Posted on 01/05/2008 7:06:01 AM PST by NYer
You're correct no Protestant denomination because those Christian Churches broke away during the Reformation and thus have been labeled Protestant (protesting what they broke away from). However, there have always been Christian Churches that were not a part of the RCC, or EO.
Even during Jesus' ministry on Earth we see in Scripture churches that were not under the authority of the Apostles, but were acceptable to Jesus.
Luke 9:49-50 Now, John answered and said, "Master, we saw someone casting out demons in Your name, and we forbade him because he does not follow with us."
But Jesus said to him,"Do not forbid him, for he who is not against us is on our side."
The Didache, which was only discovered around 150 years ago reveals the local autonomy of early Christian Churches. Prior to the Reformation the Donatist's left. The Montanists, Novatians, Paulicians, Albigenses, Paterines, Petrobrussians, Henricians, Waldenses and Anabaptists all existed prior to the Reformation. Our understanding of these various Christian Churches is limited because during this period the RCC had emerged as the dominant State sponsored church. It was never in the RCC best interest to keep accurate records of these various Christian Churches and if they became large enough they were treated as a threat to the State.
Emerging from the Anabaptists you have Baptists, Quakers and Mennonite churches today.
The less liberal the Catholic Church in America becomes, the easier it will be to keep your parishoners.
I’m Assembly of God. I have good friends who are devout Catholics.
Each Church needs to preach the Gospel of Jesus Christ and lift up him name.
There are plenty of unsaved amongst all categories of people to fill all believeing Churches with worshipping Christians if we keep our eyes on Christ and stop bickering over petty things.
I do succumb from time to time - the ego does love to attack but I recognize the futility.
(1)Lofty goals but utimately even more sublime traps on the path. (2)See above ;-)
Ah, OK. Now I see what you meant. Then the second shooter wasn't perfect either. However, he still came closer to "perfection" than the first shooter did, because his shots landed closer to his intended targets (the first shooter's bullet holes) than her shots did to her intended target (the bullseye).
He hit dead center of the target no more accurately than she had.
But the center of the target isn't his standard for accuracy, becuase that's not what he aimed for.
Precision is about replication. But, you say, he replicated all of her shots. That is true, but in doing so he failed to replicate any of his own.
It doesn't matter, because it wasn't his goal to repeatedly hit a single point; he was trying to replicate HER shots, one by one. Again, I'm talking about the precision of his aim: The distribution of his shots is a measurement of that precision. But instead of comparing his bullet holes to the bullseye, we compare them to their intended targets, i.e. the first shooter's bullet holes.
A shot is accurate if it hits its mark, i.e. if it hits where the shooter wants it to. This depends on the precision of the shooter's aim, but is also affected by things like the calibration of certain parts of the gun. However, if the aim is imprecise, then the shots will tend to deviate from their intended marks (one may land a bit to the right, another up and to the left, etc.), and thus be inaccurate.
***
All true, but you're just throwing extra noise at me. Accounting for the throw of the weapon makes attaining accuracy & precision more difficult, but we're only dealing with the end results here.
See post 91 for the analogy describing accuracy and precision in an empirical sense.
If you're talking about measuring many things, the precision of your standard wouldn't be knowable.
Not necassarily. Like I said above, for this current example we can compare the second shooter's bullet holes to to his intended targets (i.e. the bullet holes of the first shooter) to obtain a measurement of his precision and accuracy.
in logic, it is meaningless to say that a statement is accurate if it is not defined precisely.
***
Meaningless or not knowable?
Perhaps not knowable, but also meaningless. We've switched to talking about logic now (instead of empiricism), and if a statement is not defined precisely enough then it is automatically false. Let's go back to your "The ball is round" statement and make it universal: "All balls are round." Now there are lots of round balls, but this statement is false due to its generality. On the other hand, if we've never seen anything like an American football, then we might not know that this statement is false, but then all we could say is "Every ball I know of is round."
The accuracy of something is unknowable unless tested against a precise standard, but something could be accurate without that test.
But I'm talking about the accuracy of the test itself. In the shooting example, we already know exactly where the bullseye is before shooting at it, but that's different than what I'm talking about. When making measurements, it's other way around: You're trying to find the bullseye by shooting at it! :)
Ah, OK. Now I see what you meant. Then the second shooter wasn't perfect either.
Whether he was "perfect" or not is an unknown. Measurements from the centers of her holes & his holes could possibly prove perfect, as her holes were only a "suggested" target for him. As I said, if he had put all of his bullets through the holes she had made, totally missing the target would have been a possible conclusion. His real targets were her holes + a distance of X from them.
However, he still came closer to "perfection" than the first shooter did, because his shots landed closer to his intended targets (the first shooter's bullet holes) than her shots did to her intended target (the bullseye).
Correct.
But the center of the target isn't his standard for accuracy, becuase that's not what he aimed for.
Doesn't matter what his standard was, as this is my hypothetical, not his. I set up the parameters in order to communicate a concept, not to discuss our shooters, their thinking or their skill. I think they used a target with a human form, so there wasn't actually a "center", but I needed a center for the purpose of my hypothetical, so I put one in.
I said, "Precision is about replication. But, you say, he replicated all of her shots. That is true, but in doing so he failed to replicate any of his own."
It doesn't matter, because it wasn't his goal to repeatedly hit a single point; he was trying to replicate HER shots, one by one.
Come up with your own hypothetical. This one's mine. Cue evil dictator laughter, "bwhahaha". Since he is my tool, I tell you his intent was exactly what I say it was, to hit the imaginary center of that target... man, did he get lucky, as he proved himself at least as good as the woman. ;o)
A graph for precision charts density. The more density you have, the more precise your standard. I was trying to get you unstuck from thinking it was only about spread by giving you an exception to that "rule", so I gave him an extra bullet. :o)
Again, I'm talking about the precision of his aim: The distribution of his shots is a measurement of that precision. But instead of comparing his bullet holes to the bullseye, we compare them to their intended targets, i.e. the first shooter's bullet holes.
I already told you that his true accuracy & the precision of his shots were better than hers. How would we know if his precision was better if she had not set standards for him first? His shots raised the shot density by each of her shots. Now, picture his shots without hers. His shot density could then be seen as the same as hers had been & we'd be talking about the spread of his shots.
No kidding, this is getting intractable! :)
Whether he was "perfect" or not is an unknown. Measurements from the centers of her holes & his holes could possibly prove perfect, as her holes were only a "suggested" target for him. As I said, if he had put all of his bullets through the holes she had made, totally missing the target would have been a possible conclusion. His real targets were her holes + a distance of X from them.
I assumed that he has aiming for her bullet holes, because given the example you provided, it seemed a reasonable assumption to make. Under this assumption, we know he wasn't "perfect" because his shots deviated ever so slightly from their intended targets. You are correct that had he been absolutely "perfect", we would have no way of knowing this by simply looking at the target; we would need some other way of tracking his shots.
Now, when you say "His real targets were her holes + a distance of X from them" do you mean that it made no difference where his bullets hit, as long as their holes overlapped the holes made by the first shooter; or do you mean that he was actually aiming for points slightly off the centers of the first shooter's bullet holes? If the former, I would say that it is true that he succeeded in "doubling" the hole in each case, thus demonstrating his precision; but still, pairs of holes with a large overlap would indicate more precision than pairs of holes with a small overlap. If the latter, then since we don't know X (nor do we know which side of the holes he was aiming at) then this makes the example somewhat ambiguous; however, X cannot be more than the diameter of a bullet hole, so although we don't know exactly where he was aiming we can still put an upper bound on his imprecision.
Doesn't matter what his standard was, as this is my hypothetical, not his. I set up the parameters in order to communicate a concept, not to discuss our shooters, their thinking or their skill. I think they used a target with a human form, so there wasn't actually a "center", but I needed a center for the purpose of my hypothetical, so I put one in.
This is your hypothetical, so of course you may set the parameters. However, you're using it as an example to discuss MY claim about certain uses of the words "precision" and "accuracy", so the example should speak to that, and not to other senses or definitions of the words. Now, the underlying assumption is that the second shooter was somehow trying to replicate the the first shooter's shots, unless...
Since he is my tool, I tell you his intent was exactly what I say it was, to hit the imaginary center of that target... man, did he get lucky, as he proved himself at least as good as the woman. ;o)
Now that's just uncanny! :)
A graph for precision charts density. The more density you have, the more precise your standard.
Yes, and here's what we can do with this example to measure his precision--that is, if you'll let me assume that he was aiming for the first shooter's bullet holes. ;) Imagine moving each one of the first shooter's bullet holes to this imaginary "center" while keeping the relative positions of the second shooter's bullet holes with respect to these holes intact. Then we obtain ONE bullet hole from the first shooter, and a very tight cluster from the second shooter, all overlapping the original hole. That's pretty darn precise!
I already told you that his true accuracy & the precision of his shots were better than hers. How would we know if his precision was better if she had not set standards for him first?
Strictly speaking, we don't know anything other than the information given in the example. However, since he was aiming at the first shooter's bullet holes--and we pretty much have to assume this if you want to say that his shots were more accurate and precise than hers--then we can pretty safely infer that if the second shooter had aimed at the same spot with each shot, then he would have made a pretty tight cluster (see above).
Now, picture his shots without hers.
Why? Since he was aiming at the first shooter's bullet holes, it is meaningless to consider the overall spread of his shots without hers there as a reference. It doesn't tell us anything about his accuracy and precision if we don't consider what he was shooting at.
I'd rather kick this around than do some of the stuff that I should be doing instead.
You realize we keep proving the first half of the statement you made back in post #48, right? A statement can be precise without being accurate, but it cannot truly be accurate without being precise. I've always been in agreement with the first half of your statement. It's the second half of the statement that I have a problem with.
Let's go back a little, to Mad Dawg's post #50 & then your response in post #63. The answer of your difference has to do with the standard each of you used. Zero Sum used the planet earth as the standard, while MD used the imaginary zero (PM @ equator) on a graph with imaginary lines we know as latitude & longitude.
Remember what I said earlier about common ground & talking past each other? One of you was shooting at the center of the target & the other was shooting at the bullet holes. Failure to recognize the other guy's standard doesn't affect the accuracy of the statements, only the ability to understand them.
I assumed that he has aiming for her bullet holes, because given the example you provided, it seemed a reasonable assumption to make.
Yes, it would be a reasonable assumption to make, but would it be the best assumption to make? If he'd replicated the holes she'd made, we would have to consider a couple of possibilities. 1) All of his shots were "perfect". 2) All of his shots missed the target. With the results we would have, there'd be no way to determine which of those two options was correct.
Under this assumption, we know he wasn't "perfect" because his shots deviated ever so slightly from their intended targets. You are correct that had he been absolutely "perfect", we would have no way of knowing this by simply looking at the target; we would need some other way of tracking his shots.
True.
Now, when you say "His real targets were her holes + a distance of X from them" do you mean that it made no difference where his bullets hit, as long as their holes overlapped the holes made by the first shooter;
No. I was giving "X" a value, but made it a variable, since I didn't know the exact value. Also, his targets could have been (center of her bullet holes) + X or (edge of her bullet holes) + X.
or do you mean that he was actually aiming for points slightly off the centers of the first shooter's bullet holes?
Yes, tho I would qualify it by saying that the edge of her bullet holes could have also been his real targets. Whether it was the center or edge would be an unknown. If he had used an edge of each bullet hole as his target, the value of X could be zero & it would be less than the radius of the bullet hole his shot would make. If it was the center of her holes, X could be the radius of the hole his bullet would make & it would be less than the diameter of his bullet holes.
If the former, I would say that it is true that he succeeded in "doubling" the hole in each case, thus demonstrating his precision; but still, pairs of holes with a large overlap would indicate more precision than pairs of holes with a small overlap.
False. Precision would be determined by the consistency of center (her holes) to center (his holes) measurements.
If the latter, then since we don't know X (nor do we know which side of the holes he was aiming at) then this makes the example somewhat ambiguous; however, X cannot be more than the diameter of a bullet hole, so although we don't know exactly where he was aiming we can still put an upper bound on his imprecision. You are correct about the upper bound, but only if he was shooting at the center of her bullet holes. Since you spoke of which "side" he was aiming for, that upper bound would be a radius & a diameter would show two unconnected holes.
This is your hypothetical, so of course you may set the parameters. However, you're using it as an example to discuss MY claim about certain uses of the words "precision" and "accuracy", so the example should speak to that, and not to other senses or definitions of the words.
Without the ability to talk about "any other senses", I'm forced into accepting your usage, as I'd be left with nothing to challenge it. Heads, you win. Tails, I lose.
Now, the underlying assumption is that the second shooter was somehow trying to replicate the the first shooter's shots, unless...
I said, "Since he is my tool, I tell you his intent was exactly what I say it was, to hit the imaginary center of that target... man, did he get lucky, as he proved himself at least as good as the woman. ;o)"
Now that's just uncanny! :)
Calculating the odds of it... his luck was astronomical!
I said, "A graph for precision charts density. The more density you have, the more precise your standard."
Yes, and here's what we can do with this example to measure his precision--that is, if you'll let me assume that he was aiming for the first shooter's bullet holes. ;) Imagine moving each one of the first shooter's bullet holes to this imaginary "center" while keeping the relative positions of the second shooter's bullet holes with respect to these holes intact. Then we obtain ONE bullet hole from the first shooter, and a very tight cluster from the second shooter, all overlapping the original hole. That's pretty darn precise!
That was a great way to express what I was saying!
I said, "I already told you that his true accuracy & the precision of his shots were better than hers. How would we know if his precision was better if she had not set standards for him first?"
Strictly speaking, we don't know anything other than the information given in the example. However, since he was aiming at the first shooter's bullet holes--and we pretty much have to assume this if you want to say that his shots were more accurate and precise than hers--then we can pretty safely infer that if the second shooter had aimed at the same spot with each shot, then he would have made a pretty tight cluster (see above).
Without her standards (**), there wouldn't be anything to gather together. That almost supports the second half of your statement in post #48, cept there you were talking about accuracy instead of precision. A statement can be precise without being accurate, but it cannot truly be accurate without being precise.
Can a statement be accurate without requiring it to be "true/false"?
I said, "Now, picture his shots without hers."
Why?
See (**) above.
And I still don't know why, since you keep using different definitions for those words than I am, so we keep talking past each other. See (*) below.
Let's go back a little, to Mad Dawg's post #50 & then your response in post #63. The answer of your difference has to do with the standard each of you used. Zero Sum used the planet earth as the standard, while MD used the imaginary zero (PM @ equator) on a graph with imaginary lines we know as latitude & longitude.
Remember what I said earlier about common ground & talking past each other? One of you was shooting at the center of the target & the other was shooting at the bullet holes. Failure to recognize the other guy's standard doesn't affect the accuracy of the statements, only the ability to understand them.
That's a good way to put it, but note the little smiley I gave in post 63: That was my little way of saying that he was correct, but that I was talking about a different definition of the word (see post 67). Don't you just love how we dragged you back into this, MD? :)
"I assumed that he has aiming for her bullet holes, because given the example you provided, it seemed a reasonable assumption to make." Yes, it would be a reasonable assumption to make, but would it be the best assumption to make?
Given my misreading of what you meant by "doubled" hole, yes. Of course I should have realized what you meant in the first place, but that's beside the point. ;)
"If the former, I would say that it is true that he succeeded in "doubling" the hole in each case, thus demonstrating his precision; but still, pairs of holes with a large overlap would indicate more precision than pairs of holes with a small overlap." False. Precision would be determined by the consistency of center (her holes) to center (his holes) measurements.
When I said, "If the former," I was referring to the hypothesis that "it made no difference where his bullets hit, as long as their holes overlapped the holes made by the first shooter." Again, it's your example so you may set the parameters, but I wasn't sure what you meant. That's why I qualified it with "if".
"If the latter, then since we don't know X (nor do we know which side of the holes he was aiming at) then this makes the example somewhat ambiguous; however, X cannot be more than the diameter of a bullet hole, so although we don't know exactly where he was aiming we can still put an upper bound on his imprecision." You are correct about the upper bound, but only if he was shooting at the center of her bullet holes. Since you spoke of which "side" he was aiming for, that upper bound would be a radius & a diameter would show two unconnected holes.
I meant with respect to the center. The second shooter could have been aiming for the edges, or he could have been aiming somewhere inside or outside the edges--talk about splitting hairs! Using center-to-center measurements, a hole with a center one diameter (2 radii) away from the center of another hole would just barely be touching the other hole. Now it's unlikely that he would aim this far away from the center since even the slightest error to the wrong side would result in a miss, but he could aim no further away if his intent was to overlap the holes.
Without the ability to talk about "any other senses", I'm forced into accepting your usage, as I'd be left with nothing to challenge it. Heads, you win. Tails, I lose.
Yes, that's the general idea. :) Actually, I already conceded in post 103 that you might be correct with respect to different meanings of the words, so why is this still a point of contention? (*)
Without her standards (**), there wouldn't be anything to gather together.
Correct. However, it is also true that without her standards the second shooter would not have aimed as he did, which is why it is meaningless to consider the overall distribution of his shots without hers there as a reference.
Now, if you want to define the "precision" of his shots by their overall spread and their "accuracy" as how close they came to their intended targets, then yes you are correct. However, in the case of his "accuracy" you take into account his intent, while in the case of his "precision" you don't, so this isn't a useful comparison--but maybe that was your point all along? Anyway, I was trying to be consistent and consider his intent in both cases. We could also be consistent and ignore it in both cases! :)
Can a statement be accurate without requiring it to be "true/false"?
Logically speaking, no it cannot. A statement is either true or false, not both (law of the excluded middle). However, a false statement can be "almost true" in the sense that it may be possible to define the statement more precisely in order to make it true.
Correction: See post 73, which was a response to post 67.
But but, MY definition is right! Because, well, because it just IS!
I trust that clears things up.
Seriously, my dirty little secret is that I was never sure that I understood the conversation in Collitch in 1965. So all these years I have blustered around pretending that I did and that I was correct in my distinction.
But since I am not really sure that I’m right (which pretty much characterizes most of my life anyway), I am watching you with gratitude as you hammer it out.
The virtue, I thought, of my way of using the words is that it seemed to present a useful pair of attributes of measurement. And, in my l’arnin’ ths topic came up in our first semester lab, as I said, the topic of which was “Theory of Measurement”.
Measurement, the attempt to associate usefully numbers with stuff, is something we take for granted, right up until we realize that if we measure the shoreline of Great Britain with rods we will get a smaller number than we get if we measure it with a foot-rule, and far smaller that if we measure it in “palms” or “digits”.
Then we have to ask, okay, what are we doing here?
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