Confused about inductive arguments

Question

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.

Example 1:

(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.

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(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?

Example 2:

(1) There is a Rose in the garden and it is white.

(2) There is a Rose in the garden and it is red.

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(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!

Answer 1

what actually determines which characteristics are in the final universal proposition?

It depends on the issue being analyzed. The context might be indicative of what the topic of interest is.

If the matter at issue is about determining what color the roses have, the statement "all roses are colored" is a trivial paraphrase of the premises/observations and does not involve induction. But if the question is whether roses have the property of color, that conclusion certainly is inductive.

The context might also indicate the [ir-]relevance of certain characteristics for purposes of the question. For instance, if the context about the issue of bachelors purports to focus on people's lifestyle, the color of their eyes likely is rather accidental and therefore bears no significance regarding the characterization of bachelors. But the color of their eyes could be a relevant variable if the context attaches to the concept of lifestyle a condition that depends on the color of their eyes, such as social acceptance or ocular health considerations.

Answer 2

You are trying to understand induction in deductive/rationalist terms. Induction is not deductive. There is not one model that can fit our observations. There are, instead likely an infinity of such models.

There is a good discussion of this problem and its solutions in encyclopedia.com: https://www.encyclopedia.com/humanities/encyclopedias-almanacs-transcripts-and-maps/underdetermination-thesis-duhem-quine-thesis

Basically, the solutions involve accepting "pragmatic truth" rather than "logical truth" as one's truth standard. Accepting empiricism is based on its success in our dealing with the world, which is an empirical standard, and is explicitly logically circular. Pragmatists accept that we have no logically valid solutions to Munchausen's Trilemma, but we must work with one or more of the logically suspect ones anyway: Is the Münchhausen trilemma really a trilemma?