  Author  Message 

Rarity Royal Guard
Posts : 622 Join date : 20110620 Location : Parker, Colorado
 Subject: 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 _________________ 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
Mayor Mare LV26 Scoundrel Healer

   Rydel Unicorn
Posts : 829 Join date : 20110811 Location : Orlando
 Subject: 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 
   Rarity Royal Guard
Posts : 622 Join date : 20110620 Location : Parker, Colorado
 Subject: 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. _________________ 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
Mayor Mare LV26 Scoundrel Healer

   Rydel Unicorn
Posts : 829 Join date : 20110811 Location : Orlando
 Subject: 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.

   Luna Pony
Posts : 95 Join date : 20110620 Location : It's not a battlestaion
 Subject: 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 
   Rydel Unicorn
Posts : 829 Join date : 20110811 Location : Orlando
 Subject: 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 
   Fluttershy Founder Mane
Posts : 1944 Join date : 20110617 Location : Redmond, Washington
 Subject: 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* _________________ 
   The Jack Colt
Posts : 161 Join date : 20110909 Location : Bergen, Norway
 Subject: 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 ) 
   Rarity Royal Guard
Posts : 622 Join date : 20110620 Location : Parker, Colorado
 Subject: 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. _________________ 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
Mayor Mare LV26 Scoundrel Healer

   Rydel Unicorn
Posts : 829 Join date : 20110811 Location : Orlando
 Subject: 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 = ℝ

   The Jack Colt
Posts : 161 Join date : 20110909 Location : Bergen, Norway
 Subject: 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 ) 
   Luna Pony
Posts : 95 Join date : 20110620 Location : It's not a battlestaion
 Subject: Re: Pony Logic Fri Sep 09, 2011 5:47 pm  
 Ok, let's do this.
 Spoiler:

What where you expecting, hm ?
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,H3 ⇒ D(T)=1, T=F
T ∈ B , ∀(E, E∈B) [ D(E)=1, E ∈ Tr] , F ∈ Tr ⇒ D(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∈Tr ⇒ T=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. 
   Rydel Unicorn
Posts : 829 Join date : 20110811 Location : Orlando
 Subject: 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. 
   Fluttershy Founder Mane
Posts : 1944 Join date : 20110617 Location : Redmond, Washington
 Subject: 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. _________________ 
   Rydel Unicorn
Posts : 829 Join date : 20110811 Location : Orlando
 Subject: 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. 
   Fluttershy Founder Mane
Posts : 1944 Join date : 20110617 Location : Redmond, Washington
 Subject: 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 precalculus, aka Math Analysis, aka Anal Math. Almost there! Right? _________________ 
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