Long Game 95: The Fire of Ado's Light

[Szeth Pancakes he/they]

Convienninent that your crypto is supposedly not a scam :eyes:

[DrakeMarshall he/him]

20 minutes ago, Szeth_Pancakes said:

Convienninent that your crypto is supposedly not a scam :eyes:

Objection!

It isn't my crypto, it isn't a scam, and it's also neither convenient nor convienninent because you're pursuing legal action over it which is very inconvenient!

Nothing about that statement is true!

[Szeth Pancakes he/they]

1 minute ago, DrakeMarshall said:

Objection!

It isn't my crypto, it isn't a scam, and it's also neither convenient nor convienninent because you're pursuing legal action over it which is very inconvenient!

Nothing about that statement is true!

But

We live in a society

Nothing is true

[xinoehp512 he/him]

2 hours ago, DrakeMarshall said:

Oh yeah??? Where's the trademark on your name then? Can you prove that one existed that you didn't retroactively add? Can you prove that (sz)ETH is even based on your name? Can you provide evidence for the allegations that I, a humble investor, am in fact involved in the conception and/or naming of the anonymously founded cryptocurrency known as (sz)ETH? Where is your evidence for any of this?????

Anyways, the coin is called (sz)ETH not Szeth_Pancakes. Even if I did come up with the name (and of course these allegations are actually false), the (sz) are in parantheses, it is in bold, it is in italics, the font size is different, the colors are different, and the highlighting is different, and there are no Pancakes or underscores. I think that is clearly sufficiently transformative to constitute fair use!! Whoever named this coin (which wasn't me) was probably perfectly within the bounds of the law.

If you are determined to pursue these accusations which are baseless on multiple fronts, I guess I will see u in court

good luck finding a prosecutor on Silverlight though

Can you believe this guy??? Xino is saying you have no friends!! How rude!! >:P

Don't listen to somebody who is that mean to you! The only sensible response is to prove him wrong!!

Prove that you have at least 3 friends by buying into my crypto investment strategy!!

What? Preposterous! There is no logical way for this to happen, because (sz)ETH is simply too colorful to go out of style.

Doing this will only further my carefully laid plans!!

When the lawsuit inevitably fails due to the accusations being obviously false, your financial loss will ruin your credit and make you unable to prop up your supposedly stable and boring ShardBux, thus conclusively proving that they don't have any True Value™

So you admit ShardBux are stable. 

[DrakeMarshall he/him]

1 minute ago, Szeth_Pancakes said:

But

We live in a society

Nothing is true

What is this "we" you speak of you might live in a society but maybe I don't  have u considered that

Besides, it is impossible for nothing to be true! If it were, then the claim "nothing is true" could not be true, because it is also a thing Therefore at least one thing is true >:P

1 minute ago, xinoehp512 said:

So you admit ShardBux are stable. 

"supposedly stable"

I am not sure why stability is something to brag about anyways since you clearly can't WIN BIG if your boring currency has a predictable amount of value, but at the same time I do not think it is as stable as u think if it is fully contingent on ur own credit which will be subject to legal expenses if u are determined to stay ur course

[Kasimir he/him]

32 minutes ago, DrakeMarshall said:

Besides, it is impossible for nothing to be true! If it were, then the claim "nothing is true" could not be true, because it is also a thing Therefore at least one thing is true >:P

I mean...

It sort of depends how you translate that into predicate logic...

Just saying :eyes:

Edited to add:

1 hour ago, DrakeMarshall said:

While there definitely most certainly is not an actual document out there somewhere that reveals my dastardly crypto related plans, because I certainly do not have any dastardly plans of any kind, I am somewhat offended by the implication that if such a document even existed, it would be that simple and short and unsophisticated. If such a document hypothetically existed (which it of course does not why would u think that), then just hypothetically it would probably be exactly 50 pages long at the present moment and still growing.

Liesssssss

Edited May 30, 2023 by Kasimir

[Ashbringer he/him]

2 hours ago, The Wandering Wizard said:

Did just receive word that a friend that's been wanting to join SE is going to be joining

He's played mafia on another site so all I ask is for a nice warm SE stab- welcome

Joining in general or joining this game? 

 

Either way... hi everyone! After talking to a few people, I think delaying signups would get us more players than not, and most people seem interested in the full, now-slightly-more-balanced ruleset. So, I am officially delaying the start of the game to 10:00 PM PDT on June 5th, or 6 days from the original signup time. I will note that I might change the actual rollover time as well, depending on how my schedule shakes out - but delaying should get us to at least 19 players (and tbh I'd run the full ruleset with 19 players, just the more the merrier / less insanier).

I'll add Araris to the player list, @TheAlpha929 could I confirm that that works for you? 

[DrakeMarshall he/him]

1 hour ago, Kasimir said:

I mean...

It sort of depends how you translate that into predicate logic...

Just saying :eyes:

"∄ (thing) ∋ (thing is true)"

How would you translate it? :eyes:

[Kasimir he/him]

1 minute ago, DrakeMarshall said:

"∄ (thing) ∋ (thing is true)"

How would you translate it? :eyes:

¬∃x Tx

Saying it's a thing sort of implies you've got in mind something like:

¬∃x (Thx → Tx)

[DrakeMarshall he/him]

6 minutes ago, Kasimir said:

¬∃x Tx

Saying it's a thing sort of implies you've got in mind something like:

¬∃x (Thx → Tx)

I do have something like that in mind, yes. You could call it a holdover from mathematics, where specifying set membership is basically compulsory whenever you use quantifiers (in other words, in a math proof you can almost literally never get away with just saying "∃x", you are required to specify "∃ x ∈ S" where S is some kind of set). I happen to think that this way of doing it is usually just plain better

So in the notation I am most comfortable with, it would be:

∄ x ∈ U ∋ Tx

And, you are correct, the closest way to express that in your notation (which is the correct formal logic notation if ur a philosophy nerd instead of a math nerd, and is in fact the notation I learned in the 1 philosophy class that a philosophy professor pressed me into taking) is indeed this:

¬∃x (Thx → Tx).

Where to make these two equivalent, "Thx" tests membership in U, i.e. it is true if and only if x is in U.

...However, it is all kind of moot, because in this case the set we are discussing is "everything."

Now there is a rather significant can of wyrms that we could open here, because there are multiple ways of defining "everything" for this problem and I will assert that not all of those ways are equally correct, but wyrm-can-opening is strictly voluntary.

 

However, the way I actually wrote it, "thing" was actually just intended as a variable name

Which makes it exactly the same as "¬∃x Tx" even if I am a rebel and used different symbols

Because, I did not want to get into the above can of wyrms, even if I was on some level thinking it Which apparently you picked up on anyways so ¯\_(ツ)_/¯

 

But in conclusion, I think you will probably agree that the RAA argument I made follows from either translation.

There is an additional possible translation I can think of where the RAA argument doesn't work, due to the English language being hopelessly ambiguous, but it requires a fairly pathological reading of the sentence

[Kasimir he/him]

2 minutes ago, DrakeMarshall said:

But in conclusion, I think you will probably agree that the RAA argument I made follows from either translation.

It doesn't if you don't think existence is a predicate  Because your argument requires it to be a predicate.

[DrakeMarshall he/him]

1 hour ago, Kasimir said:

It doesn't if you don't think existence is a predicate  Because your argument requires it to be a predicate.

Not a predictate for "x exists" per se but a predicate for "x is a thing."

Very technically, these are not the same, because not all things exist. However, everything that exists is a thing

Regardless, I don't think including the predicate breaks anything? Here I'll even do the proof all verbose and fancy and proper like and you can tell me what you don't like

 

1. Th("¬∃x (Thx → Tx)")                                             premise

2. ∀x Tx ↔ x                                                       premise

3.     ¬∃x (Thx → Tx)                                               assume to the contrary

4.     ∀x ¬(Thx → Tx)                                               quantifier negation, 3

5.     ¬(Th("¬∃x (Thx → Tx)") → T("¬∃x (Thx → Tx)"))                universal instantiation, 4

6.     ¬(¬Th("¬∃x (Thx → Tx)") ∨ T("¬∃x (Thx → Tx)"))               material implication, 5

7.     ¬¬Th("¬∃x (Thx → Tx)") ∧ ¬T("¬∃x (Thx → Tx)"))               DeMorgan's Law, 6

8.     Th("¬∃x (Thx → Tx)") ∧ ¬T("¬∃x (Thx → Tx)"))                 double negative, 7

9.     ¬T("¬∃x (Thx → Tx)"))                                        simplification, 8

10.    T("¬∃x (Thx → Tx)") ↔ ¬∃x (Thx → Tx)                        universal instantiation, 2

11.    ¬∃x (Thx → Tx) → T("¬∃x (Thx → Tx)"))                        biconditional elimination, 10

12.    T("¬∃x (Thx → Tx)"))                                         modus ponens, 3, 11

13.    T("¬∃x (Thx → Tx)")) ∧ ¬T("¬∃x (Thx → Tx)"))                 adjunction, 9, 12

14. ¬¬∃x (Thx → Tx)                                                 reductio ad absurdum, 3-13

 

I'm a bit rusty with this style of proof, it has been a while but hopefully this is reasonably clear

edit: wait

this needs changes

its been a while ok >>

edit2: fixed

that's better >>

it is a very silly proof when u think about it

that is because the translation of ∄ x ∈ U ∋ Tx from math nerd symbols into philosophy nerd symbols is not actually ¬∃x (Thx → Tx), a more correct mapping would probably be ¬∃x (Thx ∧ Tx)

and ¬∃x (Thx → Tx) is actually a very silly statement

storm it Kas why'd you put ¬∃x (Thx → Tx) in my head ur doing me a confusion

BUT the RAA argument still works even if you use the silly translation I have just proven as much I am fairly sure

Edited May 30, 2023 by DrakeMarshall

[Drake Inferno]

It's not too late to join in, is it? Sorry I came in so late!

[xinoehp512 he/him]

19 minutes ago, Drake Inferno said:

It's not too late to join in, is it? Sorry I came in so late!

Xorial sidled up to the newcomer to the canteen. "Hello," he said, extending his hand.

 

3 hours ago, DrakeMarshall said:

∄ x ∈ U ∋ Tx

Okay, now I'm confused. What the heck does T mean? (Same for Th)

[Kasimir he/him]

4 hours ago, DrakeMarshall said:

Very technically, these are not the same, because not all things exist. However, everything that exists is a thing

See, it's like you're translating this twice because you're not just using an existential quantifier, but you're also predicating thingness to it, but that's just doing double work. That's sort of the problem with Anselm's Ontological Argument but in reverse, because he sort of wants existence to do work over and above thingness, and then argues for existence predication when you could disagree with the idea existence really does any of that sort of work beyond thingness. Arguably, your argument depends on literal wordplay from 'thingness' to 'nothing

You can argue not all things exist, but that's just the Kripke unicorn problem repackaged

4 hours ago, DrakeMarshall said:

and ¬∃x (Thx → Tx) is actually a very silly statement

Because you sort of have to do that if you're saying 'is a thing' - at least that's the notation I was taught and I stick with it  But when it's spelled out, I also thought you were doing a 'is a thing' from 'nothing' semantic move and I just realised you're not, so I don't disagree either.

4 hours ago, DrakeMarshall said:

that is because the translation of ∄ x ∈ U ∋ Tx from math nerd symbols into philosophy nerd symbols is not actually ¬∃x (Thx → Tx), a more correct mapping would probably be ¬∃x (Thx ∧ Tx)

Probably but again, we used ^ in propositional but not predicate. I never asked why, I was too busy trying to understand everything else

Tbh, I do think it's better translated as "It is not the case that a something exists such that it is a thing and it is true", but also thought you were explicitly using thingness to make the inference that "Nothing is true" violates the premise due to also being a thing, rather than just arguing it violates via the existential quantifier. Cf. the more direct something being along the lines of postulating ¬∃x (Tx), using modal logic to show that there is one thing (using this term here to suggest use of ∃ rather than thingness) in that world at least that is true, and then closing that branch of the tree.

4 hours ago, DrakeMarshall said:

3.     ¬∃x (Thx → Tx)                                               assume to the contrary

Not clear how this is the negation of premises. Could be your notation being weird given the translations to and fro  

4 hours ago, DrakeMarshall said:

7.     ¬¬Th("¬∃x (Thx → Tx)") ∧ ¬T("¬∃x (Thx → Tx)"))               DeMorgan's Law, 6

Interesting as this isn't a move that we're allowed. Maybe fancy maths nerds can but you'd have to tree and truth table at this point for this move. 

Edited May 30, 2023 by Kasimir

[DrakeMarshall he/him]

3 hours ago, Drake Inferno said:

It's not too late to join in, is it? Sorry I came in so late!

You have a great name

Somebody more official than me should probably answer this, but: We are actually kinda desperate for more people, and are postponing the start of the game because we're waiting on getting more people, so I'm pretty sure we would really love to have you

Fair warning though, this is kind of a crazy complex game to have as your first time in Sanderson Elimination. There are games with much simpler rules than this one.

3 hours ago, xinoehp512 said:

Okay, now I'm confused. What the heck does T mean? (Same for Th)

That is a very good question

T(x) means "x is true"

Th(x) means "x is a thing"

The parantheses are sometimes left off bc we're lazy

 

EDIT:

52 minutes ago, Kasimir said:

See, it's like you're translating this twice because you're not just using an existential quantifier, but you're also predicating thingness to it, but that's just doing double work.

Ye that's why I didn't make thingness into a predicate when I provided my initial translation, bc even though I wanted to I recognize it isn't really useful

Quote

Because you sort of have to do that if you're saying 'is a thing' - at least that's the notation I was taught and I stick with it  But when it's spelled out, I also thought you were doing a 'is a thing' from 'nothing' semantic move and I just realised you're not, so I don't disagree either.

Well maybe I'm getting something wrong, but I am fairly sure statements that look like ∀x (Px → Qx) make quite a lot more sense than ones that look like ¬∃x (Px → Qx). Like, let's say Dx = "x is a dog" and Mx = "x is a mammal."

∀x (Dx → Mx) means all dogs are mammals.

¬∀x (Mx → Dx) means not all mammals are dogs.

¬∃x (Dx → Mx) means everything in the universe is a dog, and also nothing in the universe is a mammal

Quote

Interesting as this isn't a move that we're allowed. Maybe fancy maths nerds can but you'd have to tree and truth table at this point for this move. 

It is in actuality a valid rule of inference that I was taught in a formal logic course, although I do not believe it is part of the most reduced set of moves, since it can be replicated using other moves. It's a bit fascinating how the minimal set of logic moves mirrors a lot of the same concepts you see in linear algebra with bases.

It is also employed by fancy math nerds though yes

Edited May 30, 2023 by DrakeMarshall

[Ashbringer he/him]

3 hours ago, Drake Inferno said:

It's not too late to join in, is it? Sorry I came in so late!

Even without the delay signups wouldn't have ended for a bit, so yes it's not too late! Welcome aboard.

I will echo Drake(Marshall) that as much as we do need the players, this is a... quite complicated ruleset. A lot of the complexities may or may not come into play, but it is complex. But if you can handle it we'd be glad to have you as a player!

[STINK he/him]

Guys this ruleset is complicated enough without delving into all this logic stuff

[Ashbringer he/him]

@TheAlpha929, can I confirm you're joining as a player with the start delay until the 5th?

[Kasimir he/him]

20 hours ago, STINK said:

Guys this ruleset is complicated enough without delving into all this logic stuff

Join us >:P

Or we could go back to crypto, if you prefer? :eyes:

21 hours ago, DrakeMarshall said:

Ye that's why I didn't make thingness into a predicate when I provided my initial translation, bc even though I wanted to I recognize it isn't really useful

Yeah but that's why I was ? because it looked like you were working specifically with thingness

21 hours ago, DrakeMarshall said:

You have a great name

Drake1 and Drake2?

ScammerDrake and NewDrake?

:eyes:

Inferno and Drake? :eyes:

21 hours ago, DrakeMarshall said:

Well maybe I'm getting something wrong, but I am fairly sure statements that look like ∀x (Px → Qx) make quite a lot more sense than ones that look like ¬∃x (Px → Qx). Like, let's say Dx = "x is a dog" and Mx = "x is a mammal."

∀x (Dx → Mx) means all dogs are mammals.

¬∀x (Mx → Dx) means not all mammals are dogs.

¬∃x (Dx → Mx) means everything in the universe is a dog, and also nothing in the universe is a mammal

Agreed with the rest, but the way I'd've read the bolded is that it's not the case that x exists such that if x is a dog, then x is a mammal. Agreed though that if you're doing a proof, you'd want to swap to not have to negate your quantifier.

21 hours ago, DrakeMarshall said:

It is in actuality a valid rule of inference that I was taught in a formal logic course, although I do not believe it is part of the most reduced set of moves, since it can be replicated using other moves. It's a bit fascinating how the minimal set of logic moves mirrors a lot of the same concepts you see in linear algebra with bases.

Can't help you there as we weren't allowed to use it, only trees

[The Paradoxical Phenomenon he/him]

7 hours ago, Ashbringer said:

@TheAlpha929, can I confirm you're joining as a player with the start delay until the 5th?

Yep, I’m in!

[DrakeMarshall he/him]

3 hours ago, Kasimir said:

Drake1 and Drake2?

ScammerDrake and NewDrake?

:eyes:

Inferno and Drake? :eyes:

I think the real solution is obviously just to never vote against either one of us so that you don't have to decide :eyes:

3 hours ago, Kasimir said:

Agreed with the rest, but the way I'd've read the bolded is that it's not the case that x exists such that if x is a dog, then x is a mammal. Agreed though that if you're doing a proof, you'd want to swap to not have to negate your quantifier.

The way you read the bolded thing is valid and more literal, but mine is logically equivalent, and I'm trying to make a point here that ¬∃x (Dx → Mx) is probably not something you would ever want to use, because there are simpler ways to express the same logic, and the use of the conditional here is rather misleading

[Mat he/him]

3 hours ago, Kasimir said:

Inferno and Drake? :eyes:

Drake and Marshall would work too tbf

Edited May 31, 2023 by Matrim's Dice

[Kasimir he/him]

31 minutes ago, DrakeMarshall said:

I think the real solution is obviously just to never vote against either one of us so that you don't have to decide :eyes:

What about 'the Drake who is a bro' and 'the Drake who is yet to be a bro'? >:P

Sir, brave of you to believe I'd even vote smh

What if I've decided to be a pacifist this game because I'm method acting a guy with a deep midlife crisis staring into the abyss of life???

What then???

Smh.

Hi converters, you've been warned :eyes:

31 minutes ago, DrakeMarshall said:

The way you read the bolded thing is valid and more literal, but mine is logically equivalent, and I'm trying to make a point here that ¬∃x (Dx → Mx) is probably not something you would ever want to use, because there are simpler ways to express the same logic, and the use of the conditional here is rather misleading

I feel like it would be but you'd basically have to rely on classical having weird results when it comes to existence claims.

And I don't disagree about that, but think that it's not even about the conditional, it just goes back to why even postulate thingness when you could just assert existential quantifier and then the predicate of being true in this case  But this was when I was reading you as wanting to make a claim about thingness when it's like...why even do that and bulk your translation up?

Edited to add:

24 minutes ago, Matrim's Dice said:

Drake and Marshall would work too tbf

Smh this is like us calling you Dice if a new Mat signs up >:P

Edited May 31, 2023 by Kasimir

[Szeth Pancakes he/they]

Inferno and Marshall. That way, nobody is confused.