Great comments on new #namethetrait video

[DrSinger]

Me and a friend worked on developing the predicate logic version of NTT. It runs as follows

H(x): x is a human
A(x): x is an animal
T(x,t): x has trait t
M(x): x has moral value

- : negation, i.e. not
-> = if, then
∄ = -∃ = there does not exist
^= and

P1: ∀x (H(x) -> M(x))
P2: ∄t (∀x∀y (((A(y) -> -T(y,t))^(H(x) ^-T(x,t))) -> -M(x)))
C: ∀y (A(y) -> M(y))

In english:

P1: for all x, if x is human then x has moral value
P2: there exists no trait 't', such that for all x and all y, if y is an animal then y does not have trait 't', and if x is a human and does not have trait 't', then x does not have moral value.
C: for all y, if y is an animal then y has moral value

Would be interested to hear any thoughts on this. If it's an accurate representation of NTT I think it's pretty clear that P2 follows from P1, and that C doesn't follow from the premises (not that this is up for contention)

[Nightcell001]

Hi DrSinger.
That's a good first attempt, I haven't explored NTT from this angle in my work in the past.
There are multiples problems with P2 that I can see, which is obviously the tricky part to translate to First order logic. First I will assume that there are only 2 closing parenthesis at the end of the premise.

The main issue is that it is the negation of a vacuously true statement. If you take as an instance "x" an animal, then the part :

(H(x) ^-T(x,t)

will be false making the implication true. The negation make the statement false.

We have to be careful when using universal/existential quantifiers in conjonction with implications and conjunctions, we most often than not end up saying what we don't want to say.

In my notes I had multiples problems with the fact that switching animals with human and vice versa ( in the instance point of view ) lead to many problems, I ended up implementing a predicate that will map a trait to a specific instance.
Anyways I do not doubt AY spent a lot of time on his argument, but in about 5 minutes you can see clearly that it is very fragile.

EDIT: Also I do not see how P2 follows from P1, do you have a derivation that I can look at ? I haven't spent much time making NTT work.

[DrSinger]

I don't see how x can be an animal in P2, since H(x) tells you x is human, and there's nothing to tell you otherwise. Perhaps I'm not fully grasping what you're saying. I have no real training in formal logic, so it's basically impossible for me to tell if it's correct until I learn more.

I haven't done any derivation to show that it follows. It's just that the animal part is effectively just 'tacked on', you could probably just tack irrelevant things on the first premise and get to P2.

Tbh I don't think there's much point working on it, if it can be debunked in words.

[Nightcell001]

I don't see how x can be an animal in P2, since H(x) tells you x is human, and there's nothing to tell you otherwise. Perhaps I'm not fully grasping what you're saying.

That's ok. I have invested quite a lot of my time on logic ( as a mathematical basis though not to argue ethically ).
The universal quantifier "∀" tells you basically that the instance you are quantifying could be anything. You can restrict the universe by using a predicate. So for example if I want to say :

- all human are mortals.

I will use informally :

∀x in {human}, M(x)

Which formally is written as :

∀x, H(x) -> M(x).

So that if x is something else than a human ( let's say a chair ), the statement is evaluated as :

∀x, False -> False

Which is vacuously true. So the statement give you information only on "x" if x is human, nothing else. That's why when using universal quantifiers, it's preferable to use implications to restrict the universe. In your P2 you use a conjonction of H() and T() which will be evaluated as False if "x" doesn't verify the predicates.( an equivalent advice apply to the existential quantifier, which should be used with conjunction rather than implication ).

Also H(x) doesn't "tell you" that x is a human. It only evaluate as true if "x" is a human. H() is a predicate ( proposition valued function )

Let me know if this is not clear enough.

I haven't done any derivation to show that it follows. It's just that the animal part is effectively just 'tacked on', you could probably just tack irrelevant things on the first premise and get to P2.

I fail to understand what you are saying here.

Tbh I don't think there's much point working on it, if it can be debunked in words.

Totally agree.

[DrSinger]

Actually I see your point now. I guess I could say for all x an element of the set all humans, for all y an element of the set all animals, as you suggested. Would it be fine then?


P1: ∀x∈H (H(x) -> M(x))
P2: ∄t∈T(∀x∈H ∀y∈A (((A(y) -> -T(y,t))^(H(x) ^-T(x,t))) -> -M(x)))
C: ∀y∈A (A(y) -> M(y))

H is the set of all humans
A is the set of all animals
T is the set of all possible traits

ignore the confusion between naming the set and the function with the same symbol

[Nightcell001]

I guess I could say for all x an element of the set all humans, for all y an element of the set all animals, as you suggested. Would it be fine then?

Yep, it's fine now. Thought you could remove the predicates H() and A() since they will evaluate to true all the time. Your statement becomes :

∄t∈T(∀x∈H ∀y∈A ((-T(y,t)^ -T(x,t)) -> -M(x)))

And now comes the second problem. This doesn't really translate P2 of AY which says there is no trait absent in animals which if absent in humans .... Meaning it is present in human. Your statement says that :
- It is false to say that there exist a trait ...
So If we managed to find a trait that evaluate the rest of the statement to True, the statement will become false by the negation.

If we take the trait to be "have two hands" : "((-T(y,t)^ -T(x,t))" evaluate to False ( because humans have two hands ), which make the implication vacuously True once again.

That falls back to my previous remarks :

( an equivalent advice apply to the existential quantifier, which should be used with conjunction rather than implication )

I hope I'm not making your brain to heat up unnecessarily, I know the feeling !

[brimstoneSalad]

I don’t agree with your last comment. “We” is supposed to represent the humans as I understand. Otherwise how would you define “we”. The addition or removal of any traits shouldn’t alter the definition of “we” because it is included in a premise. There can be no free variables in an axiom.

It's not altering the definition.

It's like saying there is no property in a square that, if removed, would make it not a square. Well, yes there is, there are many in fact, if you permit the hypothetical that one thing could become something that it wasn't prior. A square could become a triangle if you removed the property of having four sides and replaced it with three. It would no longer be a square.

So even if we accept P1 that all humans must have moral value, there are certain properties -- like humanity -- that we humans have that, if removed, would make us no longer humans.

We can not simultaneously be human and not human, but we humans could potentially become not-human.

I agree that to make a good argument you need to start from scratch, the logic laid down by AY is terribly informal.

Trying to fix it makes a pretty messy argument, but it's what was there to work with.
It wouldn't be a correction anymore if all of the original text were removed... it would just be a completely different argument.
The attempt at correction was to preserve the titular premise as much as possible.

[brimstoneSalad]

Tbh I don't think there's much point working on it, if it can be debunked in words.

Totally agree.

Actually, I'd love to include it in the Wiki article if we can figure out a formal translation.

I know Ask Yourself will just call it Chinese and ignore it, but it's nice to have so it's undeniable that C does not follow (This should be obvious, but is still being denied).

[Nightcell001]

I know Ask Yourself will just call it Chinese and ignore it, but it's nice to have so it's undeniable that C does not follow (This should be obvious, but is still being denied).

The thing is, I've made a fool of myself assuming AY had actually a formal derivation of his argument on paper and formulated it on screen for the convenience of the audience. When trying to derive C from P1, P2 I just couldn't do it.

I can provide a formal translation in First order logic of his argument, but I'm predicting his answers to be :

• This is Chinese please translate into english

• This is probably a faulty translation of my argument

• I am not a logician

• You haven't shown how my argument doesn't follow

I am predicting these answers based on an other person ( I apologize for forgetting his name ) which provided a translation of his argument but in propositional logic, and even though it was mostly incorrect, AY shut all doors to critical thinking.

I think the best strategy is to find a case which doesn't produce a contradiction, but again brimstoneSalad you have already done that, and the answer of AY have been to sneak in premises to invalidate your suggestions.

[Nightcell001]

It's not altering the definition.

It's like saying there is no property in a square that, if removed, would make it not a square. Well, yes there is, there are many in fact, if you permit the hypothetical that one thing could become something that it wasn't prior. A square could become a triangle if you removed the property of having four sides and replaced it with three. It would no longer be a square.

So even if we accept P1 that all humans must have moral value, there are certain properties -- like humanity -- that we humans have that, if removed, would make us no longer humans.

We can not simultaneously be human and not human, but we humans could potentially become not-human.

I still don't quite agree. This is not similar as the square scenario you mention because there are no self referencing word. To make it clear, if the statement was something like "there is a trait which if absent in human would make them not humans" I would have no problem with that. The problem here is the "we". If you introduce the trait as being "humanity" then if the trait is absent in humans they will no longer be humans. But what does "we" refer to in this case ? This is a self referencing problem, and is heavily avoided when talking about sets ( here I mean sets of humans ). If you consider the set of humans in the arguments and denote by "we" all the entities in it, removing the trait humanity introduce profound definition issues because the set you are left with is no more the set of humans.

I do not know if you are familiar with the work of Russell and his most famous paradox. We do not allow self referencing statement in our "classical" logic because of this. So you have multiple choices here :

• Do no consider the trait humanity

• Come up with another non-classical logic

• Alter P2 to avoid the use of "we"