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Rarity
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PostSubject: Pony Logic   Thu Sep 01, 2011 12:13 am

Ok, here's my logic for the day.

∵ Twilight is a Book.

∵ Books are Dead Trees.

∵ Fluttershy is a Tree

∴ Twilight is Dead Fluttershy

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Rydel
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PostSubject: Re: Pony Logic   Thu Sep 01, 2011 12:15 am


There is logic in what he says

EDIT: Wait - one must first prove that Twilight is a book
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PostSubject: Re: Pony Logic   Thu Sep 01, 2011 12:41 am

Ok, proving Twilight is a book.

∵ Twilight Reads a lot of books

∵ What you do defines you

∵ Fluttershy is good with nature and is a tree

∴ Twilight Sparkle is good at reading and is a book Q.E.D.

More comprehensive version coming when I have too much free time on my hands, and decide to work on it.

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Rarity is NOT part marshmallow. Where ever did you get the idea that I was darling?

Current Rariquest: Taking the butterscotch bonbons through the elusive tunnel of shining dusk.
In the end of the Beta day, I just want to use my Beta greeting, to basically say a Beta statement.
I'm tired from the tired

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Rydel
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PostSubject: Re: Pony Logic   Thu Sep 01, 2011 12:47 am

More comprehensive? I'll help.

Start with this:

The proof starts from the Peano Postulates, which define the natural
numbers N. N is the smallest set satisfying these postulates:

P1. 1 is in N.
P2. If x is in N, then its "successor" x' is in N.
P3. There is no x such that x' = 1.
P4. If x isn't 1, then there is a y in N such that y' = x.
P5. If S is a subset of N, 1 is in S, and the implication
(x in S => x' in S) holds, then S = N.

Then you have to define addition recursively:
Def: Let a and b be in N. If b = 1, then define a + b = a'
(using P1 and P2). If b isn't 1, then let c' = b, with c in N
(using P4), and define a + b = (a + c)'.

Then you have to define 2:
Def: 2 = 1'

2 is in N by P1, P2, and the definition of 2.

Theorem: 1 + 1 = 2

Proof: Use the first part of the definition of + with a = b = 1.
Then 1 + 1 = 1' = 2 Q.E.D.


You can now use addition in your proof.
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PostSubject: Re: Pony Logic   Thu Sep 01, 2011 4:37 am

Now, I understand that Peano's axioms are indeed a good starting point, but I have to add a remark concerning your conclusion.

What you define as 'addition' isn't the operation usualy called by that name. It's only a function f:N²->N . Since you define 2, it doesn't have 'numerical' value as well, because it could be any mathematical object as well.

If you want to have a classic addition, you might want to prove that this operation is:
- commutative (ie a+b = b+a)
- associative (ie a + (b+c) = (a+b) + c)
- possession of an additive identity (ie x where a+x=a)

That's the third point that bugs me, right ? Because you took the Peano's version where 0 is not in the set, so you can't prove that. It means everything you said is correct, but define an operation where (N,+) is not a group, but rather "a set and an operation".

It totally works with many problems, but just pointing it out, so rarity can use it the way it should.


/completlymissingthepoint
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PostSubject: Re: Pony Logic   Thu Sep 01, 2011 4:11 pm

While I probably could adjust this to address Luna's concerns,

1. That's a lot of work and I'm busy/lazy
2. Making Rarity work having only partially proven addition should be more amusing

Also, in the way of "assuming nothing," I have remembered a great quote from textbook: "So far, we have assumed reality. Henceforth, we will no longer constrain ourselves."

Unfortunately, it was just talking about real numbers
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PostSubject: Re: Pony Logic   Thu Sep 01, 2011 7:43 pm

>Opens thread
>Sees logic
>Sees math
>Sees theory craft on this subject
>"Pinkie Pie is Pee Wee Herman!"
>*shot*

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PostSubject: Re: Pony Logic   Fri Sep 09, 2011 1:53 pm

Rarity wrote:
Ok, here's my logic for the day.

∵ Twilight is a Book.

∵ Books are Dead Trees.

∵ Fluttershy is a Tree

∴ Twilight is Dead Fluttershy

The best thing is; this is logically correct. xD (I have just recently learned a bit on formal logic in my philosophy classes xD )
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PostSubject: Re: Pony Logic   Fri Sep 09, 2011 1:58 pm

The Jack wrote:
Rarity wrote:
Ok, here's my logic for the day.

∵ Twilight is a Book.

∵ Books are Dead Trees.

∵ Fluttershy is a Tree

∴ Twilight is Dead Fluttershy

The best thing is; this is logically correct. xD (I have just recently learned a bit on formal logic in my philosophy classes xD )

Yes, it is logically correct. Problem is that as I have not proven Twilight is a Book (Or Fluttershy as a Tree for that matter, or even that Books are Dead Trees. Man, I've got a lot of work still ahead of me) It's flimsy logic at best. Don't worry, I'm trying to get it working to a decent enough level that I can prove that Twilight is a Book, Fluttershy is a Tree, and Books are Dead Trees. Hopefully in a sufficiently complicated matter that makes anyone who looks at it wonder why I went to all that work.

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Rarity is NOT part marshmallow. Where ever did you get the idea that I was darling?

Current Rariquest: Taking the butterscotch bonbons through the elusive tunnel of shining dusk.
In the end of the Beta day, I just want to use my Beta greeting, to basically say a Beta statement.
I'm tired from the tired

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Rydel
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PostSubject: Re: Pony Logic   Fri Sep 09, 2011 4:48 pm

It's also not logically correct.
It's stating (A ∈ C) ∧ (B ∈ C) ∴ A = B with
A = Books
B = Fluttershy
C = Trees or tree products

This can be easily disproven:
A = 1
B = 2
C =
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PostSubject: Re: Pony Logic   Fri Sep 09, 2011 5:12 pm

Rarity wrote:
The Jack wrote:
Rarity wrote:
Ok, here's my logic for the day.

∵ Twilight is a Book.

∵ Books are Dead Trees.

∵ Fluttershy is a Tree

∴ Twilight is Dead Fluttershy

The best thing is; this is logically correct. xD (I have just recently learned a bit on formal logic in my philosophy classes xD )

Yes, it is logically correct. Problem is that as I have not proven Twilight is a Book (Or Fluttershy as a Tree for that matter, or even that Books are Dead Trees. Man, I've got a lot of work still ahead of me) It's flimsy logic at best. Don't worry, I'm trying to get it working to a decent enough level that I can prove that Twilight is a Book, Fluttershy is a Tree, and Books are Dead Trees. Hopefully in a sufficiently complicated matter that makes anyone who looks at it wonder why I went to all that work.

Nonono; it's not flimsy logic. Infact, it's a perfectly viably logical syllogism, if I remember the name correctly.
The problem is, it's not neccesarely TRUE. xD
For that, you'll have to prove that Twilight is a book and that Fluttershy is a tree. If those two are correct, then the conclusion MUST be correct. =D
(I never knew I'd actually USE this stuff they teach us. I mean, WTH? Why do they have a philosophy course that's mandatory in a physics education? xD )
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PostSubject: Re: Pony Logic   Fri Sep 09, 2011 5:47 pm

Ok, let's do this.

Spoiler:
 

T : twilight
F : fluttershy
D : Ω -> [0,1], state of being dead (0: alive, 1: dead)
Tr : (Tr ⊂ Ω) , trees
B : (B ⊂ Ω) , books


H1 ∵ Twilight is a Book.
H1 ⇒ T ∈ B


H2 ∵ Books are Dead Trees.
H2 ⇒ ∀(E, E∈B) [ D(E)=1, E ∈ Tr]


H3 ∵ Fluttershy is a Tree
H3 ⇒ F ∈ Tr


We want to prove :
P1 ∴ Twilight is Dead Fluttershy
P1 ⇒ T=F, D(T)=1


Which means :
H1,H2,H3D(T)=1, T=F

T ∈ B , ∀(E, E∈B) [ D(E)=1, E ∈ Tr] , F ∈ TrD(T)=1, T=F


Let's begin with proving D(T)=1

T ∈ B , ∀(E, E∈B) [ D(E)=1, E ∈ Tr]
Instantiate in
D(T)=1, T∈Tr

Proven.

T ∈ B , ∀(E, E∈B) [ D(E)=1, E ∈ Tr] , F ∈ Tr , T∈TrT=F

Now let's prove T=F
A bit more tricky, this can't be done logicaly.
We do have :
F ∈ Tr , T∈Tr (Fluttershy and Twilight are both trees)
But that's about it. That joins
Rydel point, if I am not assuming too much. We can manage it by proving that Tr is composed of only one element (there is only one tree).

Short of only one tree in Equestria, I don't think it's possible to prove anything further in P1 with only H1->3.
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PostSubject: Re: Pony Logic   Fri Sep 09, 2011 6:22 pm

Instead of proving that there is only one element in Tr, we could also prove that T and F are the same element in Tr, that is that Twilight and Fluttershy are the same object.
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PostSubject: Re: Pony Logic   Sat Sep 10, 2011 2:10 am

Okay, really now.

You guys are making me feel like I have learned nothing in my years of public education.

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PostSubject: Re: Pony Logic   Sat Sep 10, 2011 2:27 am

Good new, that's college level discrete mathematics, so you shouldn't feel bad.

Well, you shouldn't feel bad about this thread at least. I don't know what else you've been up to.
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PostSubject: Re: Pony Logic   Sat Sep 10, 2011 2:32 am

Rydel wrote:
Good new, that's college level discrete mathematics, so you shouldn't feel bad.

Well, you shouldn't feel bad about this thread at least. I don't know what else you've been up to.
Umm I'm up to pre-calculus, aka Math Analysis, aka Anal Math. Almost there! Right?

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