Penrose Star of David B

 

Penrose Star of David A

 

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.

 

My Resolution Score

My Resolution Score

 

 

On December 31, 2022, I made three New Year’s resolutions:

1. Not to make any New Year’s resolutions;

2. To get to bed before midnight;

3. To break all of my New Year’s resolutions.

I broke resolution #1 when I made it; I broke resolution #2 at midnight; and I broke resolution #3 as much as I did not.

I figure that I kept 1/2 out of 3, which equals 1 out of 6. That’s a relatively good ratio.

 

Amoeba’s Dilemma

Amoeba’s Dilemma

 

Lou Kauffman:

Replacement Perplexity

 

An intelligent amoeba confided

That he was perplexed and besided.

Which one is me,

said he to he

And where do I go when divided?

 

 

Nathaniel Hellerstein:

Divided Multiplication

 

The other amoeba replied

It is you you are floating beside

For surely you see,

I am you, you are me

By dividing, you-I multiplied.

 

Does Money Exist? 12 of 12

         Part 12. Critique of an alleged science, and a self-validation.

 

            If money might not exist, then is there a science of money? Is economics truly a science? For science requires objectivity, and who can be objective about money? Certainly not those paid to study it; for they are paid by those who have money, rather than those who do not, and he who pays the piper calls the tune. By its own logic, professional economics must be corrupt. Therefore it has a built-in plutic bias; it must ignore aplutic doubts, and attack antiplutic norms.

             To be objective, an economist must not expect to reap personal gain from his or her findings. Therefore scientific economics, if it exists, must be done aplutically, moneyless, in the public domain. Otherwise it is not science, but is instead pseudo-science, propaganda, deceptions and delusions paid for by the rich.

            Professional economics must hide its useful insights, if any. Amateur economics like this essay lacks plutic bias, but is incomplete, marginally competent, and under-marketed. Either way, truly scientific economics is scarce - as befits a science of scarcity.

             Truly scientific economics is scarce; so this essay just might be the only scientific economics treatise that you have ever read. Therefore this essay declares that this essay is necessary!