Posted by
Steve Smith on
URL: http://friam.383.s1.nabble.com/36-hour-online-game-research-exercise-tp7583780p7583788.html
Eric -
Where I got into this was actually the problem of the
excluded middle.
When I was first introduced to this
di-lemma (self-reference
intended) through the limitations of Aristotelian logic, I simply
dismissed A logic as an incomplete model of semantics. Either all
questions can be answered true or false or they cannot: true, or
false?
This just primed me for Tarski and eventually Zadeh on infinite
valued logics and "fuzzy set/logic" and then yet more fun things
like Dempster-Shafer and the Yager-Liu variants.
I was cringing that I had committed a rude thread
hijack,
As someone who hijacks his own sentences within a thread, it didn't
offend me, it represented an interesting (to me) tangent. The
pivot was the subtle homonym "game" as you point out.
since the use of "game" on the thread had emphasized
the interface and the method for pooling participant inputs. I
was using the notion of "game" more in the sense of a defined
interaction in which the structure is designed to solve a certain
problem in a way that the designer hopes he has some theory of.
I would claim the two are tied in the sense that the point of
pooling participant inputs and engaging a large pool through a
"playful" interface were used specifically to try to solve a
"certain problem in a way that the designer hopes he has some theory
of." Aside from the superficial motivations for making "everything
into a game", I think that the game theoretic (and other formal)
underpinnings are useful. In the vision cast by the SFSU teaser,
one would imagine that there *might very well be* an underlying game
theoretic abstraction of problem solving which structures the
interactions between the various players in the drama to help direct
their efforts toward actual problem solving, keep them out of cycles
and even "obvious dead ends"?
I did a little reading of Hintikka a long time ago, and will
try to say something correct, but caveat lector, because I get a
lot of stuff wrong.
Welcome to the club. I even get called on mine from time to time!
It is obvious (meaning, I think) that most of the struggle in
saying anything is not even to be right, but to say something
that has enough meaning to admit a right/wrong distinction.
Hence, while in di-lemma logic, it is fine to say that
statements which are not true are thereby false, that seems to
do very little good for a lot of what I find confusing and seek
clarity on, in the world. (Here I hope there is at least a
peripheral relevance to the problem of pooling inputs).
Yes, very much so. Crowd sourcing (pooling inputs?) problem
solving is more than eliciting a million thumbs-up/down like/dislike
votes... especially if you want to solve real world problems such
as "deciding what the real problem is and how it relates to the real
world, independent of any specific answer to the problem/question."
Hence, you can make Godel-like claims about unprovable but
true assertions, but they rely on assumptions that a suitable
notion of meaning must be assignable to any syntactically valid
construction, which then has an excluded middle.
Or maybe more to the point, the generalized
"law of excluded n+1th" . I twigged early in life to the
realization that yes/no true/false tests/questions were often
designed to reframe the test-taker answerer's perspective ("do you
still beat your wife?") and by extension, the multiple choice tests
tend to have the same flaw.
Whether one is to worry about that or not is a matter of
what you like to worry about, but clearly it is far from the
kinds of uses of truth values that I mostly worry about in
practical work.
Hmm... I felt I was tracking you right up until this one... I do
agree with the spirit of "we worry about what we choose to worry
about"... but are you saying that Godel's incompleteness is sort of
a parlor trick or that it just defers the real question to a higher
level of abstraction, not really settling (or unsettling) anything?
(this is my suspicion and I do have some hope that the line of
inquiry/discussion you allude to here might help sort that a bit?)
Hintikka's approach was to define "that which is true" by
claiming it must have a mapping to a strategy that is sure to
win in some appropriately defined game. "that which is false"
is a strategy that can surely be beaten by some other strategy.
All the other stuff, which can neither surely win nor surely be
beaten, is the middle, now not excluded.
Smacks of Wolfram's Class I-IV cellular automata. All CA are
either A) uninteresting because they achieve a steady (Class I) or
cyclic state (Class II) in finite time or B) uninteresting because
they are chaotic and random (Class III)... *EXCEPT* those which
magically appear to be actually *interesting* (Class IV), whatever
that (actually interesting) means.
The pleasing thing about this would be that, for large
games, the middle will probably grow combinatorially a lot
faster than the things that are either true or false. So I was
hoping that learning something about that in the context of
designed games might address some subset of the ways in which it
is possible to generate statements that seem to satisfy various
rules of syntax, but should not be presumed to have any
associated truth values (but best to show that if one _can_ give
them a proper semantics as strategies, in which nonsense has a
defined status).
Interesting... when you use the term "designed games" I think of
"evolved design of games". While there is a lot of intentionality
in those who seem to design the games (e.g. social customs,
political, religious, legal systems) we play within, it seems as if
the actual "large games" are evolved with a combination of something
like "natural selection" and very "directed selection" at play. I
like the phrase here "in which nonsense has a defined status". I
would claim that there is a meta-game in play where this is
literally and obviously the truth... it is why we have so many words
for "bullshit" to refer to utterances deliberately crafted to sound
meaningful while being meaningless. I *think* this is the bread and
butter of marketing and of politics (which contemporarily is
significantly driven by marketing?)
This was peripheral to a different topic about the relation
of the formal status of syntax and semantics as referees for the
content of expressions, where Jay Garfield from Smith College
pointed me at Montague Grammar, an attempt to define a syntax
for natural language that would be ensured of a self-assigned
semantics.
All I can think to say about this is "Lambdas really changed my
life" ...
Jay said it was a spectacular and informative failure, and
from what was learned, people could finally relax and
acknowledge that the syntax and the semantics of natural
language have different and at-least-in-part independent
origins. I think I was pestering Cosma about how to think about
that when he (who has read all things and understands most of
them) pointed me at Hintikka as a place to look for something
else interesting.
I didn't realize it was considered (by the community?) a spectacular
failure: Although I can believe that the following "
Montague held
the view that natural language was a formal language very much in
the
same sense as predicate logic was a formal language." has been
demonstrated to undervalue the richness of natural language. I
personally don't believe that natural language can be separated from
A) Culture and B) Embodiment. That does not mean, however, that
Montague's (and that derived from his) work isn't very useful and
important.
As a side note, my daughters and I collectively enjoy variations on
the traditional game of Scrabble, some of which allow the use of
proper names with the added benefit of being able to lay down tiles
such as "
Jaakko Hintikka"... makes me want to pour a
shot of
Koskenkorva Viina with an Absinthe chaser.
All best,
And some of the mediocre, not to allow the law of the excluded
middle to overdefine us!
Eric
- Steve
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