When Jesus saw the crowds, he went up on a mountain. The disciples followed and gathered around Him when He sat down. So began the Sermon on the Mount.
Though the text does not clearly say, I believe it was just Jesus and the disciples on the mountain. Jesus was sitting, and the disciples were around Him. there was no room for the crowds to gather, and they could not hear Him as He sat with the disciples around Him.
The Sermon on the Mount, therefore, was not for the crowds, but for the followers of Jesus.
In this context, Jesus said:
The followers of Christ who sit at His feet (not the crowds) are the light of the world. We cannot be confused about this. Letting your light shine is not something anyone can do without Jesus. Jesus is the light, and only His followers have the light. He made this clear when he said, “I am the Light of the world; he who follows Me will not walk in darkness, but will have the Light of life.” (John 8:12)
Jesus was not talking to the crowds; He was talking to His twelve disciples when He said these things. He was not speaking of the crowds; He was speaking of His close followers.
In Christ is life, and the life in Christ is the light of men. (John 1:4) Jesus is the Light that came into the world. (John 1:9) His followers are the light of the world. If we abide [live] in Him, and He [His word] abides [lives] in us (John 15:7), we are the light of the world.
As Jesus is the Light, we are the light reflecting the life that is in Jesus. Jesus, the Light, shines in the darkness, and the darkness did not comprehend it. (John 8:12) We also, now, shine the light of Christ in a dark world that does not comprehend it. We should shine nevertheless.
Lamps are not made to be hidden under a basket. (Matthew 5:15) There are made to be put on a lamp stand to light up the darkness. We are made to be a city set on a hill that cannot be hidden.
In this world, there is darkness. The world as God created it to be is not the world we live in. We live in a world that has rejected God and His order, that has been corrupted by sin. We live in the disorder caused by the self-governance of men. This is the same world into which Jesus came as the Light and in which He now instructs us to shine.
So shine, knowing that the light overcomes the darkness. (John 1:5) So shine knowing that the light in us has overcome the world. (1 John 5:4) So shine knowing that unto us a child was born, and the government of this world will one day be on his shoulders. (Isaiah 9:6) So shine knowing that the kingdom of the world will one day become the kingdom of our our Lord and of His Christ, and He will reign for ever and ever! (Rev. 11:15)
 5457/phōs (a neuter noun) – properly, light (stressing its results, what it manifests). In Scripture, phōs (“light”) is the manifestation of God’s self-existent life. See John 1:4-5 “In Him [Christ] was life, and the life was the light [phōs] of men. The light (phōs) shines in the darkness, and the darkness did not comprehend it.” John 8:12: “Then Jesus again spoke to them, saying, ‘I am the Light (phōs) of the world; he who follows Me will not walk in the darkness, but will have the Light (phōs) of life.'” (NASB)
God’s light (phōs) reveals His presence and preferences. In contrast, darkness obscures God’s will and presence. Through the light of faith, God reveals and shares His life which overcomes all spiritual darkness. We can not see things as they really are, unless God gives us light. God’s light alone reveals reality so the Psalmist proclaims, “In Thy light, we see light.” (Ps 36:9) Phōs preeminently conveys the manifestation of God’s life (Jn 1:4) so believers can perceive true reality, through faith. Without divine light, we would all be shut up to spiritual (eternal) obscurity. Light is in Christ and emanates from Him (cf. Heb 1:3). We do not turn on a flashlight (or light a candle) to see the flashlight or the candle! Light makes what is spiritual (eternal) become intelligible (“visible”). God shares light so He Himself becomes visible to the eye of the soul.
 2889/kósmos (literally, “something ordered”) – properly, an “ordered system” (like the universe, creation); the world. Kosmos (“world”) occurs 187 times in the NT and usually refers to the world-system, i.e. unaided humanity operating in the “flesh” (rejecting the lordship of Christ). Thus the world is in perpetual, spiritual chaos (alienation from God) – a “disordered order.” The world as we know it is not the ordered system God made it to be, but God through Jesus Christ stands restore the order that has become chaos. “Then the seventh angel sounded; and there were loud voices in heaven, saying, ‘The kingdom of the world (kósmos) has become the kingdom of our Lord and of His Christ; and He will reign forever and ever.'” (Rev. 11:15 NASB) This is foretold by the Prophet Isaiah – “For a child will be born to us, a son will be given to us; And the government will rest on His shoulders; And His name will be called Wonderful Counselor, Mighty God, Eternal Father, Prince of Peace.” (Is. 9:6 NASB). The fundamental idea of kosmos is “beautiful because ordered.” The godless world (kosmos) however operates in “organized chaos” from rejecting Christ the King. Only His government brings true order to the cosmos. Kósmos (“world”), literally a “disordered order,” refers to people (society) persisting in self-government – “human society running in its own (unrighteous) direction.” (See 1 John 2:15 (“Do not love the world not the things in the world”); James 4:4 (“friendship with the world is hostility toward God”); 2 Peter 2:20))
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