are mixed right in with the symbols themselves, whereas on paper, the
symbols are static entities, and the rules are in our heads.
It is important not to get the idea, from the rather strict nature of all
the formal systems we have seen, that the isomorphism between symbols
and real things is a rigid, one-to-one mapping, like the strings which link a
marionette and the hand guiding it. In TNT, the notion "fifty" can be
expressed in different symbolic ways; for example,
((SSSSSSSO· SSSSSSSO) + (SO' SO))
((SSSSSO. SSSSSO) + (SSSSSO. SSSSSO))That these both represent the same number is not a priori clear. You can
manipulate each expression independently, and at some point stumble
across a theorem which makes you exclaim, "Oh-it's that number!"
In your mind, you can also have different mental descriptions for a
single person; for example,
The person whose book I sent to a friend in Poland a while back.
The stranger who started talking with me and my friends tonight
in this coffee house.That they both represent the same person is not a priori clear. Both
descriptions may sit in your mind, unconnected. At some point during the
evening you may stumble across a topic of conversation which leads to the
revelation that they designate the same person, making you exclaim,
"Oh-you're that person!"
Not all descriptions of a person need be attached to some central
symbol for that person, which stores the person's name. Descriptions can be
manufactured and manipulated in themselves. We can invent nonexistent
people by making descriptions of them; we can merge two descriptions
when we find they represent a single entity; we can split one description
into two when we find it represents two things, not one-and so on. This
"calculus of descriptions" is at the heart of thinking. It is said to be inten-
sional and not extensional, which means that descriptions can "float" without
being anchored down to specific, known objects. The intensionality of
thought is connected to its flexibility; it gives us the ability to imagine
hypothetical worlds, to amalgamate different descriptions or chop one
description into separate pieces, and so on.
Suppose a friend who has borrowed your car telephones you to say
that your car skidded off a wet mountain road, careened against a bank,
and overturned, and she narrowly escaped death. You conjure up a series
of images in your mind, which get progressively more vivid as she adds
details, and in the end you "see it all in your mind's eye". Then she tells you
that it's all been an April Fool's joke, and both she and the car are fine! In
many ways that is irrelevant. The story and the images lose nothing of their
vividness, and the memory will stay with you for a long, long time. Later,
you may even think of her as an unsafe driver because of the strength of(^338) Brains and Thoughts