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Reflexive relationships in the Bible
1. Reflexive property
A relation
R on set
A is
reflexive if for every
x in
A,
x R x.
This can be written in mathematical form as follows.
This is read as "
for all x in (set) A, (condition) x R x (is true)"
2. Universal quantification
Universal quantification involves "
for all" within a certain domain set.
The symbol "
∀" is read as "
for all".
An example is as follows.
∀ x ∈ { 1 , 3 , 5 } : x is an odd number
This is read as "
for all x in the set 1, 3, 5, x is an add number"
The symbol "∈" is read as "in" which is short for "is an element of" (the domain set that follows).
The symbol ":" (colon) can be thought of as saying "such that" or "it is true that" (what follows).
3. Peano: symbols
The "
there exists" symbol "
∃", and many others, were created by the Italian mathematician Giuseppe Peano (1858-1932), many by reversing letters or turning them upside down.
Peano created the "
or" symbol as "
∨" from the letter "
v" starting the Latin word
"vel" ≈ "or". The "
and" symbol "
∧" is an upside down "
or" symbol.
Other mathematicians then followed this convention in creating more symbols over time. One such symbol was the "
for all" symbol "
∀" first used in 1935 by logician Gerhard Gentzen (1909-1945) and called it, in German, "
All-Zeichen", the "
all character"
4. Management
Rather than specify what one has done, management may generalize what you have done as "
Thank you for all that you do".
Translation: It is too hard to actually determine what you did or list everything that you did. It is much less for us to make a vague general statement that covers everything that you might have done.
Here is the math for "
Thank you for all that you do".
∀ x ∈ {
what you do } :
thank you
5. Thank and think
6. Reflexive laughing
An example of a
reflexive rule is the following.
It is good to be able to laugh at oneself.
Have you heard that being able to laugh at yourself may help
lengthen your life?
Here, the "
laugh at" relation is applied
reflexively to itself. That is, relating "
laugh at" from "
you" to "
you".
7. Not reflexive laughing
Have you heard that laughing at your spouse may help
shorten your life?
Here, the "
laugh at" relation is not applied reflexively.
8. Laughing summary
Here is the diagram to summarize these laughing ideas.
The relation
R as "
is the same sex/gender as" is reflexive, since
person
x "
is the same sex/gender as" person
x.
Does a rule apply to itself? If so, the rule is reflexive.
9. Self reference
Are you the same sex or gender, whatever that is, as yourself?
Except for negation, most logical (not human) rules are reflexive.
Do some people apply rules to others but not to themselves?
10. Do as I say
Whenever someone says, "
Do as I say, not as I do" they are applying a rule to others but not to them-self. That is, the rule, to them, is not a reflexive rule. In such a case, one might call the person a "
hypocrite" using the modern sense of the word.
11. Everyone do this
The pattern becomes more clear with a diagram. The rule applies to everyone, which includes self. Negation results in interesting ideas.
Math proof that disproves itself (incompleteness)
Halting problem that detects itself halting (incomputability)
Minimal programs that detect randomness
12. Deuteronomy 34:5 Moses
Does Moses write reflexively about himself in this verse?
Deuteronomy 34:5 So Moses the servant of the LORD died there in the land of Moab, according to the word of the LORD. [kjv]
… ετελευτησεν … οικετης … ρηματος … [lxx]
Did Moses write about this before it happened?
Did someone add this after it happened? If so, did Moses write Deuteronomy?
Does it really matter who write this last verse?
13. Deuteronomy 34:5
KJV: So Moses the servant of the LORD died there in the land of Moab, according to the word of the LORD.
Hebrew: וימת שם משה עבד יהוה בארץ מואב על פי יהוה׃
Greek: και ετελευτησεν μωυσης οικετης κυριου εν γη μωαβ δια ρηματος κυριου
14. Self-reference and recursion
There is an entire field of self-reference having to do with self-similar objects call fractals and with recursive references of code to (smaller instances) of similar or the same code.
These topics are left for another time, though some examples here could be considered under that category. For example, "
ditches" in "
ditches".
15. Meta prefixes
16. Self-referential and reflexive
Here are some places where one might see self-referential and reflexive ideas (and which could fit as "
meta" prefixes).
News about news
Actors playing actors
Movies about movies
17. Silence
“Silence in the face of evil is itself evil: God will not hold us guiltless. Not to speak is to speak. Not to act is to act. Dietrich Bonhoeffer (German Lutheran pastor, theologian and anti-Nazi dissident)
18. 1 Timothy 6:15 Repetitive phrase
1 Timothy 6:15 Which in his times he shall shew, who is the blessed and only Potentate, the King of kings, and Lord of lords; [kjv]
… βασιλευς των βασιλευοντων … κυριος των κυριευοντων [gnt]
Some phrases are repeated in a reflexive self-referential or "
meta" way.
King of Kings
Lord of Lords
This can be for emphasis. Could it be a reflexive reference in any way?
19. 1 Timothy 6:15
KJV: Which in his times he shall shew, who is the blessed and only Potentate, the King of kings, and Lord of lords;
Greek: ην καιροις ιδιοις δειξει ο μακαριος και μονος δυναστης ο βασιλευς των βασιλευοντων και κυριος των κυριευοντων
Latin: quem suis temporibus ostendet beatus et solus potens rex regum et Dominus dominantium
Wycliffe: whom the blessid and aloone miyti king of kyngis and Lord of lordis schal schewe in his tymes.
Luther: welche wird zeigen zu seiner Zeit der Selige und allein Gewaltige, der König aller Könige, und Herr aller Herren,
20. Blind leading the blind
Matthew 15:14 Let them alone: they be blind leaders of the blind. And if the blind lead the blind, both shall fall into the ditch. [kjv]
… τυφλος … βοθυνον … [gnt]
In Matthew 15:14, Jesus uses the example of the "
blind" leading the "
blind".
This is an example of a reflexive relationship since the blind are leading both others who are blind and themselves who are blind.
21. Exodus 3:14
At the time that Moses asks God to identify himself, Moses receives the following reply.
Exodus 3:14 And God said unto Moses, I AM THAT I AM: and he said, Thus shalt thou say unto the children of Israel, I AM hath sent me unto you. [kjv]
… εγω ειμι ο ων … [lxx]
What exactly might the saying "
I am that I am" mean?
Is this similar or different to a saying of the cartoon character "
Popeye"? "
I yam what I yam and that's all what I yam" is the saying of Popeye the sailor man.
22. Exodus 3:14
KJV: And God said unto Moses, I AM THAT I AM: and he said, Thus shalt thou say unto the children of Israel, I AM hath sent me unto you.
Hebrew: ויאמר אלהים אל משה אהיה אשר אהיה ויאמר כה תאמר לבני ישראל אהיה שלחני אליכם׃
Greek: και ειπεν ο θεος προς μωυσην εγω ειμι ο ων και ειπεν ουτως ερεις τοις υιοις ισραηλ ο ων απεσταλκεν με προς υμας
Latin: dixit Deus ad Mosen ego sum qui sum ait sic dices filiis Israhel qui est misit me ad vos
Wycliffe: The Lord seide to Moises, Y am that am. The Lord seide, Thus thou schalt seie to the sones of Israel, He that is sente me to you.
Luther: Gott sprach zu Mose: Ich werde sein, der ich sein werde. Und sprach: Also sollst du den Kindern Israel sagen: Ich werd's sein, der hat mich zu euch gesandt.
Spanish: Y respondió Dios a Moisés: YO SOY EL QUE SOY. Y dijo: Así dirás a los hijos de Israel: YO SOY me ha enviado a vosotros.
23. An actor as a hypocrite is not real
Many times Jesus appears to rebuke the Pharisees as "
hypocrites", in the modern sense, because the apply rules to others but not to themselves, reflexively. On closer inspection, and using the definition of "
hypocrite" at the time, this is not quite what is happening.
The modern definition of "
hypocrite" appears to come from a misinterpretation of what Jesus says in Matthew 7:3-5 (plank or splinter in the eye).
When Jesus says "
You hypocrites", instead of the modern sense, it might be better read as "
You actors" as in "
You pretenders" or "
Get real" or "
Get in touch with reality" or "
Get in touch with the truth". Substituting "
actors" or "
pretenders" might make for a better translation than "
hypocrites".
24. Matthew 7:1-2 Here comes the judge, but just barley
Matthew 7:1 Judge not, that ye be not judged. [kjv]
… κρινετε … κριθητε [gnt]
Barley is a cereal grain, known from ancient times, that has many uses. The usual process is to
seed it,
grow it,
harvest it, break it up, and winnow to separate the grain (fruit) from the chaff so that the grain can be used.
The ancient Greek word
"κρίνω" ≈ "separate" appears to be the source of the ancient Greek word
"κριθή" ≈ "barley" in that the grain needed to be separated to be used - allowing a play on words
"κριθήτε" ≈ "judged" as used by Jesus.
Since separation is an important and sometimes misunderstood part of the three-step judgment process (separation of guilt or innocence, sentence, punishment) the connections can be interesting in, say, the context of Matthew 7.
25. Thou shalt not murder
Exodus 20:13 Thou shalt not kill. [kjv]
לא … [he]
… φονευσεις [lxx]
One of the 10 commandments has to do with killing or murder. The Hebrew appears to be against unlawful killing resulting in a blood guilt.
The Hebrew word
"לא תרצח" (lo tirt-zach) ≈ "murder, blood guilt" allows killing in certain circumstances such as war, capital punishment, self-defense, etc.
26. 1 John 1:10 We say we have no sin
1 John 1:10 If we say that we have not sinned, we make him a liar, and his word is not in us. [kjv]
… ημαρτηκαμεν … [gnt]
Whenever we say that we have no sin, we are making a self-referential reflexive statement.
27. 1 John 1:10
KJV: If we say that we have not sinned, we make him a liar, and his word is not in us.
Greek: εαν ειπωμεν οτι ουχ ημαρτηκαμεν ψευστην ποιουμεν αυτον και ο λογος αυτου ουκ εστιν εν ημιν
Latin: si dixerimus quoniam non peccavimus mendacem facimus eum et verbum eius non est in nobis
Wycliffe: And if we seien, we han not synned, we maken hym a liere, and his word is not in vs.
Luther: So wir sagen, wir haben nicht gesündiget, so machen wir ihn zum Lügner, und sein Wort ist nicht in uns.
28. Romans 3:23 For all
Romans 3:23 For all have sinned, and come short of the glory of God; [kjv]
The term "
for all" is a universal quantifier that applies to all.
Therefore, it applies to individuals.
Discuss the statement "
I am good" in terms of reflexive self-reference.
29. Romans 3:23
KJV: For all have sinned, and come short of the glory of God;
Greek: παντες γαρ ημαρτον και υστερουνται της δοξης του θεου
Latin: omnes enim peccaverunt et egent gloriam Dei
Wycliffe: For alle men synneden, and han nede to the glorie of God;
Tyndale: for all have synned and lacke the prayse yt is of valoure before God:
Luther: Denn es ist hier kein Unterschied; sie sind allzumal Sünder und mangeln des Ruhms, den sie an Gott haben sollten,
30. Luke 18:13 Myself a sinner
Luke 18:13 And the publican, standing afar off, would not lift up so much as his eyes unto heaven, but smote upon his breast, saying, God be merciful to me a sinner. [kjv]
… μοι … αμαρτωλω [gnt]
A "
sinner" can call himself a "
sinner".
31. Luke 18:13
KJV: And the publican, standing afar off, would not lift up so much as his eyes unto heaven, but smote upon his breast, saying, God be merciful to me a sinner.
Greek: και ο δε τελωνης μακροθεν εστως ουκ ηθελεν ουδε τους οφθαλμους επαραι εις τον ουρανον επαραι αλλ ετυπτεν εις το στηθος αυτου εαυτου λεγων ο θεος ιλασθητι μοι τω αμαρτωλω
32. Matthew 27:42 Save oneself
Matthew 27:42 He saved others; himself he cannot save. If he be the King of Israel, let him now come down from the cross, and we will believe him. [kjv]
αλλους … σωσαι… [gnt]
alios … salvum … [v]
While Jesus was on the cross, some mocked him as saving others but not himself.
In effect, Jesus was not saving himself to save others.
The Latin word
"salvos" ≈ "save" and is the origin of the English word "
salvation".
33. Matthew 27:42
KJV: He saved others; himself he cannot save. If he be the King of Israel, let him now come down from the cross, and we will believe him.
Greek: αλλους εσωσεν εαυτον ου δυναται σωσαιει βασιλευς ισραηλ εστιν καταβατω νυν απο του σταυρου και πιστευσομεν αυτω επ αυτον
Latin: alios salvos fecit se ipsum non potest salvum facere si rex Israhel est descendat nunc de cruce et credemus ei
Luther: Andern hat er geholfen und kann sich selber nicht helfen. Ist er der König Israels, so steige er nun vom Kreuz, so wollen wir ihm glauben.
34. Reflexive deception
2 Timothy 3:13 But evil men and seducers shall wax worse and worse, deceiving, and being deceived. [kjv]
πονηροι … γοητες … πλανωντες … πλανωμενοι [gnt]
mali … seductores … peius errantes … errorem … [v]
… ubilai … airzjai … airzjandans… [got]
Timothy was Bishop of Ephesus. In 2 Timothy 3:13, Paul warns Timothy of "
evil" men "
deceiving" and "
being deceived". The word for "
evil" appears to be that of being burdened down with the cares and concerns of this world.
Deception can be reflexive in that one may start to believe one's own lies. This often happens when, in deceiving others, one starts to believe the deception being used.
35. Vladimir Lenin
36. 2 Timothy 3:13
KJV: But evil men and seducers shall wax worse and worse, deceiving, and being deceived.
Greek: πονηροι δε ανθρωποι και γοητες προκοψουσιν επι το χειρον πλανωντες και πλανωμενοι
Latin: mali autem homines et seductores proficient in peius errantes et in errorem mittentes
Wycliffe: But yuele men and disseyueris schulen encreese in to worse, errynge, and sendinge in to errour.
Gothic: ith ubilai mannans jah liutai theihand du wairsizin, airzjai jah airzjandans.
37. 1 Timothy 1:8
1 Timothy 1:8 But we know that the law is good, if a man use it lawfully; [kjv]
… νομος … νομιμως … [gnt]
Using the "
law" "
lawfully" is a self-referential reflexive way of using the law.
Can you measure a ruler (e.g., yardstick) using a ruler? How about the same yardstick reflexively? Does that make sense?
In general, one might use a higher standard ruler to measure a lower standard ruler. With the security after the 911 attacks, it became harder to transport the "
official" platinum metal ruler standards around the world.
38. 1 Timothy 1:8
KJV: But we know that the law is good, if a man use it lawfully;
Greek: οιδαμεν δε οτι καλος ο νομος εαν τις αυτω νομιμως χρηται
Latin: scimus autem quia bona est lex si quis ea legitime utatur
Wycliffe: And we witen that the lawe is good, if ony man vse it lawefulli;
Luther: Wir wissen aber, daß das Gesetz gut ist, so sein jemand recht brauchet,
39. Deceiving heart
40. Matthew 19:16-17 Only one is good
Matthew 19:16 And, behold, one came and said unto him, Good Master, what good thing shall I do, that I may have eternal life? [kjv]
… αγαθον … [gnt]
19:17 And he said unto him, Why callest thou me good? there is none good but one, that is, God: but if thou wilt enter into life, keep the commandments. [kjv]
… αγαθου … αγαθος … εντολας [gnt]
Jesus says that no one is
"good" but God. If Jesus is God, then if no one is good but God, then is Jesus good? Is the inference of a reflexive relationship appropriate here? Jesus uses the Greek word for "
bad" for those who are "
fallen" and need the "
good news" or "
Gospel".
41. Matthew 19:16
KJV: And, behold, one came and said unto him, Good Master, what good thing shall I do, that I may have eternal life?
Greek: και ιδου εις προσελθων ειπεν αυτω ειπεν διδασκαλε αγαθε τι αγαθον ποιησω ινα εχω σχω ζωην αιωνιον
42. Matthew 19:17
KJV: And he said unto him, Why callest thou me good? there is none good but one, that is, God: but if thou wilt enter into life, keep the commandments.
Greek: ο δε ειπεν αυτω τι με λεγεις αγαθον ουδεις αγαθος ει μη ερωτας περι του αγαθου εις εστιν ο θεος αγαθος ει δε θελεις εισελθειν εις την ζωην τηρησον εισελθειν τηρει τας εντολας
Some ideas can be done reflexively that might not be what was intended.
Suffer for Christ - inflict pain on oneself.
Don't hide your light under a bushel basket. Form an exclusive monastery.
43. Matthew 5:15 Light a candle
Matthew 5:15 Neither do men light a candle, and put it under a bushel, but on a candlestick; and it giveth light unto all that are in the house. [kjv]
… καιουσιν λυχνον … μοδιον … λαμπει … [gnt]
44. Matthew 5:15
KJV: Neither do men light a candle, and put it under a bushel, but on a candlestick; and it giveth light unto all that are in the house.
Greek: ουδε καιουσιν λυχνον και τιθεασιν αυτον υπο τον μοδιον αλλ επι την λυχνιαν και λαμπει πασιν τοις εν τη οικια
45. Self-inflicted suffering
Philippians 1:29 For unto you it is given in the behalf of Christ, not only to believe on him, but also to suffer for his sake; [kjv]
… χριστου … πασχειν [gnt]
1 Peter 2:21 For even hereunto were ye called: because Christ also suffered for us, leaving us an example, that ye should follow his steps: [kjv]
… χριστος επαθεν … [gnt]
Martin Luther, and others, would, at times, self-inflict pain on themselves to "
suffer for Christ".
Consider the following verses.
Is this an appropriate response? Why or why not? Explain.
46. Philippians 1:29
KJV: For unto you it is given in the behalf of Christ, not only to believe on him, but also to suffer for his sake;
Greek: οτι υμιν εχαρισθη το υπερ χριστου ου μονον το εις αυτον πιστευειν αλλα και το υπερ αυτου πασχειν
Latin: quia vobis donatum est pro Christo non solum ut in eum credatis sed ut etiam pro illo patiamini
Wycliffe: but to you cause of heelthe. And this thing is of God. For it is youun to you for Crist, that not oneli ye bileuen in hym, but also that ye suffren for hym;
Luther: Denn euch ist gegeben, um Christi willen zu tun, daß ihr nicht allein an ihn glaubet, sondern auch um seinetwillen leidet,
47. 1 Peter 2:21
KJV: For even hereunto were ye called: because Christ also suffered for us, leaving us an example, that ye should follow his steps:
Greek: εις τουτο γαρ εκληθητε οτι και χριστος επαθεν υπερ ημων ημιν υμων υμιν υπολιμπανων υπογραμμον ινα επακολουθησητε τοις ιχνεσιν αυτου
Latin: in hoc enim vocati estis quia et Christus passus est pro vobis vobis relinquens exemplum ut sequamini vestigia eius
Wycliffe: For to this thing ye ben clepid. For also Crist suffride for vs, and lefte ensaumple to you, that ye folewe the steppis of hym.
48. Compare you to yourself
According to Paul, instead of comparing our work to others, one should compare one's work to one's own work.
Galatians 6:4 But let every man prove his own work, and then shall he have rejoicing in himself alone, and not in another. [kjv]
… εργον … δοκιμαζετω … [gnt]
The word for "
prove" here is that of "
testing" and not a mathematical "
proof".
49. Galatians 6:4
KJV: But let every man prove his own work, and then shall he have rejoicing in himself alone, and not in another.
Greek: το δε εργον εαυτου δοκιμαζετω εκαστος και τοτε εις εαυτον μονον το καυχημα εξει και ουκ εις τον ετερον
Latin: opus autem suum probet unusquisque et sic in semet ipso tantum gloriam habebit et non in altero
Wycliffe: But ech man preue his owne werk, and so he schal haue glorie in him silf, and not in an othere.
Luther: Ein jeglicher aber prüfe sein selbst Werk, und alsdann wird er an sich selber Ruhm haben und nicht an einem andern.
50. Exercise
In exercise physiology, such as strength training, one should keep records of one's workouts and compare one's performance to oneself, and not to another person.
If someone lifts a lot of weight, one should not try to match that weight (which may cause injury). Rather, one should try to improve one's own performance to a prior performance.
51. Thought question
Can you think of any other reflexive relationships that might not be an appropriate interpretation of scripture?
52. End of page
