Q. What is the difference between παλαιός and ἀρχαῖος? and how do they stand in relation to νεός and καινός?
A. Παλαιός = more “the former,” ἀρχαῖος “ancient, antique.” You could not say ἀρχαῖος ἂνθρωπος in the sense of παλαιός. 'Aρχαῖος is opposed to νέος but cannot be so absolutely to καινός. But ἀρχαῖος can be neither νέος nor καινός. It may be opposed to both: so may be παλαιός. It is contrasted with καινός but it is not the νἐος—what now begins. In 2 Cor. 5 ἀρχαῖα are things which have been of old, a long time; we have a new system or creation. So in Matt. 13:52: they are things καινὰ καἱ παλαιά, the old scribe knowledge, and other new things.