ABSTRACT
After briefly looking at how the past three crises of mathematics had appeared and resolved in the foundations of mathematics in the previous chapter, this chapter focuses on the concepts of potential and actual infinite and relevant matters. In particular, the concept of infinite touches on those matters that seem to be beyond our finitary reach, no matter whether they are so small that we have to use our imagination to divide once and again without an end in sight, or they are so big that any chosen bound will be surpassed again and again forever, or that seem to fall in between the crack between parts and whole, where parts represent many while the whole a one. This last part actually provides an explanation for why systems science only started to appear as a systematic scientific investigation in the recent past, although the basic concepts of systems can be traced back as far as the recorded history can go and isolated studied on systems have been kept popping up at different times throughout the history.
