometer and pressure with a pressure gauge. But at the microscopic or molecular level the system is composed of trillions of molecules and it’s the motion of these molecules that produce what we see as temperature and pressure at a macroscopic level. The thermal energy of the system is distributed between its trillions of molecules and every possible, particular distribution of thermal energy between each of these molecules is an individual microstate. The number of ways that thermal energy of a system can be distributed among its molecules is an unfathomably huge number. But the vast majority of them make absolutely no difference at a macroscopic level. The vast majority of the different possible microstates correspond to the same macrostate and are macroscopically indistinguishable.

To dig a little further into what this looks like at the molecular level, the motion of a molecule can take the form of translation, rotation, and vibration. Actually, in monatomic molecules it only takes the form of translation, which is just its movement from one position to another. Polyatomic molecules can also undergo rotation and vibration, with the number of vibrational patterns increasing as the number of atoms increases and shape of the molecule becomes more complicated. All these possibilities for all the molecules in a system are potential microstates. And there’s a huge number of them. Huge, but also finite. A fundamental postulate of quantum mechanics is that energy is quantized. Energy levels are not continuous but actually come in discrete levels. So there is a finite number of accessible microstates, even if it’s a very huge finite number.

For a system like a piston we can set its entropy by setting its energy (U), volume (V), and number of atoms (N); its U-V-N conditions. If we know these conditions we can predict what the entropy of the system is going to be. The reason for this is that these conditions set the number of accessible microstates. The reason that the number of accessible microstates would correlate with the number of atoms and with energy should be clear enough. Obviously having more atoms in a system will make it possible for that system to be in more states. The molecules these atoms make up can undergo translation, rotation, and vibration and more energy makes more of that motion happen. The effect of volume is a little less obvious but it has to do with the amount of energy separating each energy level. When a set number of molecules expand into a larger volume the energy difference between the energy levels decreases. So there are more energy levels accessible for the same amount of energy. So the number of accessible microstates increases.

The entropies for many different substances have been calculated at various temperatures and pressures. There’s especially an abundance of data for steam, which has had the most practical need for such data in industry. Let’s look at some examples with water at standard pressure and temperature conditions. The entropy of

Solid Water (Ice): 41 J/mol-K

Liquid Water: 69.95 J/mol-K

Gas Water (Steam): 188.84 J/mol-K

One mole of water is 18 grams. So how many microstates does 18 grams of water have in each of these cases?

First, solid water (ice):

S = k ln W

41 J/K = 1.38 x 10^-23 J/K * ln W

Divide 41 J/K by 1.38 x 10^-23 J/K and the units cancel

ln W = 2.97 x 10²⁴

That’s already a big number but we’re not done yet.

Raise e (about 2.718) to the power of both sides

W = 10^(1.29 x 10^24) microstates

W = 10^{1,290,000,000,000,000,000,000,000} microstates

That is an insanely huge number.

Using the same method, the value for liquid water is:

W = 10^(2.2 x 10^24) microstates

W = 10^{2,200,000,000,000,000,000,000,000} microstates

And the value for steam is:

W = 10^(5.94 x 10^24) microstates

W = 10^{5,940,000,000,000,000,000,000,000} microstates

In each case the increased thermal energy makes additional microstates accessible. The fact that these are all really big numbers makes it a little difficult to see that, since these are differences in exponents, each number is astronomically larger than the previous one. Liquid water has 10^(9.1 x 10^23) times as many accessible microstates as ice. And steam has 10^(3.74 x 10^24) times as many accessible microstates as liquid water.

With these numbers in hand let’s stop a moment to think about the connection between entropy and probability. Let’s say we set the U-V-N conditions for a system of water such that it would be in the gas phase. So we have a container of steam. We saw that 18 grams of steam has 10^(5.94 x 10^24) microstates. The overwhelming majority of these microstates are macroscopically indistinguishable. In most of the microstates the distribution of the velocities of the molecules is Gaussian; they’re not all at identical velocity but they are distributed around a mean along each spatial axis. That being said, there are possible microstates with different distributions. For example, there are 10^(1.29 x 10^24) microstates in which that amount of water would be solid ice. That’s a lot! And they’re still accessible. There’s plenty of energy there to access them. And a single microstate for ice is just as probable as a single microstate for steam. But there are 10^(4.65 x 10^24) times as many microstates for steam than there are for ice. It’s not that any one microstate for steam is more probable than any one microstate for ice. It’s just that there are a lot, lot more microstates for steam. The percentage of microstates that take the form of steam is not 99% or 99.99%. It’s much, much closer than that to 100%. Under the U-V-N conditions that make those steam microstates accessible they will absolutely dominate at equilibrium.

What if we start away from equilibrium? Say we start our container with half ice and half steam by mass. But with the same U-V-N conditions for steam. So it has the same amount of energy. What will happen? The initial conditions won’t last. The ice will melt and boil until the system just flips among the vast number of microstates for steam. If the energy of the system remains constant it will never return to ice. Why? It’s not actually absolutely impossible in principle. But it’s just unimaginably improbable.

That’s what’s going on at the molecular level. Macroscopically entropy is a few levels removed from tangible, measured properties. What we see macroscopically are relations between heat flow, temperature, pressure, and volume. But we can calculate the change in entropy between states using various equations expressed in terms of these macroscopic properties that we can measure with our instruments.

For example, we can calculate the change in entropy of an ideal gas using the following equation:

Here s is entropy, cp is heat capacity at constant pressure, T is temperature, R is the ideal gas constant, and P is pressure. We can see from this equation that, all other things being equal, entropy increases with temperature and decreases with pressure. And this matches what we saw earlier. Recall that if the volume of a system of gas increases with a set quantity of material the energy difference between the energy levels decreases and there are more energy levels accessible for the same amount of energy. Under these circumstances pressure would decrease so entropy would decrease with pressure.

For solids and liquids we can assume that they are incompressible and leave off the pressure terms. So the change in entropy for a solid or liquid is given by the equation:

Let’s do an example with liquid water. What’s the change in entropy, and the increase in the number of accessible microstates, that comes from increasing the temperature of liquid water one degree Celsius? Let’s say we’re increasing 1 mole (18 grams) of water from 25 to 26 degrees Celsius. At this temperature the heat capacity of water is 75.3 J/mol-K.

Now that we have the increase in entropy we can find the increase in the number of microstates using the equation

Setting this equal to 0.252 J/mol-K

The increase is not as high as it was with phase changes, but it’s still a very big change.

We’ll wrap up the definition section here but conclude with some general intuitions we can gather from these equations and calculations:

1. All other things being equal, entropy increases with temperature.

2. All other things being equal, entropy decreases with pressure.

3. Entropy increases with phase changes from solid to liquid to gas.

Keeping these intuitions in mind will help as we move to applications with steam

Applications with Steam

The first two examples in this section are thermodynamic cycles. All thermodynamic cycles have 4 processes.

1. Compression

2. Heat addition

3. Expansion

4. Heat rejection

These processes circle back on each other so that the cycle can be repeated. Think, for example, of pistons in a car engine. Each cycle of the piston is going through each of these processes over and over again, several times per second.

There are many kinds of thermodynamic cycles. The idealized cycle is the Carnot cycle, which gives the upper limit on the efficiency of conversion from heat to work. Otto cycles and diesel cycles are the cyles used in gasoline and diesel engines. Our steam examples will be from the Rankine cycle. In a Rankine cycle the 4 processes take the following form:

1. Isentropic compression

2. Isobaric heat addition

3. Isentropic expansion

4. Isobaric heat rejection

An isobaric process is one that occurs at constant pressure. An adiabatic process is one that occurs at constant entropy.

An example of a Rankine cycle is a steam turbine or steam engine. Liquid water passes through a boiler, the steam passes through a turbine, expanding and turning the turbine, The fluid passes through a condenser, and then is pumped back to the boiler, where the cycle repeats. In such problems the fact that entropy is the same before and after expansion through the turbine reduces the number of unknown variables in our equations.

Let’s look at an example problem. Superheated steam at 6 MPa at 600 degrees Celsius expands through a turbine at a rate of 2 kg/s and drops in pressure to 10 kPa. What’s the power output from the turbine?

We can take advantage of the fact that the entropy of the fluid is the same before and after expansion. We just have to look up the entropy of superheated steam in a steam table. The entropy of steam at 6 MPa at 600 degrees Celsius is:

The entropy of the fluid before and after expansion is the same but some of it condenses. This isn’t good for the turbines but it happens nonetheless. Ideally, most of the fluid is still vapor so the ratio of the mass that is saturated vapor to the total fluid mass is called “quality”. The entropies of saturated liquid, sf, and of evaporation, sfg, are very different. So we can use algebra to calculate the quality, x2, of the fluid. The total entropy of the expanded fluid is given by the equation:

s2 we already know because the entropy of the fluid exiting the turbine is the same as that of the fluid entering the turbine. And we can look up the other values in steam tables.

Solving for quality we find that

Now that we know the quality we can find the work output from the turbine. The equation for the work output of the turbine is:

h1 and h2 and enthalpies before and after expansion. If you’re not familiar with enthalpy don’t worry about it (we’re getting into enough for now). It roughly corresponds to the substance’s energy. We can look up the enthalpy of the superheated steam in a steam table.

For the fluid leaving the turbine we need to calculate the enthalpy using the quality, since it’s part liquid, part vapor. We need the enthalpy of saturated liquid, hf, and of evaporation, hfg. The total enthalpy of the fluid leaving the turbine is given by the formula

From the steam tables

And now we can plug this in to get the work output of the turbine.

So here’s an example where we used the value of entropy to calculate other observable quantities in a physical system. Since the entropy was the same before and after expansion we could use that fact to calculate the quality of the fluid leaving the turbine, use quality to calculate the enthalpy of the fluid, and use the enthalpy to calculate the work output of the turbine.

A second example. Superheated steam at 2 MPa and 400 degrees Celsius expands through a turbine to 10 kPa. What’s the maximum possible efficiency from the cycle? Efficiency is work output divided by heat input. We have to input work as well to compress the fluid with the pump so that will subtract from the work output from the turbine. Let’s calculate the work used by the pump first. Pump work is:

Where v is the specific volume of water, 0.001 m³/kg. Plugging in our pressures in kPa:

So there’s our pump work input.

The enthalpy of saturated liquid is:

Plus the pump work input is:

Now we need heat input. The enthalpy of superheated steam at 2 MPa and 400 degrees Celsius is:

So the heat input required is:

The entropy before and after expansion through the turbine is the entropy of superheated steam at 2 MPa and 400 degrees Celsius is:

As in the last example, we can use this to calculate the quality of the steam with the equation:

Looking up these values in a steam table:

Plugging these in we get:

And

Now we can calculate the enthalpy of the expanded fluid.

And the work output of the turbine.

So we have the work input of the pump, the heat input of the boiler, and the work output of the turbine. The maximum possible efficiency is:

So efficiency is 32.32%.

Again, we used entropy to get quality, quality to get enthalpy, enthalpy to get work, and work to get efficiency. In this example we didn’t even need the mass flux of the system. Everything was on a per kilogram basis. But that was sufficient to calculate efficiency.

One last example with steam. The second law of thermodynamics has various forms. One form is that the entropy of the universe can never decrease. It is certainly not the case that entropy can never decrease at all. Entropy decreases all the time within certain systems. In fact, all the remaining examples in this episode will be cases in which entropy decreases within certain systems. But the total entropy of the universe cannot decrease. Any decrease in entropy must have a corresponding increase in entropy somewhere else. It’s easier to see this in terms of an entropy balance.

The entropy change in a system can be negative but the balance of the change in system entropy, entropy in, entropy out, and entropy of the surroundings will never be negative. We can look at the change of entropy of the universe as a function of the entropy change of a system and the entropy change of the system’s surroundings.

So let’s look at an example. Take 2 kg of superheated steam at 400 degrees Celsius and 600 kPa and condense it by pulling heat out of the system. The surroundings have a constant temperature of 25 degrees Celsius. From steam tables the entropy of the superheated steam and saturated steam are:

With these values we can calculate the change in entropy inside the system using the following equation;

The entropy decreases inside the system. Nothing wrong with this. Entropy can definitely decrease locally. But what happens in the surroundings? We condensed the steam by pulling heat out of the system and into the surroundings. So there is positive heat flow, Q, out into the surroundings. We can find the change in entropy in the surroundings using the equation:

We know the surroundings have a constant temperature, so we know T. We just need the heat flow Q. We can calculate the heat flow into the surroundings by calculating the heat flow out of the system using the equation

So we need the enthalpies of the superheated steam and saturated steam.

And plugging these in

Q = mΔh=(2)3270.2-670.6=5199 J

Now that we have Q we can find the change in entropy in the surroundings:

The entropy of the surroundings increases. And the total entropy change of the universe is:

So even though entropy decreases in the system the total entropy change in the universe is positive.

I like these examples with steam because they’re very readily calculable. The thermodynamics of steam engines have been extensively studied for over 200 years, with scientists and engineers gathering empirical data. So we have abundant data on entropy values for steam in steam tables. I actually think just flipping through steam tables and looking at the patterns is a good way to get a grasp on the way entropy works. Maybe it’s not something you’d do for light reading on the beach but if you’re ever unable to fall asleep you might give it a try.

With these examples we’ve looked at entropy for a single substance, water, at different temperatures, pressures, and phases, and observed the differences of the value of entropy at these different states.

To review some general observations:

1. All other things being equal, entropy increases with temperature.

2. All other things being equal, entropy decreases with pressure.

3. Entropy increases with phase changes from solid to liquid to gas.

In the next section we’ll look at entropies for changing substances in chemical reactions.

Applications with Chemical Reactions

The most important equation for the thermodynamics of chemical reactions is the Gibbs Free Energy equation:

ΔG=ΔH-TΔS

Where H, T, S are enthalpy, temperature, and entropy. ΔG is the change in Gibbs free energy. Gibbs free energy is a thermodynamic potential. It is minimized when a system reaches chemical equilibrium. For a reaction to be spontaneous the value for ΔG has to be negative, meaning that during the reaction the Gibbs free energy is decreasing and moving closer to equilibrium.

We can see from the Gibbs free energy equation

ΔG=ΔH-TΔS

That the value of the change in Gibbs free energy is influenced by both enthalpy and entropy. The change in enthalpy tells us whether a reaction is exothermic (negative ΔH) or endothermic (positive ΔH). Exothermic reactions release heat while endothermic reactions absorb heat. This has to do with the total change in the chemical bond energies in all the reactants against all the products. In exothermic reactions the energy released from breaking chemical bonds is greater than the energy used to form new chemical bonds. This extra energy is converted to heat. We can see from the Gibbs free energy equation that exothermic reactions are more thermodynamically favored. Nevertheless, entropy can override enthalpy.

The minus sign in front of the TS term tells us that an increase in entropy where ΔS is positive will be more thermodynamically favored. This makes sense with what we know about entropy from the second law of thermodynamics and from statistical mechanics. The effect is proportional to temperature. At low temperatures entropy won’t have much influence and enthalpy will dominate. But at higher temperatures entropy will start to dominate and override enthalpic effects. This makes it possible for endothermic reactions to proceed spontaneously. If the increase in entropy for a chemical reaction is large enough and the temperature is high enough endothermic reactions can proceed spontaneously, even though the energy required to form the chemical bonds of the products is more than the energy released from the chemical bonds in the reactants.

Let’s look at an example. The chemical reaction for the production of water from oxygen and hydrogen is:

We can look up the enthalpies and entropies of the reactants and products in chemical reference literature. What we need are the standard enthalpies of formation and the standard molar entropies of each of the components.

The standard enthalpies of formation of oxygen and hydrogen are both 0 kJ/mol. By definition, all elements in their standard states have a standard enthalpy of formation of zero. The standard enthalpy of formation for water is -241.83 kJ/mol. The total change in enthalpy for this reaction is

It’s negative which means that the reaction is exothermic and enthalpically favored.

The standard molar entropies for hydrogen, oxygen, and water are, respectively, 130.59 J/mol-K, 205.03 J/mol-K, and 188.84 J/mol-K. The total change in entropy for this reaction is

It’s negative so entropy decreases in this reaction, which means the reaction is entropically disfavored. So enthalpy and entropy oppose each other in this reaction. Which will dominate depends on temperature? At 25 degrees Celsius (298 K) the change in Gibbs free energy is

The reaction is thermodynamically favored. Even though entropy is reduced in this reaction, at this temperature that effect is overwhelmed by the favorable reduction in enthalpy as chemical bond energy of the reactants is released as thermal energy.

Where’s the tradeoff point where entropy overtakes enthalpy? This is a question commonly addressed in polymer chemistry with what’s called the ceiling temperature. Polymers are macromolecules in which smaller molecular constituents called monomers are consolidated into larger molecules. We can see intuitively that this kind of molecular consolidation constitutes a reduction in entropy. It corresponds with the rough analogy of greater order from “disorder” as disparate parts are assembled into a more organized totality. And that analogy isn’t bad. So in polymer production it’s important to run polymerization reactions at temperatures where exothermic, enthalpy effects dominate. The upper end of this temperature range is the ceiling temperature.

The ceiling temperature is easily calculable from the Gibbs free energy equation for polymerization

Set ΔGp to zero.

And solve for Tc

At this temperature enthalpic and entropic effects are balanced. Below this temperature polymerization can proceed spontaneously. Above this temperature depolymerization can proceed spontaneously.

Here’s an example using polyethylene. The enthalpies and entropies of polymerization for polyethylene are

Using our equation for the ceiling temperature we find

So for a polyethylene polymerization reaction you want to run the reaction below 610 degrees Celsius so that the exothermic, enthalpic benefit overcomes your decrease in entropy.

Conclusion

A friend and I used to get together on weekends to take turns playing the piano, sight reading music. We were both pretty good at it and could play songs reasonably well on a first pass, even though we’d never played or seen the music before. One time when someone was watching us she asked, “How do you do that?” My friend had a good explanation I think. He explained it as familiarity with the patterns of music and the piano. When you spend years playing songs and practicing scales you just come to know how things work. Another friend of mine said something similar about watching chess games. He could easily memorize entire games of chess because he knew the kinds of moves that players would tend to make. John Von Neumann once said: “In mathematics you don’t understand things. You just get used to them.” I would change that slightly to say that you understand things by getting used to them. Also true for thermodynamics. Entropy is a complex property and one that’s not easy to understand. But I think it’s easiest to get a grasp on it by using it.

The Unintelligible Remainder

Could anything truly exist in such a fashion that it could never be either perceived or thought of, even if only in principle? How would such a reality be distinct from absolute nothingness? A look into the philosophical issues of being and knowing with John Locke, Immanuel Kant, Martin Heidegger, Joseph Ratzinger, and David Bentley Hart.

“Could anything truly exist in such a fashion that it could never be either perceived or thought of, even if only in principle? How would such a reality be distinct from absolute nothingness?”

This is a question posed by David Bentley Hart in his recent book You Are Gods: On Nature and Supernature. I think it’s an interesting question and it touches on some of the most foundational issues in philosophy.

I’ll call that which could never be either perceived or thought of the “intelligible remainder”. It’s that which is left unperceived and unknown in all our perception and knowledge of things because it is intrinsically imperceptible, unknowable, and unintelligible to intelligent beings. To frame this idea it’s helpful to refer to the philosophy of John Locke and Immanuel Kant. The concepts of subject and object are important to both. Philosophically, a subject is a being who has a unique consciousness and unique personal experiences. An object is something that the subject observes, perceives, or relates to in some way. Both Locke and Kant concerned themselves with how thinking subjects relate to the objects of their experience, and in particular the limitations, or unintelligible remainder, of the subject’s grasp of the object.

In An Essay Concerning Human Understanding John Locke introduced what he called the primary and secondary qualities of things. As an example, for a light wave or a sound wave one primary quality would be its wavelength. Those are things that are in the objects themselves, independent of our perceptions of them. A secondary quality, by contrast, would be like the color of light or the pitch of a sound. These secondary qualities are not in the objects themselves but are products of our modes of perception. Secondary qualities are our own quirky human ways of perceiving things.

Immanuel Kant had some similar ideas. Instead of primary and secondary qualities, in his Critique of Pure Reason he used the terms noumena and phenomena. The noumenon is the thing-in-itself, the object as it really is, independent of our perception. The phenomenon is what we perceive of it. Kant stressed that we cannot know the noumena, the things themselves as they really are. We can only know the phenomena. Our knowledge of the world outside our heads is necessarily filtered or mediated.

Sometimes you might hear this in the form of the claim that we never actually see things themselves. What’s really happening is our brains are responding to a series of physical processes and biochemical reactions, as photons impinge on our retina and induce phototransduction in photoreceptor cells, resulting in a cascade of signals carried via the optic nerve to the visual cortex, and so on. In effect we are several layers of mediation removed from the world outside our heads. And a lot is left out in the process of translation.

What I call the unintelligible remainder is a feature of this kind of philosophy in which there is a gulf between things in themselves and our perceptions of them. There’s always something inaccessible to us. A remainder that is inaccessible or unintelligible. To put it in the form of a conceptual equation.

Things In Themselves – Our Perceptions of the Them = The Unintelligible Remainder

The unintelligible remainder is what’s left over; the aspect of things that remains inaccessible and unintelligible to us. What would that unintelligible remainder be? Well, it’s impossible to say because it’s intrinsically inaccessible and unintelligible to us. But then there’s another question. Why should we think that there is such an intelligible remainder? Why should we think that any such remainder exists if it’s something we can never really know anything about?

Let’s break such remainders down into two different types:

1. Things that we don’t know about but could know about
2. Things that we don’t know about and never could know about

How different are these? Maybe the difference is slight. Or maybe it’s huge, even ontological.

We can reason inductively that there are a lot of things that we don’t know about but that we could know about because in the past there have been things that we didn’t know about at one point but later came to know about.

For example, even though we’ve always been able to see light and color we weren’t always aware of the quantifiable spectrum of wavelengths, and that it extended into wavelengths that we can’t see with our eyes, like with infrared and ultraviolet wavelengths. But we can quantify and detect those wavelengths now. The fields of optics and quantum mechanics have further increased our understanding of light.

We can reason that we will continue to come to know about more things that we don’t currently know about. For example, we’ll certainly continue to learn more about the nature of light. Such things are obviously knowable and intelligible because we have come to know about them.

But we can’t reason inductively in the same way about things that we could never know about. Trivially, we’ve never come to know about something that is unknowable. Obviously. Why should we think that such unknowable things exist as an unintelligible remainder?

I think the reasoning about these two kinds of remainders is quite different so I want to dwell on this difference for a bit.

In the case of things that we don’t know about but could know about, we can reason that such things exist through inductive reasoning. We know this is how things have worked in the past. There have been aspects of things that we didn’t know about before that we’ve come to know about later. For any particular thing we can’t conclude deductively that there’s nothing left about it that we don’t know. But we kind of expect that there’s more there because that’s how it’s always been before.

But this kind of inductive reasoning doesn’t work for things that we don’t know about and never could know about. Why is that? Because we’ve never come to know about something that we could never know about. So it’s completely different.

But we kind of want to say still that things exist that we could never know about. Or that there are aspects of things that we could never know about. Why is that? Part of it may be a spill-over effect of our inductive reasoning about things that we didn’t know about but later came to know about. It seems like if there’s all this unknown stuff there should be stuff that we could never know about. And maybe there is a lot of stuff that we never will know about. But that’s different from stuff that we never could know about. Maybe another reason is humility, recognition of our own finitude and limited capacities. Humility is certainly admirable. But I’m not sure it’s enough to make that kind of positive claim. The only way I can see that we could really conclude that there do exist such unknowables would be some kind of indirect argument of impossibility, similar to the halting problem or Gödel’s incompleteness theorems. I don’t know of any such argument of impossibility for unintelligible remainders but it’s an intriguing possibility.

What about the alternative possibility that there is no unintelligible remainder? That everything that exists is intrinsically intelligible and could be perceived and thought of? Are there reasons to think that could be the case?

We can call the foregoing picture with Locke and Kant one of the “Cartesian subject”, which owes its name to the philosopher Rene Descartes. The basic model is of me here “inside” my head as a thinking subject, receiving sense data from objects “outside” in the world. So there’s this stark division between subject and object. This model of the Cartesian subject is quite powerful and intuitive. And it fits with the idea that there is an unintelligible remainder to the objects in the outside world, albeit inconclusively as previously discussed. But there are alternatives. I’ll talk about two: the philosophy of Martin Heidegger and the classical philosophy of Logos.

Martin Heidegger was working out of the field of phenomenology, which is the philosophical study of the structures of experience and consciousness. But his primary focus was ontology, the philosophy of being. His work was an effort to explain the meaning of being, what it means for a thing to be. In Being and Time he first approached this question through the being of human beings, what he called “Dasein”, a German neologism for “there being”. He discarded the concept of the Cartesian subject, a subject separated from the world of objects, with its split between subject and object. Instead, for Heidegger we are “being in the world”.

The philosophy of Being and Time and Heidegger’s later philosophy is extremely vast so I’m only sticking to a few key points related to my topic. One way he describes being is as disclosure, as things being revealed. Many of his circumlocutions have the effect of keeping the active role away from any kind of Cartesian subject. Instead of us as subjects perceiving objects there is disclosure and being revealing things. Another interesting concept of his is the “clearing”, like a clearing in the woods. In the dense forest it is dark and obscure but in the clearing there is space to see things. I am like a clearing in the woods, a site of disclosure and revealing, where things are revealed around me. It’s a very unusual way of speaking but these circumlocutions have the aim of directing our thinking away from the subject-object split.

Another important Heideggerian idea is that the disclosure of being to us comes in terms of our projects and interests. Things like tools are disclosed to us in the first place as tools rather than as atomic facts that we then deduce to be tools in a secondary way. Heidegger’s example is a hammer. In the Kantian view we’d receive raw sense data, percepts, that our minds would use “categories”, sort of like mental modules, to process into concepts. We’d see the raw sense data first and then our minds would process that it is a hammer. But Heidegger rejects that idea. For Heidegger we’re not isolated in our own minds looking out at the world, receiving raw sense impressions. We’re already in the world. We’re already in the workshop, smelling the sawdust, engaged in the activity of building something. The hammer is a tool for hammering as part of our project. We may not even “see” it when we’re using it if we’re really in the zone. It’s just part of a seamless flow of activity. This is a very different way of thinking.

One of the fascinating things about this is that it has very tangible implications in the field of artificial intelligence. If you think about the different approaches I’ve described here you can imagine that it will make a really big difference whether you approach AI in a Lockean, Kantian way versus a Heideggerian way. And I think this is actually one of the best ways to approach Heidegger’s thought. One of the major players in 20th century artificial intelligence was the Heideggerian philosopher Hubert Dreyfus. Here’s his account:

“In 1963 I was invited by the RAND Corporation to evaluate the pioneering work of Alan Newell and Herbert Simon in a new field called Cognitive Simulation (CS). Newell and Simon claimed that both digital computers and the human mind could be understood as physical symbol systems, using strings of bits or streams of neuron pulses as symbols representing the external world. Intelligence, they claimed, merely required making the appropriate inferences from these internal representations… As I studied the RAND papers and memos, I found to my surprise that, far from replacing philosophy, the pioneers in CS had learned a lot, directly and indirectly from the philosophers. They had taken over Hobbes’ claim that reasoning was calculating, Descartes’ mental representations, Leibniz’s idea of a ‘universal characteristic’ – a set of primitives in which all knowledge could be expressed, – Kant’s claim that concepts were rules, Frege’s formalization of such rules, and Russell’s postulation of logical atoms as the building blocks of reality. In short, without realizing it, AI researchers were hard at work turning rationalist philosophy into a research program.”

“…I began to suspect that the critical insights formulated in existentialist armchairs, especially Heidegger’s and Merleau-Ponty’s, were bad news for those working in AI laboratories – that, by combining rationalism, representationalism, conceptualism, formalism, and logical atomism into a research program, AI researchers had condemned their enterprise to reenact a failure.”

“…To say a hammer has the function of being for hammering leaves out the defining relation of hammers to nails and other equipment, to the point of building things, and to the skills required when actually using the hammer – all of which reveal the way of being of the hammer which Heidegger called readiness-to-hand.”

“…It seemed to me, however, that the deep problem wasn’t storing millions of facts; it was knowing which facts were relevant in any given situation. One version of this relevance problem was called ‘the frame problem.’ If the computer is running a representation of the current state of the world and something in the world changes, how does the program determine which of its represented facts can be assumed to have stayed the same, and which would have to be updated?”

I think that’s quite fascinating and one of the best examples I’m aware of where we can see that the opaque writing of a Continental philosopher is not just meaningless gibberish or gratuitous navel gazing without any actual implications. If we ever end up creating artificial intelligence with true self-consciousness – and I think we will – I suspect that one of these approaches will work and the other will not. And in the process that will tell us a lot about the generalized nature of self-consciousness as such, including the nature of our own self-consciousness. It may also tell us about the nature of being itself, what it means for things to be.

How does this relate to the question of the unintelligible remainder? I don’t think Heideggerian ontology addresses that as much as the approach I’ll be talking about next but I think there are some interesting things here to think about. What I see with Heidegger isn’t as much the elimination of a remainder as much as the presence of certain indispensables. And these are indispensables that in other frameworks seem less real or fundamental to the being of things; in other words, quite dispensable. We might think that what a hammer “really” is is a meaningless collocation of atoms. But in Heidegger’s ontology this is not how the being of the hammer is revealed to us. Far from it. That may not seem like a big deal. Why should the way we see things be so important or say anything about the way things really are? But here I’d go back to AI. For a self-conscious AI certain things are going to be indispensable for it to make its way around in the world. AI without the indispensables won’t work. And I’d say that’s because it won’t approach the world correctly. A self-conscious AI will have to see the world in terms of projects, activities, and interests, populated with things in terms of these interests. Those are the indispensables that make up the reality of our world. So in a reverse sort of way it may be that the Lockean-Kantian approach does have a remainder that the Heiderggerian approach is able to account for.

The second alternative to the Cartesian subject I’d like to talk about is the classical philosophy of Logos. I talked about this in some detail in a previous episode, “Logos: The Intellectual Structure of Being”. Logos has its roots in Greek philosophy but has since been most developed in Christian philosophy. The two philosopher-theologians I’ll refer to here are Joseph Ratzinger and David Bentley Hart.

Joseph Ratzinger, later Pope Benedict XVI, gave an excellent overview of Logos in his book Introduction to Christianity, in which he calls Logos the “intellectual structure of being”. He says, “All being is a product of thought and, indeed, in its innermost structure is itself thought.” What implication does this have for the way we perceive and understand things? Ratzinger says: “There is also expressed the perception that even matter is not simply non-sense that eludes understanding, that it too bears in itself truth and comprehensibility that makes intellectual comprehension possible.” That’s the key. With the Logos all of reality is intellectual or, in other words, thought. There can be no unintelligible remainder to things when all of reality is itself thought in its innermost structure.

The process of perceiving the world in this view is not one of processing mere matter with our mental faculties. It’s a process that is parallel to the structure of reality itself. As Ratzinger says: “All our thinking is, indeed, only a rethinking of what in reality has already been thought out beforehand.” As we conceive of the world through thought we are retracing the thought that comprises its essence. “The intellectual structure that being possesses and that we can re-think is the expression of a creative pre-meditation, to which they owe their existence.”

Does this kind of intellectual structure to all of reality entail the existence of God? Ultimately it may. But I think there are a couple other ways to think about it. Consider three possibilities:

1. The rationality of reality is a conditional property, conditional on there being intelligent beings in reality.
2. The rationality of reality is independent of any intelligent beings.
3. The rationality of reality is the rationality of a mind that grounds reality.

Only the third requires God.

In the first option the rationality of reality is a conditional feature, a feature that reality would have if certain conditions were met, even if they are not otherwise actualized. Something of the form:

1. IF there are intelligent beings in reality.
2. AND IF any existing intelligent beings obtain some degree of accurate understanding of reality.
3. THEN such intelligent beings will find reality to be intelligible and rational.

This is probably the option that seems most immediately plausible and straightforward.

The second option moves away from a subjective understanding of rationality to an objective understanding. We can think of this just as consistency. For intelligent beings instrumental rationality is consistency between actions and intentions. But apart from intelligent beings we could think of consistency between states of affairs. At a most basic level, noncontradiction. For some state of affairs, S, it won’t be the case that both S and not-S.

Ratzinger calls this kind of objective consistency “objective mind”. There is at least an “as-if” quality to the intelligibility of reality. It is structured “as if” rationally constructed. I think it’s possible to work within that framework. But ultimately I follow Ratzinger in his view that “objective mind is the product of subjective mind and can only exist at all as the declension of it, that, in other words, being-thought (as we find it present in the structure of the world) is not possible without thinking.”

Let’s turn now to David Bentley Hart and his discussion of this in his book You Are Gods. He says:

“We are accustomed, here in modernity’s evening twilight, to conceive of our knowledge of the world principally as a regime of representation, according to which sensory intuitions are transformed into symbolic images by some kind of neurological and perceptual metabolism, and then subjected to whatever formal conceptual determinations our transcendental apperception and apparatus of perception might permit.”

This is a restatement of the fundamental problem at hand. As a thinking subject, I’m stuck inside my head, separated from the world out there, receiving and processing raw sense data, and trying to come up with a picture of the objects out in the world as best I can. But that picture is always incomplete and eludes intelligibility. As Hart says:

“Being in itself possesses an occult adversity or resistance to being known. All that we experience in experiencing the world, then, is an obscure, logically inexplicable, but unremitting correspondence between mind and world, one whose ontological basis is not a presumed primordial identity between them, but rather something like a pre-established harmony or purely fortuitous synchrony—or inexplicably coherent illusion.”

Some opaque language here but I’ll explain. What Hart calls the “occult adversity or resistance to being known” is what I’m calling the unintelligible remainder. As I sit isolated inside my head looking out into the world putting a picture of it together, the picture that I see has order and regularity. But why? Ratzinger says it’s because the world is intrinsically rational. If that were not the case the order and regularity would be remarkable indeed. This is what Hart means when he says it would be “purely fortuitous synchrony–or inexplicably coherent illusion.” But Hart rejects that idea and, like Ratzinger, sees reality as intrinsically rational. Like Ratzinger he understands our perception and knowledge of things to be a process that is parallel to the structure of reality itself.

“Mind and world must belong to one another from the first, as flowing from and continuously participating in a single source.”

“Being and knowing must, then, coincide in some principle of form.”

Being and knowing are fundamentally linked in such a way that ontology, the philosophy of being, and epistemology, the philosophy of knowledge, “coincide as a single event of manifestation, of Being’s disclosure, which is to say also, of the full existence of what is made manifest.” There are some interesting similarities here with Heidegger in Hart’s idea of the “disclosure” of Being. In Hart’s view, being and knowing are ultimately one and the same. He’s very skeptical of the idea that the way things “really” are is something intrinsically unintelligible that we could never access or perceive.

“Under the regime of representation, the intelligible is a veil drawn before the abyss of the unintelligible, and the unintelligible is more real than the intelligible.”

This is the view he is going to criticize. That the unintelligible is more real than the intelligible.

“But what would it really mean to say that something exists that is, of its nature, alien to intelligibility? Can Being and knowing be wholly severed from one another without creating an intolerable contradiction? Could anything truly exist in such a fashion that it could never be either perceived or thought of, even if only in principle?”

“In principle” is a modifier that should not be overused but I think it’s appropriate here. The issue is not whether something currently is or can be perceived and thought of by finite human beings. As I said before, there’s been a lot of stuff that we haven’t been able to perceive or know about in the past that we’ve since gained the ability to perceive or know about by extending the reach of our innate capacities. Our innate capacities are the same as those of our ancestors 10,000 years ago. The things that are, in fact, perceivable and knowable to us were, in principle, perceivable and knowable to them. By analogy, there are things that are, in principle, perceivable and knowable to us that are not currently perceivable and knowable to us, in fact. With that in mind, Hart is asking if, with this most expansive possible understanding of the perceptive and intellectual capacities of intelligent beings, could anything exist that eludes them? That would be the unintelligible reminder. And he asks:

“How would such a reality be distinct from absolute nothingness?”

I’ll bring up again my distinction between things that we don’t know about but could know about and things that we don’t know about and never could know about. Certainly the first of these is distinct from absolute nothingness. We can reasonably conclude by inductive reasoning that lots of things exist that we don’t know about. But we cannot conclude with that same kind of inductive logic that there are things that exist that we never could know about. We might want to say that there are such unknowables out of humility. Or maybe we can reason toward their existence through some kind of argument of impossibility. But Hart thinks that: “The more rational assumption is… that in fact mind and world must belong to one another from the first, as flowing from and continuously participating in a single source.”

“It certainly seems reasonable to assume that Being must also be manifestation, that real subsistence must also be real disclosure, that to exist is to be perceptible, conceivable, knowable, and that to exist fully is to be manifest to consciousness.”

Why is that the more rational assumption? Hart doesn’t really explain that but I don’t disagree. Everything we do know about the world indicates that it is rationally structured and we have no knowledge of anything that isn’t. That’s not an absolutely conclusive reason but I think it’s a compelling reason to think that everything that exists is rationally structured, perceivable, and intelligible.

“So long as any absolute qualitative disproportion remains between Being and knowing, then, Being cannot become manifest, and so is not. Being must be intelligible, or even intelligibility itself. The perfectly unintelligible is a logical and ontological contradiction.”

There are some interesting ideas here that I think could use some further development. If the perfectly unintelligible, what I’ve been calling the unintelligible remainder, really is a logical and ontological contradiction that would be a compelling refutation of the existence of the unintelligible remainder. It looks like that argument for such logical and ontological contradiction would involve a demonstration of the necessary connection between being and manifestation, or being and disclosure as Heidegger put it. That what it means for something to be is a process of unconcealment and disclosure.

So going back to the opening question. “Could anything truly exist in such a fashion that it could never be either perceived or thought of, even if only in principle?” Is there an ineliminable, unintelligible remainder to all our knowledge and perception? I don’t think there is. I suspect that a great deal falls into the class of things that we don’t know about. Probably the vast majority of the things that make up reality. Nevertheless, I think they are all things that we don’t know about but could know about because all of reality is rationally structured and mind and world, thought and being, flow in parallel from the same source.