Logic: syllogisms

Logical reasoning in Greek philosophy often took the form of a syllogism that uses deductive reasoning to arrive at a conclusion.

Some people think syllogisms are "silly" and will use the pun "sillygism" to refer to a "syllogism".

Refined by Aristotle, the English word "syllogism" comes from the ancient Greek word "συλλογισμός" ≈ "syllogism".

The English word "sully" comes from an Old English word meaning "mud".

To "sully" a reputation is to make it as if "mud" were added to it.

The ancient Greek word "συλλογισμός" ≈ "syllogism" comes from the ancient Greek word "συλλογίζομαι" ≈ "compute, calculate" and appears in the GNT (Greek New Testament) as G4817 (see below). The word is made of the following.

"σύν" ≈ "together".
"λογίζομαι" ≈ "count, reckon".
"λόγος" ≈ "word, reasoning" and many other meanings. In Greek philosophy, the word is often refers to a explanation of reality.

The modern Greek word "συλλογισμός" (seel-lo-y-SMOS) ≈ "syllogism".

*G4817 *1 συλλογίζομαι (sool-log-id'-zom-ahee) : from G4862 and G3049; to reckon together (with oneself), i.e. deliberate:--reason with.

Usage

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συνελογισαντο

Luke 20:5 And they reasoned with themselves, saying, If ...

The ancient Greek word "λογίζομαι" ≈ "count, reckon", the root word for "syllogism", appears in Luke 20:5.

Luke 20:5 And they reasoned with themselves, saying, If we shall say, From heaven; he will say, Why then believed ye him not? [kjv]

οι δε συνελογισαντο προς εαυτους λεγοντες οτι εαν ειπωμεν εξ ουρανου ερει δια τι ουκ επιστευσατε αυτω [gnt]

Luke 20:5

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KJV: And they reasoned with themselves, saying, If we shall say, From heaven; he will say, Why then believed ye him not?

Greek: οι δε συνελογισαντο προς εαυτους λεγοντες οτι εαν ειπωμεν εξ ουρανου ερει δια τι ουν ουκ επιστευσατε αυτω

*G3049 *40 λογίζομαι (log-id'-zom-ahee) : middle voice from G3056; to take an inventory, i.e. estimate (literally or figuratively):--conclude, (ac-)count (of), + despise, esteem, impute, lay, number, reason, reckon, suppose, think (on).

Words: ελογιζομην ελογισθη=8 ελογισθημεν λογιζεσθαι λογιζεσθε=3 λογιζεσθω=3 λογιζεται=5 λογιζη λογιζομαι=5 λογιζομεθα λογιζομενος λογιζομενους λογιζομενω λογισαμενος λογισασθαι λογισηται=2 λογισθειη λογισθηναι=2 λογισθησεται

The Greek word for "syllogism" comes from the ancient Greek word "συλλογίζομαι" ≈ "compute, calculate" (as a group - together).

Colossians 2:4 And this I say, lest any man should beguile you with enticing words. [kjv]

τουτο λεγω ινα μηδεις υμας παραλογιζηται εν πιθανολογια [gnt]

… decipiat … subtilitate sermonum [v]

Aristotle developed the "syllogism" as a way to reason logically.

The Greek word for "syllogism" comes from the ancient Greek word "συλλογίζομαι" ≈ "compute, calculate" (as a group - together).

Both of these Greek words for "beguile" as "reason falsely" and "syllogism" have the same root word "λογίζομαι" ≈ "count, reckon".

More: Colossians 2:1-23 Philosophy and false reasoning through subtle sermons

This Greek word for "count" as in a "reasoning process" and the root word from which "syllogism" is derived appears 8 times in the LXX (Septuagint). Here are a few.

Exodus 30:12 When thou takest the sum of the children of Israel after their number, then shall they give every man a ransom for his soul unto the LORD, when thou numberest them; that there be no plague among them, when thou numberest them. [kjv]

εαν λαβης τον συλλογισμον των υιων ισραηλ εν τη επισκοπη αυτων και δωσουσιν εκαστος λυτρα της ψυχης αυτου τω κυριω και ουκ εσται εν αυτοις πτωσις εν τη επισκοπη αυτων [lxx]

Isaiah 43:18 Remember ye not the former things, neither consider the things of old. [kjv]

μη μνημονευετε τα πρωτα και τα αρχαια μη συλλογιζεσθε [lxx]

Exodus 30:12

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KJV: When thou takest the sum of the children of Israel after their number, then shall they give every man a ransom for his soul unto the LORD, when thou numberest them; that there be no plague among them, when thou numberest them.

Hebrew: כי תשא את ראש בני ישראל לפקדיהם ונתנו איש כפר נפשו ליהוה בפקד אתם ולא יהיה בהם נגף בפקד אתם׃

Greek: εαν λαβης τον συλλογισμον των υιων ισραηλ εν τη επισκοπη αυτων και δωσουσιν εκαστος λυτρα της ψυχης αυτου τω κυριω και ουκ εσται εν αυτοις πτωσις εν τη επισκοπη αυτων

Isaiah 43:18

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KJV: Remember ye not the former things, neither consider the things of old.

Hebrew: אל תזכרו ראשנות וקדמניות אל תתבננו׃

Greek: μη μνημονευετε τα πρωτα και τα αρχαια μη συλλογιζεσθε

Brenton: Remember you° not the former things, and consider not the ancient things.

The Greek philosopher Aristotle, personal tutor to Alexander the Great, developed and refined the syllogism.

Major premise (claim, proposition)
Minor premise (claim, proposition)
Conclusion (from premises)

A common syllogism is the following.

All men are mortal
Socrates is a man
Therefore, Socrates is mortal.

This particular syllogism, as many, relies on what is today called set theory and often depicted using Venn diagrams.

There are four basic constructs of premises about S and P.

SaP: all S are P	SiP: some S are P

SeP: no S is P	ScP: some S is not P

A difficulty in reasoning with syllogisms today is that there was not a good understanding of nothing as in "zero" in ancient times.

Here is an example.

Syllogism
Category	As stated	Abstracted
Major premise	All men are mortal	All M are P
Minor premise	Socrates is a man	All S are M
Conclusion	Socrates is mortal	All S are P

P is "mortal".
M is "men".
S is "Socrates".

Syllogism
Category	As stated	Abstracted
Major premise	All mortals die	All M are P
Minor premise	All men are mortals	All S are M
Conclusion	All men die	All S are P

P is "die".
M is "mortal".
S is "men".

Note that some people throughout time have had trouble doing abstracting. That is, substituting symbols for words (that often represent meanings).

The field of algebra involves a lot of abstraction (using placeholder names and then substitution and simplification). Those who do not like algebra tend not to like syllogisms, formal logic, computer programming, etc.

A deductive reasoning method is top-down, backward chaining from the ending point, the goal, to the starting point.

In modern times, the syllogism has been replaced by a more general and refined predicate logic, but that is beyond what is covered here.

By contrast, an inductive reasoning method is bottom-up, forward chaining, from the starting point to the ending point, the goal.

The field of science was traditionally deductive in that evidence was gathered to formulate ideas or laws about how the universe works.

A connected logic argument that uses transitivity is as follows.

If "Mary is the mother of Jesus"
and "Jesus is the lamb of God",
then "Mary had a little lamb".

Mary is the mother of Jesus.
Jesus is the lamb of God.
So Mary had a little lamb.

If "God is truth"
and "truth is reality"
then "God is reality".

Mark 10:18 And Jesus said unto him, Why callest thou me good? there is none good but one, that is, God. [kjv]

ο δε ιησους ειπεν αυτω τι με λεγεις αγαθον ουδεις αγαθος ει μη εις ο θεος [gnt]

… bonum … bonus … Deus [v]

Let us look at the idea of God being "good" is commented on by Jesus.

Mark 10:18

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KJV: And Jesus said unto him, Why callest thou me good? there is none good but one, that is, God.

Greek: ο δε ιησους ειπεν αυτω τι με λεγεις αγαθον ουδεις αγαθος ει μη εις ο θεος

Latin: Iesus autem dixit ei quid me dicis bonum nemo bonus nisi unus Deus

Wessex: Þa cwaeð se haelend hwi saigst þu me godne; nis nan man god buton god ane.

The Latin word "bonus" ≈ "good" which became the English "bonus", something that is "good".

Note that the Old English word "god" ≈ "good" is not related to the Middle English word "god" ≈ "God". The had to be distinguished by context. Eventually, an additional "o" was added to "god" to become "good".

Here is a possible syllogism form.

No one is good but God.
Socrates is a man (human).
Socrates is not good.

Here is a generalization.

No one is good but God.
X is a man (human) who is not God.
X is not good.

Now let us see what happens with Jesus as the "man".

No one is good but God.
Jesus is a man.
Jesus is God.
Jesus is good.

What Jesus says, in the overall context, does not result in a contradiction.

Note that Jesus leaves part of the reasoning not directly stated, but inferable.

Romans 3:23 For all have sinned, and come short of the glory of God; [kjv]

παντες γαρ ημαρτον και υστερουνται της δοξης του θεου [gnt]

If sinners were not allowed in church, there would be no one allowed in church.

The Greek here for "all" is plural which means there may be exceptions. Who might be an exception?
The ancient Greek word "ἁμαρτία" ≈ "error, mistake, fault, sin" as in, literally, "not a witness". The Greek for "glory" is that of "opinion". Anything that is "not a witness" for God "falls short" or "lags behind" of God's "opinion" or "expectation".

In logical reasoning, one should not universally quantify something without specifying the domain to which it applies and how it applies. The "for all" would appear to refer to "men" who are not "God" (as in "Jesus").

More: A martyred witness to a translation error

More: Whether this or that: What is your opinion on glory?

More: Expectation of a glorious Greek opinion on a doxology

Paraphrase: For all have not been a (good) witness (of God) and not approached the opinion of God

More: Whether this or that: What is your opinion on glory?

Romans 3:23 For all have sinned, and come short of the glory of God; [kjv]

παντες γαρ ημαρτον και υστερουνται της δοξης του θεου [gnt]

Do we need to come up to the "glory" of God? Perhaps a pastor could help us with that seemingly unattainable quest.

"υστερούντα" ≈ "lag behind, be late".
"δόξα" ≈ "opinion, expectation".

Paraphrase: All (with possible exceptions) have not been a (good) witness (for God) and have lagged behind the opinion/expectation of God.

It appears we do not have to reach the level of God. God has an expectation/opinion of where we should be and we are lagging behind that expectation/opinion. This appears to be in line with Eastern Orthodox thought.

More: Sin and good people

More: Everything and all things: But wait, there's more

Romans 5:12 Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned: [kjv]

Romans 5:12

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KJV: Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned:

Greek: δια τουτο ωσπερ δι ενος ανθρωπου η αμαρτια εις τον κοσμον εισηλθεν και δια της αμαρτιας ο θανατος και ουτως εις παντας ανθρωπους ο θανατος διηλθεν εφ ω παντες ημαρτον

Genesis 6:5 And GOD saw that the wickedness of man was great in the earth, and that every imagination of the thoughts of his heart was only evil continually. [kjv]

Genesis 6:5

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KJV: And GOD saw that the wickedness of man was great in the earth, and that every imagination of the thoughts of his heart was only evil continually.

Hebrew: וירא יהוה כי רבה רעת האדם בארץ וכל יצר מחשבת לבו רק רע כל היום׃

Greek: ιδων δε κυριος ο θεος οτι επληθυνθησαν αι κακιαι των ανθρωπων επι της γης και πας τις διανοειται εν τη καρδια αυτου επιμελως επι τα πονηρα πασας τας ημερας

Jeremiah 17:9 The heart is deceitful above all things, and desperately wicked: who can know it? [kjv]

Jeremiah 17:9

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KJV: The heart is deceitful above all things, and desperately wicked: who can know it?

Hebrew: עקב הלב מכל ואנש הוא מי ידענו׃

Greek: βαθεια η καρδια παρα παντα και ανθρωπος εστιν και τις γνωσεται αυτον