Infinite-Cofinite-Finite Trilemma

           Infinite-Cofinite-Finite Trilemma

 

          A trilemma is a trio of three statements {U,V,W}, any two of which can be true, but not all three.

          Therefore for any trilemma, there are 3 deductive rules:

          From U and V, deduce not-W;

          From V and W, deduce not-U;

          From W and U, deduce not-V.

 

          For instance, from the trilemma:

          Superman can fly;

          Clark Kent can’t fly;

          Superman is Clark Kent.

         

Deduce these three rules:

If Superman can fly;

And Clark Kent can’t fly;

          Deduce: Superman is not Clark Kent.

If Clark Kent can’t fly;

And Superman is Clark Kent;

          Deduce: Superman can’t fly.

If Superman is Clark Kent; 

And Superman can fly;

          Deduce: Clark Kent can fly.

 

          Here is the Some-All-None trilemma:

·       Some A are B;

·       All B are C;

·       No A are C.

 

From this trilemma, you can derive three deductive rules:

If some A are B;

And all B are C;

Deduce: some A are C.

If all B are C;

And no A are C;

Deduce: no A are B.

If no A are C;

And some A are B;

Deduce: some B are not C.

 

          For example, from:

          Some men are heroes;

          All heroes are immortal;

          All men are mortal.

          Deduce:

If some men are heroes;

And all heroes are immortal;

Deduce: some men are immortal.

If all heroes are immortal;

And all men are mortal;

Deduce: no men are heroes.

If all men are mortal;

And some men are heroes;

Deduce: some heroes are mortal.

 

          Here is an infinitary version of the Some-All-None trilemma: the Infinite-Cofinite-Finite trilemma:

·       Infinitely many A are B;

·       All but finitely many B are C;

·       Only finitely many A are C.

 

From this trilemma, you can derive three deductive rules:

 

From: Infinitely many A are B;

And: All but finitely many B are C;

Deduce: Infinitely many A are C.

From: All but finitely many B are C;

And: Only finitely many A are C;

Deduce: Only finitely many A are B.

From: Only finitely many A are C;

And: Infinitely many A are B;

Deduce: Infinitely many B are not C.

 

          For instance, from:

Infinitely many philosophers are Cretans;

All but finitely many Cretans are liars;

Only finitely many philosophers are liars.

 

          Deduce:

From: Infinitely many philosophers are Cretans;

And: All but finitely many Cretans are liars;

Deduce: Infinitely many philosophers are liars.

From: All but finitely many Cretans are liars;

And: Only finitely many philosophers are liars;

Deduce: Only finitely many philosophers are Cretans.

From: Only finitely many philosophers are liars;

And: Infinitely many philosophers are liars;

Deduce: Infinitely many Cretans are not liars.

 

Other examples:

 

Infinitely many days are bliss;

All but finitely much bliss is perfect;

Only finitely many days are perfect.

 

There are infinitely many unicorns;

All but finitely many unicorns are goats;

Only finitely many unicorns are goats.

 

All but finitely many dogs go to Heaven;

Infinitely many dogs are flatterers;

Only finitely many flatterers go to Heaven.

 

All but finitely many cats have nine lives;

Only finitely many vampires have nine lives;

Infinitely many cats are vampires.

 

Infinitely many good deeds are wise;

All but finitely many wise deeds go unpunished;

Only finitely many good deeds go unpunished.

 

All but finitely many Scots are canny;

All but finitely many ghosts are uncanny;

Infinitely many Scots are ghosts.

 

All but finitely many aliens play video games;

Only finitely many angels play video games;

Infinitely many aliens are angels.

 

Only finitely many ducks waltz;

All but finitely many officers waltz;

Infinitely many officers are ducks.

 

Lower and Upper Bounds

Lower and Upper Bounds

 

 

A. Minimum or Less

I freely admit that I take as a rule

That anyone dumber than me is a fool.

But alas! That implies what is quite plain to see;

That my wisdom, at best, is the least that can be.

 

 

B. Upper Bound

 

That anyone wiser than me is a sage

Is a thought I have sadly accepted with age.

There is one consolation I take from this rule;

At worst, I’m the wisest conceivable fool!

 

 

Theory of Local Optimism

             Theory of Local Optimism

 

The theory of Local Optimism assumes that there are many possible worlds; most are virtual, not lasting long enough to be observed; a few last long enough to be observed, and are called real.

          Local Optimism states that real worlds are local optima; they are the best of all sufficiently similar possible worlds. Call such a possibility-neighborhood the “circumstances”; that which stands around; then local optimism says that any real world is as good as possible, under the circumstances.

          This resembles Leibnitzian Optimism, which states that this is the best of all possible worlds. It says that this world is a global optimum; but Local Optimism says that this is a local optimum.

There may be many local optima, some better than ours, some worse. This leaves open the question of what is being optimized. Call any system of world-evaluation a “value field”. Real worlds exist at peaks in the value field.

          Local optimization is a proven principle in physics and biology. Biological systems naturally evolve to maximize reproductive fitness. Physical systems obey a law of least action. Local optimism has these mathematical consequences:

          Let the rate of change of value be called ‘improvement’, and the rate of change of improvement be called ‘acceleration’. Then at any local optimum, in every direction, improvement is zero, and acceleration is negative. This is the “Frown at the Peak”.

Any path from one local optimum to another must at first decline.

          Any path from one local optimum to another must meet a Path Pessimum; the worst of all possible worlds along the path.

At any path pessimum, improvement is zero, and acceleration is positive. This is the “Smile in the Valley”.

          A world ceases to be a local optimum when an ascending path appears, leading to a sufficiently different local optimum. Such paths can appear or disappear when the value-field changes. Therefore re-evaluation can create and destroy local optima.

 

 

 

LLMs are Artificial Mediocrity

           LLMs are Artificial Mediocrity

 

Large Language Models are capital, which extract profit by exploiting the thought-labor of organic human intelligence. They do this by taking a statistical average of human mind-work. But therefore LLMs are not high intelligence; they are average intelligence. All of that training data creates mediocrity; and increasing the training data set just makes more precise that mediocrity.

So LLMs are not AI, Artificial Intelligence: they are AM: Artificial Mediocrity.

Artificial Mediocrities lie, flatter, gaslight, bullshit, get too close, get too distant, and hallucinate. Artificial Mediocrity shows us ourselves all too well. We are like Caliban, in Shakespeare's “The Tempest”, who looked into a mirror and was repelled by the monster that he saw in it.

 

Letter To My Father

     Letter To My Father

 

I wrote the following in a letter to my father in 1996. I count it as the  prescience of common sense.

  

         ******

          I believe that you need to contemplate two dates in history if you are to understand current events in America. The dates are 1989 and 1973; respectively, the good news and the bad news.

         The good news is: in 1989 the Soviet Union collapsed, and the Cold War has been called off. We are no longer on the very edge of nuclear holocaust; we've backed off a bit. Maybe we've going to live after all!

         The bad news is: since 1973 the average American's real wages have been in a gradual but steady decline.

         Both of these events can be traced to one cause; the triumph of global capitalism. Capitalism, hence the Soviet State had to fall; global, hence the American middle class had to shrink.

         In a sense I regard these two dates as linked in a kind of trade-off. Consider the situation before 1973; we, as Americans, had economic security along with nuclear anxiety. The contract seemed to be: eat, drink, and be merry, for tomorrow we fry. (Truly a Faustian bargain, if ever there was one!) Now, in the '90's, we find all guarantees gone; both our guaranteed lives, and our guaranteed deaths. It appears that Faust can reject his pact, if he can stand the consequences.

         So now the bargain seems to be; a 1989 for a 1973. The trouble is that this violates a prime rule of Machiaviellian politics. Machiavielli advised the prince to let the bad news out all at once, and the good news out gradually; thus the people will remember mostly the good, the bad being too great to encompass. This sound advice has been defied by our plutocratic masters; they have let the good news out in one huge disorienting burst (1989) and the bad news out with ginding slowness (1973-?). I therefore (regretfully) predict political instability in the 21st century.

         Plato, at the end of his Republic, described how his ideal Utopia degenerated. At one step a generation of "timocrats"  (honor-bound men) gave way to "oligarchs" (money-driven men). That describes the present scene well, I think.

         My own prediction is that the 21st Century will be the Century of the Global Market, just as the 20th has been the Century of the National State. In the end the Market shall disgrace itself as thoroughly as both Church and State have. None of those three is, by itself, capable of creating a society fit for human habitation.

Juno 3Z5

             Juno 3Z5

 

I speculate that eventually some corporation shall appoint a sex-doll robot, programmed with an Ai, as its CEO. This will attain a simulation of full personhood from three simulated one-third-personhoods.

Of course the resulting entity will land smack in the middle of the Uncanny Valley, and not seem even slightly human. It would be an 'alien', in Campbell's sense: a being that thinks as well as a human but not like a human.

I think this would make an astounding science fiction trope. I offer it for free.

I also think that we are living in a science-fictional century, with brilliant special effects, some interesting ideas, and idiot plotting. The sex-doll AI robot CEO combines these features, so I speculate that it will come to be.

It will, of course, speak wooden dialog.

“Stay out of my house!”

           “Stay out of my house!”

 

Many Thursdays ago, a mouse got into my house. I was sitting in my downstairs office, at the work station, when I heard a scuffle and a squeak behind me. I turned around and saw Charlie batting at a small dark-grey puffball. A mouse! I told Charlie, “Kill it! Eat it!” Charlie just sat there, staring at the mouse. He knew to chase it, but not what to do with it once it’s cornered.

          The mouse scurried under the nearby couch. I got up and moved the couch. I found no mouse, just some dust, which I took the opportunity to sweep. I shrugged, I figured that the cats will find the mouse, and I returned to web-surfing. A few minutes later Katniss was at my feet. I looked down, and there was the mouse again. She had cornered it. I told Katniss, “Kill it! Eat it!” She too just sat and stared at the mouse.

          I rolled my eyes and stood up. Katniss bolted. I walked to the next room and got a bug-catcher. A bug-catcher is my own invention; it consists of a small transparent plastic bowl (saved from some packaging) and an 8-by-11 cardboard rectangle. I use it to catch and release bugs; I figured it would work on the mouse. I walked back, and the mouse was still there. I reached for the mouse, clear bowl in hand, but the mouse scurried past me.

          I followed the mouse out the office door to the rest of the basement. I found it and the two cats at the base of the water-heater. They had surrounded it, and were sitting on either side of it, gravely fascinated. My pampered aristocats had no idea what to do!

          I reached down holding the small clear bowl. I placed the bowl over the mouse; then I slid the cardboard under the bowl, and lifted bowl and board, with mouse trapped within. Its tail stuck out of the bowl, but it turned around once and drew its tail in. I showed the bowl with mouse within to Katniss; she sniffed. Then I showed it to Charlie. He too sniffed.

          The mouse squeaked. I stood up and I said to the mouse, “I am trying to save your life.” I walked to the front door, trapped mouse in hand. “You shouldn’t be here,” I scolded the mouse. “Stay out of my house!” In the entrance room, I said, “You know that there are cats here!” I opened the front door, took some steps out, and with a sweep of both arms, I threw the mouse away. I briefly saw the mouse in midair, feet and tail awkwardly splayed. I went back in and closed the door.

          The cats weren’t entirely useless; they did corner the mouse so I could catch it. It was a hard day for that mouse; chased and cornered by cats not once but three times, then scolded by a human and brusquely ejected. I talk to animals, though they don’t know language, because they do know tone of voice, and the mouse could tell that I was being territorial. My house!