## Individuals and categories

If I say “there’s a stray dog in our garden,” you will understand “dog” as referring to some member of the dog category, rather than to a particular dog.  Of course, it is referring to the particular dog that is in the garden, but it is only its being in the garden that makes it particular.  We might say that it is a reference to a member of the category of dogs in the garden.

At another time, I might say something that seems to single out a very specific entity, so I might seem to be talking about a particular individual.

In this post, I want to argue that most ordinary language use is really about categories rather than about individuals.  And, moreover, when it seems to be about an individual, it is really about a very small category.

### An example from mathematics

I’ll illustrate the distinction with an example from mathematics, where the distinction I am making is clearer.

The standard view, in mathematics, is that there is only one number 5.  We make a distinction between numerals and numbers.  So if I write down “5”, then the resulting ink mark on paper is a numeral, not a number.  It represents or refers to the actual number.  There are many possible ways of making that ink mark on paper, with 5, 5, 5 as just three of them.  With a variety of fonts or handwriting styles there can be many numerals.  But, on the standard view, there is only one number five, so that all of those written ink marks refer to the same number.  The number, itself, is considered an abstract entity.  If I write

3 + 2 = 5

then I am understanding that as saying that “3 + 2” and “5” are two different ways of describing the same (or identical) number.

If I write the identity

$(a + b)^2 = a^2 + 2ab + b^2$

then I call that an identity, because the expression on the left of the “=” refers to exactly the same (or identical) number as the expression on the right of the “=”.

With this standard way of talking about mathematics, the numbers that we refer to are indivuals, while the numerals that we use to reference them, are categories (or members of categories).  I’ll generally say “categories” rather than “member of categories”, because it is shorter.  We don’t care about the indivuality of a numeral.  We only care that it references an individual number.

### Examples from ordinary life

In ordinary life, things are far murkier than they are in mathematics.  In mathematics, we use “identical” to mean “the same entity”.  But that is not what we do in ordinary life.  We talk of identical twins, yet we assume that the twins are two different indviduals.  We are using “identical” to mean that we are unable to distinguish between them.  Natural language developed for use in ordinary life, so is tied to our perceptual abilities.  We say two things are identical if we are unable to perceive any significant differences between the two.

We often talk as if we are talking of individuals rather than categories.  Yet we are limited by our perceptual abilities.  There was an episode of the Star Trek series on TV, where Captain Kirk was beamed down.  But something went wrong, and the result was that there were two Kirks, one beamed down to the ground and the other remaining on the star ship.  This made for an interesting plot twist.  But it was possible only because we recognize that as a potential problem.  We can only recognize individuals with our perceptual abilities.  So if two apparent individuals are indistinguishable, we are left with the puzzle of which one is the individual that we thought we were referring to.  Or, in Star Trek term, which was the real Captain Kirk.

Star Trek is, of course, fiction.  But we can recognize the problem.  What if we could make an exact duplicate of a person, copying them atom by atom.  It is widely held that the resulting duplicate would be indistinguishable, would have all of the same memories and quirks of personality.  The situation would seem paradoxical, precisely because we think of persons as being individuals but we are limited by our perception to only be able to perceive them as categories.  What we think of as an individual in ordinary life, is just a member of a very small category.  And thought experiments, similar to that Star Trek episode, remind us that our perception limits us to dealing with categories.

### Summary

With abstract thought, such as in mathematics, we can know entities (such as the number 5) by acquaintance.  We can know them as individuals, on the basis of that acquaintance.  In ordinary life, we are limited by perception.  And perception works by making distinctions based on various criteria.  The application of a single criterion allows us to divide the world into those parts that meet the criterion and those that do not.  Perceiving an object amounts to dividing many ways based on different criteria.  So what we recognize as an object amounts to the intersection of the various categories that result from these dividings.  So what we perceive is, in effect, a very small category derived as the intersection of larger categories.

Perhaps someone who believes that people have an immaterial spiritual soul, might think that they can know an individual by acquaintance with that soul.  For myself, I am skeptical of the idea of immaterial souls, except as metaphor.  But even if you believe in the reality of a spiritual soul, that does not solve the problem except for entities with such souls.  Should we credit an automobile with having an immaterial soul?  Should we credit a golf ball with having an immaterial soul?  In short, we cannot escape the limitations of our perception, which limit us to knowing entities as categories.

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### 5 Comments to “Individuals and categories”

1. The personal identity question isn’t really a matter of whether somebody would know whether they were dealing with you or not. It’s a question of whether you’d mind if somebody created an exact copy of you and then snuffed you. Most people don’t like that idea: they don’t care if there’s an exact copy–it’s still not, you know, THEM. For one thing, while these copies are said to have the same quasi-memories, in their cases, not a single one of them is true. E.g., they weren’t really in St. Louis last week–they couldn’t have been, since they were only created this morning.

W

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