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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