> I don’t have any sense for the various properties of inductive arguments

You can easily find a lot of resources on this topic, but I can't think of any to particularly recommend. To give my own high-level summary, there are three main types of logical arguments:

- Deductive arguments: from the premises, the conclusion necessarily follows. If the premises are true, and the argument is valid, the conclusion must be true. These are the kinds of arguments found in mathematical proofs, and classical syllogisms such as "All men are mortal, Socrates is a man, therefore Socrates is mortal"

- Inductive arguments: from many particulars, infer a generalisation. If all swans so far have been observed to be white, it is reasonable to conclude that "All swans are white" – and the more observations you make, the stronger the conclusion becomes – but that conclusion can never be certain, only probable, because maybe tomorrow someone will discover a black swan, proving the conclusion to be false after all–which is of course what actually happened, when Europeans came to Australia and found swans which were black. (Also, confusingly, "mathematical induction" is a type of deductive argument, not induction in the logical sense.)

- Abductive arguments: from a situation, infer the truth of its most plausible explanation: If I walk into a room and find toys spread all over the floor, I am going to conclude that our four year old did it. Now, maybe some crazy stranger broke into our house, threw toys everywhere, then left – not absolutely impossible, but far less likely than it being our four year old.

The big difference: in deductive arguments, if the argument is good, and the premises are true, the conclusion must be true; in non-deductive arguments, the argument can be good, and the premises can be completely true, and yet the conclusion can still be false. A deductive argument which produces a false conclusion from true premises is by definition a bad one; a non-deductive argument which produces a false conclusion from true premises can still be a perfectly good one, provided that unfortunate outcome is improbable.

The natural sciences use all three, but rely heavily on induction and abduction. Historians primarily use abduction – induction works best for repeatable events, whereas many of the events historians study are essentially unique and unrepeatable (World War II was in many ways a unique event in human history, nothing quite like it had ever happened before, even World War I was different in many ways, and if World War III ever happens it is going to be very different again).

I think a lot of moral reasoning must be non-deductive, because deductive arguments generally deal with certainties, whereas it is quite natural for people to say about moral issues "I think it is probably wrong but I'm not 100% sure". I think moral reasoning often involves some degree of induction – if you repeatedly encounter particular situations which offend your conscience, you are likely to adopt a moral principle which condemns whatever those particular situations have in common – generalising a principle out of particular cases, which is essentially what inductive reasoning is. But, as in all inductive reasoning, you can never be sure that there will not be some case which might convince you that your generalisation needs an exception – a moral black swan.

> This is the first time that I’ve heard of normative epistemology, which I gather is what you are talking about.

Yes, exactly. A lot of the concepts traditionally used in epistemology appear to be normative. For example, in the classical definition of knowledge as "justified true belief", justification appears to be a normative concept – a belief which is justified given some evidence is a belief which one ought to hold (or, at least, one is permitted to hold) given that evidence, a belief which is unjustified given some evidence is a belief which one ought not to hold given that evidence.

> One thing I will say though, thinking about this seems smoother than thinking about normative morality because (I think) I don’t have as many childhood memories of people telling me what I ought to think compared to those of people telling me what I ought to do.

I think a lot of people grow up exposed to conservative religious approaches to morality, which they often experienced as being pushed on them inflexibly and never with any convincing justification–and it is unsurprising many such people become attracted to the idea that "morality is subjective". However, I wonder, is that "throwing the baby out with the bathwater"? Most of these people would feel strongly that genocide, slavery, apartheid, torture, child abuse, theocratic totalitarianism, etc, are immoral – yet, having accepted "morality is subjective", those moral positions they endorse must be just as subjective as those which they've rejected. Subjective morality weakens their own moral positions. Indeed, once you believe that morality is subjective, you can no longer claim (in any objective sense) that anyone else's morality is wrong, including that of various religious conservatives – the most you can consistently say about their morality is that you don't like it – but why should they (or anyone else) care about what you like?