Created Already In Motion

Fol­lowup to: No Univer­sally Com­pel­ling Ar­gu­ments, Pass­ing the Re­cur­sive Buck

Lewis Car­roll, who was also a math­e­mat­i­cian, once wrote a short di­alogue called What the Tor­toise said to Achilles. If you have not yet read this an­cient clas­sic, con­sider do­ing so now.

The Tor­toise offers Achilles a step of rea­son­ing drawn from Eu­clid’s First Propo­si­tion:

(A) Things that are equal to the same are equal to each other.
(B) The two sides of this Tri­an­gle are things that are equal to the same.
(Z) The two sides of this Tri­an­gle are equal to each other.

Tor­toise: “And if some reader had not yet ac­cepted A and B as true, he might still ac­cept the se­quence as a valid one, I sup­pose?”

Achilles: “No doubt such a reader might ex­ist. He might say, ‘I ac­cept as true the Hy­po­thet­i­cal Propo­si­tion that, if A and B be true, Z must be true; but, I don’t ac­cept A and B as true.’ Such a reader would do wisely in aban­don­ing Eu­clid, and tak­ing to foot­ball.”

Tor­toise: “And might there not also be some reader who would say, ‘I ac­cept A and B as true, but I don’t ac­cept the Hy­po­thet­i­cal’?”

Achilles, un­wisely, con­cedes this; and so asks the Tor­toise to ac­cept an­other propo­si­tion:

(C) If A and B are true, Z must be true.

But, asks, the Tor­toise, sup­pose that he ac­cepts A and B and C, but not Z?

Then, says, Achilles, he must ask the Tor­toise to ac­cept one more hy­po­thet­i­cal:

(D) If A and B and C are true, Z must be true.

Dou­glas Hofs­tadter para­phrased the ar­gu­ment some time later:

Achilles: If you have [(A⋀B)→Z], and you also have (A⋀B), then surely you have Z.
Tor­toise: Oh! You mean <{(A⋀B)⋀[(A⋀B)→Z]}→Z>, don’t you?

As Hofs­tadter says, “What­ever Achilles con­sid­ers a rule of in­fer­ence, the Tor­toise im­me­di­ately flat­tens into a mere string of the sys­tem. If you use only the let­ters A, B, and Z, you will get a re­cur­sive pat­tern of longer and longer strings.”

By now you should rec­og­nize the anti-pat­tern Pass­ing the Re­cur­sive Buck; and though the coun­ter­spell is some­times hard to find, when found, it gen­er­ally takes the form The Buck Stops Im­me­di­ately.

The Tor­toise’s mind needs the dy­namic of adding Y to the be­lief pool when X and (X→Y) are pre­vi­ously in the be­lief pool. If this dy­namic is not pre­sent—a rock, for ex­am­ple, lacks it—then you can go on adding in X and (X→Y) and (X⋀(X→Y))→Y un­til the end of eter­nity, with­out ever get­ting to Y.

The phrase that once came into my mind to de­scribe this re­quire­ment, is that a mind must be cre­ated already in mo­tion. There is no ar­gu­ment so com­pel­ling that it will give dy­nam­ics to a static thing. There is no com­puter pro­gram so per­sua­sive that you can run it on a rock.

And even if you have a mind that does carry out modus po­nens, it is fu­tile for it to have such be­liefs as...

(A) If a tod­dler is on the train tracks, then pul­ling them off is fuz­zle.
(B) There is a tod­dler on the train tracks.

...un­less the mind also im­ple­ments:

Dy­namic: When the be­lief pool con­tains “X is fuz­zle”, send X to the ac­tion sys­tem.

(Added: Ap­par­ently this wasn’t clear… By “dy­namic” I mean a prop­erty of a phys­i­cally im­ple­mented cog­ni­tive sys­tem’s de­vel­op­ment over time. A “dy­namic” is some­thing that hap­pens in­side a cog­ni­tive sys­tem, not data that it stores in mem­ory and ma­nipu­lates. Dy­nam­ics are the ma­nipu­la­tions. There is no way to write a dy­namic on a piece of pa­per, be­cause the pa­per will just lie there. So the text im­me­di­ately above, which says “dy­namic”, is not dy­namic. If I wanted the text to be dy­namic and not just say “dy­namic”, I would have to write a Java ap­plet.)

Need­less to say, hav­ing the be­lief...

(C) If the be­lief pool con­tains “X is fuz­zle”, then “send ‘X’ to the ac­tion sys­tem” is fuz­zle.

...won’t help un­less the mind already im­ple­ments the be­hav­ior of trans­lat­ing hy­po­thet­i­cal ac­tions la­beled ‘fuz­zle’ into ac­tual mo­tor ac­tions.

By dint of care­ful ar­gu­ments about the na­ture of cog­ni­tive sys­tems, you might be able to prove...

(D) A mind with a dy­namic that sends plans la­beled “fuz­zle” to the ac­tion sys­tem, is more fuz­zle than minds that don’t.

...but that still won’t help, un­less the listen­ing mind pre­vi­ously pos­sessed the dy­namic of swap­ping out its cur­rent source code for al­ter­na­tive source code that is be­lieved to be more fuz­zle.

This is why you can’t ar­gue fuz­zle­ness into a rock.

Part of The Me­taethics Sequence

Next post: “The Be­drock of Fair­ness

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