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Friday, January 13, 2012

Grice and Turing

Speranza

Grice relies on a functionalist theory of mind alla Turing in his "Method in philosophical psychology."

This from wiki, functionalism (philosophy of mind).

Types of functionalism

Machine-state functionalism

Figure:

Artistic representation of a Turing machine.

The broad position of "functionalism" can be articulated in many different varieties.

The first formulation of a functionalist theory of mind was put forth by Hilary Putnam.[5][6]

This formulation, which is now called "machine-state functionalism" (or "machine functionalism" for short) was inspired by the analogies which Putnam and others noted between the mind and the theoretical "machines" or computers capable of computing any given algorithm which were developed by Turing (a "Universal Turing machine").

In non-technical terms, a "universal Turing machine" can be visualized as an indefinitely and infinitely long tape divided into rectangles (the memory) with a box-shaped scanning device that sits over and scans one component of the memory at a time.

Each unit is either blank (B) or has a 1 written on it.

These are the inputs to the machine. The possible outputs are:

1. Halt: Do nothing.

2. R: move one square to the right.

3. L: move one square to the left.

4. B: erase whatever is on the square.

5. 1: erase whatever is on the square and print a '1.

An extremely simple example of a universal Turing machine which writes out the sequence

111

after scanning three blank squares and then stops is specified by the following machine table:

State One State Two State Three

B write 1

stay in state 1 write 1

stay in state 2 write 1

stay in state 3

1 go right

go to state 2 go right

go to state 3

halt

This table states that if the machine is in state one and scans a blank square (B), it will print a 1 and remain in state one.

If it is in state one and reads a 1, it will move one square to the right and also go into state two.

If it is in state two and reads a B, it will print a 1 and stay in state two.

If it is in state two and reads a 1, it will move one square to the right and go into state three.

If it is in state three and reads a B, it prints a 1 and remains in state three.

Finally, if it is in state three and reads a 1, then it will stay in state three.

The essential point to consider here is the nature of the states of the universal Turing machine.

Each state can be defined exclusively in terms of its relations to the other states as well as inputs and outputs.

State one, for example, is simply the state in which the machine, if it reads a B, writes a 1 and stays in that state, and in which, if it reads a 1, it moves one square to the right and goes into a different state.

This is the

"functional definition"

of state one.

It is its causal role in the overall system.

The details of how it accomplishes what it accomplishes and of its material constitution are completely irrelevant.

According to "Machine-state Functionalism,"

the nature of a mental state is just like the nature of the automaton states described above.

Just as state one simply is

the state in which, given an input B, such

and such happens, so"

"being in pain" (or thinking that Christmas is white)

is the state which disposes one to cry "ouch"

-- or sing, "I'm thinking of a white Christmas") become distracted, wonder what the cause is, and so forth.

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