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Although inductive and analogical reasoning work, they work depending on some notion of similarity.

For example, the argument that "All swans observed have been black. The next swan we observe will be black" is considered to have inductive weight to it the more and more swans we observe. But what is a swan? Each and every "swan" is a different object. We just assign the word "swan" to them because all these objects have some notion of shared properties that conceptualize as a swan in our head. Those objects are similar in some sense.

With simple examples like these, it doesn't seem so intuitive that we do this, but with more complicated examples, it becomes more obvious. But given that similarity is fundamentally subjective and there is no reason to think it is a mind independent feature, how can we know for sure when our inductive inferences are reliable or not? In the case of swans atleast, one could argue that it is a "natural" kind, but what about kinds that don't seem natural? How can we use proper inductive references with these?

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  • Per Hume's famous problem of induction, even public events of extremely objective nature such as the sun rise each day on earth from inductive reasoning based on numerous observations is a weak point if not the weakest point, no analogy here is involved... Dec 26, 2022 at 0:31
  • Yes, I'm aware of that problem of induction. I'm talking about a different problem, that is a different problem with the notion of similarity. "The sun rising today on earth" is not the same event as "the sun rising yesterday". They are different events
    – user62907
    Dec 26, 2022 at 0:52
  • I've felt for a long time that this is a significant issue in philosophy, but I've never seen it dealt with directly. Dec 26, 2022 at 4:11
  • Indeed your two propositions are describing two empirically different while similar events, but inductive reasoning is more about arriving at generalized proposition mostly in probability form which by definition is already different (but similar) to each sample observation your suspected (conjectured) generalization supposed to base upon, thus your subjective similarity thesis easily refutes such reasoning even without any testing effort. Carnap's degree of confirmation logic seeks to track your black swans or ravens to calculate the strength of your evidence to support your hypothesis. Dec 26, 2022 at 4:52
  • @DoubleKnot, from your comment, it's not clear that you understand the problem he is posing. No form of induction, including Carnap's can even get off the ground until you have decided which events to include in the data, and it is that choice which is in question. Dec 26, 2022 at 7:08

2 Answers 2

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Is the subjective nature of similarity a weak point of analogical / inductive reasoning?

Yes. Grouping (apparently) similar things is the part of the process that introduces "noise" into an otherwise clean set of data. The messier the data set, the more noise. The more noise, the more arbitrary the conclusion will be in relation to the true situation.

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Point to a white swan and say "This is a swan". Point to other five white swans and say the same phrase. Its well understood by listener what a swan is: a swan is whatever shape, color, properties those six objects pointed to have in common.

Now point to a black swan and say "This is a swan". Your listener will say "Aha, so the color is not what define a swan. I will update my definition of swan by minusing color property from it".

This is inductive reasoning. Bottom-up approach. We go from known to unknown, changing our definitions and learning / updating our concepts, thereby making unknown known.

Lets put in subjectiveness. Suppose your listener can only see in infra-red. He cannot see colours. Therefore his definition not get broaden when introduced to a black swan.

Subjective nature of similarity is therefore a weak point indeed of analogical/inductive reasoning. The listener dont understand the analogy because he cannot generalize. He cannot generalize because he dont see different things. So, he dont pick common properties. He see all properties as common so there is nothing to pick. The set dont get smaller. He is not moving up from the bottom so there is no bottom-up approach.

Ofcourse this example deals with colour only. If one of the six white swans is injured or crippled or fat or significantly younger than others then ofcourse the infra-red observer can generalize in those terms.

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