Sunday Morning Greek Blog

June 28, 2023

A Plentiful Harvest (Matthew 9:35–10:23)

Filed under: Biblical Studies,Christology,Christology,Evangelism,Hebrews,Matthew Gospel of — Scott Stocking @ 10:25 pm
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My brother and I went on a fishing trip a few weeks ago up to South Dakota. We went through an outfitter, which meant they provided a boat for us with a guide who knew where to fish for the walleye we were targeting. Now I hadn’t been fishing for about 15 years before that, and that had only been at Louisville Lakes down by the Platte River with my son. So you might imagine I was pretty grateful to have a guide. Not only did the outfitter provide the boat and driver, but the fishing poles and the bait as well.

But it didn’t stop there. Our guide knew where the fish were biting. We had to go about 10 miles down from Chamberlain where we launched, and we hung out there until the three of us hit our limit. Our guide also baited the hook for us every time. If we caught a fish, we’d get to reel it in ourselves, which of course is the most exciting part. The guide, however, would always take the fish off the hook for us, put it on a “marker” or hook if it was a keeper, and placed it in the water storage compartment in the boat.

Afterwards, the guide wasn’t done. He even cleaned the fish for us, put it in Ziploc bags, and kept it in a freezer for us until we were ready to go home. All my brother and I really had to do was show up and reel in the fish. That’s my kind of fishing!

Now you probably know where I’m going with this. When Jesus called his first two disciples in Matthew 4:19, Simon Peter and Andrew, he said, “Come, follow me, and I will send you out to fish for people.” Now of course, we have to be careful about carrying this metaphor too far. The endpoint of the metaphor is that we need to gather people into the kingdom.

In our gospel passage today, Jesus switches up the metaphor in those last few verses of Matthew 9 from fishing to farming. Verse 35 reads almost like a summary of what Jesus’s ministry had been like up to that point, which is a nice transition into chapter 10, where get a formal introduction to Jesus’s 12 chosen harvesters: the disciples, or apostles if you will. One for each tribe of Israel, as it were.

Now to put a little more meat on the bones here, let’s quickly review what Jesus had been doing since he called his first two disciples, at least from Matthew’s perspective. He’d preached the longest sermon we have recorded in the Gospels in chapters 5 through 7. In chapter 8, he healed a man with leprosy, a centurion’s servant, and Simon Peter’s mother-in-law, along with many others. He talked about the cost of following him, so that those who chose to do so knew what they’d be signing up for.

Later in chapter 8, he calms the storm at sea, cast out demons from two men, and in chapter 9 he forgives and heals a paralyzed man, raises Jairus’s daughter from the dead, and heals a woman who’d had a bleeding condition for 12 years. And to put the icing on the cake, he heals two men of their physical blindness and a man who couldn’t speak because he was possessed by a demon. In the midst of all that activity in chapter 9, Jesus also calls Matthew out of his tax collector booth to follow him and answers a theological question on the side about fasting.

Now Matthew makes it sound like all these events leading up to our passage of the day could have happened in somewhat rapid succession, perhaps covering a time frame of three to seven days or more. Matthew’s rapid-fire collection of stories about Jesus set the stage for us about the scope, breadth, and depth of the challenge of “fishing for men.” Any disciples who’d been with Jesus up to that point could recognize this was not going to an easy road to walk down.

But with Jesus, it would not be so hard as they might imagine. We only need to jump ahead one chapter to see that Jesus says his yoke is easy and his burden is light. Just like my brother and I had a guide to help us on our fishing trip, Jesus and his heavenly father have already done much to prepare the fields for the harvest. And the more workers they have for the harvest, the easier the task becomes.

A poll by the Pew Research Center in March of this year, as you might expect, showed church attendance dropped off slightly over the pandemic. Here’s a summary of what the poll said:

“The poll found that the share of U.S. adults typically attending religious services at least once a month dropped from 33% in 2019, before the COVID-19 outbreak, to 30% in 2022. About 20% of Americans say they now attend in person less often than they did before the pandemic.”[1] According to the same article, the largest drop by demographic was among Black Protestants: the percentage attending at least once per month was down 15 percentage from pre-pandemic levels, from 61% to 46%. A pastor friend of mine has said for several years now that only about 20% of Omahans attend church on Sundays.

Now the survey didn’t go into what the causes of that were. But the point is that there are a lot of people out there who aren’t going to church, and many of them need not only the hope we have in Jesus but also the friendship and fellowship we have with one another in the name of Jesus. But over the years, I’ve noticed that among people who do go to church, they increasingly say they’re going there not necessarily because of the denomination of the church or what “brand” of Christianity they practice; they go and keep going when they feel a sense of connection with others in the church.

One of the things they beat into our heads in seminary was that, when you have a new person or family come into your congregation to “check it out,” if they don’t form any significant relationships within the first one to two months there, they’ll probably not come back. They may agree 100% with your doctrine, but if they’re not connecting with others, they’re not sticking around.

The author of Hebrews hints at this 10:24–25:

24 And let us consider how we may spur one another on toward love and good deeds, 25 not giving up meeting together, as some are in the habit of doing, but encouraging one another—and all the more as you see the Day approaching.[2]

I spent most of my pastor career in small rural congregations much like Mt. View here. They have very traditional worship, usually have an active core of people, and typically draw an older crowd, because the young people are always looking for something new and exciting. Their attention spans are shorter than ever these days. In some cases, those smaller congregations actually have a significant role or mission in their community or that their members are involved in. That’s a beautiful thing!

Larger churches may have fancier worship with a full band and lights and big video screens and other fancy tech, but they don’t stay big because of all that. They stay big because they’ve found success in connecting with people and connecting those people to other like-minded people. They typically have a large small-group network where members get the bulk of their spiritual support. It’s challenging enough for a full-time pastor to manage a congregation of about 50 to 100 parishioners. It’s quite another thing to manage and maintain a congregation of 2–3,000 people. They just can’t do it on their own, obviously. That’s where the small groups fit in. The leaders of the small group I’m in at my church have turned over the membership in their group several times over in the 12 years I’ve been there. That’s because their small group members go out and start their own small groups. Before the pandemic, they would have an annual “reunion” of those who’d been in their small groups over the years. That would usually draw about 30 to 50 people.

Getting back to our gospel passage today: Jesus understood that dynamic of the small group, which is why he chose his own small group in Matthew 10. He needed a group of disciples he could train so that when he was gone, the church would have established leadership at its birth on Pentecost. Not only does he train them, though, he gives them authority to do the miracles he himself was doing. In other words, they had a drawing card that would attract people to the good news: not just in words, but in miraculous deeds as well.

He tells them to go to the Jews first, because they were the ones who had known and clung tight to the hope of a coming Messiah all those years. And the most challenging part: he tells them to go out in faith and not to take any money or extra clothes. That had to be scary. When people go out today to plant a new church, they have a whole big plan of where’s the best spot and what their trajectory would look like even before they hold their first worship service. But Jesus wants them to trust him and, in reality, the power of the Holy Spirit, who was already starting to work in the hearts and minds of the disciples, even though he hadn’t come in all his fullness yet.

He also says to seek out a worthy person wherever they go and stay with them for a few days. That’s an important note there I want to emphasize: If you want to grow the church, do everything you can to attract quality people who will do the hard work of building the framework for success. Sure, we can welcome anyone who comes through our doors, but not everyone is going to be a leader. When you find those with leadership potential, do everything but kidnap them to help attract people to the kingdom.

The last section of our passage this morning is a warning that is becoming more and more relevant for Christians today. Let’s look at that again:

Jesus says his disciples are entering into a danger zone when he sends them out. “Sheep among wolves”; floggings; arrests and depositions before the highest rulers in the land; family betrayals; and universal hatred toward them. What Jesus is saying here isn’t political. After all, Jesus told his disciples to go to the Jews first, and this is how the Jews, their own flesh and blood, would treat them. It really didn’t have much to do with Roman rule, although the Romans would have been suspicious of large crowds, like those at Pentecost. In the dictatorship Rome had become under a Caesar who considered himself divine, people tended to toe the line out of fear and survival instinct. You’ll notice that Jesus never once spoke out against Roman rule.

But in a free society like ours, where traditionally there has been no attempt to force any unity of thought or behavior, we have become either accepting or tolerant of people’s free will choices, some of which have no respect for God, his followers, or his creation. Jesus is speaking of a godlessness that has infected the Jews, and that such godlessness will lead to hatred and persecution. Are we not beginning to experience that godlessness today?

Just like Jesus, I’m not trying to be political here. What I’m talking about isn’t politics, it’s paganism at best, and at worst, it’s just plain evil. America has lost track of 85,000 unaccompanied minors who’ve crossed into our country in the last two years. We know many of these children are being trafficked for labor and sex, which is unspeakable. Children are exposed to sexualized content, and not just in books, at a young age, something that would have been considered child abuse 20 years ago. And the operations that are being performed on some kids who haven’t even reached puberty yet that will scar them for life? That was unthinkable even 20 years ago. All in denial of the fact that God created two biological genders, each with their unique and divine purpose and form. How have we gotten to this point where we’ve objectified children and gender for godless ideologies? The church must be a light in this darkness.

And yet, when we speak out against such evils, the wolves come after us. We’re cancelled, banned, brought before judges to defend what we believe. It is happening just as Jesus said it would for those who would proclaim that the kingdom of heaven is near. But Jesus doesn’t expect us to sit back and take it. He says we need to be shrewd as serpents and innocent as doves. Keep your head on a swivel. Don’t worry about the material things; God will provide for your needs as you find people worthy of your greeting and your peace. He also promises the words to say when dragged before rulers and authorities. The Holy Spirit will speak for you and through you in those moments if you stand firm.

The promise in Matthew 10:22 is still true today: “The one who stands firm to the end will be saved.” That sounds like what Paul says in Ephesians 6: “Put on the full armor of God so you can take your stand against the devil’s schemes.” It’s a spiritual war we’re fighting, not a political one. We need spiritual armor and spiritual weapons. The armor of God is the armor that God himself is said to wear in the Old Testament. I know I got a little heavy there, but know that your own ministry efforts here are winning battles as well, especially by bringing warmth and comfort to those who need it most through your quilting ministry and the other ways you reach out to the poor, lonely, and needy.

In reality, we can only influence one heart at a time. Where we plant a seed of hope, someone else may come along and water it and cultivate it. But in all cases, God causes the growth. Let us remain steadfast and faithful in the ministries that God has called us to so that we can continue to spread the good news that the kingdom of heaven is near. We are his hands and feet, may the Lord bless us to his service. Amen.

[1] Poll: Religious service attendance a bit down after pandemic (omaha.com)

[2] The New International Version. 2011. Grand Rapids, MI: Zondervan.

June 2, 2023

Reflections on Fishing for Future Followers of Christ

Filed under: Biblical Studies,Evangelism,Matthew Gospel of — Scott Stocking @ 10:32 pm
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A quick article to get back in the saddle on the ultimate purpose of my blog.

It’s Friday night after two days of a “guided” walleye fishing excursion with my brother. We went to Chamberlain, South Dakota, and our guides took us out on Lake Francis Case on the Missouri River. This is the first time I’ve gone fishing in 15 years, so I wasn’t sure what to expect. My brother had told me our guides (wound up with a different one each day) would do most of the work for us, and they did.

Of course, as a pastor, I couldn’t help but think about Jesus telling (strongly suggesting?) Peter and Andrew, “Come, follow me, and I will send you out to fish for men” (Matthew 4:19). I see some definite parallels between the guided fishing experience and Jesus’s call for Peter and Andrew, and indeed all of us, to be fishers of future followers of Christ (how’s that for alliteration!).

One thing that struck me as my brother and talked about the experience was when my brother said, “If I had brought a boat up here to fish on my own, I wouldn’t have had a clue where to go to find the walleye biting.” The guides, of course, knew the perfect spot to catch them, and it was about 10 miles downstream from Chamberlain. If my brother and I had come on our own, there’s no telling what kind of success or failure we would have had without a guide.

Another benefit of having the guide was that they handled all the “dirty work” of fishing for us; ALL of it. They provided the boat, the bait, and the fishing poles. They put the bait on the hook for us every time. They removed the fish from the hook when we caught them. Some were too small to keep and had to be thrown back; the keepers went in the “box” to keep them fresh while we were on the lake. They even cleaned the fish for us at the end of the day, put the flesh in zip-locked bags, and held them in a freezer for us to pick up and take home at the end of our trip. The only thing we had to do was drop the line in the water (no casting, since we were trolling in a boat) and wait for the fish to bite. And we didn’t have to wait long. We each caught our limit, including the guide, both days, so we were quite pleased with our experience, and plan on doing it again.

It was a wonderful experience and a chance to spend some quality time with my brother. I hadn’t had many opportunities to do that most of my adult life, because I had lived in a different State for 23 years. As I get older, I find I value this family time more and more. That was the main purpose and goal of the trip, and we accomplished that.

But the preacher in me wanted to reflect on this first and foremost, because I won’t be preaching again until Father’s Day, so I wanted to put up a post in the interim. The second reason for making this post is that my little diversion down the rabbit hole of PEMDAS has been causing quite a stir it seems. This weekend, as it did two weeks ago, is seeing an incredible spike in people accessing my article on a viral math problem. Something is definitely afoot. More on that later. Basically, I wanted to assure you that my blog has not been abducted by a math nerd (I’m the math nerd who owns the blog) and that I’m not converting the blog permanently to a math blog.

Back to fishing: Perhaps you’ve already figured out where I’m going with all this talk about a fishing expedition. Jesus told us: “The harvest is plentiful but the workers are few. Ask the Lord of the harvest, therefore, to send out workers into his harvest field” (Matthew 9:37–38). Jesus knows the best places to fish for men, just like our guides knew the best place to go to catch walleye. Jesus says the harvest is ready: those who are called to go out and fish for men don’t necessarily have to do the hard work of preparing a field (or a lake) for harvest. God has already taken care of that. This isn’t to say that we shouldn’t go where God has not (at least to the casual observer) prepared something, namely because discerning what or whom God has prepared is not always obvious to the naked eye.

Our job, then, is to put the “line in the water,” so to speak. As Christians, we may need to put something shiny and sparkly in front of people to get their attention and draw them in. When it comes time for us to fish for future followers, we don’t always know how people have been brought to a place to where they’ll respond to the enticing message of the gospel.

Of course, we don’t want to take this analogy too far. We don’t (or at least, I hope we don’t) flay those who’ve responded positively to the Gospel message, dip them in batter, and fry them. Let’s not be ridiculous now. The “throwbacks” are akin to those who have responded to the gospel in some way, but for whatever reason, they’re not ready to jump in fully. This is made apparent by the parable of the sower (Matthew 13:1–15). Not everyone is going to be immediately convinced by the signs and situations God is putting in their paths, so it’s okay to let them go and grow for now. God may still be working on them.

Jesus is our guide for when we’re called to fish for men. We don’t need to have any special knowledge necessarily, just the willingness to cast the line and hopefully draw them in. Others who have been convinced in that manner should do just fine sharing that hope with future followers. If you do happen to be one of those who is laying the groundwork for the gospel in a place that needs quite a bit of preparation, God bless you! Your apostolic mission is what keeps the body of Christ advancing on earth.

I do hope you’ll forgive me for my little math diversion. I wish you all happy fishing as you reach out and share the love of Christ with those whose hearts and souls have been prepared to receive it, and to those who still need more preparation.

Peace,

Pastor Scott Stocking, M.Div.

My opinions are my own.

 

May 29, 2023

Toward an “Active” PEMDAS: Strengthening Its Theoretical Foundation

Filed under: Numbers (Cardinal & Ordinal),PEMDAS — Scott Stocking @ 11:56 pm
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If you like this article, you may also like 8 ÷ 2(2 + 2) = 1: Why PEMDAS Alone Is Not Enough or 8 ÷ 2(2 + 2) = 1, Part 2: A Defense of the Linguistic Argument.

I’ve gotten caught up in the PEMDAS/Order of Operations (Parentheses/Brackets, etc.; Exponents; Multiplication & Division [left-to-right]; Addition & Subtraction [left-to-right]) discussions on social media. I must admit it is frustrating to see how religiously some people cling to an imperfect and almost thoughtless understanding of PEMDAS. It is a convention that, as currently practiced, has no theoretical soundness and is clearly NOT intuitive. In linguistic terms, I would describe the current application of PEMDAS as passive, that is, it doesn’t seek to recognize certain theoretical and intuitive constructs in mathematics, and even undermines them, and as such represents a primitive view of mathematics.

By “primitive,” I mean that some of the proponents of a strict PEMDAS are childlike in its defense, resorting to emotion and circular arguments based on their assumptions. No one has offered any proof that what they believe about its inner workings is in fact how people have historically interpreted some of these expressions. Nor have they offered anything to counter the various arguments and peer-reviewed documentation I have offered except by returning to their assumption and repeatedly showing us how they think the target expression should be worked even as we question their premise. PEMDAS pays too much attention to the individual signs and symbols, but it lacks the sophistication to understand the “syntax” or intention of certain conventions of expression we have developed over the centuries.

PEMDAS as practiced today is like reading the synoptic gospels of the New Testament without reading the gospel of John, or like reading the New Testament without also reading the Old Testament to understand its foundations. If you’re not biblically minded, it’s like reading Shakespeare without a 16th century dictionary at hand. I aim to fill that void here and make PEMDAS something so theoretically reliable that we won’t need to have wasteful discussions in social media about who’s right and who needs to go back to elementary school. My purpose is to propose such a theoretical structure whereby we can agree on one rule to address the issue of these viral problems.

Properties

I want to begin with a discussion about the basic mathematical properties we all had to learn at the beginning of the semester in Algebra. Properties are demonstrable principles in mathematics that will help lay the foundation for what some have begun categorizing as “grouping.” But more on that later.

Associative and commutative properties are intuitive. By that I mean that it’s obvious to most that if we have the expression

a * b * c

it does not matter how we “group” the terms, that is, how we “associate” them within parentheses or how we “commute” terms in the order of presentation, we get the same result. Every permutation of the variables multiplied together yields the same result. They’re all cofactors of the product, after all, so you get the same result every time. As such the following expressions are ALL literal identities of each other.

(a * b) * c ≡ (a * b)c ≡ (ab)c ≡ a * (b * c) ≡ a(b * c) ≡ a(bc) ≡ c * (a * b) ≡ c(a * b) ≡ c(ab) ≡ b * (c * a) ≡ b(c * a) ≡ b(ca), etc.

Distributive property is intuitive as well because it’s the undoing of factoring:

a(b+c) ≡ (ab+ac)

That expression represents implied (or implicit) multiplication, and the result demonstrates that the distributive property is a form of grouping equivalent to putting parentheses or brackets around the entire expression. As a type of grouping, then, it belongs to the P in PEMDAS. In addition, I would argue that even when there is an explicit multiplication sign used for the distributive property:

a * (b+c) ≡ (ab + ac)

this does NOT negate or override the application of the distributive property, and the expression thus written is also considered grouped and should be treated as if it has parentheses or brackets around it. Why? Because we know that if two expressions are equal or identical to a third expression, the other two expressions are identical as well:

a(b+c) ≡ a * (b+c).

Since both expressions are identical, it is necessary to consider both as grouped, as implied multiplication by the action of the distributive property at least, and in the case of the first one, by the syntax of implied multiplication. As such, my first proposal to strengthen PEMDAS and place it on a sounder theoretical ground is this:

Proposition 1: Mathematical properties should be considered at the same level of grouping as parentheses in PEMDAS, and when so recognized, the human person working such expressions has both the responsibility and authority, by virtue of any applicable mathematical properties, to place such expressions within the appropriate form of brackets to indicate priority given to the calculation. In doing so, the human person working the expression should ensure that any units of measurement or counting associated with the expression are not affected by so organizing.

The Trouble With Computers and Calculators. Most calculators do not recognize grouping characterized by this implicit syntax (I know syntax is primarily a linguistic concept, but for math, it refers to the arrangement of the signs and symbols, including the numbers, of an expression and how those influence the interpretation of the expression). You typically must apply the parentheses or brackets around the expression to force it to do so. Without parentheses, calculators assume all else in the syntax of an expression is explicit.

Implicit Multiplication Generally

Having trouble accepting implied multiplication is a form of grouping? What is a number with an exponent if not implied multiplication? The term 33, or in calculator language, 3^3 is 3 * 3 * 3, but we don’t undo the exponent notation if a division sign comes before it. Why? Because we’ve given this form of implied multiplication priority over signed multiplication in PEMDAS. The implied multiplication is grouped into the simple expression, algebraically speaking, of an. If you do deconstruct the implicit multiplication of an exponent, you’ve obviously taken PEMDAS to an unacceptable extreme.

PEMDAS does not address what to do with a factorial expression.

4! = 4 * 3 * 2 * 1

Algebraically, this is expressed as

n! = nPr =n(n – 1)(n – 2)…(n – r + 1])

where nPr is the number of permutations (P) of n things taken r at a time and n = r.

The factorial is also considered a form of implied multiplication, then. However, since PEMDAS doesn’t explicitly deal with factorials in the order of operations, how should we treat it? Algebraically, the first term in the grouping doesn’t have parentheses around it, so if we come across a ÷ n!, are we going to treat that as (a/n) * (n – 1)! then? Absolutely not! I’ve already hinted at why. It’s considered a grouping of factors implicitly multiplied. Because it’s a grouping, then, we would also treat it as if it were either an exponent or within parentheses. If these two types of implicit multiplication (powers and factorials) are generally treated at the E level in PEMDAS, why shouldn’t the implicitly multiplied expressions a(b + c) or even ab for that matter, or any variation thereof as described above, be treated at least at the E level, if not the P level of PEMDAS?

This leads me to my second proposition and a subsequent corollary to strengthen PEMDAS and place it on a more solid theoretical ground:

Proposition 2: In the absence of properties, any terms or expressions using implied multiplication should be considered at the grouping level of Parentheses in PEMDAS, and when so recognized, the human person working such expressions has both the responsibility and authority, by virtue of the implied multiplication, to place such expressions within the appropriate form of brackets to indicate priority given to the calculation. In doing so, the human person working the expression should ensure that any units of measurement or counting associated with the expression are not affected by so organizing. [Added 7/6/23] Within the grouping level, exponents and factorials should be processed first, then any implied multiplication would follow. So 3x^2 (without parentheses) should be evaluated as 3(x^2) and NOT (3x)^2.

Corollary 1: Any expression using explicit or implicit grouping markers (parentheses, brackets, juxtaposition, etc.) should NOT be rearranged in such a way as to undo the intention of the syntax or to fit certain elements into the framework of a property. For example, an expression in the form a/(bc) (explicit grouping) or a/bc (implicit grouping) should not be undone and reworked to become (a/b) * c or (ac)/b. NOTE: Some on social media tried to say the distributive property worked as follows:

b ÷ a(x+y+z) = [b * (x+y+z)]/a.

It’s ridiculous to think that a coefficient (or cofactor) should become a divisor in this situation.[1]

Let me also add here a call to return to standards. If the ISO standards don’t recognize the obelus anymore, then let’s just stop using it altogether. We can retain references to it for historical purposes, but in formal education (including textbooks), edit it out. People have tried saying the obelus is different from the vinculum, but again, I’ve never seen any formal explanation as to why this is, because the obelus isn’t a standard! I’m using it in this article because that’s how the expressions appear in the social media threads.

Excursus on Implicit Functions—Added 08/29/23 (from a post I made on Facebook), and lightly edited on 04/01/24.

Exponential terms don’t require a standard operator sign (+-x÷/) but rely on juxtaposition of the exponent.

Roots do not require a standard operator sign but the juxtaposition of the superscripted power and value in relation to the radical or of a fractional exponent. In some settings, the radical is NOT fully evaluated unless the answer can be expressed as a rational number. If the not-fully-evaluated radical is in the denominator of a fraction, the fraction must be rewritten so the radical is only in the numerator.

Factorials don’t require a standard operator sign but rely on the juxtaposition of a punctuation mark.

Cosine, sine, tangent, etc. don’t require a standard operator sign, but rely on the position of the measurement next to an abbreviated form of the word, and in the case of inverse trig functions, the juxtaposition of a -1 “exponent.”

Logarithms don’t require a standard operator sign but rely on the juxtaposition of a subscripted base (as needed) next to the abbreviated form of the word and the position of the value after the word/base combination.

Absolute value does not require a standard operator sign but juxtaposes, or brackets, the value between two pipes.

A fraction written with a vinculum does not require a standard operator sign that typically disappears when the operation is performed. The vinculum typically only disappears when the fraction can be represented as a whole number (mixed numbers, which consist of a juxtaposed whole number and fraction [implicit addition!!], typically have to be converted to an improper fraction when working them in an expression) or when, during the evaluation of the expression, the denominator divides evenly into the numerator. The fraction is a vertical juxtaposition of the two values with the vinculum indicating the grouping in the denominator and the relationship with the numerator. This is implicit division without actually dividing the two values to create a decimal. A fraction is considered a single value and NOT necessarily a division problem in the context of an expression. [This paragraph expanded from original on 04/01/24.]

Now while some of these functions do require parentheses to group the values being evaluated, NONE of them have a standard operator sign extant outside of any values in parentheses. These are all implicit functions, that is, they essentially have an implied set of brackets (or parentheses or some other grouping symbol) around them so they’re taken as a unit, or operand if you will. We don’t break out the implied multiplication of the exponent or factorial and supply the signs when evaluating the expression. Neither do we break out the implied addition when dividing by a mixed number, except in the manipulation of the mixed number to an improper fraction. In my opinion, that belongs in the P (parentheses) step of PEMDAS.

In the same way, an expression such as 2(2+2) is an implicit notation (no operational sign outside of the parentheses), so it belongs in the category of implicit functions. Operator signs break up an expression into operands. All this talk about “terms” that some have promulgated in the social media pages is meaningless, especially since the given expression above is technically one term by their own definition. We can debunk the contention 8 ÷ 2 should be treated as a fractional coefficient to what’s in parentheses. The obelus indicates we have two operands: 8 and 2(2+2). As an implicit function, with presumed parentheses around it, the 2(2+2) stands alone as the divisor in the expression. It should NOT be separated.

By the way, here’s how Wolfram defines “operand”: “A mathematical object upon which an operator acts. For example, in the expression 1×2, the multiplication operator acts upon the operands 1 and 2.” Implicit functions should have priority over explicitly signed operations and would need to have its own priority in PEMDAS for the functions included in that category.

End excursus.

Creating the Theoretical Foundation for PEMDAS.

Are you following me so far? Because I’m about to make it even more interesting. PEMDAS is neither intuitive nor theoretical (at least as applied) because there’s no proof to show why any one operation should be given preference over another. It is a convention that has rather haphazardly come into being historically without, as far as I can tell, any serious discussion about its theoretical or practical validity. As such, it does NOT mathematically or logically carry the same weight as properties.

The “intuitive” thing for a person to do just seeing a complex expression for the first time would be to simply work left-to-right through the symbols because we learn to read left-to-right in most languages. So such a person would treat the following as if it were in a series of brackets:

2 * 3 + 4 ÷ 5 – 6 = –4

becomes

{[(2 * 3) + 4] ÷ 5} – 6 = –4.

We used to play a game like that in 5th & 6th grade math class, where the teacher would give a string of numbers and operators (occasionally they’d put some operation in parentheses to see if we were paying attention) and we’d have to keep up with the math by taking the total as each new operator-number combination was announced and perform that operation on the running total. There was no going back through the string and figuring out PEMDAS or whether the distributive property applied. Whoever spit out the correct answer first got to advance toward the front of the class.

When we’re talking about PEMDAS, then, we’re talking about pedagogical construct that, historically speaking, seems to have been formulated rather hastily and loosely without much theoretical forethought. First, PEMDAS doesn’t account for everything that could be happening in an expression. I used the example of the factorial expression above. I’ve never seen anything in any explanation of PEMDAS that suggests where such an expression would fall. The factorial is important, for example, for calculating permutations. Treating a factorial in the wrong level of PEMDAS can potentially create false expectations about the probability of some event, like drawing winning lottery numbers. Exponents seems to be the most logical place because the factorial is a form of grouping by implied multiplication just like exponents are.

Second, in practice, PEMDAS is decidedly passive. It leaves too much room for interpretation, especially when historically, people have considered terms with implied multiplication to be grouped, bound, and inseparable. The PEMDAS absolutists in the social media threads on such problems have no respect for that historical reality. They suggest that the older generation’s understanding of PEMDAS is outdated when the real problem is their methodology and lack of critical thinking skills. This lack of critical thinking is becoming increasingly prevalent in American education today. Instead of a passive PEMDAS, we need an active, robust PEMDAS that focuses more on intentional grouping and a more sophisticated definition of grouping based on the assumptions made in the syntax of algebra.

Third, strict PEMDAS, at least as practiced by the absolutists, is no better than a calculator, because it fails to consider the implications of implicit multiplication. A calculator may be able to perform calculations quickly, but it doesn’t have a “mind” like you and I do to analyze the syntax and context of an expression.

The Priority of Operational Signs. Now that we have addressed the grouping issue and the weak nature of PEMDAS as currently practiced (if the absolutists are to be believed, anyway), it’s time to address the basic functions of mathematics: multiplication and addition. Since multiplication and addition are the primary operations mathematics, division and subtraction are respectively subordinate to them. We all can agree, I suppose, that division is multiplication by the inverse of the divisor, and subtraction is addition performed on a negative number. So while we’re beefing up the order of operations with a more active and robust use of parentheses to ensure any expression is solved the way its creator intended, let’s get rid of the obelus and the slash (solidus) as well and make everything about multiplication and addition. After all, isn’t that what we do when we divide by a fraction? We manipulate the expression (invert and multiply) to perform multiplication first, so wouldn’t that argue for the priority of multiplication in that instance? Let’s use only the vinculum to indicate “division,” and let’s put parentheses around a fraction with a vinculum so there’s no question that the vinculum is grouped. Fractions are, after all, more accurate than decimals if the decimal equivalent is not finite.

Let’s change all subtraction expressions to adding negative numbers expressions. Let’s keep all expressions with radicals as exponent expressions as much as possible. Let’s focus more on ensuring the proper ORDER of operations using parentheses and brackets rather than assuming everyone treats every expression in a uniform way. Obviously, that’s not happening right now. We can’t have a system of math where people are coming up with two (or more) answers to the same expression because they’ve been taught different things about it or work from a different set of assumptions. We need to firm up PEMDAS so we can have a uniform understanding of what fits where and restore uniformity. Without that, we’re wasting precious time arguing about ambiguities. It’s time someone cleared those ambiguities up. That’s why I’m stepping forward here to offer a theoretical solution.

One more question: If multiplication and addition are the primary operations of mathematics with division and subtraction respectively subservient to them, what is the theoretical reason then that multiplication and division are treated equally left-to-right? Why wouldn’t multiplication and addition be given priority over division and subtraction? I’ve never seen an explanation for this. After all, there are some out there who have a multiplication-first view of PEMDAS. I’m not sure I can fault that view given that multiplication has formal properties associated with it while division does not.

Conclusion

This whole process of “thinking out loud” in the social media posts has been, in my mind, anyway, a helpful discussion. In the process, I have more firmly codified my own beliefs about PEMDAS, as I’ve done here, and have continued to do so over the past year. I am even more firmly convinced that those who haven’t gotten the same answer as me on the more popular manifestations of this PEMDAS debate have a lack of theoretical understanding that should be corrected. I hope that I have filled that gap and that I have convinced at least some of you that the answer is 1, not the square of the numbers in parentheses (see Demonstration Proofs 1 & 2 below). I offer my proofs below of the three most popular expressions as a demonstration of application to my principles.

I do think PEMDAS is a valuable pedagogical tool, when properly understood with solid theoretical underpinnings. Professor Oliver Knill has repeatedly said the only way to ensure a problem is worked the way one means to is to overuse, if necessary, parentheses and other groupings.[2] Otherwise, ambiguous problems remain open to interpretation, and we’ll never get any kind of uniformity. My attempt here is to promote a uniformity of understanding so that we only get one answer for each unique expression.

Demonstration Proofs.

Proof

Given

36 ÷ 6(2 + 2 + 2)

Grouping by distributive property and implied multiplication

36 ÷ [6(2 + 2 + 2)]

Multiplication by inverse and grouping under vinculum

36×16(2+2+2)36 \times \frac{1}{6(2 + 2 + 2)}

Application of distributive property

36×16(2)+6(2)+6(2)36 \times \frac{1}{6(2) + 6(2) + 6(2)}

 Multiply terms in brackets

 

36×112+12+1236 \times \frac{1}{12 + 12 + 12}

Add terms in brackets

 

36×13636 \times \frac{1}{36}

Cancel common factors and simplify

1

QED

Proof

Given

8 ÷ 2(2 + 2)

Grouping by distributive property and implied multiplication

8 ÷ [2(2 + 2)]

Multiplication by inverse and grouping under vinculum

8×12(2+2)8 \times \frac{1}{2(2 + 2)}

Application of distributive property

36×12(2)+2(2)36 \times \frac{1}{2(2) + 2(2)}

Multiply within brackets

36×14+436 \times \frac{1}{4 + 4}

Add terms in brackets

36×1836 \times \frac{1}{8}

Cancel common factors and simplify

1

QED

Proof (From Professor Oliver Knill’s “Ambiguous PEMDAS” Web page. When presented with this problem, 58 of his 60 calculus students got the following result indicated in the proof. The other two treated (3y – 1) as the expression under the vinculum. NONE got the answer promoted by the PEMDAS absolutists.)[3]

Given

2x/3y – 1; x = 9, y = 2

Group by implicit multiplication and vinculum

2x3y−1\frac{2x}{3y} – 1

Substitute

2(9)3(2)−1\frac{2(9)}{3(2)} – 1

Multiply in brackets

186−1\frac{18}{6} – 1

Simplify

3 – 1

Subtract

2

[1] Professor Oliver Knill from Harvard (Ambiguous PEMDAS (harvard.edu)) cites Lennes, 1917. [No title given]: “When a mode of expression has become wide-spread, one may not change it at will. It is the business of the lexicographer and grammarian to record, not what he may think an expression should mean but what it is actually understood to mean by those who use it. The language of algebra contains certain idioms and in formulating the grammar of the language we must note them. For example that 9a2 ÷ 3a is understood to mean 3a and not 3a3 is such an idiom. The matter is not logical but historical” (emphasis in original). In scans from Lennes printed article, these statements appear: “A series of operations involving multiplication and division alone shall be performed in the order in which they occur from left to right.” However, the subheading in the very next paragraph says: “The Above Rule Contrary to Actual Usage,” and the author goes on to say: “It would, however, follow from this rule for carrying out multiplications and divisions in order from left to right, that

9a2 ÷ 3a = (9a2 ÷ 3) × a = 3a3.

But I have not been able to find a single instance where this is so interpreted. The fact is that the rule requiring the operations of multiplication and division to be carried out from left to right in all cases, is not followed by anyone. For example, in case an indicated product follows the sign ÷ the whole product is always used as divisor, except in the theoretical statement of the case” (emphasis in original).

The following section of the text has the subheading “The Established Usage” reconfirms that the obelus indeed means the entire product after it is intended to be the divisor, and not just the first term. (Who says the obelus has no grouping power!) He also goes on to say “All multiplications are to be performed first and the divisions next.”

I’ve also found similar analysis in a 1935 textbook Second-Year Algebra by Hawkes, Luby, & Touton, p. 19. That’s how I understood it the late 70s and early 80s in high school and college and in the early 2000s when I taught JH & HS math and algebra. I seriously doubt nearly 100 years of history (at least) of this understanding has changed in the past ten years or so.

[2] Ambiguous PEMDAS (harvard.edu); see also https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html

[3] Knill, Oliver. “Ambiguous PEMDAS.” Ambiguous PEMDAS (harvard.edu), retrieved May 29, 2023.

May 28, 2023

Divine Number Patterns: Chiasms and Perfect Squares

Filed under: Biblical Studies,Greek,Numbers (Cardinal & Ordinal) — Scott Stocking @ 2:44 pm
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If there’s one pattern in math more than any other that makes me realize we have an intelligent, perfect creator, it’s the concept of the perfect square. Consider the following:

1. The perfect squares (1, 4, 9, 16, 25, etc.), represented algebraically by n^2, are the sum of the first n odd numbers. So 5^2 is 1 + 3 + 5 + 7 + 9 = 25. I know this sounds cheesy, but God takes what is odd, orders it, and sums it all up into something perfect: everything is “squared away.” By the way, this is very easy to visualize as well. If you start with a single square shape, in order to make the next square, you would add one square to the left, one on top, and one diagonally to make the next square. Then you would add 2, 2, and 1 diagonally to get the next square, and so on.

2. Looking at the first 50 perfect squares, you can also see a complex chiasm of numbers, notably in the last two digits of each number. A chiasm is typically a literary pattern where the author lays out a certain number of points or premises, then repeats them in reverse order. The idea is that whatever is mentioned in the middle of the chiasm is typically the focus of the narrative.

a. Now look at the pattern, first of the final digit of each set of 10 numbers, from 0 to 10, 10 to 20, etc.: 1, 4, 9, 6, 5, 6, 9, 4, 1. Of course, all multiples of 10, when squared, end in a zero (0), so they’re sort of the “fence posts” for the chiasm, anchoring what precedes and what follows.

b. Now look at the pattern from 0 to 50. Notice the last 2 numbers of 0 through 10: 00, 01, 04, 09, 16, 25, 36, 49, 64, 81, 00. Now look at 40 through 50: 00, 81, 64, 49, 36, 25, 16, 09, 04, 01, 00. A chiasm with 0 through 10. You’ll see the next sets, 10 through 20 and 30 through 40, respectively, have a similar pattern, and the whole set of 50 has 25 as its crux point. If you look at the next 50 numbers, you’ll see the same pattern repeated, and thus it repeats through all 100 numbers.

c. When you look at these numbers in systems used for computers (e.g., binary, octo, hex), you find similar chiastic patterns. In binary, you see the pattern in the last three digits.

3. The chiasm is significant for several reasons I can think of:

a. God created us with 10 fingers and 10 toes. Having a number system in base 10 (even the Jewish and Greek alphabets, which doubled as symbols for numbers, are calculated on base 10) seems like it fits a divine pattern.

b. God created the human body with a symmetrical appearance, mirroring right and left sides. If you hold your hands in front of you (both palms out or in, but not one each way), you can see the chiastic pattern yourself.

c. The scriptures themselves have chiasms throughout. Some have even identified an macro-chiastic pattern across all 66 books. One need only search “chiastic patterns in the Bible” to see dozens of examples and images of such patterns. It’s so prevalent, that one might even say it was an intentional mnemonic device used in the literature of the day to help remember and tell the stories of faith.

d. I believe there is so much more that could be discovered about Scripture by looking at these number patterns. I’m not talking about numerology, though. For example, most of us know that the number of the beast is 666. But did you know that the Greek letters in the Greek spelling of Jesus Christ add up to 888? And look at the number of those from the tribes of Israel in Revelation: 144,000, or 122 x 103. I believe that’s just the tip of the iceberg!

My conclusion, then, is that the mathematical rules that God put in place in creation are, in part, revealed in, or perhaps modeled in, our Scriptures to demonstrate the divine-design (read “inspiration”) component of God’s word. I haven’t even scratched the surface yet, but I intend to do much more exploring on this topic.

Peace,

Pastor Scott Stocking, M.Div.

My opinions are my own.

May 17, 2023

Life in the Spirit (John 14:15–21)

Filed under: 1 John,Biblical Studies,Christology,Ephesians,Greek,John Gospel of,Life of Christ,New Testament,Pneumatology,Soteriology,Textual Criticism,Theology, Biblical — Scott Stocking @ 11:35 pm
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Message preached on Sixth Sunday of Easter 2023 (May 14) at Mt. View Presbyterian Church. I added some technical details about the text for the blog article that I did not cover in my sermon.

Acts 17 is perhaps the most significant event we have recorded from the life of Paul in terms of his ministry. No, that chapter doesn’t recount any of his appearances before Roman rulers in defense of his faith and ministry. Rather, Paul attends a meeting of philosophers at a place called the Areopagus in Athens. It is safe to say that the Areopagus represented the “melting pot,” as it were, of worldviews and ideas on the meaning of life and purpose of humankind. Two of the more prominent philosophies mentioned in Acts 17 are Epicureanism, which originally focused on pursuing happiness, and Stoicism, which originally focused on living according to nature and suppressing one’s desires. Now I say “originally,” because by Paul’s time, Epicureanism had become more focused on sensuality than happiness, and Stoicism had just made its adherents prideful.

But we also learn from Acts 17 that most of the Roman gods and goddesses, or at least the Roman versions of the ancient Greek gods and goddesses, were still quite popular still in the day, so much so that Paul comments on and is distressed by the number of idols and other symbols of pagan worship that fill the city. Apparently, the Athenians were even afraid of leaving out a forgotten deity, so they had a statue with the inscription: “to an unknown god” (Acts 17:23).

Paul would use that statue as an object lesson to introduce these philosophers to a God they knew virtually nothing about: the God of the Jews, Yahweh, the Lord of Hosts, the One True God. Paul spoke of the resurrection of Jesus, a truly foreign concept to them. He spoke of the Creator God who “does not live in temples built by human hands.” Paul’s message certainly stirred the philosophical pot of thought in Athens, as a several who’d heard him at that meeting wanted more information from him, and an even smaller group actually started following Paul.

In our gospel passage today, Jesus stirs the pot in his own way by talking about someone called “The Advocate.” Sounds like a John Grisham or James Patterson title, right? Jesus introduces his disciples to a familiar concept with an unfamiliar application: the concept of the Holy Spirit guiding each of us, not just the prophets. Let’s take a closer look at the passage, beginning in John 14:15.

Our reading printed in the bulletin is from the New Revised Standard Version. Depending on which version you read, you may see a few different English words in your translation, so I want to help clear that up a bit. These differences by themselves don’t mean that any one version is better than another. Translation committees often will have a certain audience in mind or a certain writing style or worldview that governs the words they choose, especially to translate complex concepts from the source language into English.

Verse 15 says: “If you love me, you will keep my commandments.” Sounds pretty straightforward, right? It seems that the last part of the sentence naturally follows from the first part. “If you love your kids, you’ll give them attention.” “If you love your mom, you’ll buy her flowers occasionally.” You get the idea, right? But if you were to read it in New International or King James Version, it sounds more like a command: “If you love me, keep my commands.” I won’t bore you with the technical details of why there is such a difference, but the end result is the same in Jesus’s mind: he wants us to obey his commandments. I do prefer the NRSV translation in our bulletin, because it’s closer to what the original language says, and it sounds less authoritarian.

[For my blog readers, I will give you some of the technical details here. First, verse 15 is a third-class conditional sentence. That means, according to Daniel Wallace in Greek Grammar Beyond the Basics (GGBB)[1], that often, “the condition [is] uncertain of fulfillment, but still likely” (emphasis in original). The third-class condition can take any mood-tense combination in the apodosis (the last part of an “if-then” or conditional statement), and therein lies the second technicality. There are three variant spellings of the verb in the phrase in question. The chosen reading is the future tense form of τηρέω (tēreō, “I keep”), τηρήσετε (“you will keep”), being found in its most prominent witness B. The Aleph (א) witness has τηρήσητε aorist subjunctive (“you would keep my commands”). The witnesses A and D have τηρήσατε imperative (“keep my commands”). Notice, for all three variants, there is a difference in spelling of one vowel, which could have easily been confused in a scriptorium where the copy was read aloud for scribes to transcribe. Metzger says the editorial committee for the UBS text felt the future tense reading best fit the context.[2]]

Verse 16 is where you really start seeing the different ways the description of the Holy Spirit is translated. In our text today, Jesus says “I will ask the Father, and he will give you another Advocate [capital A], to be with you forever.” The current version of the NIV, which was updated in 2011, has “another advocate [lower case A] to help you and be with you.” So the NIV uses a phrase to translate the word to uncover a bit of the meaning behind what the role of the advocate is. Notice that the NIV doesn’t interpret it as a title like our current text in this verse, but later in the chapter, they do treat it as a title. Some other translations of this word you might see are “Comforter” (KJV); “Counselor” (older version of the NIV); or “Helper” (ESV, NASB).

If you’ve been in the church for a while, you’ve probably heard the Greek term that is behind these English translations: paraclete. The word is not used in the Greek version of the Old Testament, so we can’t make a connection to the “Wonderful Counselor” in Isaiah 9. In ancient Greece, it carried the idea of a helper or assistant in a court of law. John is the only NT writer who uses the word. He uses it of Jesus in 1 John 2:1–2 to speak of Jesus’s role in advocating for us before the Father: “If anybody does sin, we have an advocate with the Father—Jesus Christ, the Righteous One. 2 He is the atoning sacrifice for our sins[3]”

But the Holy Spirit’s role as the Advocate in our lives is different than that of Jesus’s role before the Father. It opens the door to a new concept: that God’s Holy Spirit would soon be available to all his disciples, and indeed to all believers, once Jesus ascended to Heaven, not just to a select few as in the Old Testament. We see that in the promise of the prophet Joel that Peter cites in his sermon on the Day of Pentecost.

The Holy Spirit’s role really does seem to be best described by the word Advocate. The NIV I think does the best job of explaining the role when the translators added “to help you” as a gloss to “advocate.” The Holy Spirit’s role is twofold: First, he is the living representative of Christ and God in us. Verse 17 says “You know him, for he lives with you and will be in you.” In verse 18, Jesus says, “I will not leave you as orphans.” The Holy Spirit’s presence will be a constant reminder that God loves us, just as he loves his one and only son. And it’s because of that love, as John indicates in vs. 15 above and reemphasizes in vs. 21. John also closes out this short section by saying Jesus will show himself to his disciples through the ministry of the Holy Spirit.

Beyond our passage, we see in 14:26 that our Advocate comes in the name of Jesus “will teach us all things and will remind us of everything [Jesus] said to us.” In saying this, Jesus also says he’ll leave us with peace and assurance that he will come and ultimately rescue us from the evil one himself.

The Holy Spirit’s first role, then, is ultimately to help us mature in our faith. As we spoke about a couple weeks ago when we looked at the “I am the door” passage, Jesus’s sheep know his voice. The Holy Spirit IS the voice of Jesus, the good shepherd, in our lives. The more we love God and Jesus, the more we will come to recognize the Holy Spirit’s voice speaking into our lives.

The second role of the Holy Spirit is to testify about Jesus through us, John 15:26–27. As we begin and continue to grow in our understanding of what life in the Holy Spirit means, we begin to recognize when the Holy Spirit is prompting us to act and to testify about who Jesus is. People will challenge us, and indeed are challenging us today, about our faith in God. According to Jesus in John 16, these challenges to our faith are not new and should not surprise us when they happen. Jesus reminds his disciples in John 16:7–11:

7 But very truly I tell you, it is for your good that I am going away. Unless I go away, the Advocate will not come to you; but if I go, I will send him to you. 8 When he comes, he will prove the world to be in the wrong about sin and righteousness and judgment: 9 about sin, because people do not believe in me; 10 about righteousness, because I am going to the Father, where you can see me no longer; 11 and about judgment, because the prince of this world now stands condemned.[4]

John goes on to say that when persecution starts to come our way, the Advocate, the Holy Spirit, will guide us into all truth. We won’t have to worry about what we’ll say, because the Holy Spirit will be directing us straight from the heavenly throne.

How does this look in real life? I want to close by giving an example from Paul’s letter to the Ephesians. Five times in that letter, Paul emphasizes that believers on earth have a connection to “the heavenly realms.” In 1:3, Paul says we, that is, the corporate body of Christ, together, have been “blessed in the heavenly realms with every spiritual blessing in Christ.” This comes from the power of the Holy Spirit dwelling in us. I want to emphasize that this a corporate gift, that is, no one person has every spiritual blessing, but as a body of believers, in the aggregate, we have on earth everything God wants us to have to carry out the ministries he’s called us to.

We learn toward the end of chapter 1 that the heavenly realms are where Christ is seated at the right hand of God, and all things have been placed under the rule and authority of Christ for benefit of the body of Christ. A few verses later, in 2:6, we find out that when Christ calls us and saves us, we too already have the blessing of being raised up and seated with Christ “in the heavenly realms.” It is from that vantage point, our souls connected to heaven, and our feet touching the ground, that we can “do good works, which God prepared in advance for us to do.”

In chapter 3 vs. 10, Paul reveals that God’s intent was that as the corporate body of Christ, the church, “the manifold wisdom of God should be made known to the rulers and authorities in the heavenly realms.” Without getting too involved in the concept of spiritual warfare, this speaks to our role of testifying about Jesus to the world as we saw in John 14–16 above. That is our purpose: to speak forth the word of God in both action and deed. In the first three chapters of Ephesians, Paul affirms who we are in Christ and what our exalted position is before him. In the last three chapters of Ephesians, he gives several examples of what it means to live in the heavenly realms, culminating with chapter 6 about putting on the armor of God, where we find his final reference to the heavenly realms:

10 Finally, be strong in the Lord and in his mighty power. 11 Put on the full armor of God, so that you can take your stand against the devil’s schemes. 12 For our struggle is not against flesh and blood, but against the rulers, against the authorities, against the powers of this dark world and against the spiritual forces of evil in the heavenly realms. 13 Therefore put on the full armor of God, so that when the day of evil comes, you may be able to stand your ground, and after you have done everything, to stand. 14 Stand firm then…”[5]

Paul goes on to describe the armor of God, for that is what it truly is. If you were to look up the references to each of the pieces of armor mentioned in the Old Testament, you would find that every one is mentioned in the context of God wearing it or wielding it. That armor isn’t a cheap imitation or a mass-produced copy. It’s the protection and strength of God himself. That’s what Jesus was affirming for us by speaking of our Advocate, the Holy Spirit, coming to dwell within us to teach us, empower us, and embolden us to speak his word.

It seems like the days of evil are fast encroaching on us. Don’t get left behind. Believe in Jesus if you don’t already. Commit yourself to loving him and receive the strength and power of the Advocate for our souls, the Holy Spirit. Maranatha! Come Lord Jesus! Amen!

[1] Wallace, Daniel B. 1996. Greek Grammar beyond the Basics: An Exegetical Syntax of the New Testament. Grand Rapids, MI: Zondervan (Logos version).

[2] Metzger, Bruce M. 1971/1975 (corrected). A Textual Commentary on the Greek New Testament. Stuttgart: United Bible Societies.

[3] 1 John 2:1–2. The New International Version. 2011. Grand Rapids, MI: Zondervan.

[4] John 16:7–11. The New International Version. 2011. Grand Rapids, MI: Zondervan.

[5] Ephesians 6:10–14a. The New International Version. 2011. Grand Rapids, MI: Zondervan.

May 12, 2023

Strength from Forgiveness (Psalm 51; 1 Timothy 1:12–17)

Filed under: 1 Timothy,2 Samuel,Biblical Studies,Faith, Faithfulness,Greek,Hebrew,Repentance,Soteriology — Scott Stocking @ 6:27 pm
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Click above to listen to message.

Sermon preached at Mt. View Presbyterian Church, September 11, 2022. Edited for publication.

There is no price we can pay or effort we can make to compel God to give us mercy or grace.

I think most of us are familiar with the story of David and Bathsheba. One evening (we don’t know how late, but the text says David had gotten out bed), David was out on the roof of his palace looking over the city when he saw at a nearby neighbor’s house the beautiful Bathsheba bathing (2 Sam 11:2–5). In that moment, David forgot he was otherwise known as a man after God’s own heart. The key word there is “forgot.” David should have known better. Bathsheba was not some exhibitionist bathing for all of Jerusalem to see. She had in that culture that valued purity and faithfulness a reasonable expectation of privacy. Most likely there were civic codes that prevented you from building your home in such a way as to risk violating your neighbor’s privacy. For example, in some Mediterranean cultures, they had rules that you couldn’t have a window in your house that allowed you to see directly into your neighbor’s house or back yard, especially if such a window was on the second floor. The palace may have been large enough to be exempted from such rules, but the principle existed nonetheless.

Add to this that shame of nakedness in that day would not have been on the one who was naked outside, especially if she had a right to privacy, but the shame would have been on the one who looked upon the nakedness. That is why Noah’s sons had to back into the tent to cover their naked, drunk father after the flood. David should have known immediately to avert his gaze and go somewhere else where such a view was not possible. It may be that David was on the roof of his palace, perhaps trying to get a view of the distant battle or the campfires of the troops or just to take in the cooler air. It would not have been a normal place for him to hang out. David had several opportunities to do the right thing in this situation, but the more he looked, the more he wanted Bathsheba. He could have done nothing at that point except walk away, but he didn’t. Instead, he sent someone to bring Bathsheba to him. He lay with her and got her pregnant.

And if that wasn’t bad enough, he tried to manipulate the situation by first giving Uriah, Bathsheba’s husband, a break from the battle in the hopes he would lay with Bathsheba and some might not question the paternity of the baby. But Uriah showed more integrity than David, so David sent him back to the battle with instructions to his commander, Joab, to manipulate the battle in such a way that Uriah would surely perish, and he did.

Of course, we know that David’s sin was exposed by the prophet Nathan, and we see David’s repentant, godly response in Psalm 51.

Read Psalm 51:1–10

1 Have mercy on me, O God, according to your unfailing love;

according to your great compassion blot out my transgressions.

2 Wash away all my iniquity and cleanse me from my sin.

3 For I know my transgressions, and my sin is always before me.

4 Against you, you only, have I sinned and done what is evil in your sight;

so you are right in your verdict and justified when you judge.

5 Surely I was sinful at birth, sinful from the time my mother conceived me.

6 Yet you desired faithfulness even in the womb; you taught me wisdom in that secret place.

7 Cleanse me with hyssop, and I will be clean; wash me, and I will be whiter than snow.

8 Let me hear joy and gladness; let the bones you have crushed rejoice.

9 Hide your face from my sins and blot out all my iniquity.

10 Create in me a pure heart, O God, and renew a steadfast spirit within me.

11 Do not cast me from your presence or take your Holy Spirit from me.

12 Restore to me the joy of your salvation and grant me a willing spirit, to sustain me. [1]

So David is busted. Found out. Exposed. It was pointless for him to deny it. And he didn’t live in a culture where such behavior, especially in the political class, would be ignored and swept under the rug. He had to face his maker. And he chose the best path, the only path, really, to put him on the road to restoration. God was giving his anointed a chance to come clean through the prophet Nathan’s intervention, and David accepted. He pleaded with God for mercy and owned up to his mistake.

This word for “mercy” here, (חָנַן ḥā·nǎn), is almost always used in the context of someone speaking, more so than in a running narrative that tells a story. The New International Version tends to translate it based on the perspective of the speaker. In the current passage, and for about one-third of the total occurrences of the word in the OT, if the speaker knows they’ve done wrong and they ask for ḥānǎn, the translators use the word “mercy.” On the other hand, if the speaker has acted justly and feels threatened by the enemy, or is referencing the goodness of God generally, the translators usually use “gracious” or “generous” for the word. That sense of the word represents about half the total occurrences of the word. These two primary meanings represent a modern distinction that some have made between “mercy” and “grace.” “Mercy” is not getting what you deserve, while “grace” is getting what you don’t deserve or didn’t earn. In both cases, it is a gift of God. And in both cases, there is no price we can pay or effort we can make to compel God to give us mercy or grace. We can ask for it, we can search for it, but the “price” for such a gift can only be paid by God, which he ultimately did through Jesus on the cross.

This is where the other key word in Psalm 51:1 comes in, a Hebrew word you’ve most likely heard before if you been in church or Bible studies for any length of time: חֶסֶד (ḥě·sěḏ), God’s “unfailing love.” Of the 245 times this word is used in the OT, well over three-fourths of the occurrences refer to God’s enduring, unfailing love and kindness. And nearly half of the uses of the word are found in the Psalms, including in the praise Psalm 136, where “His love (ḥěsěḏ) endures forever” is a repeated refrain at the end of each of its 26 verses.

As one Bible dictionary puts it, ḥěsěḏ is not a “disposition,” that is, it’s not just a feeling or a certain way of thinking. It is in the end a helpful act of God rooted in his covenant relationship to us, or when applied to us mortals, our helpful acts of love toward family and friends. It is an overflow of his righteousness, mercy, and shalom peace. As a covenant responsibility, David expects to and has a certain level of assurance that he will be forgiven. This is the same assurance we have when we come to Jesus: “If we confess our sins, he is faithful and just to forgive us our sins and purify us from all unrighteousness” (1 John 1:9). As I said above, there’s nothing we can do to earn this, but we can and should respond to it with a ḥěsěḏ of our own. “We love because he first loved us” (1 John 4:19). Not only is this ḥěsěḏ toward God, but toward our family and friends as well.

In vv. 5–6, David gives us a contrast between the way we are and the way God wants us to be. I want to use the English Standard Version translation of these two verses here because I think they’re a little less interpretive of the Hebrew text, and come much closer to what David was trying to convey:

5  Behold, I was brought forth in iniquity, and in sin did my mother conceive me.

6  Behold, you delight in truth in the inward being, and you teach me wisdom in the secret heart.[2]

On the one hand, David realizes he is a sinner in need of God’s grace. But on the other hand, David knows that only God can transform his inner being into the godly character he desires. God knew David was a sinner in need of his grace, and that David might fall short of the ḥěsěḏ standard miserably at times, but he still chooses him anyway to lead his people. Verse 5 is similar to Paul’s essay in Romans 7 about doing what he doesn’t want to do and recognizing that sin still may try to get a stranglehold on him. But by sending the prophet to David, God is giving David a chance to come clean, to repent, and he does. God doesn’t ostracize or “cancel” his anointed because of one or two or five or ten mistakes. God’s ḥěsěḏ requires our willingness to be taught and to seek his truth to transform our inner being. God is forever the God of the next chance. God’s gift and his calling on our lives are without repentance, “irrevocable” (Romans 11:29). So no matter how many times you think you’ve failed or fallen short, know that he has called you for a purpose, and that he is guiding you and strengthening you in his ḥěsěḏ love to bring about his will.

Verses 10–12 give us a glimpse of how we get God’s truth in our inward being and his wisdom in our “secret” heart. After forgiving us and cleansing us, David recognizes that he must immerse himself in the presence of God to experience the restoration and renewal that awaits him. This is not a passive process: David goes on in the psalm to commit himself to teaching others about God’s ways and singing the praises of God aloud.

Verse 12, then, ties into our Gospel reading this morning from Luke 15: Both the shepherd and the woman have lost something of value. In the case of the shepherd, he leaves behind everything of value he does have, that is, the flock, to find the one sheep that is missing. This is what God does for us to bring us back to him.

In the case of the woman, she must clean her whole household to find the missing coin. David asked God to “cleanse” him with hyssop and remove from him all that would keep him from experiencing God to the fullest. Notice that he didn’t pledge to clean up his own life. God doesn’t need to wait for us to do that on our own. He meets us where we are and works with us from that point forward to bring restoration.

For both the shepherd and woman, there is rejoicing for finding what was lost and restoring it to its rightful place. Jesus draws the parallels there with both stories to the heavens rejoicing when one sinner repents. When we know God is with us, we can feel assured of our salvation, our calling, and the power of his ḥěsěḏ love.

Before I wrap up this morning, I want to bring in a passage that shows how this transformation from sin to victory worked itself out in Paul’s life. Let’s look at 1 Timothy 1:12–17:

12 I thank Christ Jesus our Lord, who has given me strength, that he considered me trustworthy, appointing me to his service. 13 Even though I was once a blasphemer and a persecutor and a violent man, I was shown mercy because I acted in ignorance and unbelief. 14 The grace of our Lord was poured out on me abundantly, along with the faith and love that are in Christ Jesus.

15 Here is a trustworthy saying that deserves full acceptance: Christ Jesus came into the world to save sinners—of whom I am the worst. 16 But for that very reason I was shown mercy so that in me, the worst of sinners, Christ Jesus might display his immense patience as an example for those who would believe in him and receive eternal life. 17 Now to the King eternal, immortal, invisible, the only God, be honor and glory for ever and ever. Amen.[3]

We only need to look at verse 13 to see how far Paul was from the Christian faith. First of all, he calls himself a blasphemer, which by itself would have been enough to get him stoned to death in Israel. But in context here, he’s probably referring to his initial denial of Christ as Lord and his approval of the stoning of Stephen, because the Jews thought Stephen had blasphemed in his final, fatal message. Paul was a persecutor. He thought this new Jesus movement was so dangerous to traditional Judaism that the followers had to be jailed or snuffed out, violently if necessary. He even admits to acting ignorantly and in unbelief, and that he was the worst of all sinners.

Yet with all that, God still chose to use Paul to be the main messenger of the faith in the northern Mediterranean region. He humbly gives thanks and praise for all that God has done for him and is doing through him. His life would be the ultimate testimony of the transforming power of God’s grace and salvation.

I want to focus for a moment here on verse 12, because I believe that parallels what David’s desire was in his psalm of repentance: “I thank Christ Jesus our Lord, who has given me strength.” I guess you could say Paul was “fortunate” enough to have a direct revelation from Jesus to set his life in the right direction. Granted, that was probably a pretty scary situation for him, as it would be for any of us, I imagine. But the attempt to turn a violent and desperate man from his ways required corresponding radical action of God to set him straight. That seems to have been enough, at least initially, to have “strengthened” Paul, because we see very soon after his conversion in Acts 9:22 that Luke tells us, “Saul (Paul) grew more and more powerful (or strengthened) and baffled the Jews living in Damascus by proving that Jesus is the Messiah.” He relates his own story here so that in 2 Timothy 2:1, he can also encourage Timothy to be strong in God’s grace as well. Having the examples of men and women of faith, both in the Bible and in our own lives, will help us stay grounded in the faith and give us strength and endurance for our Christian walk. The author of Hebrews said it well:

Therefore, since we are surrounded by such a great cloud of witnesses, let us throw off everything that hinders and the sin that so easily entangles. And let us run with perseverance the race marked out for us, 2 fixing our eyes on Jesus, the pioneer and perfecter of faith. For the joy set before him he endured the cross, scorning its shame, and sat down at the right hand of the throne of God. 3 Consider him who endured such opposition from sinners, so that you will not grow weary and lose heart.[4]

My friends, do not lose heart. Every day, lift up the Lord Jesus in your life through word and deed, and give God the praise and glory he deserves.

Now to the King eternal, immortal, invisible, the only God, be honor and glory for ever and ever. Amen.[5]

[1] The New International Version. 2011. Grand Rapids, MI: Zondervan.

[2] The Holy Bible: English Standard Version. 2016. Wheaton, IL: Crossway Bibles.

[3] The New International Version. 2011. Grand Rapids, MI: Zondervan.

[4] The New International Version. 2011. Grand Rapids, MI: Zondervan.

[5] The New International Version. 2011. Grand Rapids, MI: Zondervan.

May 6, 2023

Of Sheep, the Shepherd, and His Open Door (John 10:1–10)

Filed under: "I Am" Statements,Christology,Ecclesiology,Evangelism,Greek,John Gospel of,Nehemiah,Soteriology — Scott Stocking @ 10:17 pm
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My message from three weeks after Easter, 4/30/23. I’ll add the audio file later.

Nehemiah was a central figure in the rebuilding of Jerusalem after the Exile. Around the year 444 BC, he had approached King Artaxerxes about returning to Jerusalem to see the city walls restored. Some families had been there for almost 70 years already, beginning to return in earnest after the new temple was completed, but they had no protection from enemies around them because of the decimated walls. Most of us, I think, are somewhat familiar with the big picture of the story of rebuilding the wall. The task was divided up among several different groups, with each group taking responsibility for a section of the wall that contained a particular gate—10 gates are mentioned as Nehemiah details the assignments.

One thing of note in this story, especially as it relates to our passage today, is that the Sheep Gate was the first section of the wall to be assigned. It was on the northeast corner of the Temple mount near the recently rebuilt Temple and adjacent to the Pool of Bethesda, and it was most likely the gate the sheep would come through when brought in for the sacrifices. This particular gate was so significant and so important that Nehemiah assigned the high priest and his fellow priests to be in charge of that section. This would be the cornerstone, as it were, for the rest of the wall. That the high priest was involved let everyone know in Jerusalem that this project was serious business. They would establish the standard and the work ethic for getting this project done in 52 days.

John doesn’t give a lot of details about where Jesus is at when he speaks the message of the sheep and the good shepherd in John 10. I can imagine, however, if he was in Jerusalem, he was probably pretty close to the Sheep Gate. Five chapters earlier, Jesus had healed an invalid of his 38-year disability at the nearby Pool of Bethesda. One might say Jesus had already rescued one of his sheep in that instance, just like the parable of the lost sheep from Luke 15.

This location was special not only to Jesus, then, but also to his followers and to those who had witnessed that miracle. Historically, there has been and continues to be an occasional sheep market near that gate, so it’s special to the shepherds as well. It’s entirely possible that Jesus had this as his backdrop while teaching his disciples.

Now the word used for “gate” here is the typical word that would have been used for the door of a house, or more figuratively, a “door” of opportunity. The Greeks had a unique word for gate that typically implied either the entrance into an outdoor enclosed area that didn’t have a frame save for the fence on either side, or a city gate, which may have been reinforced to withstand attacks. In the context of shepherding, a “door” for the sheep may have referred to a corral that had some sort of sheltered area the sheep entered through and could stay under in bad weather.

Regardless, the purpose of the door or gate was to keep the predators out. Verse 1 makes that plain: “Anyone who does not enter the sheep pen by the gate, but climbs in some other way, is a thief and a robber.” In verse 8, Jesus tells his listeners that “all who have come before me are thieves and robbers,” and he finishes off this section by warning them of their purpose: “The thief comes only to steal and kill and destroy.”

That sounds pretty scary, right? But in this story, we also get a glimpse of the relationship between the sheep and the shepherd that has helped the sheep develop a sense of when danger is near so they know when to flee. In verse 8, Jesus says the sheep won’t even listen to the thieves and robbers, and in fact, as verse 5 says, they will run away from the thieves and robbers because they don’t recognize the stranger’s voice.

But they do recognize the shepherd’s voice, and they will follow the shepherd. If they’re out in the field grazing, they know when it’s time to come in. If they get lost, they can listen for the shepherd’s call and follow their voice to get home safely.

I think the parallels here for our own lives are obvious to most people, but they always bear repeating. How do you recognize the Shepherd’s voice? How many times have we caught ourselves saying something like, “I just wish God would tell me what to do!” If you’ve spent enough time reading and studying Scripture, praying to God, and hiding his word in your heart, you probably already have the ability to discern God’s voice. You may not hear an audible voice, but sometimes the Holy Spirit’s promptings are so powerful, you cannot help but pay attention and act accordingly. We’ll talk about that some more in a couple weeks.

Another way to hear God’s voice is to read the Bible out loud for yourself. This same John who wrote this gospel says in the introduction to the book of Revelation, “Blessed is the one who reads aloud the words of this prophecy, and blessed are those who hear it and take to heart what is written in it, because the time is near[1]” Did you know that reading out loud takes longer than reading without speaking? When I’m reviewing my sermon to put the finishing touches on it, I can read through it on paper in about 5 minutes just in my head. But when I read it out loud, it forces me to consider how my words sound as they come out of my mouth. What seems perfectly normal to me on paper may have a slightly different nuance when I read it out loud.

When we read silently, we typically read in monotone in our minds. When we read out loud, especially if we’re familiar with the passage, we begin to understand where the author may have intended to inflect their voice one way or the other. When we speak, we tend to emphasize certain words by raising our voice, or maybe drop it to a whisper if we want to add some more drama to it. We raise our voice at the end of a question, right? When we’re getting to our conclusion, we tend to slow down a bit to make sure every word is clearly understood. I do love it that we read whole passages out loud here every Sunday. I think that’s important for any church to do that. And those of you do read up here on Sundays do a great job of putting expression and emotion into the passages you’re reading. That brings God’s word alive and gives all of us a chance to learn it and take it to heart even more fully.

Finally, hearing God’s word read or seeing it portrayed in a movie or television show adds extra depth to God’s word, because you can see an interpretation of the historical and cultural setting in which it’s spoken. A few weeks ago, when I spoke on the woman at the well, instead of reading that long passage from John chapter 4, a passage filled with drama, emotion, and suspense, I thought it much better to show you the clip from The Chosen series about that passage. I think I’m a pretty good reader, but my speaking skills just were not up to the task of trying to portray a frustrated, heart-broken, oppressed woman who’s had five husbands. I just can’t do that role justice! Watching a series like The Chosen, or any of the movies depicting the biblical stories like Mel Gibson’s The Passion of the Christ or Cecil B. DeMille’s The Ten Commandments, can help bring the biblical story to life for us and give us a new and deeper understanding of God’s word. They help us hear God’s voice in a different way.

Another way we can hear his voice is by fellowshipping with one another. Since we’re called to be part of the body of Christ, fellowshipping with one another allows us to share our experiences with each other and learn from each other how God has worked in and spoken in their lives. We are not alone, and I don’t mean there are aliens out there. We have a great cloud of witnesses surrounding us to give us their historical perspective through their lives, their written or recorded word, and the fruit of their ministry.

If you’re more of a politically or civically minded person, you might be hearing God’s voice if you find you have a passion for some social justice cause on any side of the issue. It’s not my job to tell you which side to take, of course. This is America, after all, and we’re all free to not only express our opinions and beliefs, but to defend and try to persuade others of our beliefs, in love of course. God’s kingdom has a diverse population, and we can’t always expect that everyone will be on the same page of every issue all the time. But let’s not resort to extremes like “cancelling” or ostracism either just because we disagree with a brother or sister in Christ. Let us speak the truth in love to each other. Even if we don’t agree with one another on something, having a robust discussion on issues of the day helps us to understand one another and develops a certain sense of empathy, even if in the end neither side budges. It helps us to see how God may be moving in others’ lives.

There’s one other aspect of this passage that is worth noting, and this really cuts to the core of what Jesus’s statement “I am the gate” is all about. Look at verse 9 again: “I am the gate; whoever enters through me will be saved. They will come in and go out, and find pasture.” First notice that Jesus says he is THE gate. He’s not just any old gate, and he’s not one of many gates; he’s the only gate. And what does that gate lead to? The salvation of our souls. It’s interesting, I think, that there is only one other time in John’s gospel where Jesus uses the phrase “through me.” It comes in the sixth “I am” statement of Jesus in John 14:6: “I am the way, the truth, and the life. No one comes to the Father except through me.”

Jesus is the only way to get to our eternal reward. But what does it mean to go “through” Jesus? It means we become part of the body of the Christ and maintain that connection by being faithful to him. We immerse ourselves in God’s word and surround ourselves with other faithful followers so we have a strong support network. But notice the other part of vs. 9: “The will come in and go out, and find pasture.” Jesus is not saying here that we move in and out of salvation. What he recognizes here is that, as Christ-followers, we can’t avoid being out in the world where wolves and thieves and robbers want to attack us. But we have a safe haven in Christ, where we can enter in and find rest from the struggles of life. Knowing we have that safe haven helps us endure in the “pasture.” In vs. 11, Jesus says he’s the good shepherd. As the good (and perfect) shepherd, he maintains the boundaries of his pen so that we can have that safe place to rest. But he also promises that he won’t abandon us when the wolves come after us in the pasture. He is watching over us, giving us a strong sense of security that he will never leave us nor forsake us. We have a wonderful shepherd, a great high priest who knows what it’s like to be us and can empathize with us in every way.

I suppose we can say that our church family is our “sheep pen.” I do hope that you all feel that sense of security and belonging being here on Sunday mornings and whenever else you gather to make quilts or carry out your other ministry activities. The church is the place where that should happen. I also hope you know that your church family can be a valuable source of support for you in times of trouble, darkness, and even despair. Even though this congregation is small in numbers right now, I have seen the impact of your ministry. I am one of the results of the ministry of this church from 50+ years ago. Many of you have been faithful to this ministry for even longer. I know the good shepherd looks down on this part of his flock and smiles, and I pray you will continue to lead others to gates of heaven, just as you have been doing. Amen.

[1] The New International Version. 2011. Grand Rapids, MI: Zondervan.

Assurance, Hope, and Power: The Disciples’ Resurrection Rebound (John 20:19–31)

Filed under: Greek,John Gospel of,Liturgical Calendar,Passion,Psalms,Resurrection,Soteriology,Theophany — Scott Stocking @ 12:20 pm
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Click the Play button below to hear the recording of the message.

My message from 4/16/23, the week after Easter, at Mt. View Presbyterian Church in Omaha.

I learned a fancy new ten-dollar word this week. “Denouement” (day new MA). If you’re into literature or are a member of book club, perhaps you already knew the term before today. It’s a French word that’s made its way into English that refers to what happens in a story after the climax or high point of the action has occurred. The meaning of denouement is “untying of the knot.” An English equivalent, at least in the context of literature, might be “resolution.” How does the story “resolve” or work itself out after the climax.

Why am I starting my message this morning with a vocabulary lesson? (Don’t worry, no quiz at the end!) Well, you may have already guessed where I’m going with this. The crucifixion, burial, and resurrection of Christ is the climax of the Gospel story in the New Testament. Like the Gospels, the Christian liturgical calendar begins with the “prequel” of the Advent, the birth of Christ, beginning the Sunday after Thanksgiving; passes through several “seasons” in which we see the nature and work of our servant-savior; and leads up to the crucifixion and resurrection.

We’ve now entered the “denouement” of the liturgical seasons, the time between the Resurrection, celebrated on Easter Sunday, and Pentecost, 50 days following. After that, aside from the first Sunday after Pentecost being “Trinity Sunday” and the last Sunday of the liturgical year being “Christ the King,” the rest of the liturgical calendar is officially “proper,” or the nth Sunday after Pentecost. That’s doesn’t sound near as exciting as all the stuff at the beginning of the liturgical year.

Of course, the Gospel is a compelling and engaging story regardless of the season, month, or day in our liturgical or regular calendars. It is made so, in part, by the way you and I live out our faith in the places we find ourselves in this world. As disciples of Christ, we have been charged with being light and salt in an increasingly dark and bland world. But it’s hard to do that if we’re not convinced and assured that the resurrection of Christ has secured that hope for us.

That is where we find ourselves in the early stages of this denouement: Jesus had appeared to the women who came to the tomb, and even to two unnamed disciples on the road to the Emmaus, but the 11 remaining apostles had not yet seen him and, according to the longer ending of Mark’s Gospel, they didn’t believe either of those reports from earlier in the day. But on the evening of that same day Jesus was resurrected, Jesus literally drops in on them in the house where they were staying; the door was locked.

All the apostles (“the Twelve”) except Thomas (and of course Judas) were there for the first visit. It’s likely that others were there as well, but the text is silent on that detail. Jesus shows his disciples his pierced hands and side and even asks his disciples to put their fingers in the holes. The disciples are not only convinced, but the text says they are overjoyed as well. Something else happens here that I think gets overlooked in the Gospel story. Jesus essentially commissions the disciples—we don’t know if this meant only those of the Twelve who were present or everyone—by giving them the Holy Spirit in advance of the day of Pentecost. He also gives them authority to forgive sins or not forgive sins. Jesus was granting them a portion of divine authority here, collectively, so that he could have an official complement of representatives to prepare the world for the coming of the Holy Spirit to believers and birth of the Church on the day of Pentecost.

This is important for a couple reasons. First, just as plant seedlings are often nurtured in the controlled environment of a greenhouse or a baby is born in sterile conditions in the hospital, so too did the church need a perfect or near-perfect spiritual environment to get started and to grow. I believe the authority Jesus gives them, again collectively, included the knowledge of the perfect, untainted Gospel on which Jesus wanted to found the church. Their proclamations were considered authoritative, and as a group, they could hold each other accountable for that perfect doctrine, instead of having all of the authority for the church rest in one person. Eight days later, Thomas would be added to that group when he finally got to see Jesus and had every doubt erased. He would be able to proclaim, “My Lord and my God!” after seeing Jesus for himself.

On the other hand, having a group of leaders thus empowered and commission would also help with the stability of the local, usually house, churches that would begin to form after the day of Pentecost. With so many hearing the Gospel in their own language that day, it would be important that someone with that kind of authority could be sort of a regional overseer for the fledgling churches and communicate officially on behalf of the apostles whenever questions arose. We see some hints of that in the middle chapters of the book of Acts. I think it’s safe to say the apostles didn’t want 3,000 new converts going back to their respective homelands without some kind of help from those who had first-hand experience with Jesus and the apostles.

Getting back to Jesus’s first appearances to the disciples, they had assurance of what we read in our passage from Psalm 16 this morning. Here’s verses 9–11 from the New International Version:

9 Therefore my heart is glad and my tongue rejoices;

my body also will rest secure,

10 because you will not abandon me to the realm of the dead,

nor will you let your faithful one see decay.

11 You make known to me the path of life;

you will fill me with joy in your presence,

with eternal pleasures at your right hand.[1]

The apostles realized that Jesus was the “faithful one” who did not see decay, and by implication, those faithful ones who had died before had also been safe from that decay. Paul tells us in Ephesians that Christ, upon his resurrection, led an army of captives out of the “lower earthly regions” into the heavenly realms. Peter would use this passage from Psalm 16 in his powerful sermon on the day of Pentecost because he had realized and experienced its truth for himself.

Peter would later write in one of his two letters about the living hope that comes through the resurrection of Jesus. He says this in the opening chapter of his first letter:

3 Praise be to the God and Father of our Lord Jesus Christ! In his great mercy he has given us new birth into a living hope through the resurrection of Jesus Christ from the dead, 4 and into an inheritance that can never perish, spoil or fade. This inheritance is kept in heaven for you, 5 who through faith are shielded by God’s power until the coming of the salvation that is ready to be revealed in the last time. 6 In all this you greatly rejoice, though now for a little while you may have had to suffer grief in all kinds of trials. 7 These have come so that the proven genuineness of your faith—of greater worth than gold, which perishes even though refined by fire—may result in praise, glory and honor when Jesus Christ is revealed. 8 Though you have not seen him, you love him; and even though you do not see him now, you believe in him and are filled with an inexpressible and glorious joy, 9 for you are receiving the end result of your faith, the salvation of your souls. [2]

Thomas had the luxury of seeing Jesus on his second appearance to the group and finally believing he had risen, even though he refused to believe his closest friends after Jesus’s first appearance convinced them. You and I will probably not have that luxury of seeing Jesus while we dwell on earth, unless he comes again in the immediate future. We would fall, then, in the second category: “Blessed are those who have not seen and yet have believed.”

As disciples of Christ, we have a wealth of resources available to us as we live and serve in God’s kingdom. We have a new birth, or as Jesus told Nicodemus, we’re “born again” of the Spirit. The old has gone; the new has come! The past no longer controls us. We have a living hope affirmed by the resurrection. The faithful in the Old Testament probably could not have even conceived of what the New Testament has revealed to us about eternal life in the heavenly kingdom. Our inheritance is permanent! No moth or rust can destroy it!

We’re shielded by God’s power (and his armor) through faith, and we have the hope of his second coming and the eternal salvation that will be ours to claim. We have this assurance even in the midst of the trials and griefs we suffer corporately and individually, for it is in standing firm through these trials that our faith is tested, purified, and proven true. Paul says in Ephesians that when we put on God’s armor, we can stand firm in the faith. We can know in part here on earth that joy we will fully know in heaven!

Even though Easter is the climax of our liturgical year, our denouement need not in any way diminish the joy and excitement of living for Christ in the hope of our resurrection and our salvation. Each and every day can be an adventure with Christ as we read his word, serve those who need an extra measure of his grace, and walk in faithful fellowship with one another. Those first few weeks after the resurrection, the believers had a lot of knots to untie to figure out their part in growing the early church. Of course, the Spirit was calling people, and that couldn’t be stopped. But they had to move quickly. For us today, we could use this season to think about how we do our own ministries. How can we use the excitement of celebrating Jesus’s resurrection to channel that energy into “untying the knots” that may be holding us back from doing more for God’s kingdom or for the local church or community? Are there others we could reach? Are there others we could invite? Are there others who need our help? Who could I talk to about my doubts and fears? These don’t have to be grandiose, but I do think the answers should be just big enough to require some faith in and reliance on God to get them done.

As we move through this season leading up to Pentecost, remember that Christ has given us assurance of his resurrection and our own, the hope of eternal life in an imperishable kingdom, and the power to minister in his name and encourage those who also need that assurance and hope. Peace to you! Amen.

[1] Psalm 16:9–11. The New International Version. 2011. Grand Rapids, MI: Zondervan.

[2] 1 Peter 1:3–9. The New International Version. 2011. Grand Rapids, MI: Zondervan.

April 28, 2023

8 ÷ 2(2 + 2) = 1: Why PEMDAS Alone Is Not Enough

Filed under: Numbers (Cardinal & Ordinal) — Scott Stocking @ 11:22 pm
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I recognize this is off-topic for my blog, but I love math. And I also discovered that Greek grammar has some features of math properties or laws, so it’s only mostly off-topic.

If you like this article, you may also like https://sundaymorninggreekblog.com/2023/05/29/toward-an-active-pemdas-strengthening-its-theoretical-foundation/ or my latest article, https://sundaymorninggreekblog.com/2024/03/16/8-%c3%b7-22-2-1-part-2-a-defense-of-the-linguistic-argument/

See also the latest article, my conversation with ChatGPT on juxtaposition in mathematics. https://sundaymorninggreekblog.com/2025/03/23/8-%c3%b7-22-2-1-a-discussion-with-chatgpt-on-the-implications-of-juxtaposition-in-mathematics/

Click here to save 10% on various Logos Bible Software packages and get five free digital books.

See my Rumble video on a similar expression at The correct way to solve viral math expressions. For a more complete explanation, see my newly released Rumble video (12/22/24) at Stocking’s Order: Why 8 ÷ 2(2 + 2) = 1

Bottom Line (added 12/20/24 6:35 am)

For expressions and equations that have elements featuring a mix of explicit and implicit operations, implicit operations should be done first without immediate regard to or influence of explicit operational signs. Implicit operations include any form of grouping that involves paired grouping symbols, any juxtapositional grouping or pairing without explicit operational signs implying a particular operation, or a combination of both.

Supporting Evidence for the Bottom Line (added 01/19/24, ~5:45 am CST)

In the .pdf file linked below, the first table describes Implicit Constructions in mathematics and demonstrates that they each have their own unique Syntax and Orientation that leads to an implication (thus the word “implicit”) for how they’re handled in any math expression, specifically that they are given priority in the Order of Operations over explicit (existing) operational signs (+ – x ÷). The second table demonstrates the actual Implicit Operations that take place (e.g., finding a common denominator; converting to an improper fraction, etc.) before addressing explicit operational signs. In ALL cases, implicit operations should be worked prior to explicit operational signs.

Implicit Constructions in MathematicsDownload

Introduction

I know this is a Greek language blog, but math uses Greek characters sometimes, so there’s at least a tenuous connection. And all truth is God’s truth, even in Mathematics, for which God created the principles, properties, and laws. Being a former high school math teacher myself, I was disappointed at the lack of knowledge of fundamental laws and properties in math that led to many people thinking Expression 1 did not equal 1 in certain viral social media threads. In an effort to restore some truth to people’s mathematical knowledge, I present the following proof that the answer to Expression 1 is ALWAYS AND FOREVER 1.

Expression 1

8 ÷ 2(2 + 2)

Conventions vs. Laws

Many people in the social media chains trying to tackle this problem were claiming that following the order of operations they learned in and impressively remembered from grade school was the correct way to approach the problem:

Parentheses

Exponents

Multiplication/Division LTR

Addition/Subtraction LTR

This order is commonly known in American math as PEMDAS and recalled by the sentence “Please Excuse My Dear Aunt Sally.” I do not deny the importance of PEMDAS, but the reality of the problem is, any basic math problem like this can only have one correct answer. It’s not and never a matter of personal interpretation. Otherwise, the foundations of mathematics would crumble into oblivion, and not even Common Core could save us (not that it ever did anyone any good). This is math; it doesn’t care about and is never affected by your feelings about it.

PEMDAS is only a tool for organizing the operations in the problem, but by itself, it is not sufficient to solve the problem correctly. In fact, PEMDAS isn’t a mathematical law at all. It is merely an agreed-upon convention to work “linear” math problems. Math does have many laws or properties that come into play and must be considered in the PEMDAS process, and PEMDAS is subservient to these laws. Nothing about the correct solution I’m about to show you violates PEMDAS, provided you correctly interpret the forms of the individual expressions within the larger expression and how the various laws and principles apply.

If you think back to your primary school math lessons, you may have a vague memory of a set of laws[1] about the relationships of numbers in certain types of expressions. For example, the Associative Properties of addition and multiplication say that no matter how you group the numbers in their respective equations, the sum (addition) or product (multiplication) will always be the same. The Commutative Properties for these two operations are similar; the order of the order or arrangement of the elements in an expression does not affect the value of either expression. These Associative Properties are represented in Expressions 2 and 3, while the Commutative Properties are in 4 and 5:

Expression 2: Associative Property of Addition:

(a + b) + c = a + (b + c)

Expression 3: Associative Property of Multiplication:

(a * b) * c = a * (b * c)

Expression 4: Commutative Property of Addition

a + b = b + a

Expression 5: Commutative Property of Multiplication.

ab = ba

The expressions on either side of the equal sign in the respective equations above reveal another principle of math, that of identical expressions. They look different, but regardless of the values assigned to each variable, they will always be equal. This is also called an identity.[2]

The other important thing to know is that PEMDAS, unlike the Associative and Commutative Properties, is not a law! It is merely a convention for solving a problem that is subject to these laws. PEMDAS does NOT usurp these laws. This is where people are getting tripped up on solving Expression 1 or similar expressions for that matter. I will demonstrate how the correct application of these laws within the framework of PEMDAS will ALWAYS yield the answer of 1, NOT 16 or some other number.

Solving the Expression

One other law must be brought to the fore to solve this expression: the Distributive Property. This is slightly different from the other four laws, in that it involves both addition and multiplication, and it establishes a common equation form that must be worked the same way every time it is found within an equation. Wolfram Research is considered one of the premier math knowledge platforms in the world, so I will draw on their examples of the Distributive Property to make my point. If anyone wants to challenge me on my conclusions drawn from this source, you’ll have to do better than a cheesy homework help Web site. The Wolfram Web sites have two different ways of writing the Distributive formula. BOTH equations are identical expressions and should be solved the same way every time regardless of where they fall in an equation.

Expression 6: Distributive with intervening multiplication operator

a * (b + c) = ab + ac (and of course, if you’re using all real numbers, combine like terms).[3],[4]

Expression 7: Distributive without intervening multiplication operator

a(b + c) =ab + ac (and of course, if you’re using all real numbers, combine like terms).[5]

Whether the expression has the multiplication operator or not, you would treat both as an expression to be solved BEFORE leaving the P step in PEMDAS. The actions UPON the parenthetical result must be completed BEFORE leaving the P step.

For purposes of demonstration later on, we can also apply the Commutative Property of Multiplication to the Distributive property form. We have two “factors” (the a and the (b + c)), so we can rearrange them and still have the same result. In the case of the current form, if we put the a term to the left as written in Expression 7 above, this form of the expression is said to be left distributive (i.e., the a multiplies through from left to right). If the a term is to the right of the parentheses, then the form is called right distributive.[6] See Expression 8 below. The right distributive form of the expression is an identical expression to the left distributive form. I will use this to demonstrate that PEMDAS is not consistent if you don’t first solve the expression in distributive property form.

Expression 8

(b + c)a = ba + ca (and combine like terms if using all real numbers).

Are you with me so far? Maybe you see where I’m going with this? The expression to the right of the division sign must be processed as and simplified to an individual, inseparable term, because it is in the form of a Distributive Property expression. It has parentheses after all, so it must be dealt with before being divided into 8. So here’s the explanation of solving the equation as written:

Expression 9

(2 + 2)2 = 2(2 + 2) = (2 * 2 + 2 * 2) = (4 + 4) = (8)

This then leaves you with the final expression (Expression 10) to be solved:

Expression 10

8 ÷ (8) = 1

QED

Why the Answer Is NEVER 16 or Any Other Number

I am going to offer several proofs or citations that demonstrate why PEMDAS is not sufficient by itself to solve this problem. The first citation comes from a 1935 textbook for advanced algebra. 7 Here is what the authors say:

“If the multiplication of two or more numbers is indicated, as in 4m or 5a2, without any symbol of multiplication, it is customary to think of the multiplication as already performed.

Thus 4m2 ÷ 2m = 4m2/2m, not (4m2/2)m.”

This equation (original to the authors’ text) has the same basic form of Expression 1, with the only difference being all real numbers are used in Expression 1. I’m guessing that all of you agree that the expression to the immediate right of the equal sign in the example above is the correct way to interpret the expression on the Left. And of course, the expression on the right simplifies down to simply 2m. The other form, which you get if you do strict PEMDAS without any other consideration, simplifies to 2m3. You all know the 2m is correct, right? That’s the way we all learned how to process variables with coefficients. So if m = 2, we should expect an answer of 4, not 16. 4(4) ÷ 2(2) = 16 ÷ 4 = 4. If you do it the strict PEMDAS only way, then you get 4(4)/2 * 2 = 16/2 * 2 = 16. Wrong answer, therefore, the wrong method to solve.

[Additional notes and evidence added 08/05/2023 (italicized).]

From Wolfram MathWorld, the following article on Precedence, which you get to from the WolframAlpha description of “Order of Operations,” discusses the concept of “advanced operations” that “bind more tightly.” It then contrasts that with “simple operations.” Although Wolfram does not detail what those two concepts embrace, multiplication by juxtaposition (or “implied multiplication”) would be one of those advanced operations that “bind more tightly” and thus have precedence (what is an exponent or factorial if not implied multiplication?), while a “simple operation” would include any expression with all operational signs extant and leave nothing to be implied.

In Wolfram MathWorld’s discussion of the “solidus,” they confirm that most textbooks teach that an equation in the form of a ÷ bc should be interpreted as a ÷ (bc) and NOT ac ÷ b, and then acknowledge that most computational languages, including Wolfram, treat the expression without parentheses in a strictly linear manner without acknowledging the implied multiplication. They say that in order to solve the problem the way the textbooks teach it, or the way most people who actually use real-world equations where it makes a difference, you MUST enter the parentheses in most computational languages (that is the context of MathWorld), including in most calculators. Here’s the definition:

This is solid evidence that the answer to Expression 1 should be 1 and not 16. I’m not blowing smoke, and I’m not trolling. Those who get the answer 16 should rethink their logic.

[Here ends the addition of new material on 08/05/23]

Let’s make the expression in question look a little more like the example I just gave, and remember, that is from an advanced algebra book written by a couple math professors from Columbia U and the U of Southern California. For the expression in question, let m = (2 + 2) and substitute it into the expression, giving us Expression 11.

Expression 11

8 ÷ 2m

You Sixteeners should see right away the error of your PEMDAS-only ways. We don’t break the coefficient away from the variable, so we wouldn’t break it away from what we substitute into the variable. It works both ways. Just like the problem from the textbook, we can clearly see that the answer to “simplified” expression is not 4m, but 4/m. Since we let m = (2 + 2), 4/(2 + 2) = 4/4 = 1. QED.

If that historical example isn’t enough to convince you that PEMDAS alone isn’t correct, consider the following based on my discussion of right- and left-distributive above. As the original equation is written, I’ve already thoroughly demonstrated that the part of the main expression right of the division sign must be treated as an inseparable expression. But for the sake of argument, let’s consider the contention that PEMDAS alone applies without calling on the Distributive Property. As many Sixteeners have demonstrated, this works out to (8/2) * (2 + 2), or 16. However, if we substitute the right-distributive form of the expression in question for the left distributive form, we get Expression 12. Remember, whether right or left, the two expressions are considered equal, or identical.

Expression 12

8 ÷ (2 + 2)2

Expression 12 is, by definition, identical to Expression 1, so we should expect the same answer, right? However, if you apply the PEMDAS-only method on this form of the equation, you get (8/4) * 2, or 4. This PROVES that PEMDAS alone is not sufficient to solve the whole expression, because you get different answers for identical expressions! That is logically impossible in a first-order math equation with real numbers. NOTE: Because I demonstrated that the expressions are themselves equal or identical before solving them, you can’t turn around and say they’re not identical because they get different answers with PEMDAS-only. Distributive property is a law; PEMDAS is a convention. Law trumps convention.

QED

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A Quick Note About Your Calculators

Most basic calculators don’t typically recognize the Distributive Property from what I’ve seen. In fact, if you read the manuals of most scientific calculators, you’ll find them admitting that you may need to use parentheses to force it to act according to the laws of mathematics in some instances. (See definition of Solidus above.) So don’t trust your calculators. In fact, I’m willing to bet whoever submitted that problem in the first place most likely knew that about calculators and is rolling on the floor laughing their butts off that many were fooled by the calculator, thus resulting in the social media melee over the problem.

A Comparison to Greek

Since this is primarily a blog about interpreting the Greek New Testament (and occasionally the Hebrew/Aramaic Old Testament), I couldn’t help but notice that the Commutative and Distributive Properties apply to Greek adjectives and nouns. In Greek, if the definite article is with the adjective and the adjective modifies a noun, then it doesn’t matter which comes first. The phrases are still translated the same way (article+adjective+noun = noun+article+adjective). The same goes for the noun. If the article is with the noun, then the noun is the subject of the phrase and the adjective is the predicate: (article+noun+adjective = adjective+article+noun). The grammatical case, number, and gender of the noun (subject, object, possessive, etc.) distribute through the article and any adjectives associated with it. Who knew solving a math problem would lead me to discover that Greek grammar has some mathematical logic to it!

My opinions are my own, but my well-reasoned conclusions are indisputable!

Scott

Addendum (added 5/14/23)

PEMDAS is shortsighted. It ignores mathematical properties (that is, laws), which take precedence over order of operations like PEMDAS (an accepted convention, not a law or property). I would suggest the “P” in PEMDAS should not only stand for Properties first, but secondarily for Parentheses. Properties are to PEMDAS what the U.S. Code is to subregulatory guidance in legislative speak. Subregulatory guidance has no authority without the force of law behind it. PEMDAS has no power without the force of mathematical properties behind it.

If you use strictly PEMDAS without recognizing the Distributive Property, you wind up with the following, as the sixteeners are interpreting this:

8 ÷ 2(2+2)

Becomes

8 ÷ 2(4)

Becomes

8 ÷ 2 * 4

But let’s not stop there. This becomes, using the multiplicative inverse to change from division to multiplication:

(8 * 1/2) * 4

And applying the Associative property of multiplication, this becomes

8 * (1/2 * 4)

Substituting back in the original parenthetical expression

8 * (1/2 * (2+2))

Look at what happens to the last half of the equation: You’re now dividing (2+2) by 2 when the syntax of the original expression clearly indicates they should be multiplied together using the Distributive Property. The sixteeners have fundamentally changed the syntax of the original expression, which is a violation of the whole process of solving the equation. That’s why 16 is incorrect!

You can’t simply dismiss the Distributive Property here. A property is a law of math that essentially requires no proof. It is superior to and has precedence over PEMDAS, which is not a property at all and, to my knowledge, has never been proven to account for all things could be going on in an expression. That’s why Property should come before parentheses in PEMDAS.

Why You Can’t Trust Graphing Calculators

Look at how Wolfram Alpha handles the basic form of the expression in question as we gradually add information. All images grabbed from Wolfram Alpha on 5/14/23 around 10:30 pm CST). NOTE: I have an acknowledged request to Wolfram Alpha to investigate why the following is happening.

Now provide the values for x, a, b.

Substitute in 8 for x.

Add parentheses with the substitution; same result; solution is 1.

Then put in the 2+2 directly. Solution again is 1. Note that it’s NOT (8/a) * (2+2)

But when I directly enter a value for a, the logic changes.

And the expression as written behaves similarly.

So clearly PEMDAS by itself is not sufficient to process the problem, because you can see that even some of the best graphing calculators don’t process the basic form of the equation consistently. Arguments from your graphing calculator don’t cut it for me. Those are just AI. This is a real demonstration of faulty logic in certain formats. You can’t have two different answers to the same expression. The answer 1 is right; 16 is wrong.

Still Not Convinced? (Added weekend of 5/20/23)

What happens to the way you solve the problem if you change the 2 to a negative sign?

8 ÷ -(2 + 2)

Because the negative sign implies that what is inside the parentheses is multiplied by-1, would you PEMDAS-only proponents then have (8 ÷ -1) x (2 + 2) = -32? ABSOLUTELY NOT! Even the Sixteeners have to admit that the problem should be read as 8 ÷ -4 = -2, thus proving my point that what is outside a parenthetical expression (in this case, -1) and multiplied by implication must be solved first to fully deal with the parentheses.

Or how about if the problem is 6 ÷ 3!? The expression 3! represents an implied multiplication relationship, just as 2(2+2) is. So if it’s implied multiplication, is it then deconstructed to 3*2*1 or 1*2*3? Do you see the problem if you deconstruct it like that? Which order?!? According to the logic of the Sixteeners, it should be. But of course that’s silly. You wouldn’t break up the factorial, just as you shouldn’t break up the two factors of 2(2+2) and make one a divisor.

Making It Real

Here are a few examples of how applying PEMDAS-only to real-world formulas could potentially be disastrous. I posted the following examples on a Facebook post dedicated to one of the viral equations and got no end of criticism for proving PEMDAS wasn’t relevant to solving the problems, because the values now had units of measurement applied, which automatically groups the expressions without the need to resort to extra parentheses or brackets. (I cleaned this up a bit because of the limitations of responding on an iPhone that doesn’t have ready access to the obelus symbol that I’ve found.)

What is the context of the equation? Is it a velocity formula, where v= d/t with d = 36 miles and t = 6(2 + 2 + 2) hours = 36 hours? Then v = 1 mile/hour. Going 36 miles in 36 hours does NOT yield a velocity of 36 miles/hour!

Is it a density formula, where D = m/V with m = 36 kg and V = 6(2 + 2 + 2) cubic cm = 36 cubic cm? Then the answer is 1 kg/cubic cm. Who says the obelus doesn’t have grouping powers!

Johnny, Freddy, Rita, Ginger, Gary, and Nancy each have two apples, two oranges, and two bananas to share with their classmates. The class has 36 people including themselves and the teacher. How many pieces of fruit may each person have? 36 classmates ÷ 6(2 + 2 + 2) classmates*pieces of fruit/classmate) = 36 classmates / 36 pieces of fruit = 1 classmate for every 1 piece of fruit. It’s not 36 pieces of fruit for each classmate!

The resulting equations are PEMDAS-naive, proving that PEMDAS is not always necessary to solve these types of expressions.

[1] Reitz, H. L. & Crathorne, A. R. College Algebra, Third Ed. New York: Henry Holt and Co., 1929, pp. 4–5.

[2] Ibid., p. 18

[3] If the parenthetical part of the expression has an exponent, you would follow PEMDAS process the exponent before distributing the a through the result (e.g., a(b + c)2 = a(b2 + 2bc + c2) à ab2 + 2abc + ac2.

[4] See the definition at Distributive — from the MathWorld Classroom (wolfram.com) (accessed 04/27/23), where Wolfram also indicates the concept is part of 5th grade math standards in California. The fact that it is a 5th grade standard may explain why the multiplication sign is used.

[5] See a more detailed description at distributive – Wolfram|Alpha (wolframalpha.com) (accessed 04/28/23). This more detailed description includes both expressions, with and without the multiplication sign.

[6] Op. Cit., Wolfram|Alpha.

[7] Hawkes, Herbert E., Luby, William A., and Touton, Frank C. Second-Year Algebra, Enlarged Edition. Boston: Ginn and Company, 1935, p. 19.

April 13, 2023

Some Thoughts on Inerrancy

Filed under: 2 Peter,2 Timothy,Biblical Studies,Deuteronomy,Faith, Faithfulness,Hebrews,John Gospel of,Luke Gospel of,Psalms,Reliability of Scripture,Romans,Textual Criticism — Scott Stocking @ 11:00 pm
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He humbled you, causing you to hunger and then feeding you with manna, which neither you nor your ancestors had known, to teach you that man does not live on bread alone but on every word that comes from the mouth of the Lord.[1]

Your word is a lamp for my feet, a light on my path.[2]

Heaven and earth will pass away, but my words will never pass away.[3]

Again Jesus said, “Peace be with you! As the Father has sent me, I am sending you.” And with that he breathed on them and said, “Receive the Holy Spirit. If you forgive anyone’s sins, their sins are forgiven; if you do not forgive them, they are not forgiven.”[4]

For I am not ashamed of the gospel, because it is the power of God that brings salvation to everyone who believes: first to the Jew, then to the Gentile. For in the gospel the righteousness of God is revealed—a righteousness that is by faith from first to last, just as it is written: “The righteous will live by faith.”[5]

All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness, so that the servant of God p may be thoroughly equipped for every good work.[6]

For the word of God is alive and active. Sharper than any double-edged sword, it penetrates even to dividing soul and spirit, joints and marrow; it judges the thoughts and attitudes of the heart.[7]

Bear in mind that our Lord’s patience means salvation, just as our dear brother Paul also wrote you with the wisdom that God gave him. He writes the same way in all his letters, speaking in them of these matters. His letters contain some things that are hard to understand, which ignorant and unstable people distort, as they do the other Scriptures, to their own destruction.[8]

The other night, just before I was ready to turn in, a long-time acquaintance and friend, Terry, IM’d me and asked me about biblical inerrancy. I hadn’t really given that much thought since seminary because I’ve been pretty settled on the issue for some time, but I thought I’d put down a few of my thoughts that came to mind as he and I briefly chatted.

  1. I believe 2 Timothy 3 that God’s word is inspired, that is, God-breathed. However, I also believe he speaks it both directly and through his fallible servants in a fallen world. He did this through his prophets in an authoritative way, but I don’t doubt that they may have added “local color” to their prophecies.
  2. I believe Jesus commissioned his apostles (and perhaps a few of their successors) with an ex cathedra authority, tempered by mutual accountability, to establish the primitive structure of the early Christian communities, the core doctrines of the faith, and vital practices to share and spread that faith. I do not believe this ex cathedra authority survived past the first or second generation of believers.
  3. I believe the historical books of the OT, from Genesis through Kings and Chronicles, were collated from extant copies of original writings and official journals. Some of these texts have obvious signs of an editor long after the recorded events took place (e.g., 2 Chronicles 20:26).
  4. I believe the Hebrews had in place a diligent process to copy their texts to ensure their accuracy and fidelity from one generation of texts to the next.
  5. I believe the NT autographs (original letters and Gospels) were without error doctrinally and textually. However, since we can be relatively certain that none of these have survived the ravagees of time, this statement has qualified significance. As the letters were copied in scriptoriums, human error inevitably made its way into the successive copies.
  6. I believe the science of the study of textual transmission is more than sufficient in most cases to identify when and where these errors entered into the text and which of the variant readings are the most reliable. I do not believe any of the disputed variations affect any doctrine of Scripture, especially since most doctrines do not rely solely on any one single text. The eclectic Greek text is the best modern version to use, as it takes into account the opinions and research of several qualified scholars.
  7. I believe “the Church of Christ on earth is essentially, intentionally, and constitutionally one”[9]; the differences we see among and within denominational traditions are reflections of the diversity of God’s kingdom. If we can appreciate the diversity in God’s creation, with hundreds of different varieties within each species, then why should we expect that the local manifestations of the church be copycats? I do not believe that such diversity, by itself, disqualifies the Scriptures in any way.
  8. I believe that anyone who can hear or read the Word of God translated into their own language, regardless of version, can understand and respond to the Gospel at its most basic level. The study of the Word of God in its original languages adds depth and color to the story and may convince some who think the principles taught therein are archaic, pedantic, or irrelevant.
  9. I believe that above all else, love for one another founded in the love God has shown and is still showing us is the highest virtue for the Christ-follower at least, and for all humanity generally, regardless of their belief. Love is necessary for the survival of the human race; faith and faithfulness are necessary for salvation; hope is necessary for our security in the faith and our strength to love one another. All other arguments pale in comparison to the power and testimony of faith, hope, and love.

Of course, this list is nowhere close to exhaustive, but I pray that it gets you, the reader, thinking about what you believe about Scripture and the testimony you bear as Christ-followers. Peace to all!

My thoughts are my own, and annotated when borrowed from elsewhere.

NOTE: If you have some other Scriptures you’d like to add on the reliability of God’s word, feel free to add them in the Comments section. I’d love to hear from you!

Pastor Scott Stocking, M.Div.

[1] Deuteronomy 8:3. The New International Version. 2011. Grand Rapids, MI: Zondervan.

[2] Psalm 119:105. The New International Version. 2011. Grand Rapids, MI: Zondervan.

[3] Luke 21:33. The New International Version. 2011. Grand Rapids, MI: Zondervan.

[4] John 20:21–23. The New International Version. 2011. Grand Rapids, MI: Zondervan.

[5] Romans 1:16–17. The New International Version. 2011. Grand Rapids, MI: Zondervan.

[6] 2 Timothy 3:16–17. The New International Version. 2011. Grand Rapids, MI: Zondervan.

[7] Hebrews 4:12. The New International Version. 2011. Grand Rapids, MI: Zondervan.

[8] 2 Peter 3:15–16. The New International Version. 2011. Grand Rapids, MI: Zondervan.

[9] Campbell, Thomas. Declaration and Address.

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