27 October 2007

Wff 'n Proof

Hi -

Have you ever played "WFF 'N PROOF: The Game of Modern Logic?" (Yes, Whiffenpoof fans, it was developed at Yale.)

When I was in elementary school, I found a copy of it at home. It purports to be a fun game, one that happens to result in teaching you something called "propositional calculus." It's designed for kids as young as six. I've tried four times to read the instruction manual for this game, and after all these years -- I'm 33 now -- I've only gotten to page 12. Of 168!

It is actually a collection of 21 games, each building upon the lessons of previous ones. I think I understand the first lesson, which teaches you to recognize WFFs, or "well-formed formulas." As the games progress, you improve your logical thinking skills. If anyone ever makes it to the 21st game, that person will be an absolute genius of logical thinking.

J-Fav and I get a kick, though, out of the 1960s linear-programming narrative in the four-page introduction:

Although the WFF 'N PROOF games were designed primarily to be fun -- to be an autotelic activity that learners would voluntarily spend time doing for its own sake -- they were also meant to provide practice in abstract thinking and to teach some mathematical logic. To the extent that WFF 'N PROF is autotelic, [Jeez, do I need to drag out my dictionary after all? -g] it will be played merely because it is fun to play - regardless of the fact that something useful is being learned in the process.
...There are a total of thirteen ideas introduced and used repeatedly in the play of the WFF 'N PROOF games: the definition of a WFF, the definition of a Proof, and eleven Rules of Inference (the Ko, Ki, Co, Ci, R, Ao, Ai, No, Ni, Eo, and Ei Rules). These thirteen ideas, which comprise one formulation of the system of logic called "propositional calculus" (abbreviated 'PC'), are presented very gradually as a learner proceeds through the series of twenty-one games. [zzzz...]


Any of you ever seen this game? It actually looks fun, and sort of kooky at the same time.

(If so, maybe you could tell me if the symbol "A" ("or"), as in "Apq", means "at least one of the following" versus "only one of the following." That is, Boolean OR is different from English OR.)

Hmm, if I were to make it to page 23, I could ponder: "The statement of what is proved by P2 is merely: From 'K-p-Kqr' and 'Kqr', it is valid to infer 'r'."

-g

9 comments:

Kaz Maslanka said...
This comment has been removed by the author.
Kaz Maslanka said...

With your recommendation I went out and bought wff'n proof ... now, I have to sit down and see if I can work through some of it.

Thanks,
Kaz

Angela said...

well, I was just Googling wff'n proof and came across your post because yes, I did learn it as kid, but in 6th grade. Up until last fall, we had an alumni Yahoo! group that if I had seen your question then, would have directed you to. Maybe you can find a coach in North Carolina (the closest league to you) that can help. Not only was wff'n proof hard for me back then but there's too many cobwebs for me to remember how to play if I tried!

Anonymous said...

"A" means at least one the following -- boolean.

I've had difficulty progressing through the games because I can't find anyone to play the games with me but I've been working on a way to make them as one-player games -- turning them into games of solitaire.

I admit the text is a little difficult to read and understand, but far from impossible. First of all, it's essential that you understand everything on one page, before you progress to the next. Don't just plow ahead thinking you'll figure it out as you continue reading. It'll just get worse and worse.

If you really don't understand the text, try something I learned while practicing the piano:

1) Start reading at "A. Introduction." Read and try to understand what you are reading. Do not turn the page if there is anything on that page that you did not understand. After 15 minutes, set the book down.
2) Go do something else for 45 minutes.
3) Pick the book up and begin reading again at the last paragraph you understood. Continue reading and re-reading for 15 minutes and then set the book down.
4) Go do something else for 45 minutes.
Continue this process until you get to the end of the first game.

Play the first game using the 15 minutes on 45 minutes off pattern until you can play the first game well.

Go back to reading, as described above, until you get to the end of the second game.

Play the second game using the 15 minutes on 45 minutes off pattern until you can play the second game well.

Continue this process, working through the book and the games. You may need to extend the "on" periods as you progress to the more advanced games. Try playing through one complete proof at a time. However, you'll find that as you progress through the games, you'll more easily understand what you are reading and doing.

Anonymous said...

ARRGGHHH! WFF'N PROOF...I found this last week at a church yard sale for fifty cents. Weird, i thought. Kooky little game from the sixties, I thought.

My wife and I had a jolly time trying to wring some fun out of it, though. We made it to game #2 before our brains shut down.

Christopher Hetkey said...

Played it a lot when I was a kid after i got kicked out of catholic school for being "LEARNING DISABLED". Must have worked. After college, graduate school, 10 years in the military and 16 years at Microsoft. I have a hot wife and am retired at 48. So...gotta get one for my kids.

Anonymous said...

i played it in high school in out advanced classes. cant remember how to play but would love to find it and see if i remember anything

Spoonwood said...

A stands for "alternation". "p" and "q" are the alternates in "Apq". If one of the alternates is true, then Apq is true. Thus, if both alternates are true, one of the alternates is true, and thus Apq is true. Comparison with "or" terms in natural language only goes so far... the Latin term "sive" means "or", but more precisely means "or equivalently".

Anonymous said...

I just purchased WFF 'n Proof for three main reasons: (1) I'm taking an upper-level philosophy course in mathematical logic and want to succeed with it, (2) I remember being intrigued by it many years ago, and (3) I want to figure out how to play it solitaire since I have no one I can play it with.

Question - does anyone know about an online version of WFF 'n Proof, either with online players or playing against the computer? Go and Chess players have such resources available so I would think that there might be something for "WFF 'n Proof" players.

My email is rms@cs.brown.edu