Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (124 page)

K
ATY
: I see your point for the category
pump
, Anna, because a pump is a complex device having numerous moving parts, but I don’t buy it for more basic categories, such as
hammer
or
plate.
Surely you aren’t going to argue that there, too, category membership depends on relationships?

A
NNA
: Oh, yes, I surely am! For something to be a hammer, we expect it to have a handle that is grasped by a human hand, and a metal head that is raised (by the human hand) above the handle and then brought down onto a nail, allowing the latter to penetrate into various materials, such as wood. So here we are talking about a
handle
, a
head
(the hammer’s), a
hand
(a person’s), a
nail
, and a piece of
wood
,
at the very least, and in order to describe the situation, one needs to refer to many relationships connecting these items. How does this differ from the case of the category
pump
(which, as we just saw, has internal parts and relationships among them)? It’s quite the same.

K
ATY
: Maybe that’s true of
hammer
, but
plate
is different! All that counts for a thing to be a plate are its size, shape, and strength, and these are just
traits
, not relationships among parts. In fact, a plate has no parts to speak of. So my point is proven: at least
some
categories
don’t
involve relationships, whereas
all
analogies
do
.

A
NNA
: Sorry, but you’ve jumped a little too fast, Katy. Relationships don’t have to hold among the
pieces
of an object; they can connect an object to its
surroundings.
Thus for an object to be a plate, it has to be able to sit on a table without tipping over, and it has to be able to hold such things as gravy without the gravy leaking off. Moreover, it has to be washable, not poisonous, not prone to shedding small flakes, not damageable by the process of cutting, not prone to dissolve in water, and so forth. These key qualities that make something be a plate bring in many other notions, such as
tables, gravity, foods that flow, water, soap, human health, knives, cutting, dissolving
, and so forth. An object is a plate by virtue of its relationships to all these other things in the world. And so we see that any category, no matter how simple, is a mental structure that involves relationships among various entities in the world, and the act of categorization depends on taking these relationships into account. And thus, dear Katy, your hoped-for distinction goes down the drain.

K
ATY
: Oh, my… You’re quite right, Anna, that on more careful analysis, hammers and even plates are no less “relational” than are hearts or pumps, and so I have no choice but to withdraw my proposed dichotomy. This is getting frustrating and confusing, but luckily I have a new dichotomy up my sleeve, and with this one I’m pretty sure I’m going to put you into something of a pickle. Are you ready?

A
NNA
: Be my guest!

Categorization involves
two levels of abstraction;
analogy involves
just one

K
ATY
: In the examples you’ve just given, whenever an analogy is involved, such as between an atom and the solar system, or between a heart and a pump, the two entities involved are both situated at the same level of abstraction. But when you categorize something, that’s not the case, because
by definition
any category is more abstract than all of its members. In other words, in contrast to what happens in analogies, there is a difference of abstraction levels between things that are being categorized and the categories into which they are getting placed.

A
NNA
: Shall we try to focus on a concrete example? That will help a lot, I think.

K
ATY
: Sure! I assume you’re sitting on a chair, right? That tangible object is a special case of the general category
chair
, which in turn is a special case of the more general category
furniture
, and on upwards it goes. And so there’s a big difference between
comparing two things of
equal
generality, such as a heart and a pump, and comparing two things that have
different
levels of generality, such as a specific chair and the abstract category
chair
, or the abstract category
chair
and the even more abstract category
furniture.
And by the way, there was a good reason that when we broached this topic, you carefully steered clear of the classic old analogy between the atom and the solar system: since both items are concrete things, thus at the same level of abstraction, there is no way that we could be dealing with a case of categorization here. To be specific, an atom is not a solar system, nor is the solar system an atom; they’re at the same level. And so to summarize, in an analogy, source and target reside
at the same level of abstraction
, while in a categorization, the category is
more abstract
than the thing being categorized. All right; the ball’s in your court now, Anna, and it’s a foregone conclusion that I’m going to win this point!

A
NNA
: Don’t be so sure, Katy. I believe I can handle your volley without too much trouble. Your claim that there is necessarily a level-distinction whenever one categorizes something is, I’m sorry to say, just a simplistic stereotype. In fact, this way of looking at things comes straight from the naïve analogy “categories are boxes”, which suggests that one should look at categories as containers and entities in the environment as things to stick in them. Your image reflects the idea that categories in the mind are like Russian dolls, one nested inside another inside another, going many levels up or down. For example: Ollie is a dog; dogs are
canines;
canines are
mammals;
mammals are
animals;
animals are
living things;
and so forth. And indeed, if categories really were boxes containing their members, then your proposed distinction might be justified. But your idea collapses as soon as it is examined carefully. I suggest you go back and take a look at the end of Chapter 3, where the mental process of categorization or analogy-making — call it whichever of these two labels you prefer — is portrayed as the construction of a mental bridge between two structures that themselves are also mental entities. This happens not only when we make a link between a heart and a pump (or more precisely, between mental structures representing them) but also when we assign an object on a shelf to the category
plate.
In either case, we take a fresh new mental representation of something and we link it to some preexisting mental structure. And as I just stressed, this process of building a link between two mental structures can be called either “analogy-making” or “categorization” — whichever label one prefers.

K
ATY
: Good grief, Anna — are you implying that categorization and analogy-making are
exactly the same thing
, and that there is no difference
at all
between them?

A
NNA
: I’m glad to see that you’re starting to catch my drift, Katy. Hopefully this will make you more receptive to my ideas. Do you recall the category of faces that looked alike, back in Chapter 3? Seeing Mark Twain’s face gave rise to a first mental structure, and subsequently, seeing Edvard Grieg’s face enriched this initial structure, making it more complex. Each time a new face is seen that resembles the previous ones, the evolving mental structure gets further enriched. There is thus no box here, but simply a mental structure growing in complexity, and as the number
of faces involved in this process increases, the mental structure starts to feel more abstract. If we step back and look at this type of process, we see that there is no box representing a category, with members neatly placed inside it, and that there is no upwards leap of abstraction involved in an act of categorization that makes it differ from the process of making an analogy.

K
ATY
: I’m not convinced. After all, human faces are very concrete, and mentally superimposing several faces has very little to do with the way categories are normally built up. More
typical
categories are much more abstract than that.

A
NNA
: All right; your healthy resistance pushes me to seek a more abstract example to get my point across. Here’s an attempt. When I was little, our family went to an amusement park where we boarded a boat that sailed down a river through a jungle filled with scary beasts. I was thrilled by this great adventure, but when we got off the boat, my father pointed out that our vessel wasn’t really floating down the river but was actually rolling on wheels on some underwater tracks, which forced it down a predetermined pathway. I realized that our boat was in truth more a
trolleycar
than a
boat
, which made me sad. The disillusionment struck me, but I didn’t dwell on it for long. Several years later, when I was in high school, some friends convinced me to take part in a talent show in which they were doing a tango number. They were all good tango dancers but I knew nothing, and I had to work like the devil in order to get the routine down. Finally I learned it, and on the big day our number came off pretty well. Everyone congratulated me for my tango-dancing talent. But I knew I didn’t have any such talent! When I explained that the only bit of tango I knew was this tiny two-minute routine that I could perform only in the most inflexible way, I suddenly recalled that boat in the park that looked as if it was freely sailing down the river but was actually rigidly constrained by tracks. My apparent tango skill was just another boat held rigidly on its course by invisible tracks and capable of taking in naïve viewers!

K
ATY
: That’s an amusing analogy, but what’s the point?

A
NNA
: Well, you’ve called it an analogy, which is fine with me, but the way I just described it, my deceptive tango skill was a new member of my childhood category
fake-boat-on-tracks
.

K
ATY
: Oh, now I see your point!
My
interpretation was that you made an
analogy
between two deceptive events in your life, whereas
yours
was that your deceptive tango skill seemed to you to belong to an old
category
that you knew — that of
boats that look free but that are actually constrained by hidden tracks
.

A
NNA
: To be more precise,
my
interpretation is that the making of the analogy was tantamount to a categorization. The two acts are one and the same thing.

K
ATY
: Aha — one can look at things either way. I frankly have to admit, that’s most provocative… I can even see how this is parallel to the example of the faces. The boat rolling on tracks established a new category during your childhood; that event in your life is parallel to seeing a photo of Mark Twain. Then your tango-dancing
fakery a few years later was the second member of the category, which is parallel to seeing a photo of Edvard Grieg, which makes the original category broader and richer. Now that you’ve transmitted to me the
constrained-boats
category, I can even think of a pretty good member of this very category in my
own
life!

A
NNA
: I’d like to hear it.

K
ATY
: Well, one time I was on a plane sitting next to an elderly gentleman from Chile who hardly spoke a word of English. Just for the fun of it, I — who had never taken even a week of Spanish — recited a couple of lines from a poem by Pablo Neruda that a high-school friend of mine who loved South American literature had once taught me by rote because I was so taken with those lines’ beautiful sonority when she recited them. The Chilean gentleman jumped to the conclusion that I was a fluent speaker of his native language, and I think he was quite disappointed when he realized that my Spanish was limited to following that very short stretch of hidden tracks. Don’t you think that my Spanish on tracks is a nice example of your
fake-boat
(and also
fake-tango)
category?

A
NNA
: Indeed! Let me be the first to welcome this new member into my childhood category, Katy. I think you now can see that any category, abstract or concrete, is launched by a first experience and then builds up gradually as, over one’s life, one runs into various analogous entities. And it’s crucial to see that there is no critical moment when the first memory suddenly switches status and turns into a category. It’s more like the process whereby a hamlet turns into a village, which may grow into a town, and possibly into a city. There isn’t a sharp baptismal moment at which one must henceforth say “town” or “city”, because the metamorphosis is gradual. And likewise, there is no hierarchical difference, no sudden jump in abstraction, between an initial memory and a category. The initial memory founds the category, just as a hamlet founds a potential city. We may be tempted to think that there is a qualitative difference between a category and its members, but that is an illusion coming from the naïve analogy “categories are boxes”.

Categorization is
objective;
analogy is
subjective

K
ATY
: I see I’m going to have to give up on this dichotomy, because your argument is persuasive. But I’m not done with you yet, Anna! I’m holding a pen in my hand. If I tell you it’s a ballpoint pen, that’s an objective fact. No one could say the opposite. Much the same holds for that sheet of paper and the paper clip that I see sitting over there on my desk.
Ballpoint pen, sheet of paper
, and
paper clip
are all categories that have the quality of total objectivity. An elephant is an elephant, an apple is an apple, and Paris will always be Paris. There are no two ways about it. When we categorize, we do something that is objective.