I am having trouble understanding inductive arguments, i'm just not sure about how particular observed occurances are supposed to combine into a single definition.
(1) My friend is a bachelor and is unmarried, adult, male, brown eyed, brown haired and European.
(2) My other friend is a bachelor and is unmarried, adult, male, blue eyed, black haired and European.
(3a) To be a bachelor is to be (unmarried, adult, male brown eyed, brown haired and European) OR (unmarried, adult, male, blue eyed, black haired and European)
(3b) To be a bachelor is to be unmarried, adult, male, and European.
But (3a) could just as easily be (3b) because we recognize that eye colour and hair colour differ, but then we have lost information during the process of induction, some of the observed particulars had characteristics that have been missed out. But additionally, on the other hand, to not lose any characteristics by OR-ing every particular's properties together (like in 3a) does not seem like the correct method, because any silly definition would count for example "To be a tree is to be not a table and .etc.etc". So what actually determines which characteristics are in the final universal proposition?
(1) There is a Rose in the garden and it is white.
(2) There is a Rose in the garden and it is red.
(3a) All Roses (in the garden) are red or white.
(3b) All Roses (in the garden) are coloured.
For (3b) I generalized the characteristics in (1) and (2) but it is different to (3a). I am not sure whether (3a) or (3b) is the 'real' inductive argument and which one isn't. Finally, what actually is the difference or similarity between just simply 'generalizing characteristics' and inductive arguments? Thanks for your time, really appreciate any help!