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I have two questions regarding Quine's paper “Natural Kinds”:
These two things are explained in the paper, but I couldn’t fully understand them. Please elaborate as much as you can.
First similarity is not a relation because it comes in degrees, two things can be similar enough in exactly the same feature for one use, but not for another. So as a relation, similarity is 'fuzzy' or statistical, even when restricted to a single focus. There may be a mathematical model for it, but that of simple relation, used in ordinary logic, is not that model.
Similarity is also not a relation, even statistically, for the same reason existence is not a predicate. The ways in which things can exist do not form a hierarchy with a single kind of existence being most basic. So there is not a single, basic, applicable definition of 'exists' under which a pizza, a perfect circle, a unicorn and a deity can all be said to either exist or not to exist consistently.
The varieties of similarity also don't cohere. Things can be similar in various ways, but the ways themselves, like the ways of existing, neither cleanly separate, nor form a hierarchy. Which is more similar the unicorn and the perfect circle or the unicorn and the pizza? Or rather, what are the ways in which each pair is more similar? There is not a collection or measure here, but an infinite-dimensional space of fuzzy measures which we expect to support a single measure. Such things rarely work even in math.
But it is impossible to formulate rules about much of anything that do not depend upon the ability to substitute similar terms for the same variable. Otherwise you do not really have a rule, you have a list of cases, which breaks down as soon as a new object comes into existence. You can imagine a rule against having pets on the furniture could be encoded by listing pets and items of furniture, specifying what is 'on', and so forth. But there will be more pets in the future, and you will have different furniture then. So that is not the real nature of the rule. There is really a slot for the pet, which can be held by pets and not human visitors, a slot for furniture that includes sofas and excludes cat baskets...
But how definite are those slots? My dog can't walk in the street for the same reason I can't, but maybe a procession of protesters can -- me and my dog are similar enough by some criterion, and the protest is different. I can't urinate in a parking lot, but my dog can, and drunken sports fans somehow get away with it -- even though I and the sports fan are more similar in almost every way (at least sometimes) than I am to my dog, somehow the categories work out that way. If asked in each case what is the real limit on why the rule applies to whom or what it applies, we can only vaguely say.
So the human notion of rules in general depends strongly on the notion of similarity, and very few of them that are truly useful can even identify the kind of similarity that is required to allow substitution into the rule. Our notion of similarity passes below our conscious reasoning, but it is the very thing that allows rules to exist. And our ability to conceive of rules is what makes logic applicable. So similarity is fundamental to logic in a very definite way.
