The (passive) "conflict" (as if within himself) is a Greek (active) word "fight" or "race" or "struggle" as used for athletic contests. The ancient Greek word "ἀγωνία" ≈ "competition, struggle" and is the source of the English word "agony".

In the past, one could "see" Paul persecuting the church. Now, one can "hear" Paul preaching the truth. This distinction is reemphasized later in Philippians. The Greek word for "hearing" assumes understanding of what is heard.

More: An opposite angle on the agony of punishment

In about 500 B.C., Pythagoras had a secret society who membership was a mystery to anyone outside the group. It was a closed group and required a special initiation.
Pythagoras had a simple proof (omitted) to show the irrationality of the square root of two. This secret was not to be revealed to anyone outside the group. The punishment for revealing this secret was death.

The Greek word for "mystery" is based on the Greek word for "initiation" as in a member to a group that is "shut" until one is "initiated". The term "mystery cult" is still heard today.

Do whole numbers exist? Do real numbers exist? Explain.

More: Initiation into an open and shut mystery

Have you ever been "beguiled" with "enticing words"?

The Greek word for "beguile" comes from the ancient Greek word "παραλογίζομαι" ≈ "reason falsely" and means, literally reasoning "beyond logic" or "beyond words" as in "false reasoning".

More: Going beyond the prefix para

The ancient Greek word "παραλογίζομαι" ≈ "reason falsely" is used often by Aristotle in his work On sophistic refutations. Paul uses this word in Colossians - a book that uses many Aristotelian words. Apparently "false reasoning" in "teaching" was a problem at the church at Colossae.
The Latin for "enticing words" is "subtle sermons".

One meaning: Beware lest anyone use false reasoning on you with subtle sermons.

More: Aristotle

The Latin word "decipio" ≈ "catch, ensnare" from the Latin word "de" ≈ "of, from" and the Latin word "capio" ≈ "capture" and is the source of the English word "capture". The "enticing words" is interesting in the Latin.

• The Latin word "subtilitate" ≈ "subtle".
• The Latin word "sermonum" ≈ "sermons" and has to do with words being spoken and is the source of the English word "sermon".

Using the Greek and Latin: See that no one uses false reasoning on you in subtle sermons. Does your pastor preach "subtle sermons"?

Might there be a reason why you seldom hear this chapter being preached?

Aristotle wrote a book called On Sophistic Refutations in which he detailed the "false reasoning" used by Sophists (from the Greek word for "wisdom") who would use invalid logic to convince others of ideas to make money for themselves. In English, "sophistic" logic or "false reasoning" is "sophistry".
One of the many types of invalid logic detailed by Aristotle was "eristic" reasoning. Paul uses that word often but it is often translated, without the "bad logic" connection, as "strife"

More: Eristic reasoning creates strife and contention

More: Aristotle

The ancient Greek word "παραλογίζομαι" ≈ "reason falsely" is used often by Aristotle in his work On sophistic refutations. Paul uses this word in Colossians - a book that uses many Aristotelian words. Apparently "false reasoning" in "teaching" was a problem at the church at Colossae.
The Latin for "enticing words" is "subtle sermons".

One meaning: Beware lest anyone use false reasoning on you with subtle sermons.

More: Aristotle

The ancient Greek word "περιπατέω" ≈ "walk around" is the source of the English word "peripatetic" and comes from two Greek words.

• The prefix "περῐ" ≈ "around" as in the English word "perimeter".
• The ancient Greek word "πάτέω" ≈ "walk" from "πάτος" ≈ "walk".

More: Matthew 11:1-6: Trapped by an offensive misinterpretation of Jesus

The ancient Greek word "περιπατέω" ≈ "walk around" .

Aristotle, from Stagira, taught in Athens in the open rather than closed environments and had a habit of walking back and forth as he talked. One tradition has it that his followers were called "peripatetics" for this reason.
Writing to a Greek audience, Paul appears to be saying that our walk should be with Jesus and not with the philosophy of man.

The ancient Greek word "ῥίζα" ≈ "root" of a plant and, later, as a math root such as the square root of two. It is related to the Latin word "radix" ≈ "root" and the English word "root" from the Old English word "wyrt" ≈ "root".
The English word "radical" comes from the Latin word "radicalis" ≈ "pertaining to the root, having roots".

The Gothic word "waurts" ≈ "root".

More: Radical square and other roots

Might Paul be making an analogy of Christ as an alternative to the "square root" and "mystery" secrets of Pythagoras and Greek philosophy?

More: Initiation into an open and shut mystery

More: Teaching and learning sound and healthy doctrine

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Today, one thinks of a "synagogue" as a place where Jewish worship takes place. The word "synagogue" is a Greek word made of up two parts.

• The prefix "syn" meaning together as in "symphony" (sounding together).
• The root "ago" meaning leading or bringing, reduplicated as is not uncommon.

The meaning, both in the LXX (Septuagint) and GNT (and today) is that of people being led to come or be brought together.

More: Matthew 25:38 Taking someone into a synagogue

The conjunction or intersection of A & B or A and B is true=1 if both of A and B are true=1, else the result is false=0.

More: Logical conjunction

The word "and" is a conjunction in that both parts (on either side) are needed.

Example: You need to buy milk and cookies at the store.
Distribute as follows.

• You need to buy milk at the store and
• you need to buy cookies at the store.

You need to do both.

The origins of this verse in the NIV (New International Version) appear to go back to Wescott and Horte who are said to have loved Greek philosophy. Instead of (all) "philosophy", as in the "wisdom of man", they used the words "hollow philosophy" or "empty philosophy" so that some Greek philosophy would not fall under this warning.

NIV: See to it that no one takes you captive through hollow and deceptive philosophy, which depends on human tradition and the elemental spiritual forces of this world rather than on Christ. Philippians 2:8.

• KJV: philosophy and empty deception (same as Greek)
• NIV : empty and deceptive philosophy (changed from Greek)

The English word "hollow" is related to the English word "hole" as in an empty space.

The Greek for "rudiments" is that of "elements" as one part of a row, series, sequence, etc.

How the "rudiments" of the "world" best be taken?

• a set of (unordered) elements (without repetition) of the world
• a sequence of (ordered) elements of the world

The modern Greek word "στοιχεία" (stee-KHEE-a) ≈ "elements" and is the origin of the English chemical term "stoichiometric".
The "rudiments of the world" would appear to include what is often taken as "natural philosophy" or, in modern terms, the "physics" as to how the world operates.