Modern science is based on induction. Our fundamental scientific laws are arrived at through observation. The law of gravity predicts that when I drop a pencil it will fall to the floor. It does not guarantee this. We are only assuming that what has happened in the past will continue to happen in the future. The law of gravity is based on our experiences with the natural world. We cannot simply deduce that an object dropped must move toward the earth.

When I first encountered inductive logic in my mathematical education, I did not trust it. It seemed too soft. I wanted cold, hard deduction. All of my mathematics up to that point had relied on deduction. I knew I could depend on it. Induction involved positing that a statement was true for one or two specific cases and then showing it was true in the general case based on those assumptions. It took a while, but I finally appreciated the power of induction. Its power is determined by the reliability of the assumptions. Since most mathematics is axiomatic, the assumptions can be shown to be true.

“Say to Hezekiah king of Judah: Do not let the god you depend on deceive you when he says, ‘Jerusalem will not be handed over to the king of Assyria.’ Surely you have heard what the kings of Assyria have done to all the countries, destroying them completely. And will you be delivered? Did the gods of the nations that were destroyed by my forefathers deliver them: the gods of Gozan, Haran, Rezeph and the people of Eden who were in Tel Assar? Where is the king of Hamath, the king of Arpad, the king of the city of Sepharvaim, or of Hena or Ivvah?” - 2 Kings 19:10-13 NIV

Those are the words that Sennacherib, King of Assyria, sent to Hezekiah as his army was preparing to attack Jerusalem. He was appealing to the logic of induction. Just as the other armies had fallen, just as their gods had failed them, so would the LORD fail to protect his people. There was just one flaw to his proof. The God of Israel is not like the gods of Gozan and Haran. His fundamental assumption that all gods are alike proved to be incorrect. The king of Assyria learned this lesson within one night through the destruction of his army. It does not appear he took this to heart since he was later assassinated by his sons while worshipping in the temple of his god Nisroch. Induction is powerful - when based on solid assumptions.