rotation of 0, 45, 90, 135, 180 that Cooper and Shepard saw in the data. Many other experiments have corroborated the idea that visual thinking uses not language but a mental graphics system, with operations that rotate, scan, zoom, pan, displace, and fill in patterns of contours.
What sense, then, can we make of the suggestion that images, numbers, kinship relations, or logic can be represented in the brain without being couched in words? In the first half of this century, philosophers had an answer: none. Reifying thoughts as things in the head was a logical error, they said. A picture or family tree or number in the head would require a little man, a homunculus, to look at it. And what would be inside his head—even smaller pictures, with an even smaller man looking at them? But the argument was unsound. It took Alan Turing, the brilliant British mathematician and philosopher, to make the idea of a mental representation scientifically respectable. Turing described a hypothetical machine that could be said to engage in reasoning. In fact this simple device, named a Turing machine in his honor, is powerful enough to solve any problem that any computer, past, present, or future, can solve. And it clearly uses an internal symbolic representation—a kind of mentalese—without requiring a little man or any occult processes. By looking at how a Turing machine works, we can get a grasp of what it would mean for a human mind to think in mentalese as opposed to English.
In essence, to reason is to deduce new pieces of knowledge from old ones. A simple example is the old chestnut from introductory logic: if you know that Socrates is a man and that all men are mortal, you can figure out that Socrates is mortal. But how could a hunk of matter like a brain accomplish this feat? The first key idea is a representation : a physical object whose parts and arrangement correspond piece for piece to some set of ideas or facts. For example, the pattern of ink on this page
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Socrates is a man
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is a representation of the idea that Socrates is a man. The shape of one group of ink marks, Socrates, is a symbol that stands for the concept of Socrates. The shape of another set of ink marks, isa, stands for the concept of being an instance of, and the shape of the third, man, stands for the concept of man. Now, it is crucial to keep one thing in mind. I have put these ink marks in the shape of English words as a courtesy to you, the reader, so that you can keep them straight as we work through the example. But all that really matters is that they have different shapes. I could have used a star of David, a smiley face, and the Mercedes Benz logo, as long as I used them consistently.
Similarly, the fact that the Socrates ink marks are to the left of the isa ink marks on the page, and the man ink marks are to the right, stands for the idea that Socrates is a man. If I change any part of the representation, like replacing isa with isasonofa, or flipping the positions of Socrates and man, we would have a representation of a different idea. Again, the left-to-right English order is just a mnemonic device for your convenience. I could have done it right-to-left or up-and-down, as long as I used that order consistently.
Keeping these conventions in mind, now imagine that the page has a second set of ink marks, representing the proposition that every man is mortal:
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Socrates is a man
Every man is mortal
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To get reasoning to happen, we now need a processor . A processor is not a little man (so one needn’t worry about an infinite regress of homunculi inside homunculi) but something much stupider: a gadget with a fixed number of reflexes. A processor can react to different pieces of a representation and do something in response, including altering the representation or making new ones. For example, imagine a machine that can move around on a printed page. It has a cutout in the shape of the letter sequence isa, and a
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