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Subject: Why use arbitrary letters instead of familiar logic symbols on the dice? rss

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Can anyone explain why this game uses arbitrary capital letters in place of the standard symbols of the propositional calculus? Is there some goal or feature of this game I'm missing?

I haven't played much, but so far it makes the game really hard to learn, and (at least seem) of questionable educational value.

EDIT: It turns out this notation is not arbitrary (in the sense of unique to this game) after all!
 
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Are your familiar logic symbols not arbitrary? I'm guessing the authors used the arbitrary symbols they were familiar with. I seem to remember reading that the authors used these extensively in teaching and testing, but I'm a bit fuzzy on it - it's been four decades since I played this.
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Sphere wrote:
Are your familiar logic symbols not arbitrary?

Well of course they are. Perhaps "not used anywhere else", at least to my knowledge, is what I should have said instead of "arbitrary".

Is "K" really used for "and" anywhere else? "A" for "or; "C" for "then"?
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There were a lot of things in use 50 years ago that aren't in use now.
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Sphere wrote:
There were a lot of things in use 50 years ago that aren't in use now.

But I want to play this game now (without any 60s weirdness).

And in any case the question remains: were these symbols (C, A, K, etc.) ever widely used in propositional calculus?
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The symbol usage is specific to the game, which was devised in the 1960s, long before computer programming languages were widespread. Back then, I believe the most commonly accepted way to indicate the logical terms and, if-then, or, and not was to use those selfsame English words. AFAIK no one used a vertical bar for or, nor an ampersand for and, nor an exclamation point for not. Did you have other symbols in mind? Maybe they wanted a prefix notation for all such operators, to provide consistency within the game. Anyone familiar with symbolic logic should have little trouble learning it.

EDIT: Maybe some mnemonics would help.

C rhymes with the French word si, which means if.
E means equivalence, that's easy.
N means not.
A remember the aorta, a blood vessel in your heart, to associate A with or.
K Remember the German philosopher Emmanuel Kand.
R means reiterate. Or something.
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twixter wrote:
The symbol usage is specific to the game, which was devised in the 1960s, long before computer programming languages were widespread. Back then, I believe the most commonly accepted way to indicate the logical terms and, if-then, or, and not was to use those selfsame English words.

The propositional calculus did not originate with computer programming languages. In any case, ~ and ¬ were certainly in use by the 1930s (in fact ~ was used before 1900); ∧ and ⇒ maybe a bit later.
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David, I don't think Aldaron is talking about computer languages, but the symbols commonly used in symbolic logic. It's a good question. My recollection of textbooks from that time were that the same operators were used then as today: "V" for "or", inverted V for "and", and "~" for "not" (although I'm not certain about the last one). I think that a one-sided arrow and two-sided arrow were used for "if-then" and "if-and-only-if", but I could be wrong about that. In any event, I've never seen the letters employed in WFF 'N PROOF used for these operators and can't imagine they ever were used, as that would have been supremely confusing.

One possible explanation is that Layman Allen wanted to use something more familiar and less bizarre looking for his audience, so he went with letters instead of symbols. The game itself is so obtuse that that seems unlikely, but you never know. It's particularly weird because I believe that the companion game for Set Theory (OP-Sets) did use standard set theoretic symbols for the operators. It's all very strange, but maybe one of the people involved with the project is still alive and will be able to address the question.

I actually played this game as a kid in the sixties, which should let you know that Geekdom starts early. It was pretty strange, but I guess I was up for just about any game if I could find a willing adult. I assume it was an extension of the push toward "modern math", the disastrous attempt to get more theoretical mathematics into elementary school courses. I've never understood why that was supposed to let us win the space race with the Sputnik-launching Rooskies, but that's what the best and the brightest seemed to think at the time. We still do a terrible job of teaching math in this country, but at least it's because of the way that it's taught and not because of the subject matter.
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Yes, those letters were definitely in use at some time, and may still be in some contexts, particularly when using Polish notation with propositional calculus.

C - Conditional "if...then"
K - Konjunction (because C was taken) "and"
A - Alternate "or"
E - Equivalence "if and only if"
N - Negation "not"

So instead of expressing "a and b" as

a ^ b

they would use

Kab

Instead of expressing "a and (b or not c)" as

a ^ (b v ~c)

they would use

KaAbNc

Polish notation eliminates the need for parentheses and other grouping symbols.
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Larry Levy wrote:
I actually played this game as a kid in the sixties, which should let you know that Geekdom starts early. It was pretty strange, but I guess I was up for just about any game if I could find a willing adult. I assume it was an extension of the push toward "modern math", the disastrous attempt to get more theoretical mathematics into elementary school courses. I've never understood why that was supposed to let us win the space race with the Sputnik-launching Rooskies, but that's what the best and the brightest seemed to think at the time. We still do a terrible job of teaching math in this country, but at least it's because of the way that it's taught and not because of the subject matter.

It wasn't meant to teach math. The marketing hoopla was all about teaching people to think more logically. I'm pretty sure promotional materials claimed that they had documented increases in S.A.T. scores or I.Q. scores (or something along those lines) for people after playing regularly for a number of weeks. I also seem to remember a connection with Princeton University... was the guy a professor there or something? Personally, I think learning the symbology is a low bar for anybody who's willing to tackle something that is (by design) that much of a brain burner.

If I had more time, I'd dig mine out of the closet and have a look. Last time I did, I recall that the foam which held the dice was turning to dust.
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I was referring to New Math, Sphere, but as you say, the intent was the same, to get people thinking more logically. I still think the whole thing was loopy (and I lived through it). The goal was fine, but the method chosen to implement it was very rigid (the opposite of logical thinking) and it was taught at far too early an age.
 
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Phil Fleischmann wrote:
Yes, those letters were definitely in use at some time, and may still be in some contexts, particularly when using Polish notation with propositional calculus.

That's interesting, Phil. I hadn't considered Polish notation. I first encountered it in the mid-seventies, because the HP calculators used it, but of course it predated that.

Looks like we've got our answer, Aldaron. Polish notation makes a certain amount of sense, since it meant the game didn't need parentheses.
 
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Phil Fleischmann wrote:
Yes, those letters were definitely in use at some time, and may still be in some contexts, particularly when using Polish notation with propositional calculus.

Excellent.
 
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Larry Levy wrote:
Looks like we've got our answer, Aldaron. Polish notation makes a certain amount of sense, since it meant the game didn't need parentheses.

Yes, but they're not connected like that. There's no reason whatsoever that the traditional symbols could not have been used for Polish notation too, and thus for this game (as they are for example on RPN calculators).
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Allen was following Łukasiewicz's original notation, which used those letters as seen in http://en.wikipedia.org/wiki/Polish_notation; I believe the rulebook refers explicitly to this source. It would have been tricky to use the traditional wedge symbols for 'and' and 'or' on dice, since they are inverts of one another. The Wikipedia article asserts (without a reference) that the traditional notation did not become well-established until the 1970s.

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The 1990 edition of the rulebook I have refers to A. N. Prior's FORMAL LOGIC from 1955 (I think the book does mention Lukasiewicz at some point in some example, but it doesn't cite any of his works). Prior's book uses Polish notation through almost the entire text. Prior's book refers to Lukasiewicz's works. Lukasiewicz came up with his symbolism and Polish notation around 1924, as the Wikipedia indicates (and he says in his own writing) http://en.wikipedia.org/wiki/Jan_%C5%81ukasiewicz. I know he used it, Jaskowski used in the first paper on natural deduction, I read somewhere that Tarski used it in some of his earlier writings, and I believe Wajsberg, and some other Polish logicians used it. Polish notation still does get used sometimes today http://web.ics.purdue.edu/~dulrich/Home-page.htm, http://www.clas.ufl.edu/users/jzeman/modallogic/ As pointed out above, the capital letters C(onditional), A(lternation), K(onjunction), E(quivalence), and N(egation) actually denote first letters for descriptive names of the connectives. If you had no knowledge of logical symbols whatsoever, these symbols would probably come as easier to remember and thus work with, than the standard symbols. I don't see, for example, how "~" corresponds to any sort of name for negation quite so easily as "N" does.
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You must remember that Layman E. Allen was neither a mathematician nor a logician; he was on the faculty of Yale Law in 1962 (he later moved on to the U. of Michigan) where he was head of something called the ALL Project (Accelerated Learning of Logic) whose intention was to teach propositional calculus (PC; no personal computers in those days) to middle and high schoolers using "autotelic" (whatever that means) methods. This, of course, was part of the reaction to Sputnik. WFF 'N PROOF and its sister games, EQUATIONS, ON-SETS, and PROPAGANDA, are still used in a few scattered places in the USA as part of "academic games" competitions.

I had an uncle who was an engineer; he gave me a 1966 copy of WFF 'N PROOF for my birthday or for Christmas, I can't remember which, either that year or shortly thereafter, and I've still got parts of it, including the rulebook. I hear, though, that the rules, particularly with respect to scoring, have changed over the years and I hope to get the most recent version to study, along with EQUATIONS and ON-SETS.

When I went off to M.I.T. in 1974 people were replacing their slide rules with hand-held calculators, some of which used Polish notation, in which "p and q" becomes "Kpq", and some of which used reverse Polish notation, in which "p and q" becomes "pqK", but it wasn't till a few years later that I made the connection between calculators and WFF 'N PROOF. Obviously Allen didn't anticipate the use of reverse Polish notation in calculators, which is just as well, since WFF 'N PROOF is tough enough using Polish; imagine trying to play it in reverse Polish.
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Sphere wrote:
If I had more time, I'd dig mine out of the closet and have a look. Last time I did, I recall that the foam which held the dice was turning to dust.


I just picked up a copy of this yesterday, and the foam was indeed dust. I scraped it off the cover, which leaves an ample, still sticky swirl of glue that seems pretty impossible to remove from the vinyl.

I'm thinking I could go to Hobby Lobby and find some new foam to paste in there. Maybe.

I first encountered this game in the 4th grade, and since there was no one to teach it to me, I gave up quickly. I found it yesterday on a lunchtime stroll of a local antique mall for $9.95 and snapped it up. Everything's pristine but the foam. Gonna figure this thing out!

By the way, Layman Allen's email address is: enswell@gmail.com. The wff n proof website is http://wffnproof.com. They still make the game. Same cheesy graphics on the cover.shake
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lgoldberg wrote:

I just picked up a copy of this yesterday, and the foam was indeed dust. I scraped it off the cover, which leaves an ample, still sticky swirl of glue that seems pretty impossible to remove from the vinyl.

....
By the way, Layman Allen's email address is: enswell@gmail.com. The wff n proof website is http://wffnproof.com. They still make the game. Same cheesy graphics on the cover.:shake:
Tea tree (or was it eucalyptus?) oil removed the glue. That was a year ago and the plastic has no signs of damage.

I was careful about the dust from that foam though.
I've got no idea what was OK in foam in the mid-sixties.
 
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Thanks, I'll try that!
 
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