Predicate Punchline
Prove ∀x (G(x) ⊢ M(x))
Choose a major premise:
[[∀x (K(x) ⊢ L(x)) |wrong]]
[[∀x (L(x) ⊢ M(x))|minor 1]]
[[∀x (G(x) ⊢ L(x)) |minor 2]]
[[∀x (L(x) ⊢ K(x))|wrong]]
[[What the hell? |Short Author's Statment]]Wrong!!
[[Try again |Start]]
Choose a minor premise:
[[∀x (K(x) ⊢ L(x)) |wrong]]
[[∀x (G(x) ⊢ L(x)) |Syllogism]]
[[∀x (L(x) ⊢ K(x))|wrong]]
Choose a minor premise:
[[∀x (K(x) ⊢ L(x)) |wrong]]
[[∀x (L(x) ⊢ M(x))|Syllogism]]
[[∀x (L(x) ⊢ K(x))|wrong]]Make an inference
[[(∀x(G(x) ⊢ L(x)) ∨ ∀x(L(x) ⊢ M(x))) ⊢ ∀x(G(x) ⊢ M(x)) |wrong]]
[[(∀x(G(x) ⊢ L(x)) ∧ ∀x(L(x) ⊢ M(x))) ⊢ ∃x(G(x) ⊢ M(x)) |wrong]]
[[(∃x(G(x) ⊢ L(x)) ∧ ∃x(L(x) ⊢ M(x))) ⊢ ∃x(G(x) ⊢ M(x)) |wrong]]
[[(∀x(G(x) ⊢ L(x)) ∧ ∀x(L(x) ⊢ M(x))) ⊢ ∀x(G(x) ⊢ M(x)) |translate]]That was hard. Let's [[translate |start2]].
Everything that follows is a direct translation of what came before.Prove that all greeks are mortal.
Choose a major premise:
[[All cats are men. |wrong2]]
[[All men are mortal. |minor2 1]]
[[All greeks are men. |minor2 2]]
[[All men are cats |wrong2]]Wrong!!
[[Try again |start2]]
Choose a minor premise:
[[All cats are men. |wrong2]]
[[All greeks are men. |Syllogism2]]
[[All men are cats |wrong2]]
Choose a major premise:
[[All cats are men |wrong2]]
[[All men are mortal.|Syllogism2]]
[[All men are cats.|wrong2]]Make an inference
[[Because all Greeks are men or all men are mortal, all Greeks are mortal. |wrong2]]
[[Because all Greeks are men, and all men are mortal, Socrates is mortal |wrong2]]
[[(Socrates was Greek, a man, and mortal. So all Greeks are mortal |wrong2]]
[[Because all Greeks are men and all men are mortal, all Greeks are mortal. |end]]Quod Erat Demonstrandum
[[Start over? |Start]]
[[Author's Statement|Long Author's Statement]] Math is infamous for its confusing, hard to read jargon. It obfuscates the most simple statements for the sake of mathematical rigor. While this end appeals to many, (author included) it has some very real drawbacks, especially when it comes to communication with the non-math population. Jargon can sometimes hide a surprising truth about math: half the battle is understanding what you’re talking about, and the other half is easier than you think. This twine attempts to show you both sides of that coin: you experience the frustration of not understanding random symbols on the screen, and the ease of the problem once you do.
[[Begin |Start]]Math is infamous for its confusing, hard to read jargon. It obfuscates the most simple statements for the sake of mathematical rigor. While this end appeals to many, (author included) it has some very real drawbacks, especially when it comes to communication with non-math people.
This is in some sense unavoidable. Mathematicians study objects far outside the realm of everyday life, and therefore must have their own set of words to describe these objects. However, jargon can sometimes hide a surprising truth about math: half the battle is understanding what you’re talking about, and the other half is easier than you think.
“The quotient of the infinite cyclic group <a> by the subgroup <a^2> has order 2.” Is a fancy way of saying “all whole numbers are either even or odd.” Once you understand that, everything about reasoning with groups becomes easier. This twine attempts to show you both sides of that coin: you experience the frustration of not understanding random symbols on the screen, and the ease of the problem once you do.
The interactive environment of Twine allows us to create a “simulated proof,” where the user attempts to prove something by choosing from multiple options. This is unlike real proofs, where there are neither options to choose from, nor a higher authority telling you what you’ve done is wrong (both of which can be helpful). However, these details are orthogonal to the purpose of the piece, and their omission is therefore excusable.
Deciding to start with symbolic logic then translate to English (rather than the other way around) was an important choice in the tiny twine. Very rarely do students gain an intuitive understanding of the topic before being introduced to the symbols and jargon. Because of this, there’s an inevitable period of extreme confusion. I wanted the twine to parallel this development, and therefore chose to begin the twine with confusion. This has the obvious drawback of not being engaging, (why would a random reader on the internet feel compelled to continue playing the twine?) but I don’t feel it would be nearly as effective were I to do it the other way.