A constraint logic system is a system of constraints whose solution needs to satisfy those constraints. One example is in the field of linear programming (which uses linear constraints) where all solutions are (points or lines) on the boundary of the convex region.

A unifier unifies the constraints without contradictions. A MGU (Most General Unifier) unifies the constraints without contradictions and has a minimal frontier in the lattice of constraints, a LFP (Least Fixed Point). If there are multiple solutions, a constraint logic system will attempt to find all MGU constraints (e.g., via backtracking).

More: Constraint logic: unification and resolution

Salt: You are the salt of the earth.
Light: You are the light of the world.
Candle: You are the candle of the _______.

Candle: You are the candle of the air.
Candle: You are the candle of heaven.
Candle: You are the kingdom of heaven.

A candle might represent a type of kingdom such as a church or group of believers. (Revelation).

[author variations]

More: Matthew 5:14: Light of the world

Some constraint logic features:

• Assumes consistent code word meanings.
• Uses most general unifiers.
• Backtracking to find additional solutions.

Model can be gradually tightened as more constraints resolved.

More: Syntax and semantics

More: Models and reality

More: Constraint logic: unification and resolution

Every language is a code. A definition is a meaning.

• Simple model: word to definition is 1 to 1.
• Realistic model: word to definition is many to many.

Constraint-logic (code-word) approach: (public and secret codes)

• Target language (to be decoded): many to many
• Source language (to be used): many to many

Approaches:

• Rules based: This does not work well.
• Pattern-based: Works well, but substantial source text in each language needed. (Google Translate)

Meta-language issues: Jokes, play on words, code-word approach, higher-level patterns, multiple meanings, etc.

It does not matter that both spoke Greek. The code-word approach may not be known to the other person.

More: Constraint logic: unification and resolution

More: Some difficulties of language translation

More: Parables and secret codes used and explained by Jesus

Two ideas of language study were discussed by Swiss linguist and philosopher Ferdinand de Saussure (1857-1913)

• diachronic refers to language change over time.
• synchronic refers to language as it was used at a specific time.

Note that these ideas apply in (at least) two ways:

• 1. to the language being studied such as Greek.
• 2. to the language being used, such as English, to analyze/describe the language being studied.
• 3. In the case of the Bible, to Latin which changed many Greek words that were then translated from Latin into English.

Examples:

• Greek: Attic, Koine, Modern (and variants)
• English: Old English, Middle English, Modern English (and variants)



More: Some difficulties of language translation

To discredit an opinion, one can find errors in the opinion. The same does not work well with a model. If a model does explain all phenomena sufficiently well, one needs to find a better model that handles those phenomena.
In desperation, those tied to opinion may question whether a model exists to explain the phenomena (even when presented with a model).

Note that some, such as flat earthers, may not accept any model but rely primarily on their opinion.

Those who believes in a flat earth have nothing to fear but sphere itself!

More: Circle of the flat earth

More: Models and reality

Precisely defining models in logic can confuse some people.
Definition: An interpretation of a first order language L consists of the following.

a. A non-empty set D, called the domain of the interpretation.
b. For each constant in L, the assignment of an element in D.
c. For each n-ary function in L, the assignment of a mapping form Dⁿ to D.
d. For each n-ary predicate in L, the assignment of a mapping from Dⁿ into { true , false } (or, equivalently, a relation in Dⁿ).

[Aristotle quote]

More: Models and reality

Definition: Let I be an interpretation of a first order language L and let F be a closed formula of L. Then I is a model for F if the truth value of F with respect to I is true.
Definition: Let T be a first order theory and let L be the language of T. A model for T is an interpretation for L which is a model for each axiom of T.

Some precise ways of dealing with symbols, languages, interpretations, models, etc., can be found in the field of logic programming. The above definitions are on pages 12-13 of: Lloyd, J. (1984). Foundations of logic programming. Berlin: Springer-Verlag. This book (about 125 pages) was used in a graduate computer science course in logic programming that I took years ago.

More: Constraint logic: unification and resolution

More: Models and reality

A logical variable represents a semantic concept. Predicates can select the part of the meaning needed for that part of a sentence fragment. Example:

• Let X be a code word logical variable.
• verb(X) is logical variable X as a verb. Mode, tense, etc., are omitted for simplicity.
• noun(X) is logical variable X as a noun. Gender, etc., are omitted for simplicity.
• adjective(X) is logical variable X as an adjective.
• (and so on)

Suppose X is the idea of "salt".

• noun(X) is "salt".
• verb(X) is "salted".
• adjective(X) is "salty".

Given the use of the logical variable for "salt", an assignment of a value to this logical variable would make sense in each place where that logical variable is used.

Note that in an actual logical programming language (think of Prolog), the implementation would be somewhat different.

• Simplified syntax model: noun(X)
• Logic programming syntax: X, noun(X)



More: Models and reality

Assume that a word is spoken by Jesus and recorded by Matthew.

The way not to decide on the meaning of a word in the GNT (Greek New Testament) is as follows.

• Assume the meaning decided in the early church and coming through the Latin is the actual meaning.
• Use opinion, in the guise of logic, to support that meaning.

Observation: Computers can never get more than about 94% accuracy on identifying the part of speech of a word. This is because human experts cannot agree more then 94% on the part of speech of a given word.

Remember the warnings (predictions) of Jesus of leaven (bad teachings) being mixed in with good teachings. Remember the warnings (predictions) of Jesus (two times) of the mountains (definitions, same Greek word) being moved.

Some think it funny to connect mountains with definitions. They think such funny mountains are just hill areas.

More: Matthew 13:33 KP4 Parable of the leaven

More: Matthew 24:15-20 Delimiting the boundary of the region of a mountain

More: Matthew 21:17-23 Connecting the fig tree curse with moving this mountain

More: Matthew Mustard seeds and moving mountains

More: How to study and understand what Jesus says in the Bible

One way, using logical reasoning, to decide the meaning of a word in the GNT might be as follows..

• Look at how that word is used by Jesus elsewhere in Matthew, then in the GNT, then in ancient Greek lexicons and works (e.g., Josephus, Aristotle, Lucian, etc.).
• Look at how the surrounding words are used by Jesus elsewhere in Matthew, then in the GNT, then in ancient Greek lexicons and works (e.g., Josephus, Aristotle, Lucian, etc.).
• If there are multiple words comprised of the same letters (diacritical marks were added later), consider each possibility.
• Decide on the probability of each meaning fitting. In considering play on words, multiple meanings may be appropriate.

When deciding the meanings of words, one is approximating a statistical fixed point in word meaning space. This is similar to a probabilistic constraint logic (programming) solution using code word semantics.

More: How to study and understand what Jesus says in the Bible

Consider the Russell Paradox. Are each of the following contradiction in terms? Can they actually exist?

• Can a "rotten" "tree" ever have "beautiful" or "raca" "fruit"?
• Can a "good" or "not eating" "tree" ever have "oppressive" "fruit"?



More: Punishment by Spoonerisms: switched consonants

More: Self-referential paradoxes

More: Bertrand Russell

More: Some shallow and deep ideas about tree structures

• "συνέδριον" ≈ "council".
• "σῠν" ≈ "with, together" and "δρῠῶν" ≈ "(of) trees" or "τρῐῶν" ≈ "(of) three"

The Greek word for "council" is a play on words of "together" "three" (in an evil/oppressive Satanic sense) of the "tree" or "three".

More: Matthew 5:22 The danger of brotherly anger

The ancient Greek word "συνέδριον" ≈ "council" as in an "advising body" or "governing body". This is a man-made organization. The word comes from two words and means, literally, "sitting together".

• "σῠν" ≈ "with, together" and "ἕδρα" ≈ "seat".

The last part of the Greek word for "council" as in "seat" is the source of the last part of the Latin phrase "ex cathedra" ≈ "from out of the chair". This phrase is used to refer to the Pope making "infallible" pronouncements from "the out of the chair". This takes God's "throne" (12 verses away) and puts it under human power.

More: Matthew 5:22 The danger of brotherly anger

The English word "raca" comes from the ancient Greek word "ῥακά" ≈ "idiot, fool, good-for-nothing" which comes from Aramaic (similar to Hebrew) word "ריקא" ≈ "worthless person".

The ancient Greek word "μωρε" ≈ "foolish, stupid" (as used) from "μωρός" ≈ "foolish, stupid" as in the English word "moron".

More: Matthew 5:22 The danger of brotherly anger

The Greek words used by Jesus for "Raca" and "fool" appear only once in this exact form in the GNT (both in this verse) and not in the LXX (Septuagint).

Perhaps Jesus is using a play on words. Perhaps a Spoonerism. Perhaps even Latin. Such a usage should fit into the context which is that of top-down or, for non-computer scientists, backwards order.

More: Top-down vs. bottom-up

More: Matthew 5:22 The danger of brotherly anger

• Greek "μωρε" ≈ "foolish, stupid".
• Latin "Rome" ≈ "Rome" (vocative) and Greek "Ῥώμη" ≈ "Rome".
• Greek "ῥώμη" ≈ "might, power, force, strength".


• Greek: "ῥακά" ≈ "idiot, fool, good-for-nothing"
• Greek "χαρά" ≈ "favor, grace" and, in context, "joy".
• Latin "hara" ≈ "animal pen, chicken coop, pigsty".



More: Punishment by Spoonerisms: switched consonants

More: Matthew 5:22 The danger of brotherly anger

More: Matthew 5:22 The danger of brotherly anger

Does it make any sense to make comparisons of the following, using Spoonerisms of the Greek with Latin (transliteration)?

• By embracing the brother Jesus, one effectively calls the council "raka" or (Latin Spoonerism) an "animal pen" or "chicken coop" or "pigsty" or (Greek Spoonerism) "grace" or "favor".
• By embracing the "council", one effectively call the brother Jesus a "fool" or (Latin Spoonerism) "Rome" or (Greek Spoonerism) "Rome" or "might" or "power" or "strength".

[chicken coop]

More: Matthew 5:22 The danger of brotherly anger

The ancient Greek word "ῥάκος" ≈ "rag, strip of cloth".

The LXX includes a word for tattered that is part of a play on words with the "teeth" part of "weeping" and "gnashing" of "teeth".

Details are left as a future topic.

More: Matthew 9:14-17 Old and new garments and bottles

More: Matthew 9:14-17 Old and new garments and bottles

As commentary added by Matthew, John the Baptist is speaking. Neither appears to be clued into the specific code meanings used by Jesus for these words. To what does the "root" and the associated "tree" refer?

☐ A person who does not bring forth good fruit (the ultimate "fish fry").
☐ A human infrastructure (empire, church, etc.) that does not bring forth good fruit where the "root" is the leader (in for a "rude" or "root" awakening).

What could this "tree" refer to historically?

☐ Rome, ☐ Judea under Herod, ☐ Israel (as the fig tree),
☐ church (sand infrastructure), ☐ other trees/empires/mountains,



More: Some shallow and deep ideas about tree structures

• "καλὰ" ≈ "beautiful, good, virtuous".
• "ῥακά" ≈ "idiot, fool, good-for-nothing"

Might the "council" make you a Saint for doing "good" "works" "before" men? What promotional value might they obtain from doing so? Might the council say, "let us give you the next steps"?

More: Wholesome and healthy sanctified saints

More: Matthew 5:16 Let the light of Jesus shine

The TR adds some words to this verse. Do the words added by the TR fit the use of the word "good" as Jesus appears to use that word?

More: Matthew 5:43-44 Love your enemies

The KJV (King James Version) translates two different Greek words as "good".

• "ἀγαθός" ≈ "good, capable, trustworthy".
• "καλός" ≈ "beautiful, good, right". The word "tasty" will be used for this quality of "fruit". Please do not get "testy" about something being "tasty" - an idea that might withstand the "taste" of time.



More: Matthew 7:17-20 Fruit trees programmed to produce fruit of their kind

The ancient Greek word "κᾰλούς" ≈ "beautiful, good, right" (accusative, masculine, plural) appears in each of three successive verses. Jesus uses this exact word in one other place in Matthew.

More: Matthew 7:17-20 Fruit trees programmed to produce fruit of their kind

The ancient Greek word "καλάμη" ≈ "reed, staff, rod" and is related to "canons" and "cannons" and "canyons". A similar Greek word refereed to a stylus on pen used for writing.
The ancient Greek word "σαλεύω" ≈ "shake up, agitate" as in "ocean waves". John was doing his share of "agitation" but was otherwise "unshaken" by what was happening in the culture.
Was John the Baptist "good"? Was John the Baptist "raca"? Explain.

More: Canons, cannons and canyons

More: Luke 21:24-28 Perplexed with problems with impossible solutions

More: Matthew 11:7-9 Shaken in the wind

More: Matthew 11:7-9 Shaken in the wind

More: Matthew 11:7-9 Shaken in the wind

The ancient Greek word "διαφέρω" ≈ "carried through, different" with a sense of a "different" way or type as in it "makes a difference".
In many places, the Latin Vulgate changed "different" to "better".

• Paraphrase: ... you are different (not better) than many of the sparrows.
• Paraphrase: ... how different (not better) is a man (than) a sheep.

The word comes from two Greek words.

• The ancient Greek prefix "δια" ≈ "through" as in the English word "diameter".
• The ancient Greek word "φέρω" ≈ "bring, carry" and is related to the English word "bear" (as in carrying something) and the Latin word "fero" ≈ "bear, carry".

The modern Greek word "διαφέρω" (thee-a-FEH-ro) ≈ "differ, be different".

More: Deferring on a difference of opinion on differences

This is commentary added by Matthew which may or may not fit the situation.

This verses uses the sense of "extinguishable" as in, for example, "not quenched".

The Greek word translated as "bruised" is similar to the "scattered" in "path" in the "path" not to take.

More: Matthew 7:13-14 Strait talk about narrow and wide gates

More: Unquenchable fire

More: Matthew 12:14-21 Comments added by Matthew

It's a tree, wooden you know! Let's make like a tree and get out of here.

• Jesus: Freely you have received. Freely give. ... Know the truth and the truth will make you free.
• Birds: Treely you have received. Treely give. ... Know the root and the root will make you (a) tree.



More: Everything being equal: To biff a translation

More: Matthew 12:30-37 Pardon the idle word counting - new

• Can one "make" the "tree" and the "fruit" "beautiful" or "raca"?
• Can one "make" the "tree" and the "fruit" "rotten" or "plastic"?
• Is the "tree" really "known" by it's "fruit"?

What is the information content? Whose POV (Point Of View) is being used?

More: Matthew 7:17-20 Fruit trees programmed to produce fruit of their kind

More: Punishment by Spoonerisms: switched consonants

More: Matthew 5:22 The danger of brotherly anger

More: Matthew 5:9 B7 Making and appeasing peaceful peacemakers

More: Matthew 12:30-37 Pardon the idle word counting - new

Notice that the Latin uses the same word for the Greek "rotten" "fruit" in verse 33 and for "evil" man in verse 35. It is reasonable to assume that if Jesus intended these two be the same, Matthew would have used the same Greek word in each verse.
A mountain represents an empire. A tree represents the human infrastructure of an empire. The root of the tree represents the human leader. In computer science, a single person would be a (degenerate) tree structure. That is, a tree with no branches and one leaf - the root of the (degenerate) tree.

More: Matthew 12:30-37 Pardon the idle word counting - new

Assume that the "tree" represents a human hierarchy as in a religious establishment such as the one Jesus is addressing. Here are the choices provided.

• Make the "tree" good and the fruit good [raca].
• Make the "tree" rotten and the fruit evil/oppressive [made in clay, plastic].

This verse would not need to be said unless something else were happening.

It appears that the "rotten" "tree" was trying to make the fruit appear as "good" fruit. Why would a "good" "tree" try to make the fruit appear as "rotten"? Might any "idle words" used to make the fruit appear "good" need an "accounting"?

Jesus is the "vine" and we are the "branches" (of the vine, not the tree).

More: Galatians 5:19-23 Abstracting the fruit of the spirit

More: Fruit of the harvest

More: Matthew 12:30-37 Pardon the idle word counting - new

The statement "The tree is known by its fruit." is an ambiguous statement based on the viewpoint of who "knows" or "infers" what.

• God "knows" (sees) both the inside and the outside of the "fruit".
• Man "knows" (sees) only the outside of the "fruit".

From computability theory, it may not be possible to always determine in all cases if the inside is "good" or "rotten". An "accounting" may be necessary for "idle words" so that a decision procedure can be used to resolve ambiguities.

The Greek word for "fruit" is masculine and takes the grammatical gender of "his".

More: Ambiguous statements and perspective

More: Matthew 12:30-37 Pardon the idle word counting - new

• Can a seed be "choked"? (not an artichoke seed)
• Can "thorns" "choke" a growing seed?

Note the decreasing productivity of the seeds: 100 then 60 then 30. Why?

More: Matthew 13:3-23 KP1 Parable of the sower

More: Matthew 13:3-23 KP1 Parable of the sower

Greek, like Hebrew, associated letters with numbers. The study of this is called gematria. The most famous instance of gematria is the 666 from Revelation 13.

• 100 = "Ρ" or "ρ" or "rho".
• 60 = "Ξ" or "ξ" or "ski".
• 30 = "Λ" or "λ" or "lambda".

Any gematria meaning of 100, 60 and 30 is not clear but may indicate some interesting connections.
Keep in mind that the historical connection of this parable is that of the time of Jesus in Judea where the Romans ruled and had let Herod (and descendent's) have some local rule.

More: Matthew 13:3-23 KP1 Parable of the sower

The symbol of Rome, the ruling power of the world at that time, in letters was SPQR (Senatus Populusque Romanus) (as an initialism) from the Latin phrase "senātus populusque rōmānus" ≈ "The Roman Senate and People".

This is just one of many possible gematria connections.

• Latin "Senatus" ≈ "Senate" and "Populusque" ≈ "people and" and "Romanus" ≈ "Rome".
• Greek "και" ≈ "and" and "λαός" ≈ "people".



More: Matthew 13:3-23 KP1 Parable of the sower

Mark repeats some of what Matthew writes but also changes and adds some things. Many details in Matthew are not in Mark (or Luke). Note the order of the numbers. Discuss:

• Who is right? Does it matter? Who copied from whom?
• How might this discrepancy have arisen?



More: Matthew 13:3-23 KP1 Parable of the sower

The "sowing" of the "seed" appears to have happened in parable #1, the parable of the sower. Those who fell by the wayside, choked by thorns, etc., do not appear to be the "tares".

It would appear that the "birds" deposited as weed seeds the weeds that appear with the wheat.

More: Matthew 13:24-30,36-43 KP2 Parable of the wheat and tares

More: Matthew 13:24-30,36-43 KP2 Parable of the wheat and tares

Revelation defines a "merchant man" as a "great one of the earth". Why might a "great" one of the earth sell everything, but not himself, to obtain "one" pearl? Are not "many" pearls needed. That is, at least two pearls, needed. If everything is sold to buy one pearl, which pearls are thus not obtained? Obtaining only one pearl is like having one link in a chain. From Matthew 18, that "one" or "sheep" or "little one" might be you! Have you been "bought" to help someone else be "great"?
Might the two most important laws identified by Jesus be two "pearls". Both are needed. What happens if one obtains only one of these "pearls"?

More: Matthew 18:2-11 Great children ensnared in the middle

More: One cookie rule: good to the last drop

More: Matthew 13:45-46 KP6 Parable of the pearl of great price

More: Matthew 13:47-50: KP7 Parable of the harvest at the end of the age

How are the "good" "arranged" into "vessels"?
What exactly is meant by "gathered" or "collected" or "arranged" into "vessels"?

Consider 10 of which 5 are "rotten" and 5 are "good". There are three obvious possibilities for "gathering" or "arranging" into "vessels". There may be more.

More: Matthew 13:47-50: KP7 Parable of the harvest at the end of the age

• "σαπρόν" ≈ "rotten, putrid" (accusative)
• "πλάσσον" ≈ "formed in clay" as in "plastic".

The ancient Greek word "σαπρός" ≈ "rotten, putrid" and comes from "σήπω" ≈ "make rotten, putrid". [Rodney Dangerfield, sap] The ancient Greek word "πράσον" ≈ "leek" (plant).

More: Matthew 13:47-50: KP7 Parable of the harvest at the end of the age

More: Matthew 13:47-50: KP7 Parable of the harvest at the end of the age

The Greek word for "hypocrite" meant "acting" or "pretending".

• Modern hypocritical behavior: Telling the disciples not to eat without washing their hands while they, in fact, eating without washing their own hands. They were not doing this. Thus, they were not "hypocrites" in the modern sense.
• Ancient hypocritical acting or pretending behavior: They believed what they were saying but were "acting" or "pretending" that this tradition was, in fact, important.

Jesus, through Isaiah, indicates the definition of the "hypocrite" as someone who "pretends" to honor God (with their "lips") but their "heart" does not do this. They can do exactly what they are saying and are then not "hypocrites" in the modern sense. Instead, they are just pretending to honor God.

More: An actor as a hypocrite is not real

More: Matthew 15:1-21 Blind leading the blind

An interesting story that appears to be related is in Matthew 15. The account in Mark 7 is similar. Let us look at Matthew 15. Jesus is speaking.
The woman replies. Then Jesus grants "bread" "crumbs" to the woman. Why might a church deny communion to those may consider "dogs"? What about a pure bred "dog"?

More: Matthew 7:6 The hunt for holy hound splits

Peter is speaking. What Peter is saying appears to not be in line with "raca".

More: Matthew 17:1-8 Transfiguration on a mountain

What is "good" to do? How might this be "raca"?

More: Matthew 18:2-11 Great children ensnared in the middle

What is "good" to do? How might this be "raca"?

More: Matthew 18:2-11 Great children ensnared in the middle

What is "good" to do? How might this be "raca"?

More: Matthew 26:17-29 Betrayal of the Last Supper tradition