On Santa and the Noble Lie

        On Santa and the Noble Lie

            Plato, in his “Republic”, admits that his ideal Republic must use what he called a “noble lie”. The lie is that there are four kinds of men; of gold, of silver, of brass and of iron. The men of gold are the philosopher-kings, the men of silver are the guardians, and the men of brass are the artisans, and the men of iron are the farmers. The upper classes of Plato’s Republic tell this to the lower classes, to reconcile themselves to their lives; but it is a lie, as Plato admits, for there is only one breed of human, not four.

            A deception this crass and self-serving is called noble? And stranger still, Plato thinks it would work? For surely artisans and farmers are wise to the world’s lies. Their livelihood is the market, so they know very well that the buyer must beware! They’ve seen brass called gold, and gold called brass! Plato’s Noble Lie can fool only the naïve and unworldly;  to wit, his Republic’s upper classes. His philosopher-kings fool only themselves.

            A lie self-serving when told, intended for permanence, ineffective to its cynical hearers, corrupting to its tellers; what is noble about any of that? I would call a lie noble only if it costs the teller, and it’s built to be temporary, and it improves the minds of the hearers when the deception inevitably fails. A lie is noble if it creates philosophers.

            Therefore consider the legend of Santa. It’s a lie, all right; a known falsehood told to the young by their parents, their peers, shopkeepers, radio, TV, the Internet, NORAD… even the President of the United States is in on the conspiracy! Stated baldly like that, it sounds weird; but that’s the plain truth. And the purpose of this elaborate prank? To collapse! Eventually, inevitably, the child discovers that there is no Santa Claus; so you shouldn’t believe just anything you hear! Santa, in the very act of vanishing, leaves behind a lasting gift: sales resistance.

            Santa Claus is a failed myth, deliberately told by unbelieving adults to their credulous children as an initiation into skepticism. His liberating revelation is that he does not exist. Santa is to the gods as a vaccine is to disease; a failure coopted into a warning. Santa is a paradoxical saint of a doubt-based culture.

            I say this as an outsider to the Santa cult; for I do not participate in the rites of shopping. However, I did initiate my daughter into skepticism via the Tooth Fairy; an equally noble lie.

On Corporate Religion

On Corporate Religion

I hear that the Supreme Court shall soon consider a case where the owners of a corporation do not wish to pay for their workers' abortions; they claim that would violate the corporation's religious rights under the first amendment.

More absurd fallout from Citizen's United! For how can corporations have religion? They don't even have souls! According to Justice Brandeis, corporations have 'no bodies to condemn or souls to damn'. So if a corporation is to have a religion, then it must be a religion for persons without souls.

What might such a religion be? Satanism, perhaps? Or Objectivism? Your suggestions are welcome!

I ask because this could be material for a fantasy story. Our hero visits Hell, he encounters a Corporation, the soulless monster expounds upon its religion, a faith suitable for soulless monsters. The satirical possibilities are endless.

Odd Logic, 5 of 5; Odd Sums of Kleenean Logic

ODD SUMS OF KLEENEAN LOGIC

        Linearity isn’t always diagonal. Non-atomic functions are always multi-linear, but needn’t be diagonal-linear.  For instance, consider odd sums on Kleenean logic.

        Kleenean Logic has three values F, I, and T; and atomic functions ‘and’, ‘or’, and ‘not’; all defined by:

        Not T = F ;  not I = I ;  not F = T

        (X and Y) = (Y and X); (X or Y) = (Y or X)   for all X and all Y

        (T and X) = (F or X) = X  for all X

        (F and X) = F  ;  (T or X) = T for all X

        (X and X) = (X or X) = X   for all X.

            not   and Y  F I T    or Y  F I T 

        X

        F    T           F F F          F I T

        I    I           F I I          I I T

        T    F           F I T          T T T

        Now consider the odd sum t+i+f: call it “j”. Then by object cancellation, any three of t,i,j,f sum to the fourth. Also:

        not(j) = not(t)+not(i)+not(f) = f+i+t = j

        T and J = (T&T)+(T&I)+(T&F)    = T+I+F = J

        T or J  = (TorT)+(TorI)+(TorF) = T+T+T = T

        F and J = (F&T)+(F&I)+(F&F)    = F+F+F = F

        F or J  = (ForT)+(ForI)+(ForF) = T+I+F = J

        I and J = (I&T)+(I&I)+(I&F)    = I+I+F = F

        I or J  = (IorT)+(IorI)+(IorF) = T+I+I = T

        J and J = (T&T)+(T&I)+(T&F)+(I&T)+(I&I)+(I&F)+(F&T)+(F&I)+(F&F)

               =  T+I+F+I+I+F+F+F+F  =  T+I+F = J

        J or J  =

         (TorT)+(TorI)+(TorF)+(IorT)+(IorI)+(IorF)+(ForT)+(ForI)+(ForF)

               =  T+T+T+T+I+I+T+I+F  =  T+I+F = J

            not   and Y  F T I J    or Y  F T I J 

        X

        F    T           F F F F          F T I J

        T    F           F T I J          T T T T

        I    I           F I I F          I T I T

        J    J           F I F J          J T T J

        In Kleenean logic, ‘x and y’ is the lesser of the two values, under the order F<I<T; and ‘x or y’ is the greater of the two values; and ‘not’ pivots the three values around the middle value I.

        When you add J, then “and” is the minimum operator, and “or” is the maximum operator, for this diamond-shaped lattice:

                       I

               <              <

        F                              T

               <              <

                       J

        Also, ‘not’ flips this diamond through its I-J axis.

        This is “diamond logic”, a paradox logic including Kleenean logic, and here derived from it by odd sums.

        Now consider the function d(x):

               d(x) = (x and not x)

        d(T) = F ; d(I) = I ;  d(F) = F

        therefore d(T)+d(I)+d(F) = F+I+F = I;

        but d(F+I+T) = (J and not J)  =  (J and J) =  J.

        d is not diagonal-linear; d(t+i+f) needs nine terms:

        d(t+i+f) =  (t+i+f) and not(t+i+f) 

        =       (t and not t) + (t and not i) +(t and not f) +

               (i and not t) + (i and not i) +(i and not f) +

               (f and not t) + (f and not i) +(f and not f)

        =       f + i + t +

               f + i + i +

               f + f + f 

        =       f+i+t  

        =       j

        Here the terms off the lower-left-to-upper-right diagonal cancel out. That counter-diagonal is f+i+t, or j; the main diagonal is f+i+f, or i. So d is multi-linear, but not diagonal-linear.

Odd Logic, 4 of 5; Odd Sums of Objects

    ODD SUMS OF OBJECTS

        To define an odd sum of objects x+y+z, we need to define predicates and functions on those objects. Let us specify certain predicates P1, P2, … and functions f1, f2, …; call those the “atomic” predicates and functions; let other predicates be defined from the atomic predicates plus the logic operators; and let other functions be defined by composition of atomic functions. And let all atomic predicates and functions be odd-linear:

       

        P(x+y+z)   =   P(x)+P(y)+P(z)

        f(x+y+z)   =   f(x)+f(y)+f(z)

        Then all predicates defined from logic operators and atomic predicates will be multi-linear, thus:

        If P and Q are atomic predicates, then

               (P and Q)(x+y+z)      

        =       P(x+y+z) and Q(x+y+z)

        =       (P(x) and Q(x)) + (P(x) and Q(y)) + (P(x) and Q(z)) +

                (P(y) and Q(x)) + (P(y) and Q(y)) + (P(y) and Q(z)) +

                (P(z) and Q(x)) + (P(z) and Q(y)) + (P(z) and Q(z))

        If f, g and h are atomic functions, then

               f(g(x+y+z), h(x+y+z))         

        =       f(g(x),h(x)) + f(g(x),h(y)) + f(g(x),h(z)) +

               f(g(y),h(x)) + f(g(y),h(y)) + f(g(y),h(z)) +

               f(g(z),h(x)) + f(g(z),h(y)) + f(g(z),h(z))

        “And” and f take two inputs, so the odd-sum had 3^2 = 9 terms. For three-imput logic functions on predicates, or three-input functions, the odd-sum will have 3^3 = 27 terms, and so on.

        Of particular importance is the equality predicate, defined extensionally from the atomic predicates:

        (x=y)   =       conjunction of (P(x) iff P(y))

        x+x+y has the same atomic properties as y;

               P(x+x+y) = P(x)+P(x)+P(y) =  P(y)

        Therefore x+x+y = y   ;  this is object cancellation.

        Object cancellation implies that if f is a commuting atomic function;  f(a,b) = f(b,a)  ;  then:

        f(x+y+z,x+y+z)

        =       f(x,x) + f(y,x) + f(z,x) +

               f(x,y) + f(y,y) + f(z,y) +

               f(x,z) + f(y,z) + f(z,z) +

        =       f(x,x) + f(y,y) + f(z,z)

        because the off-diagonal terms cancel out. This is diagonal linearity.