A Game for Gaining Logical Fluency
Matthias Jenny, who recently received his PhD in philosophy from MIT, has started working in the tech industry. He wrote to share with Daily Nous readers a game he created to help people develop basic logical fluency.
The game, Andor, has players drag and drop parts of a statement so to arrange them into a true statement. It can be played here or downloaded for iOS here, for Android here, and for Amazon Kindle Fire here.
Dr. Jenny explains why he thinks the game is useful, and provides a further description of it:
One thing that sets people experienced with logic apart from novices is fluency. A fluent speaker of a natural language doesn’t have to think twice about how to use simple words. Likewise, people experienced with logic don’t stumble over simple facts such as that logical disjunction is inclusive. Andor is a free mobile game that aims to teach fluency in the use of the Boolean connectives and introduce the formalism of sentential logic along the way. It is intended to be played by people without any formal training in logic or be used alongside a formal introductory logic curriculum.
Andor contains three hundred levels; the first thirty-one comprise a tutorial that introduces players to the truth-conditions of the Boolean connectives, the use of parentheses, and formal notation. A significant portion of the tutorial pays special attention to scope ambiguities that can be resolved with parentheses.
Each level consists of a number of atomic sentences, connectives, and parentheses. The goal is to rearrange these pieces to construct a true sentence. Upon completing the tutorial, players will encounter levels that increasingly demand greater fluency in the use of the Boolean connectives. But the levels increase in difficulty slowly enough to ensure steady improvements in fluency.
Dr. Jenny says that he welcomes feedback on any aspects of the game. You can email him or comment here. He adds: “I would especially be curious to hear from logic teachers who decide to use the game in the classroom.”
Here’s a video showing how the game is played (note, this video was updated on 3/17/2018):
This looks useful—thanks Dr. Jenny for this resource, and thanks Justin for linking it.
I have two suggestions after few minutes messing around with the web version. First, when the sentences are arranged correctly, the screen changes immediately, without giving time to read the completed version of the sentence. I wonder if a brief delay might help — maybe the ‘correct’ sound should make available a button to continue to the explanation, rather than simply going straight to it.
Second, level 10 treats this as a correct answer:
(it’s false that the Milky Way is on Earth)
And this as an incorrect answer:
it’s false that (the Milky Way is on Earth)
From the syntax explanation provided up to that point, I didn’t see why the latter shouldn’t also be counted as correct.
Thanks again for this—I will play around with it more. It looks like something I may well want to incorporate into my logic course.
This is really great. Related to Jonathan’s first comment, something that might help is a `Submit Answer’ button. That would additionally partially suppress the strategy of simply rearranging the elements until one gets the `correct answer’ pop-up.
I would also note that it is much more pleasant to play on a computer than on a phone. One reason for this is that wrapping from the small screen of a phone makes it more difficult to see the structure of the sentence. Perhaps forcing the app into landscape would help, as I imagine some users might not realize the benefit of doing so. Another (partial) solution would be to reduce the text size. A second reason, though perhaps not fixable, is that on a computer when you drag an element it moves with your cursor, while on the phone it does not move with your finger but only shifts position once you release.
“First, when the sentences are arranged correctly, the screen changes immediately, without giving time to read the completed version of the sentence.”
Click the “x” instead of “On to level n.” You can review the correct answer at leisure.
Thanks to Jonathan and Bryce for the feedback!
Jonathan, I built in a short timeout between marking a level as complete and changing the screen. I’ll experiment with making the timeout longer. In the meantime, as Michael points out, clicking the “x” (or clicking anywhere outside of the pop-up screen) allows the player to see the completed level. I tried to walk the line between giving sufficiently detailed instructions and being verbose. I may erred a bit too much on avoiding verbosity. In the same vein, I tried not to throw all of the syntax for parentheses at the player right at the beginning. The instructions for level 14 explain that one can’t put parentheses around atomic sentences.
Bryce, I worry that a “Submit Answer” button would slow down the flow of the game, but I’ll experiment with that, as well as with enforcing landscape screen orientation.
This looks great! I think I’ll use it as a quick way of getting folks up to speed wrt the standard (first-cab-off-the-block) account of logical consequence, and then get said folks to reflect on the wide-open question of whether that account is anywhere near the right account.
[Minor but sincere suggestion: It’s great that you explicitly use logic’s falsity operator. I’d recommend, for symmetry, that you explicitly add logic’s (usually implicit) truth operator, viz., “it’s true that…”. You can then let folks correctly infer that logic’s truth operator is — as far as logical consequence goes — redundant, as Ramsey and so many others have said. But it’d be nice to have the full boolean quartet of dual connectives — the two unary (truth and falsity operators) and two binary (disjunction and conjunction) early on.]
Thanks, Jc! I’ll definitely think about incorporating the truth operator. By the way, I’m also considering making a version of the game for three-valued logics.
If you’re going to go three valued, you’ll probably have to choose between two options that, on closer inspection, are somewhat odd: K3 and LP. These are both cool logics, but weirdly `unbalanced’, as I think Jc would say. Pedagogically, it might make just as much sense to jump all the way to the four-valued logic FDE rather than pausing at either the LP or the K3 waystation.
Why not do all three!
Definitely do FDE if you do a so-called many-valued version! (And you should. Morally, you should.) With FDE in hand, you can then have three sub-games:
1. Allow the truth and falsity operator to be only exhaustive and not exclusive (LP).
2. Allow the truth and falsity operator to be only exclusive and not exhaustive (K3).
3. Demand that the truth and falsity operators be both exhaustive and exclusive — the standard “classical” account. (This just loops back to your original game as it now stands.)
There’s also an added benefit (and I am completely serious here): FDE is truly logical consequence; it’s God’s logic. So, you can’t go wrong with a game in that direction!
All good. So happy that you’re creating all this.
Thank you for this- great project and a great cause!
my suggestions:
1. in my opinion, which was only enforced while playing the game, it much better pedagogically to have fixed elements and being able to change only one type of element at a time. So, for example, only being able to swap the statements/connectives/parentheses while everything else is fixed. If not that, it would still be much better to have all the elements layed-out already in a wff. having to deal with things like “()” or “~&” just makes it frustrating to me, especially as the statements get more complex.
2. i second the suggestions of a submit button. sometimes i get a right answer without even knowing i’m going to.
3. it would be great if one could play it just using the keyboard (also being able to scroll through the instructions with the keyboard). and also being able to mute the game.
oh, and also to be able to skip levels or save the game.
Thank you for these suggestions!
The ability to skip levels or view the answer to see where you’re wrong or why you’re wrong would be great in my opinion as I’m stuck in a level at the moment and don’t know why.
Hi Sam,
Have you completed the first 31 levels? If so, then you should see a “Shuffle” button. When stuck, I recommend hitting that and starting the level you’re stuck on from scratch.