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From: PADIN@FNALB.BITNET
Newsgroups: mod.ai
Subject: THE PSEUDOMATH OF THE TURING TEST
Message-ID: <8610270723.AA05463@ucbvax.Berkeley.EDU>
Date: Fri, 24-Oct-86 21:09:00 EST
Article-I.D.: ucbvax.8610270723.AA05463
Posted: Fri Oct 24 21:09:00 1986
Date-Received: Mon, 27-Oct-86 05:59:50 EST
Sender: daemon@ucbvax.BERKELEY.EDU
Organization: The ARPA Internet
Lines: 54
Approved: ailist@sri-stripe.arpa


        LETS PUT THE TURING TEST INTO PSEUDO MATHEMATICAL TERMS.

        DEFINE THE SET Q={question1,question2,...}.  LETS NOTE THAT
FOR EACH q IN Q, THERE IS AN INFINITE NUMBER OF RESPONSES ( THE RESPONSES
NEED NOT BE RELEVANT TO THE QUESTION, THEY JUST NEED TO BE RESPONSES).
IN FACT, WE CAN DEFINE A SET R={EVERY POSSIBLE RESPONSE TO ANY QUESTION}, i.e.,
        R={r1,r2,r3,...}.

        WE CAN DEFINE THE TURING TEST AS A FUNCTION T THAT MAPS QUESTIONS
q in Q TO A SET RR IN R OF ALL RESPONSES ( i.e., RR IS A SUBSET OF R).
WE CAN THEN WRITE
                        T(q) --> RR

WHICH STATES THAT THERE EXISTS A FUNCTION T THAT MAPS A QUESTION q TO A
SET OF RESPONSES RR.  THE EXISTENCE OF T FOR ALL QUESTIONS q IS EVIDENCE FOR
THE PRESENCE OF MIND SINCE T CHOOSES, OUT OF AN INFINITE NUMBER OF RESPONSES,
THOSE RESPONSES THAT ARE APPROPRIATE TO AN ENTITY WITH A MIND.

        NOTE: T IS THE SET

{(question1,{resp1-1,resp2-1,...,respn-1}),
 (question2,{resp1-2,resp2-2,...,respk-2}),
 ...
 (questionj,{resp1-j,resp2-j,...,respj-h}),
 }

WE USE A SET (RR) OF RESPONSES BECAUSE THERE ARE ,FOR MOST QUESTIONS, MORE
THEN ONE RESPONSE. THERE ARE TIMES OF COURSE WHEN THERE IS JUST ONE ELEMENT IN
RR, SUCH AS, THE RESPONSE TO THE QUESTION, 'IS IT RAINING OUTSIDE?'.

NOW A PROBLEM ARRISES: WHO IS TO DECIDE WHICH SUBSET OF RESPONSES INDICATES
THE EXISTENCE OF MIND?  WHO WILL DECIDE WHICH SET IS APPROPRIATE TO INDICATE
AN ENTITY OTHER THAN OURSELVES IS OUT THERE RESPONDING?
FOR EXAMPLE, IF WE DEFINE THE SET RR AS

                RR={r(i) | r(i) is randomly chosen from R}

THEN TO EACH QUESTION q IN THE SET OF QUESTIONS USED TO DETERMINE THE EXISTENCE
OF MIND, WE GET A RESPONSE WHICH APPEARS TO BE RANDOM, THAT IS , WE CAN MAKE NO
SENSE OF THE RESPONSE WITH RESPECT TO THE QUESTION ASKED.  IT WOULD SEEM THAT
THIS WOULD BE SUFFICIENT TO LABEL TO RESPONDENT A MINDLESS ENTITY. HOWEVER,
IT IS THE EXACT RESPONSE ONE WOULD EXPECT OF A SCHIZOPHRENIC.  NOW WHAT DO WE
DO?  DO WE CHOSE TO DEFINE SCHIZOPHRENICS AS MINDLESS PEOPLE?  THIS IS NOT
MORALLY PALATABLE.  DO WE CHOSE TO ALLOW THE 'RANDOM SET' TO BE USED AS
CRITERIA FOR ASSESSING THE QUALITY OF MINDEDNESS?  THIS CHOICE IS NOT
ACCEPTABLE EITHER BECAUSE IT SIMPLY RESULTS IN WHAT MAY BE CALLED TURING NOISE,
YIELDING NO USEFUL INFORMATION.
        IF WE ARE UNWILLING TO ACCEPT ANOTHER'S DECISION AS TO THE SET OF
ACCEPTABLE RESPONSES, THEN WE ARE COMPELLED TO DO THE DETERMINATION OURSELVES.
NOW IF WE ARE TO USE OUR JUDGEMENT IN DETERMINING THE PRESENCE OF ANOTHER MIND,
THEN WE MUST ACCEPT THE POSSIBILITY OF ERROR INHERENT IN THE HUMAN DECISION
MAKING PROCESS. AT BEST,THEN, THE TURING TEST WILL BE ABLE TO GIVE US ONLY A
HINT AT THE PRESENCE OF ANOTHER MIND; A LEVEL OF PROBABILITY.