Turing Machines

and

Functionalism Alan M. Turing

1912-1954 English mathematician, logician, cryptanalyst, creator of computer science In 1954, Alan Turing committed suicide, eating an apple laced with cyanide. The symbolism of the knowledge of good and evil, and of Snow White, Turing’s favorite fairy tale, are thought to be intentional. Turing was essential in the breaking of the German Naval Enigma code “Computing machinery and intelligence” (Mind, October 1950) The Turing Test ...for Machine Intelligence: With the human, C, communicating via typed text with a human, B, and computer, A, could the computer fool C into believing that it (and not B) was the human? If so, the machine should be considered intelligent. In 1952, the British government found Turing guilty of being gay. He lost his security clearance and was forced to choose between prison or chemical castration through estrogen injections. He chose chemical castration. 55 years later, in 2009, after a long internet and petition campaign, Prime Minister Gordon Brown issued a full and heartfelt apology on behalf of the British government. Brown stated that the country and humankind owes Turing a huge debt, his treatment was “horrifying” and “utterly unfair”. He ended the letter with,

“I am very proud to say: we’re sorry. You deserved so much better. ” Church–Turing Thesis about the nature of functions whose values are effectively computable. In simple terms, it states that “everything computable is computable by a Turing Machine.”

(more on Turing Machines later) at any point in the computation the read/write head is in one of a finite number of internal states {q0, q1,...,qn} the machine table of a Turing machine fully specifies its functional economy—and it does so independently of its physical realization

indeed, the internal states of the machine qis are defined in exactly the way the functionalist wants to define mental states—in virtue of their relation to inputs, outputs, and other internal states

thus, just as one can reason and investigate the nature of a particular Turing machine, or Turing machines generally, without worrying about the physical realization, so the (traditional machine) functionalist wants to claim that we can develop an autonomous psychology which investigates the functional psychology of organisms without having to worry about physics, biology, or neurology

Traditional machine functionalists claim that the mind can be correctly described, and explained as a complex Turing machine or probabilistic automaton A Turing Machine An abstract specification of a universal computing device. Turing hypothesized that any effectively computable function is Turing Computable (i.e., computable by a Turning Machine (Church-Turing Thesis)) an infinite tape divided into squares a read/write head (or scanner head) that can move along the tape and, well... read and write! (and erase) :P is made up of.... is... non-blanks can have a 1 or 0 in them all but a finite number of squares are blank the program is basically a set of conditionals:

IF in state qn and scanning an x, THEN...

move left one square, or

move right one square, or

write a 1, or

write a 0, or

write a blank,

AND...

stay in current state, or

change to state qi the program is usually specified as a machine table:

B 0 1

q1 1q1 Bq1 Rq2

q2 1q2 Bq2 Rq3

q3 1q3 Bq3 if in this state and scanning this symbol This is a VERY simple machine, can you tell what it does? The set of Turing computable functions is provably equivalent to the set of abacus computable functions and the set of recursive functions; indeed, Turing computability is equivalent to every known formalization of the notion of computability. This is important because Church (1903-1995) and Turing proposed that any computable function is Turing computable. I.e., any mechanically computable operation can be carried out by some Turing machine. This claim (known as the Church-Turing Thesis) cannot be proved, since it involves an intuitive, non-formal notion of mechanical computability; however, it could be refuted if a formal notion of computability were developed, and there were a function computable by that method, but not Turing computable. But every formal notion of computability developed so far is equivalent to Turing computability, and this is taken as strong evidence for the Church-Turing Thesis. then carry out these instructions So What...!? The complexity of an abstractly specified Turing machine is effectively unlimited (though not infinite), so they are amazingly powerful Power & Complexity A variant on the notion of Turing machine, is that of the probabilistic automaton—here, rather than the internal state and input determining the subsequent behavior, it determines a set of behaviors each one of which has a certain probability weighting, and the outcome is generated according to those weightings

(note that, strictly speaking, this is still a deterministic system) Multiple Realizability The machine table of a Turing machine fully specifies its functional economy—and it does so independently of its physical realization.

One can reason about the nature and properties of a Turing Machine (the software) without worrying about the details of its realization (the hardware) Abstractness This same abstractness of the software means that there are many ways a Turing Machine could be realized, so long as the physical (or even non-physical!) system has states which carry out the abstractly specified state transitions Of utmost importance is the network of interrelations between

inputs

internal states

outputs

And the states of the system are defined in terms of these interrelations the complexity and power of an actually realized Turing Machine are limited only by resources and technology Functionalism Every mental state is physically realized

mental state token = physical state token, but

Mental state types ≠ brain state types

because of multiple realizability, rather

Mental states are identified by their functional relations to

inputs

outputs

other mental state types Definition: three types

nine tokens two tokens of one type three tokens of another type Contrasts... With Behaviorism

behaviorism attempts to define mental states solely in terms of inputs and outputs—stimulus and response

in functionalism mental states are real and can be referred to in defining other mental states

acknowledges the holistic nature of mental state definitions With Identity Theory

identity theory committed to m.s. type = b.s. type

functionalism is committed only to token identity and denies type identity Non-Reductive Materialism

&

Multiple Realizability

&

Methodological Autonomy the multiple realizability of mental states and the denial of type identity make functionalism a non-reductive theory because of multiple realizability, a full understanding of mental states (across various types of creatures) is neither dependent on nor reducible to physics or neurology or chemistry four tokens of another type note the mutiple realizability exemplefied here! Semantics from Syntax Syntactic/causal relations are purely physical, and therefore can be mechanized in various ways,

But they can be designed or evolved to be meaning-respecting and reason-respecting

P → Q

P

---------

Q

Reason-Respecting Causal/Physical Devices Formal Abstraction Grounded in Multiple Realizations Clark—Formal Systems/Turing Machines Liberate in 2 Ways: Reason-Respecting Physical Devices

computers just one way such a system can come about

various physical systems (e.g., an organism) can have an economy of inner states which causally produce flexible purposeful behavior in virtue of some of those internal states being about other internal and external states

such a system exhibits inteligence Avoiding Homuncular Regress Via a Village of Idiots Type Identity vs Token Identity Many Varieties of Functionalism What is important is the causal economy of internal states, their interrelations among themselves and the inputs and outputs

Turing machines/serial computation was the original model for functionalists

But that economy need not be understood in terms of Turing machines

Any systematic specification of causal roles can comprise a functional system

If appropriately arranged, the functionalist claims, such a system would be a mind

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# Turing Machines and Functionalism

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