BINARY VALUES
COMBINATORIAL LOGIC (ie TRUTH TABLES or BOOLEAN LOGIC)
OPERATORS (ie OPERATIONS)
The Test:
These are concepts. Can we do what Babbage did and imagine a computer using these concepts applied to a machine which combines the bead abacus and simple household electric circuitry? Would it work?
But first another historical note.
Kurzweil's 1990 book, "The Age of Intelligent Machines" contains an excellent unit on truth tables and computing, although the present hypothesis disagrees with its conclusion. It is titled, "A NOR B: The Basis of Intelligence?" Here is what Kurzweil is saying: "To the extent that one accepts the Church-Turing thesis, the simple NOR gate can be considered (at least in theory) the basis of human intelligence". (page 152). What is the Church-Turing thesis? "The Church-Turing thesis states that all problems solvable by a 'sentient being' are REDUCIBLE TO A SET OF ALGORITHMS. Another way of expressing this thesis is that machine intelligence and human intelligence are essentially equivalent." (ibid). The present hypothesis disagrees because it states that yes/no, 1/0, T/F is the the basis (in formal logic) of human intelligence which is essentially what Aristotle said and that the logic gates of computing, based on Boolean logic at the conceptual level, are a redundancy, albeit a very practical redundancy. "Boolean algebra and truth tables are closely related, as we have seen. One can always be expressed in terms of the other." (Warring, page 92 of "Logic Made Easy", 1985).
Why such interest in Truth Tables? George Boole himself said it: "The mathematics we have to construct are the mathematics of the human intellect." (page 7 of "Mathematical Analysis of Logic" by George Boole, 1847).
Is this the very foundation of human thinking and if so, can we not construct a machine to simulate it? SI or simulated intelligence may be a better expression than AI or artificial intelligence since a very advanced machine capable of manipulating Truth Tables better than any human would have very real super-human intelligence.
TRUTH: THE HEART OF PHILOSOPHY OF LOGIC
Stephen Reed writes in "Philosophy of Logic" that "We start, therefore, at the heart of philosophy of logic, with the concept of truth." (page 3).
When the Greek philosopher, Cratylus of the Heraclitean School, was asked, "What is truth?" he would answer only by raising one finger. Some might interpret this as a kind of sarcasm, a way of dismissing the question. But it may also be that he was expressing binary notation. Finger up =1; finger down = 0. Aristotle said essentially the same in his "Metaphysics" when he wrote, "To say that (either) that which is is not or that which is not is, is a falsehood; and to say that that which is is and that which is not is not, is true." (101b26). We have the same logic-philosophy position expressed by another historical figure, Jesus Christ, reported by his biographer, St. Matthew to have said, Let your yeses be yes and your nos be no, because more than this comes from evil (Matthew 5:37). COMBINATIONS of T/F give us the complete picture of truth and falsehood from the perspective of formal logic. The only OPERATION required is to correctly connect to the T's and the F's as expressed in the Truth Tables or expressed by a machine or expressed by a human. The computer then, is a giant connection machine. It connects and reconnects at an amazing speed and with amazing numbers of T/F values but would it not yield the same result if it worked more slowly as long as it contained the same number of POSITIONS from which those T/F VALUES can be expressed? That is the present hypothesis expressed in one sentence.
In "Logic" by Wesley C. Salmon, we read: "All of these connectives are known as truth-functional CONNECTIVES, for the truth value of any compound statement constructed by means of these connectives is completely determined by (is a function of) the truth VALUE of the parts." (page 35). So here we have two of the four key concepts for a logic machine as listed at the top of this section. In Runes' Dictionary of Philosophy, we find under "Logic Machines" a brief history, including the statement that "Such devices would indicate that the logical process is mechanical to a notable degree" and the note that William Stanley Jevons in 1869 came up with "a species of logical abacus".
Warring, in "Logic Made Easy" says "Boolean algebra and truth tables are closely related, as we have seen. One can always be expressed in terms of the other." (page 92). Moreover, on page 85 he links the VALUES as expressed above in terms of T/F, Yes/No at the level of human thinking with the On/Off connections of a machine. "These (logic expressions) can be evaluated as true or false, yes or no, in the case of general subjects (eg premises); or on or off, go or stop, in the case of signals".
Now we only have to use Truth Tables or matrices if you prefer, to establish the valid chain of T/F, Yes/No
VALUES and make sure that our CONNECTION MACHINE makes the correct connections so that each POSITION in the table/matrix is filled with the correct value. Doing this in logic is called a "Truth Function". In hardware it is the circuitry of an Electric Abacus.
http://www.geocities.com/ELECTRIC_ABACUS/page3