An Overview of Kurt Gödel’s Ontological Argument

Perhaps I’ve not given it enough thought, but I must confess that I find Gödel’s ontological argument to be one of the most powerful and persuasive pieces of evidence for the existence of God — evidence that really is hard to ignore. I focus on Gödel, by the way, since his is the version I’ve looked at the most, though Leibniz offered a similar one in correction of Descartes’ which, along with Anselm’s, posited existence as a predicate and never wrestled with the question of whether or not the perfect being in question was itself logically possible. At any rate, it does make a good bit of sense, and the objection that positive properties are subjective and undefinable somehow doesn’t sit well with me, though it’s hard to say why. I’m sure there must be an answer, but it seems that we can all intuitively agree with his own explanation that appeals to the moral aesthetic of of such properties.

Formally, the argument is written thusly:

Ax. 1.    {[Pφ ⋄ ▢(∀x)(φx → ψx)] → Pψ}
Ax. 2.    {P~φ ↔ ~Pφ}
Th. 1.       ∴ {Pφ →♢(∃x)φx}
Df. 1.     {G(x) ↔ (∀φ)(Pφ → φx)}
Ax. 3.     P(G)
Th. 2.       ∴♢(∃x)G(x)
Df. 2.     {φ ess. x ↔ [φx ⋄ (∀ψ)(ψx → ▢(∀y)(φy → ψy)]}
Ax. 4.     {Pφ → ▢Pφ}
Th. 3.       ∴G(x) → G ess. x
Df. 3.     {E(x) ↔ (∀φ)(φ ess. x → ▢(∃y)φy)}
Ax. 5      P(E)
Th. 4.       ∴▢(∃x)Gx

All of these formulas can be restated in more colloquial English, however, so that one doesn’t need to know the symbolic language to understand the argument.

Ax. 1. If a property is positive and the instantiation of that property entails the instantiation of another property, that other property is also positive.
Ax. 2. A negation of a property is positive if and only if the property itself is not positive.
Th. 1. Therefore, if a property is positive, it is possible that such a property exists.
Df. 1. A thing is Godlike if and only if that thing has all positive properties and only positive properties.
Ax. 3. Being Godlike is a positive property.
Th. 2. Therefore, it is possible that something Godlike exists.
Df. 2. A property is an essential feature of something if and only if that property entails every other property that thing has.
Ax. 4. If a property is positive, it is necessarily positive.
Th. 3. Therefore, if something is Godlike, being Godlike is an essence of that thing.
Df. 3. Something necessarily exists if and only if every essential feature of that thing necessarily exists.
Ax. 5. Necessary existence is a positive property.
Th. 4. Therefore, something Godlike necessarily exists.

If that still seems like a bit much to handle, don’t worry. It took me a while to understand it too. Keep in mind, also, that philosophy has its own language so that those who haven’t been acquainted with that language might find some of the arguments difficult to grasp. That sounds a bit demeaning perhaps, but I only say it so that no one feels stupid if they’re having a hard time following along. Oftentimes philosophers use very common words in very precise ways so that most of us think their sentences are incoherent mumbo jumbo until we realize that they’re actually defining words differently than we expected. I’ve tried to be relatively straight forward in my interpretation of the argument that I wrote above while remaining true to the premises as they were written formally, and I think I’ve been successful, even though the argument itself is a bit dense and abstract. It might be worth keeping in mind, however, that the words “necessarily” and “possibly” carry with them certain connotations so that they refer to things that are logically necessary or logically possible in some possible world. Or, to put it another way, something is logically possible if, in some hypothetical world, it can exist without logical contradiction. For example, it is conceivable that in some possible world the continent of North America is shaped like a perfect triangle. Bizarre though it may seem, there is no inherent contradiction in this idea, meaning that it is logically possible and not an absolute impossibility. On the other hand, in no possible world is there a triangle that has any more or less than three angles, since a triangle is by definition something with three angles. If it has four angles it would be a quadrilateral and no longer a triangle. This is, then, a necessary truth since in all possible worlds triangles will always have three angles — no more; no less. And while we’re at it, I might as well clarify what is meant by the term “essence” or “essential.” The essence of something is that which makes a thing what it is. A triangle, to use the last example, is a geometrical figure of three angles, and these three angles are the essence of that geometrical figure called the triangle. It may be a blue triangle or a green triangle or even a metal triangle used to make noise, but these are not essential properties of the triangle since they don’t define what it actually is. So, if what I’ve written doesn’t make sense, try reading it with these ideas in mind and see if it doesn’t help.

To boil it all down, though, the core of the argument goes like this:

1. Something that is Godlike has all positive properties and only positive properties.
2. We can prove that these so-called “positive properties” are at least logically possible.
3. Furthermore, since being Godlike is a positive property, we can conclude that something Godlike possibly exists.
4. Now, if something is Godlike, then this Godlike thing entails all positive properties, since positive properties are the essence of being Godlike.
5. Necessary existence is a positive property.
6. Therefore, something Godlike necessarily exists. This is because being Godlike entails all positive properties and necessarily existence is a positive property, meaning that something Godlike necessarily exists.

As far as I can tell, all of this is a very solid piece of reasoning (far better than the moral argument, which simply doesn’t hold up, or even the Kalam Cosmological argument, which has some pretty clear weaknesses), making it hard for me to seriously deny the existence of some Godlike being.

Trinitarianism in Second Temple Judaism

I’m currently reading Alan Segal’s Two Powers in Heaven in which he argues that certain strains of Jewish theology during the Second Temple and Rabbinic periods believed in multiple divine figures — divine hypostases — which was perceived by some as violating the standard of traditional monotheism. Next semester I hope to do my final research project on the development of Trinitarian thinking during this time, indicating that it was not at all a uniquely Christian invention, but had its roots in a variety of Judaic traditions, such as Philo’s Logos doctrine, second God, and divine triad. Michael Heiser has a nice, small article with a couple good links that I’m quite pleased to have found.

You’ll Never Look at a Nativity Scene the Same Way Again.

For a lot of us it’s not uncommon to hear someone mention interesting tidbits about the Christmas holiday that highlight the inaccuracies of our most cherished traditions, such as the absence of an innkeeper or donkey/camel in the biblical account, and even the likelihood that Christ was born in the spring rather than the winter, which would mean that there was never a “cold winter’s night that was so deep”. Perhaps the latter aberration was the result of Church authorities placing the Christmas celebration in proximity to the feast of Saturnalia, though such a popular story has seriously come into question among scholars, and the notion that many western, early Christians truly believed December to be the month of Jesus’ birth has gained a good amount of acceptance. Nevertheless, one of my favorite factoids that will ruin just about every nativity scene you encounter this winter is the very real possibility that Jesus was born in a house, not a stable.

I know; it kind of sounds crazy at first, but a couple points work in favor of this theory and make it more plausible than any other at this point. First to note, the Greek word καταὺματι can just as easily mean “guest room” as it does “inn”, which in itself doesn’t fully establish my point, though does start us off, especially since it’s the same word used for the upper room of the Last Supper later on in the story. In other words, Luke is not saying that there was no room in the inn, but rather that there was no space in the guest room. But what guest room? Probably the guest room in a house owned by one of Joseph’s relatives in the area, which leads us to the second point.

When we consider that that Joseph almost certainly had family in Bethlehem (it was his hometown after all), it would almost be inconceivable that he couldn’t find someone to take them in for the short time they would be in town. And even if he had no family in the area, ancient, Middle Eastern codes of hospitality would have never allowed for a pregnant woman to take shelter in an outdoor stable, at least not if there were any other options. But what of the manger? Surely he was laid where animals were fed, correct? Well yes, that’s true; but the poor would often keep their animals in the house, and it’s no stretch to believe that Joseph’s family were more lower class than upper, hence being among those who kept their livestock indoors.

So then, what we have is Joseph, Mary, and whoever else might have been in attendance, constructing a sort of make-shift crib out of a manger in a house that could have easily been a bit overcrowded as it was, due to the census and the resultant travelers. Don’t worry. This doesn’t detract from the biblical story. The point ultimately remains the same: the savior of the world – the God of the universe – became like us and was born into conditions completely unfit for a king.

Brief Thoughts on Paul, the Law, and the Gospel, Written Primarily for My Own Benefit

The main contribution by scholars who promote the New Perspective on Paul is that the Apostle, contrary to Reformation and Evangelical doctrine, had little concern in his letters for good works as such, but was rather focusing on works of the Mosaic Torah, which were being promoted as a necessary concomitant to faith for the purpose of maintain one’s covenant status before God. In other words, the controversy was not over good deeds in a addition to faith, but instead over becoming essentially Jewish in addition to faith. That’s why such an emphasis is placed on circumcision, which was the defining feature of Jewish adherents and became an essentially short-handed way of describing one who identified as a Jew. So it goes that when one reads Pauline literature, one needs to remember that certain terms can generally be taken as synonyms for the Torah (the Law of Moses), such as “circumcision”, “works of the Law”, and even the word “works” in most cases.

Another crucial point to remember is that Palestinian Judaism of the first century didn’t really teach that good works earned salvation at all in the way that is often thought in the modern Christianized world. The Reformers transferred the abuses of the Catholic Church and the emphasis on merit back into Paul’s day, and saw in the Bible a fight between those who wanted to earn eternal life through good works and those who taught that faith alone led to eternal life, when in fact Judaism very much believed that their place within the covenant was on the basis of God’s electing grace, apart from anything they did on their own. The catch was that in order to maintain this covenant status, an individual was obligated to follow the precepts of the Mosaic Law, which was also unfortunately interpreted in an overly-rigid and legalistic manner, and therefore turned into an incredible burden for many of the common people. Some might argue that there really isn’t any distinction at all between obedience to earn a right covenant status and obedience to maintain a right covenant status, since both are based on working to earn the favor of God; but as subtle as the distinction may be, it is indeed there, and was carried over into Christianity by many of the early Jewish converts, who taught that obedience to the Torah was necessary in addition to faith in Messiah Jesus. The Jerusalem Council (Acts 15:1-35) was called to address this matter, and the Galatian Christians were starting to fall back into this mindset at the time Paul wrote the canonical letter to them. The same issue is being addressed in Romans when Paul spends so much time writing about works, faith, and the place of Israel in relation to this new church being filled with Gentiles.

This is part of the rich and multifaceted background of the New Testament, which one needs to keep in mind when reading and studying its contents. For by understanding these facts, one can get a better grasp on the role of the Law within Paul’s thought and consequently the role of the Law for the Christian today. Jews felt a certain pride in their Torah and boasted in it as something which made them superior to the nations around them — something that made them better than “Gentile sinners” — and eventually found themselves interpreting its contents in a way that diminished the spirit of love and faith behind it, while at the same time increasing the emphasis on rules and literal commands, which further led to a spirit of exclusivity, leading Gentiles to consider Jews “haters of men”. It may well have been that the converts to Christianity weren’t quite as hard-nosed as the traditionalists from whom they separated; but to Paul, maintaining such ethnic exclusivity and requiring Gentile believers to essentially become Jewish was in direct contrast to the Gospel preached, not only by Christ, but to Abraham. The Torah was never intended to add or change one’s covenant status before God. A right relationship with him always came by trusting in him and living in love toward others. The Torah simply served as a guide to lead people toward that trust by not only showing them what to do, but also by showing them that they couldn’t do it. Remember, sin is anything that detracts from God’s intended best for humanity but isn’t counted where there is no law (Rom. 5:13). In other words, one can’t be held accountable for doing something he didn’t know was wrong. Sin is counted against the person, however, when that individual knows it is wrong, which turns that mere sin into transgression. Before the Law, humanity was aware of certain ways to behave and ultimately had no excuse for their wickedness (Rom. 1:18-32); but the Torah gave a fuller code, which at the same time also turned people’s sin into transgression since they were more aware of their breach of love and justice. This is what Paul meant when he said the Law was given to increase sin and make it utterly sinful (Rom. 7:13), for our innate moral sense renders us without excuse to begin with; but with the Law, we become even more convicted, which should, in turn, lead us to simply trust the mercies of God (Gal. 3:22). It never justified and never will.

Now under the New Covenant, however, we are no longer need that Law to lead us to faith, since the Spirit has been given, while its use as a moral code (which was always incomplete and limited from the beginning, due to the limited nature of humanity) is now reduced, since the Law of the Spirit serves as our code within the heart, thus breaking the bond and dependency we once had with and on the commandments written in stone (2 Cor. 3:3). For Paul, it is the Spirit of God that brings the most profound change, turning the Law into a relic of the past — a valuable relic, mind you, and one that provides wonderful insight, but no longer the schoolmaster it once was (Gal. 3:24).

The Death of Jesus and the Kingdom of God

* I’m indebted to David Brondos for the bulk of what I propose below, and virtually all of the ideas below come from his book Paul on the Cross and Redeeming the Gospel. He is certainly not the only theologian to reject classical atonement theories, and I am uncertain how unique his holistic understanding of Christ’s salvation message is. Nevertheless, I thought it fair to at least give credit where credit is due and to not pass these ideas off as my own, though I may have deviated from his thought in certain minor areas, such as my brief speculation regarding the possibility of Christ not being crucified and the small detail that the Kingdom began after Christ left earth, not while he was on it. As for the former, I don’t think he ever addressed such a possibility, and as for the latter, I don’t recall what he held regarding the Kingdom, whether it was present with Christ or not until after.

It would also be prudent to add that due to the controversial nature of alternate atonement theories, I don’t ask anyone to take my word for it. Whether or not my views will change in the future, I find this position to be one of the most reasonable and elegant I’ve been exposed to so far; but one should think for himself and examine the evidence in a more thorough manner than by reading a single blog.

When I was in college I asked one of my professors how the classic Protestant doctrine of penal substitution could be in accordance with justice – a question many have asked since the 16th century when it was first expounded by John Calvin and others during the Reformation. You see, it’s often said that since God is just, he must punish sin; and since all humans are sinners, all humans must be punished; but if all humans are punished for their sin, then they cannot inherit eternal life since the punishment for sin must also be infinite and eternal, which means that God cannot save people as he wishes until that punishment is somehow meted out. Obviously those whom he wants to save can’t take the punishment, since an offense against an infinite God requires an infinite punishment, which, as I already mentioned, would require eternal punishment for the offenders.

As a solution, the Son of God became incarnate in the man Jesus, lived without sin (ensuring that he didn’t deserve the punishment himself, which would have made him just another human), and then vicariously took that punishment on the cross for the sins of humanity. This was, as I said earlier, to satisfy justice since God apparently could not simply forgive of his own accord. The problem, however, is that this isn’t really justice at all. Justice demands that the offender be punished, not just anybody. I can’t take the place of an inmate on death-row for a murder I didn’t commit. Everyone would agree that this is entirely contrary to the whole purpose of the death penalty, whatever purpose you might ascribe to it. In the case of restitution I’ll admit that one could argue that another can vicariously pay back a debt, which is different than taking punishment; but this is more akin to Anselm’s satisfaction theory, which is similar, but also different to Calvin’s. If you don’t know much about satisfaction or penal substitution, it’s okay. My real purpose in writing this entry is not so much to critique other theories as it is to lay down an alternate system that makes sense of Christ’s life and death.

I think it’s safe to say that in order to understand what happened on the cross, one first needs to understand the nature of salvation itself, which is far more holistic than people often recognize. We see in the Gospels that Jesus came announcing the Kingdom of God, which was at hand, that he came “to proclaim release to the captives, give sight to the blind, and set free those who are oppressed” (Luke 4:18 cf. Isa. 61:1)  In saying this, he was not just offering forgiveness from sins and entrance to some ethereal heaven after death. He was setting up the kingdom on earth – planting the mustard seed that would grow into a large tree (Matt 13:31-32). In this sense, salvation included a great deal more than just some future salvation from hell, but salvation from our sins here on earth and the consequences that arise from them, along with all manner of ills and suffering that have plagued us for ages. Salvation is not just spiritual, it is also physical; and this holistic salvation is to be brought to earth through the church/kingdom, which began with the coming of the Holy Spirit.

In setting the stage for this future kingdom, we see on page after page of scripture that Jesus came into frequent conflict with the religious authorities of his day. Not all were against him, of course, but a substantial portion evidently were due to both His vicious condemnation of them as hypocrites and His understanding of the Law of Moses as something which embodied principles, rather than rules. To them he was seen as a lawless rebel who was leading the people astray. This ostensibly radical departure from standard Jewish religious thought eventually led to his execution at the hands of the Jewish and Roman leaders as is heard every Easter in churches around the world. At that point it was over. He died, never having fulfilled his goal of starting the kingdom that would one day embody the fullest principles of love and justice, or so it seemed. It wasn’t until days later that the disciples were shocked to find that this “failed” Messiah wasn’t even in his tomb anymore, and that he was in fact alive.

Obviously such events needed to be understood since they were such a drastic departure not only from their religious expectations, but also from the ordinary course of human life. Unfortunately we don’t know what Jesus told the disciples when “he opened their minds to understand the Scriptures” (Luke 24: 27, 32, 45), but we still have the writings of the Apostles from which to learn and infer what was believed among first century Christians.

I am going to here suggest that the death of Jesus was not, strictly speaking, actually and atoning sacrifice and did not serve as a means in taking away the sins of the world. Jesus died in fighting for a cause – the cause of God’s kingdom, which he was seeking to inaugurate. But much as we would say a soldier who died in battle sacrificed his life, so too can we say that Jesus’ death was a sacrifice, which is why the Apostles use sacrificial language in describing what took place. God is free to “have mercy on whom he will have mercy” (Rom 9:15) and doesn’t require any satisfaction of justice. He requires no balancing of the scales to remit sin. Jesus died in seeking to alleviate our suffering, much of which is the result of our sin, while also teaching us how to live right and whole lives. In this way, he died for our sins. He was obedient to God unto death, thereby showing us true perfection and holy living, which serves as our example as we follow him.

What if Jesus hadn’t been crucified? I maintain that he would have died anyway, after which the Holy Spirit would have been sent and the Kingdom inaugurated. But if he had died in an accident or from natural causes, we would have never seen a perfect example of faithfulness. Yes, he still would have been perfect, but the example he left us wouldn’t have been one of obedience unto death, which is the highest and most dedicated form, and it is for this reason that God ordained his execution rather than a natural death. Nevertheless, he was not to remain in death but was raised on the third day, according to the Scriptures, so that He could return and fully establish the kingdom he set into motion.

Those who believe this message are counted among the covenant people of God, that is, they are justified. It’s not by believing that Christ appeased the Father’s wrath as a sacrifice. It’s by believing in the promises of God — the promise that God will mercifully forgive our sins and someday establish his just kingdom in its fullness throughout the world. To believe in Jesus is to believe in his cause and to believe that he has been raised to one day return to not only champion that cause but to complete it — to believe that God made good on his word once and will do so again. In so doing we are counted righteous, and as such we will one day partake of a new and restored physical creation free from the suffering and evil we experience here.

Oh, and in case you’re wondering. The professor didn’t have an answer for me. He could only say that it must have been different in the case of Jesus. I guess he would pretty much have to say that, wouldn’t he?