(Google Books) The Problems of Philosophy By Bertrand Russell
Answering as you do that the principle is based on probabilities, not certainties and that reflects the real world, is also to miss the point because both Hume and Russell realized that we don't have certainty about all matters of science - in fact Russell explicitly discusses probabilities in the section referenced above. The point is that we have no logical right to affirm on the basis of our past experiences that even probability is true of the natural order. So the principle of induction is left without a foundation.
Russell was a much better writer than I am (a gross understatement, to be sure - he was an immensely talented writer) Maybe you will get the point if you read what he wrote about this particular philosophical problem.
There is a difference between confidence based on evidence and blind faith. Faith that is not based on verifiable, repeatable evidence is based on hope and nothing more. It's a shot in the dark.
I'm sure you must realize that all existence or factual questions are not established or disconfirmed in the same way in every case. It should be obvious that historians use methodologies different from those of biologists or philosophers, etc. The type of evidence in existence or factual claims is determined by the field of discussion and by the metaphysical nature of the entity in the claim under question. If "repeatable evidence" were always required to prove something you could never prove that George Washington crossed the Delaware river because historical events like that are not repeatable.
Again, my major point was that the principle of induction cannot be justified by induction, or pure reason, Reasoning itself rests upon presupposition of faith. Faith is not "blind". It is, as the Bible describes it, the substance of things hoped for, the evidence of things unseen." or, "Faith is the title deed to things hoped for, the evidence of things not seen".
- Hupostasis} is a very common word from Aristotle on and comes from upisthmi (upo, under, isthmi, intransitive), what stands under anything (a building, a contract, a promise). See the philosophical use of it in 1:3, the sense of assurance (une assurance certaine, Menegoz) in 3:14, that steadiness of mind which holds one firm (2 Corinthians 9:4). It is common in the papyri in business documents as the basis or guarantee of transactions. "And as this is the essential meaning in Hebrews 11:1 we venture to suggest the translation 'Faith is the title-deed of things hoped for'" (Moulton and Milligan, Vocabulary, etc.). {The proving of things not seen (pragmatwn elegxov ou blepomenwn).
Robertson's Word Pictures - Hebrews 11:1
Cordially,
Offering philosophy is a waste of time to me and a luxury most people can't afford. Thank God we don't have to depend on philosophers for real life solutions.
You can not only predict certain behavior, but you can even predict the speed with which it will be acquired and the speed at which it will be extinguished by properly applied conditioning.
This is part of the reason why I have zero tolerance for philosophical niceties. You are the one who introduced this inductive principle, which to me means nothing of any substance. I deal in real terms. I said I could show you how I know or came to know, and if you don't believe me you are free to try it yourself.
Now as to not being able t know historical events, much of hisotry is doubtful and cluded in mystery. There is no comparable obligation or need to believe hisotry religiously, no pun intended. Everything historical must be taken with a grain of salt, especially ancient history, and yield to new evidence. That's why new discoveries change what we know about history. But the same is not the case when it comes to faith.
Not only does faith not have a working model, where you can tell me "if you don't believe me, do this..." but faith will not yield to reason even when evidence points to it being in error. Because it's hope against all odds. It's desperation, and to a large extent fear that drives it, and just like anything fear-driven it resists reason.
"Faith is the title deed to things hoped for, the evidence of things not seen"
And that makes it true? What an anonymous human wrote 2000 years ago? What do you have to show for it except solitary hope?
Compare my proof with the stove top and yours. Night and day. Apples and oranges. Substance vs. hot air. But, don't take my word for it, lay BOTH of your hands on a red hot stove top! I bet you won't be writing for a while. Maybe that will give you more time to think what is real and what wishful tinkling, inductive or deductive, doesn't matter.