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From persistence to God

Edward Feser’s book Five Proofs of the Existence of God (2017) includes his version of the Aristotelian proof, which looks at the existence of change. There is a similar proof that looks at the existence of persistence. Aristotle, with a static world-picture, wanted to explain change. Someone with a dynamic world-picture might want an explanation for persistence. As time is required for change, so a place or space is required for persistence. Below I sketch this argument by modifying some words in Feser’s text (with page references to his book):

Persistence happens. Examples are all around us. The coffee in your cup is still warm after you step away for a minute. A leaf on the tree outside your window is in the same place it was yesterday. A puddle is the same size it was ten minutes ago. You swat a fly and miss, so it keeps buzzing around.

These examples illustrate four kinds of persistence: qualitative persistence (the coffee doesn’t change temperature); persistence with respect to location (the leaf is in the same place); quantitative persistence (the puddle is the same size); and substantial persistence (a living thing keeps on living). That persistences of these sorts occur is evident from our sensory experience of the world outside our minds. (p.17)

What persistence involves is, for pseudo-Aristotle, the actualization of a potential. The coffee has the potential to stay warm. A leaf has the potential to stay in the same place. A puddle has the potential to remain the same size. A fly has the potential to stay alive. (p.18)

Persistence requires a ‘persistentizer’. We find examples all around us in everyday experience. The warm air in the room keeps the temperature of the coffee the same. The connection to the tree keeps the leaf in the same place. But the thesis that persistence requires a ‘persistentizer’ is not merely a generalization from instances like these. It follows from what persistence is: the actualization of a potential. (p. 19)

Consider next that series of persistences that extend across space, in what we might think of as a linear fashion. The coffee is still warm because the air in the room is warm; the air is warm because the air conditioner switch is in the off position; and so forth. (p. 20)

There is another kind of series—let us call it the hierarchical kind—which must have a first member. … Consider the coffee cup as it sits on your desk. It is, we may suppose three feet above the floor. Why? Because the desk is holding it up, naturally. But what holds the desk up? The floor, of course. The floor, in turn is held up by the foundation of the house, and the foundation of the house by the earth. (p.21, same text fits persistence)

First of all, since the cause of things is pure actuality and therefore devoid of potentiality, it cannot go from potentiality to actuality or from potentially persistent to actually persistent and is thus ever-new or inexhaustible. Since existing within space entails persistence, an ever-new cause must be transcendent in the sense of existing outside of space altogether. It neither comes to be nor passes away but simply is, spacelessly, without origin or destination. (p.29)

Let’s skip ahead to a few modifications of Feser’s more formal statement of the argument (p.34ff):

1. Persistence is a real feature of the world.
2. But persistence is the actualization of a potential.
3. So, the actualization of potential is a real feature of the world.
4. No potential can be actualized unless something already actual actualizes it (the principle of causality).
5. So, any persistence is caused by something already actual.
6. The occurrence of any persistence C presupposes some thing or substance S which persists.

19. In order for this purely actual actualizer to be capable of persistence, it would have to have potentials capable of actualization.
20. But being purely actual, it lacks any such potentials.
21. So it is ever-new or inexhaustible.
22. If this purely actual actualizer existed in space, then it would be capable of persistence, which it is not.
23. So, this purely actual actualizer is transcendent, existing outside of space.
24. If the purely actual actualizer were material, then it would be persistent and exist in space, which it does not.
25. So, the purely actual actualizer is immaterial. (p.35-36)

The main difference between this argument and Feser’s is the conclusion that God is ever-new or inexhaustible. Does that contradict Aristotle or the Bible? Not necessarily; divine newness and faithfulness are compatible, as in Lamentations 3:22-23:

The steadfast love of the Lord never ceases;
his mercies never come to an end;
they are new every morning;
great is your faithfulness.

Gregory of Nyssa compares God to a spring (Commentary on the Song of Songs, Homily 11):

It is just as if you could see that spring which Scripture tells us rose from the earth at the beginning in such quantities that it watered the entire face of the earth (Gen. 2:10 ff.). As you came near the spring you would marvel, seeing that the water was endless, as it constantly gushed up and poured forth. Yet you could never say that you had seen all the water. How could you see what was still hidden in the bosom of the earth? Hence no matter how long you might stay at the spring you would always be beginning to see the water. For the water never stops flowing, and it is always beginning to bubble up again.

It is the same with one who fixes his gaze on the infinite beauty of God. It is constantly being discovered anew, and it is always seen as something new and strange in comparison with what the mind has already understood. And as God continues to reveal himself, man continues to wonder; and he never exhausts his desire to see more, since what he is waiting for is always more magnificent, more divine, than all that he has already seen.

Luther at 500

October 31, 2017, is the 500th anniversary of the Reformation. Phillip Cary’s excellent article in First Things places this in perspective. While the full article is behind a paywall, here are some excerpts:

It all did start with the ninety-five theses, in a sense. Luther probably did not actually nail them to the church door—at least no one at the time tells us so. And if he did, it was not in anger or protest against the church. He was trying to arrange an academic discussion, and evidently that’s where the bulletin board was. What we do know is that he mailed them off to his archbishop, together with a treatise on indulgences and a cover letter dated October 31, 1517, so that is the date remembered as the beginning of the Protestant Reformation.

What Luther did not know at the time is that the pope and the archbishop were the ones profiting from this merchandise, each claiming half of the take. So it is not surprising that events took a turn he did not anticipate. Within five years, this intensely obedient monk had concluded that obedience to God precluded obedience to the pope, and a schism in the Church followed.

At the starting point in 1517, Luther’s pastoral concern was unfamiliar and hardly Protestant. He thought indulgences made penance seem much too easy, undermining the lifelong work, required of all Christians, of contrition, which he identified with heartfelt self-hatred.

By the end of 1518, he was teaching that Christians hearing the word of absolution in the sacrament of penance (“I absolve you of your sins in the name of the Father, the Son, and the Holy Spirit”) should simply believe their sins are absolved.

Faith comes by hearing, says the apostle (Rom. 10:17), and Luther is the greatest and most obsessive theologian of hearing in the Christian tradition. For Luther, everything depends on hearing the Word of God, taking hold of it, clinging to it, and not talking back—not calling God a liar. His treatment of the doctrine of justification always turns on the conviction that “God is true, though every man be a liar” (Rom. 3:4). Everything depends on God being true to his word and keeping his promise, which the deceitfulness of our unworthy hearts cannot overturn.

What happens in 1518 is that Luther’s fierce conviction that we must never talk back against God’s word meets the medieval doctrine of sacramental efficacy, and results in the Protestant conception of the power of the Gospel.

When Luther teaches justification by faith alone, he is not requiring us to put faith in faith. On the contrary, he wants us putting faith in the Gospel alone. Any account of faith that focuses on the experience of faith—any theological turn to subjectivity, such as in liberal theology—has missed Luther’s point. What we experience, for the most part, is our own sin and unbelief. Faith means turning away from our experience to take hold of Christ alone by believing, against all doubt and temptation, that what the Gospel tells us about Christ given for us is really true.

Justification by faith alone is thus justification by Christ alone. This has everything to do with hearing the Gospel spoken aloud in external words, through which Christ claims each of us by saying “you” in a way that includes me.

Luther accepts the traditional metaphysical attributes of God, such as eternity, immutability, omnipresence, and so on, but these are not objects of his devotion. Above all, he has no use for the rich notion of intellectual vision shared by Augustine and Aquinas, going back ultimately to Plato’s metaphor of seeing the supreme Good with the mind’s eye. Luther does not aim to see God’s essence but to hear him speak, for it is in his word that God gives himself to be known.

If God is a person rather than a principle, coming to us in the person of his own Son, isn’t believing what he has to say about himself the deepest and most appropriate way to know who he is?

Most important, Luther’s challenge affects Christian life by freeing Christian love to be love, removing the kind of performance anxiety that makes it about ourselves. If we are justified by faith alone, then works of love serve our neighbors, not our desire to justify ourselves or make ourselves holy. We are holy because Christ claims us as his own through word and sacrament, and Christian love takes root in our hearts because we believe what Christ has done.

How we have always been justified by faith alone is best seen in light of Luther’s distinction between law and Gospel. Both the law of God and the Gospel of Christ are God’s word, but the former only gives us instructions while the latter gives us Christ. For the law tells us what to do, but the Gospel tells us what Christ does. The distinction grows out of Augustine’s insistence, in his great treatise On the Spirit and the Letter, that telling us to obey the law of love does not help us do it from the depths of our hearts; only the grace of Christ can give us such a heart. Luther merely adds: The place to find the grace of Christ is in the Gospel of Christ.

E. W. Kenyon, part 4

The previous post in this series is here. McIntyre next introduces theological defenses of divine healing. in 1881 William Boardman (1810-1886) authored The Great Physician (Jehovah Rophi).

Boardman’s earlier work, The Higher Christian Life (1859) was tremendously influential in bringing the message of sanctification into non-Methodist circles. … Boardman expressed the idea that everything we need is already a reality in Christ, only awaiting the believer’s faith to claim it. … He later came to see healing as a part of our redemption and applied this same premise (that sanctification and everything we need is already true in Christ and awaiting our claiming it by faith) to healing. This is exactly what Kenyon taught. p.85

A. J. Gordon … wrote a book titled, The Ministry of Healing: Miracles of Cure in All Ages, which [Charles] Cullis published in 1882. It was a historical and doctrinal study of faith healing from the early church fathers, the post-Reformation period, and modern ministries of healing. p.86

Kenyon certainly read this book since he quoted from Gordon’s writings more frequently than any other author. p.86

Gordon believed that healing was included in the atonement of Christ. Even the critics of the doctrine acknowledged Gordon’s skillful treatment of the subject. Gordon wrote:

 The yoke of His cross by which He lifted our iniquities took hold also of our diseases; so that it is in some sense true that as God “made Him to be sin for us who knew no sin,” so He made Him to be sick for us who knew no sickness. …

If now it be true that our Redeemer and substitute bore our sicknesses, it would be natural to reason at once that He bore them that we might not bear them.

But, it is asked, if the privilege and promise in this matter are so clear, how is it that the cases of recovery through the prayer of faith are so rare? Probably because the prayer of faith itself is so rare, and especially because when found it receives almost no support in the church as a whole. p.86-87

Healing in the atonement became widely regarded as the basis for claiming healing as the believer’s covenant privilege. p.87

R. L. Stanton and R. Kelso Carter also wrote books defending divine healing in the atonement.

Kenyon would later state his belief about deliverance from sin and sickness being included in the finished work of Christ in his book, Jesus the Healer. p.89

Kenyon, like most of the voices in the Faith-Cure movement, saw in the work of Christ at Calvary a basis for holy living and healing and health. Claiming the provisions of Christ’s work by faith and confessing them before men was common practice among them. Acting on the promise without any apparent change was also regularly encouraged. p.89

McIntyre covers much more but let’s skip to the controversy that ensued.

Anyone teaching divine healing in the latter part of the nineteenth-century faced the inevitable comparison with Christian Science and the other metaphysical cults. Unfortunately, many leaders in the orthodox church who were opposed to healing in general failed to distinguish any significant difference between the two approaches to healing. p.239

In this climate, divine healing teachers had to be able to show the differences between biblical healing and metaphysical healing. p. 240

McIntyre then documents the following points:

  • The Faith-Cure movement predated the metaphysical cults by a number of years.
  • The practices of the Faith-Cure movement were established before the metaphysical cults were visible as distinct movements.
  • The Faith-Cure movement, which was rooted in the evangelical church, had distinctly different teachings than the cults.
  • E. W. Kenyon’s teachings are in the Faith-Cure tradition.

I will end this brief introduction to McIntyre’s book with this quote from Kenyon about affirmations:

You see the vast difference between an affirmation based upon your own will or philosophy and an affirmation backed up by God Himself.

The affirmations based upon sense knowledge philosophy have no more value or ability to make good than is in the will and mind of the maker of the affirmation. But the affirmation that is based upon the living Word has God back of it to make it good. p.259

E. W. Kenyon, part 3

The previous post in this series is here. McIntyre next turns to the Faith-Cure movement.

This revival of healing, known as the Faith-Cure movement[,] lasted from around 1873 until its teachings were absorbed into the Pentecostal movement in the early 1900s. Its earliest advocates began teaching divine healing by faith as early as 1846. p.64

It is only because so few today are aware of this revival that Kenyon’s critics have been as influential as they have been. A review of its teachers and teaching reveals a great similarity between the Faith-Cure movement and the [Word of] Faith movement. p.64-65

Kenyon helped bridge the gap between the two movements. Others who bridged the gap included F. F. Bosworth, John G. Lake, and Carrie Judd Montgomery. p.65

Kenyon was influenced by the three most prominent leaders of the Faith-Cure movement—A. B. Simpson, Charles Cullis, and John Alexander Dowie. p.65

McIntyre points out that Kenyon and his wife Evva were initially reluctant to pray for the sick. Kenyon later wrote:

Before this I had always been suspicious of anyone who claimed their prayers were answered along the line of healing. I felt we had doctors and surgeons and sanitariums for that purpose. p.66

But sick people asked Kenyon to pray for them, and when he started to do so, people were healed.

From that day on healings came—not many, for not many people asked to be prayed for. … One day I discovered the use of the name of Jesus. Then miracles became a daily occurrence. p.67

Kenyon cautiously introduced divine healing to [his] new nondenominational church, called the Tabernacle. p.67

McIntyre describes leaders of the Faith-Cure movement, A. B. Simpson (the founder of the Christian and Missionary Alliance), Charles Cullis, and John A. Dowie.

[A. B.] Simpson, like so many of those involved in the Faith-Cure movement, advocated testimony and actions of faith before the healing was manifested. p.70

[Charles] Cullis shared his discovery of divine healing with many leaders in the Holiness movement who also embraced the doctrine. p.72

Arguably the most gifted—and the most tragic—character in the Faith-Cure movement was John Alexander Dowie. Used mightily of God for a season, Dowie came to believe in his latter years (from 1901 until his death in 1907) that he was Elijah the Restorer, the great end-time prophet. p.72

In one of his books, Kenyon referred again to the power of God in Dowie’s ministry. He wrote, “You and God and linked together. You become invincible. We see a glimpse of this in Luther’s ministry. We saw it in John Alexander Dowie’s ministry. We have seen it in individuals here and there—God and man linked together, doing the impossible. p.73

McIntyre notes there was debate about the role of doctors in divine healing.

An aspect of healing ministry that is still debated today is the use of medical treatment. The abysmal state of medicine was probably one of the underlying reasons why some Faith-Cure healers rejected medical treatment. p.73

It was common in both the Holiness movement and the early Pentecostal movement to trust God alone for physical health and healing. p.74

McIntyre then tells of other leaders of the Faith-Cure movement, starting with Ethan O. Allen.

Ethan O. Allen [1813-1903], known as the father of divine in the United States, was the first American known to have a full-time traveling ministry focused on healing. For fifty years he traveled throughout the Eastern United States praying for the sick and teaching divine healing. Allen was also a frequent guest at A. B. Simpson’s conferences. p.77

Kenyon’s teaching is strikingly similar to Allen’s. … Let’s review the steps Allen took. He claimed the promise of God by faith and stated that the “evidence” of his healing “was very clear.” The “evidence was the witness of the Holy Spirit that his prayer was heard and that God had given the healing to him by faith. Note that he said, “I have got the evidence, pain or no pain.” p.78

Allen applied the Methodist understanding of faith for receiving sanctification to receiving healing. He spoke out of the witness of the Spirit rather than his physical condition. Some people today call this “sensory denial;” the Methodists and Faith-Cure people called it faith in God and His Word. p.78-79

Allen, also in the Methodist tradition, stressed the need for confession that a healing is received. p.79

McIntyre points out that this principle was in line with Phoebe Palmer and “older Methodists such as Hester Ann Rogers and John Fletcher” who “taught that sanctification was kept by continual public confession. This idea was normative in Methodism as early as 1846.” (p.79)

McIntyre gives other examples of this teaching: Elizabeth Mix, Carrie Judd Montgomery, and, surprisingly, Andrew Murray.

Having lost his voice and reportedly finished his career as a preacher, Murray sought out the truth of divine healing. Eventually he went to London to the divine healing home established by William Boardman called Bethshan. He was so completely healed he was never troubled again by any weakness of the throat or voice. … In 1884 Murray wrote the Dutch version of his book on divine healing called Jesus, The Physician of the Sick. It was published in English in 1900. Concerning faith and healing Murray wrote:

Prayer without faith is powerless… If you have already asked for healing from the Lord, or if others have asked it for you, you must, before you are conscious of any change, be able to say with faith, “On the authority of God’s Word, I have the assurance that He hears me, and that I am healed.”

Here another respected leader whose devotional writings are still popular today, expressed himself in terms that Kenyon could easily have used. p.83

The next post in this series is here.

E. W. Kenyon, part 2

This post continues the previous post here. McIntyre’s book provides more 19th century history and shows how E. W. Kenyon’s teachings reflected his background in the Holiness movement.

The Holiness movement in America was rooted in the Methodist church, which was the largest Protestant denomination during the nineteenth century. John Wesley had taught the doctrine of Christian perfection in earlier years, and many voices were calling the church, within and without Methodism, back to a “higher Christian life.” p.46

The most distinctive doctrine of the Holiness movement was what was known as the second work of grace. At conversion the believer’s sins were forgiven. He was justified. Then the convert was to seek an experience known as entire sanctification. This was the “second work of grace.” It consisted of an instantaneous crisis of consecration, or total abandonment to the Lord, believed to remove the sin nature which was not affected by conversion. After this crisis the believer was able to live without sinning. This experience was often referred to as the baptism of the Holy Spirit. p.46-47

We can easily establish that Kenyon was exposed to these teachings. Kenyon was converted in a Methodist church. He spent his first years with the Lord attending a Methodist church and other Holiness meetings. He also attended services with The Salvation Army (who were among the second-work-of-grace Holiness advocates). p.46

Kenyon was, for the most part, a Holiness preacher when he pastored the Free Will Baptist church in Springville, New York (1894–1897). p.47-48

Personally, and as a pastor, Kenyon attempted to enter into an experience of entire sanctification. “In a church of which I was pastor we used to have consecration services from one to three times a week. I cannot tell you how many times I personally tried to do this,” the mourned. p.48

McIntyre then describes the teachings of the influential Phoebe Palmer (1807–1874) and others:

Palmer advocated what she called the “shorter way” into the experience of holiness. She taught that holiness was available, like justification, on the basis of faith alone. The necessary thing was to meet the conditions set forth in the Scriptures and then to believe the promises, accepting the Word of God alone as the evidence. p.50

The Free Will Baptists, with whom Kenyon was aligned at the time, were one of the denominations that embraced this teaching on holiness by faith. p.51

A positive confession of receiving the grace of sanctification was widely taught and practiced in the Holiness movement. … Palmer wrote in 1848, many years before Christian Science or New Thought developed:

But do not forget that believing with the heart, and confessing with the mouth, stand closely connected, and “what God hath joined together, let not man put asunder.” To the degree that you rely on the faithfulness of God, O hasten to make confession with the mouth of your confidence; and to the degree you honor God, by reposing on His faithfulness, will God honor you, by conferring on you the graces of His Holy Spirit in their rich plenitude. p.51-52

Other influential teachers, including Kenyon, later reflected Palmer’s ideas of faith as a law and an unchanging principle of the kingdom [of God]. … The “law of faith” was not some rigid demand that caused God to bow to the believer’s whim, but rather a principle by which the believer met the conditions of God’s covenant promises and God performed His promise for them every time (Rom. 3:27) P.52-53

[Hannah Whitall] Smith (1832-1911) is a respected and well-known author still today. Her book The Christian’s Secret of a Happy Life is still quite widely read. … Smith’s book and its teachings on faith and consecration are a great representation of the teaching of the Higher Life movement, as it was often called. The idea of confession is not missing from her teaching either. She encouraged her readers:

To begin at once to reckon that you are His, that He has taken you, and that He is working in you to will and to do His good pleasure. And keep on reckoning this. You will find it a great help to put your reckoning into words, and say over and over to yourself and to your God, “Lord, I am Thine; I do yield myself up entirely to Thee, and I believe that Thou dost take me. p.58-59

Kenyon, like many other Christians of his day, had a crisis of consecration and wrote his own statement of consecration. He referred to this experience a number of times, mostly in his unpublished articles, so this event in his life is not widely known. p.60

Kenyon, while struggling with the issue of Christ’s Lordship or the necessity of total consecration of his life to God, faced … a number of what he described as “life-threatening” illnesses. He surrendered to the best of his ability to Jesus. He was dramatically healed as a result of this surrender and of the prayer of an unknown brother. … In this episode of Kenyon’s life we see both the influence of the Holiness movement and a definite experience with divine healing. p.62, 63

The next post in this series is here.

E. W. Kenyon, part 1

D. R. McConnell in A Different Gospel, 1988, and Hank Hanegraff in Christianity in Crisis, 1993, accused E. W. Kenyon of promoting heresies such as those found in New Thought. However, Joe McIntyre in E. W. Kenyon and His Message of Faith: The True Story, 1997 (rev. 2010), documented how Kenyon’s teachings were well within evangelical Christianity. Since Kenyon is considered to have influenced the controversial Word of Faith (or simply Faith) movement, an assessment of this requires a closer look at Kenyon and his teachings. This series of posts will include excerpts from McIntyre’s book and Kenyon’s writings.

McIntyre quotes Kenyon on his seven-fold test for the truth of Christian doctrines (p.33-34):

This danger of being led into false teaching stood at the threshold of every new truth in the early days of my Bible study, and I prayed much that the Lord would give me a real testing tube, scales, weight, and measure, whereby every step could be satisfactorily proved. (May 1916)

All New Testament teaching conforms to Old Testament types, and if all doctrine were built of the units of testimony of the whole Word, much false teaching would be done away with.

Take this sevenfold test. All New Testament doctrines must be found:

1) In Genesis, in germ (or seed) form;
2) In the Law, in type;
3) In Psalms, in sacred song;
4) In the Prophets, as prophecy;
5) In the Gospels, taught by Christ;
6) In Acts, practiced by the Apostles;
7) In the Epistles, as doctrine.

… Every truth, or doctrine taught in the New Testament can be found by the Spirit-taught student in these sevenfold steps. It gives the Christian an entire Bible. Then let us see, if the whole Word sends forth clear tones in perfect harmony with each other as we ascend the scale from Genesis to Revelation. (Oct. 1898)

McIntyre notes (p.35):

All the metaphysical cults, particularly Christian Science and New Thought, handle the Scriptures quite loosely, employing much fanciful interpretation, probably to avoid the implications of the text taken literally. In contrast, unless he was interpreting the types, Kenyon consistently took the text in its most obvious, literal sense. In this he reflected the influence of J. N. Darby and other Brethren authors whom he greatly respected. A little closer to home, we see the influence of A. J. Gordon, A. T. Pierson, R. A. Torrey, and A. B. Simpson, all of whom Kenyon greatly admired.

Regarding the baptism of the Holy Spirit (p. 37):

[Kenyon] taught that immediately after one was born again one should ask the Holy Spirit to come and live in his body. Statements of this idea are in almost every book he wrote. What Kenyon did not believe was that the experience of receiving the Holy Spirit was the baptism of the Holy Spirit. He believed that the phrase baptism of the Holy Spirit referred to conversion.

Regarding speaking in tongues (p. 37-38):

Kenyon believed that speaking in tongues was a valid experience, but for him the evidence for being filled, or receiving the Holy Spirit, was the promise of Scripture itself. Kenyon wanted people to look to the word of God alone as evidence that they had received the Holy Spirit.

McIntyre points out that in this matter Kenyon was influenced by four Christian teachers: A. J. Gordon, A. T. Pierson, R. A. Torrey, and A. B. Simpson. (p.38ff)

The next post in this series is here.

Speed vs. velocity

For some background, see here and here.

Velocity is defined as: “The time rate of change of position of a body; it is a vector quantity having direction as well as magnitude.” Speed is defined as: “The time rate of change of position of a body without regard to direction; in other words, the magnitude of the velocity vector.” (McGraw-Hill Dictionary of Physics, 3rd ed.)

However, it’s not that simple. A common example shows the problem:

When something moves in a circular path (at a constant speed …) and returns to its starting point, its average velocity is zero but its average speed is found by dividing the circumference of the circle by the time taken to move around the circle. This is because the average velocity is calculated by only considering the displacement between the starting and the end points while the average speed considers only the total distance traveled. Wikipedia

So the average speed is not the magnitude of the velocity (which is zero in this case) but something else – the travel distance divided by the travel time.

The question is whether the speed over a finite interval should be the magnitude of the displacement divided by the time interval or the arc length divided by the time interval (i.e., the integral of the norm of the velocity function over the time interval). The answer should be the latter, although the former is implied by the common definition of speed.

It is better to define speed as the ratio of the arc length (travel distance) divided by the arc time (travel time). In short, speed is that which is measured by a speedometer.

Dimensions and units

A dimension is informally regarded as the number of coordinates needed to specify the location of a body or point. That may suffice for a mathematical dimension, but a physical dimension is a dimension of something, that is, some unit. In that sense, the dimensions of force are different from the dimensions of velocity.

However, units such as force and velocity use the same dimensions of space and time. They have a common notion of direction as their basis. A northward force and a northward velocity are in the same direction. In that sense, it is common to speak of space and time as the only physical dimensions.

It is possible to use the speed of light to translate spatial units into temporal units and vice versa. This is done in relativity: the invariant interval may be expressed in length units by multiplying time by the speed of light or in time units by dividing lengths by the speed of light. So space and time are integrated as spacetime dimensions.

Outside the technical usage of relativity, length and time units are distinguished because they are physically different. The method of measuring them differs. The common measures of motion are related to time, not space. The philosophy of time is different from the philosophy of space.

For vectors of rates, such as velocity, different component rates lead to different vectors. Consider a displacement/distimement north 90 km in 3 hrs and east 30 km in 2 hours. The rates for each component dimension are 90/3 = 30 km/hr north and 60/2 = 30 km/hr east. However, the time rates use the overall time of 5 hrs and get 90/5 = 18 km/hr north and 60/5 = 12 km/hr east. The space rates use the total distance of 150 km to get 150/3 = 50 km/hr north and 150/2 = 75 km/hr east (which would normally be expressed as hr/km).

That is, for time rates, the dimensions apply to space, and for space rates the dimensions apply to time. For the rates by component, the dimensions apply to velocity itself rather than space or time.

Addendum: If we consider the progress in the direction of the end point in time, the velocity denominator would be the square root of (3²+2²) = √13. The corresponding numerator would be the square root of 90²+30² = √95. The resulting velocity magnitude would be √(95/13) = 7.2 km/hr.

Centrists and extremists

There are a variety of centrists, as there are a variety of means (e.g., arithmetic, geometric, harmonic, etc.). But all centrists share certain characteristics, which differ markedly from all extremists.

Centrists reside in the center, the middle, from a long-term perspective. Unlike moderates, who go with the flow of current politics and culture, centrists resist change away from the center. As I’ve noted before, that often makes centrists contrarians, trying to turn society away from movement toward any extreme.

Centrists see extremes as contraries, not contradictories. This logical point is the justification for seeking to balance opposites rather than eliminate any of them. It’s not that extremes are all wrong; it’s that extremes substitute the part for the whole. Extremists see their opponents as permanent contradictions, which leads them to desire to eliminate them rather than compromise with them.

One commentator on Hegel put his dialectic this way:

Logical unification is the application of the same dialectic relationship in the realm of logic. Consciousness is taken as ‘thesis’ and Being as ‘antithesis’. Thesis and antithesis are identical because antithesis is derived from thesis, and different as antithesis is something other than thesis. This contradiction between them is, however, resolved and superseded in their unity understood as ‘synthesis’.

This logic is exactly wrong. The problem is not antithetical propositions, that is, contradictions, but contraries that are treated as contradictories. Contraries can be reconciled at a higher level of consciousness but contradictories cannot be reconciled because one is true and the other is false. There is a direct line from Hegel’s logic to the Marxist liquidation of classes of people considered to be in contradiction to the cause.

Centrists welcome balanced compromise between contraries. There is no formula for what this is or how to achieve it. Each case must be considered separately, and care must be taken so that weaker parties are represented as much as stronger parties. Balance is not a fixed equilibrium but an oscillation around a center, like a balance beam rocking back and forth.

Centrists are patriots. A patriot is one who supports the good of the whole country, rather than just a part or faction. The problem of politics is the tendency for factions to gain power and the good of the whole to decline. Constitutions and elections are supposed to reduce the danger of that happening, but it takes vigilance by patriots to make sure it doesn’t.

Centrists keep the whole in mind at all times: the whole of society, the whole of civilization, the whole of life. Extremists take a part for the whole, and end up trying to eliminate the other parts. The ultimate extreme is idolatry: putting something other than God in the place of God. Centrists keep God in the center at all times.

Algebraic relativity

Relativity may be derived as an algebraic relation among differentials. Consider motion in the x spatial dimension, with a differential displacement, dx, differential velocity displacement, dv, and arc (elapsed) time t:

dx² = (dx/dt)²dt² = dv²dt² =  d(vt)².

Let there be a constant, c:

dx² = d(vt)² = d(cvt)²/c² = d(ct)² (v/c)² = d(ct)² (1 – (1 – v²/c²)).

Let γ² = 1/(1 – v²/c²). Then

dx² = d(vt)² = d(ct)² (1 – 1/γ²) = d(ct)² – d(ct)²/γ² = d(ct)² – d(ct/γ)² = d(ct)² – d()²,

where τ = t/γ. This may be rearranged as

d()² = d(ct)² – dx²,

which equals the Lorentz invariant, d()² = ds².

Alternately, consider motion in the t temporal dimension, with a differential displacement, dt, differential velocity displacement, dv, and arc length x:

dt² = (dt/dx)²dx² = d(1/v)²dx² =  d(x/v)².

Let there be a constant, c:

dt² = d(x/v)² = d(x/cvc² = d(x/c)² (c/v)² = d(x/c)² (1 – (1 – c²/v²)).

Let λ² = 1/(1 – c²/v²). Then

dt² = d(x/v)² = d(x/c)² (1 – 1/λ²) = d(x/c)² – dx²/(λc)² = d(x/c)² – d(x/λc)² = d(x/c)² – d(σ/c)²,

where σ = x/λ. This may be rearranged as

d(σ/c)² = d(x/c)² – dt²,

which equals the Lorentz invariant, d(σ/c)² = dw².

Equivalently, consider motion in the ξ temporal dimension, with a differential displacement, , differential celerity displacement, du, and elapsed space x:

² = (/dx)²dx² = du²dx² =  d(ux)².

Let there be a constant, k = 1/c:

² = d(ux)² = d(kux)²/k² = d(kx)² (u/k)² = d(kx)² (1 – (1 – u²/k²)).

Let λ² = 1/(1 – u²/k²). Then

² = d(ux)² = d(kx)² (1 – 1/λ²) = d(kx)² – d(kx)²/λ² = d(kx)² – d(kx/λ)² = d(kx)² – d()²,

where σ = x/λ. This may be rearranged as

d()² = d(kx)² – ²,

which equals the Lorentz invariant, d()² = dw².