Us from Computers (part 5) It's only logical

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     Okay, so Functionalism as a Philosophic theory took another 60 years and a computer to develop.  They didn’t use the computer to figure anything out nor was it just any kind of computer, after all the Greeks had computers.  The computer that got philosophers thinking was a digital (as in counting), non-analog, general-purpose computer that could, theoretically, do anything.   Half a century later, my computer plays a mean game of chess, but still can’t make a decent gin martini, well, not the way I like them. 

     The thought went like this, if we make a machine that can read a bunch of ones and zeros that are actually a code of really simple instructions, even complex tasks, once broken down into the smallest possible operations of intellect, the computer could emulate the thinking process.  (It’s too bad early computer engineers didn’t have some machine to do their thinking for them, we could have had the digital highway generations ago—too bad that it’s really the Jersey turnpike.)  The man that brought you the thing that you use to find out how your friends are, what today’s meme the meme of three seconds ago, and see cute pictures of cats doing stupid things, was Alan Turing.  He was also the man that argued quite loudly that one day, in the far distant year of 2000, that human intellect would be challenged by our own creations and that we’d have to deal with this new artificial intelligence. 

     What Shelley’s imagination had done almost two fourscore before was being proposed again, just this time with physics, logic and math replacing chemistry and occult.  Just like Victor, Alan forgot to make his creation … not hideous.  It would take an a little over half a fourscore for computers to become beautiful but only a few decades to put most bookkeepers out of a job.   Maybe that was Dr. Frankenstein’s problem, he stopped at creature version 0.1. 

     So how did an overly complex calculator cause philosophers to think up Functionalism?  Enter Hilary Putnam (and like René, they’re both men, sorry this is still history, not herstory) and his concept of machine state functionalism.  Like Hobbes, Putnam thinks that we really are just calculating machines, but instead of slide rules, abacuses or whatever Hobbes had in his day, Putnam viewed all things that have a mind are really Turing machines.   

     Turing’s still theoretical concept of the thinking machine was based on algorithms of logic-based mathematics. Math is, in many ways, only one-step removed from the Philosophy of Logic’s attempts to model human intuition, specifically semantic logic (logic operations done in plain language).  According to some, Aristotle was one of the four greatest logicians.  (If Aristotle didn’t say it first, and get it wrong, it isn’t worth saying, or fixing.)

     Lucky for math majors the world wide, he did, and lucky for the rest of us normal people, Alfred Tarski (and others) was busy perfecting the field of Logic so that Turing’s machines might be able to do something more useful than a TI-25.  They were all working at nearly the same time, well Turing was building vacuum-tubed frankensteins during WWII, Tarski was exploiting… I mean utilizing his Berkley graduate students in the fifties, and Putnam didn’t coin his philosophic term until 1960, but given the previous timescales of advancement, that is partially at the exact same moment.

(For those still reading to find out why ‘can’ is a bad word, hopefully the following will explain that.)

     What Tarski did was to build on the works of previous Logicians and push the field into a form that would enable the first real-world abstract application apart from mathematics and philosophy, advanced computer science.  The thing he introduced was a way to model truth in both formal and natural language.  What’s the difference?  Well, if I say, Socrates was a man, all men are mortal, and therefore Socrates is mortal (Aristotle said this first), I have made a logical statement in my natural language, English.  I could express the same concept by saying,

Ax: all things that are x (because for some reason upside down “A” isn’t a standard character)

→: if ____, then ____.

s: Socrates

Ix: x is a man

Mx: x is mortal

1. Is

2. (Ax)(Ix → Mx)

3. (Is → Ms) (normally omitted from natural language argument)

 ∆ Ms

     Both statements are the exact same, or as close as you can get in any translation.  Both are equally true.  Both are useful in their own “native” language; computers don’t really speak English and most of us don’t speak Logic notation.  What Tarski did in logic was prove a set of rules that we can use to look at all that nonsense and figure out if it was true or not.  The above example is an easy one because like a good number of statements it is either true or it is false because we’re really only talking about one member of a larger group and as long as men are mortal and Socrates is a man, then he has to be mortal.  If he were a robot, then it would be false.  If men were immortal, it would be false.  So, statements in that form are either true or false all the time, all depending on how accurately the premises reflect reality as it actually is.  However, some statements are true at one level and false at another.

     His modeling system allowed a person to fairly quickly take logical notation and figure out if All/Some statements are false, and how many members you need in your set of objects to make it true or false.  One of the really cool things about Logic, most of the time a statement like that will be true if you only have one member in your set, but be false in the second and subsequent sets of increasing size, or they will be false in the first set and true in the rest. 

     For instance, if everyone trusts everyone, and you only have one really, truly honest and trustworthy person that you are considering, then it is true.  If you have one Christian and one Atheist, there is a damn good chance the statement will be false.  If you add in one tax collector, you’re guaranteed to have a false statement.

     Way back at the beginning we were talking about ‘can’ and the deterministic universe (I know it was a lot of word ago), the claim was that a mechanical universe, with mechanical parts in it, shouldn’t produce non-mechanical minds.  That is a lie; or rather it isn’t true in all possible worlds.  The basic claim that we live in a mechanical cosmos is that all things in the universe are deterministic.  However, it is conceivable that something truly random and apparently non-mechanical could result even from physical interactions (in fact any and all interactions at a small enough level) even in a seemingly deterministic universe.  And before all you Einstein fans out there jump down my throat about this, I have two words for you, Quantum Mechanics. 


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