NameTheTrait 2.0

This article is intended to be an improvement on the original (logically invalid) NameTheTrait argument. It is possible to correct the NTT argument and preserve its persuasive force by adding a premise that rejects double standards and by changing the first premise to require human moral value (or some other moral consideration) to be based on a trait. This makes NTT valid, and allows it to be presented in the same way as it was intended.

NTT 2.0 In English

In the following 'x has minimal moral status' means at least that we are morally required not to treat x in the ways that consuming animal products treats non-human animals - for instance, x is such that we are morally required not to inflict enormous suffering upon and / or kill x for relatively trivial reasons (like taste-pleasure).

(Having such 'minimal moral status' could be one way of understanding having "moral value," but for a more ambitious argument 'minimal moral status' could be replaced in what follows by something stronger, such as having the right to the equal consideration of one's interests, etc.)

(P1) Humans have minimal moral status just in case and because they have a certain trait.

This may or may not include all humans (e.g. brain-dead humans or human embryos).

(P2) If humans have minimal moral status just in case and because they have a certain trait, then all beings have minimal moral status just in case and because they have that trait.

If the trait is the full explanation of humans' minimal moral status, it must be sufficient to give minimal moral status to other beings that have it. To think otherwise would be to embrace a double-standard as arbitrary as that involved in thinking that traits that give moral status to members of one ethnicity or sex fail to give the same moral status to members of another ethnicity or sex, even when they are just as present in both cases.

(P3) There is no trait absent in non-human animals, which, if absent in a human, would cause the human to not have minimal moral status.

or equivalently

(P3) Sentient non-human animals have the trait that gives minimal moral status to humans.

When we consider such things as sentient but intellectually less able humans in various circumstances, various ways in which intellectual ability is vs. is not morally relevant, and what bare-biological species membership amounts to, it seems clear that sentience is sufficient for minimal moral status in humans and non-human animals.

Therefore

(C) Sentient nonhuman animals have minimal moral status

which, given what minimal moral status amounts to, entails that we are morally required to go vegan.

Defense of Premises

Premise 1

All that is necessary here is to convince the opponent that humans who have R, have R in virtue of some trait that they possess, it is not necessary to specify which trait. But examples may include example sentience, capacity for sentience, moral agency etc. Furthermore all humans may or may not possess this trait.

Premise 2

Most people would reject moral double standards, it is unlikely that one would face much resistance on this premise.

Premise 3

If one can convince an opponent that sentience, or the capacity for sentience, or similar, is what grants humans R, then they must accept the premise, as sentient animals possess these traits. A strategy to get people to agree that traits such as these grant humans R, is to consider traits commonly used as justifications for denying animals moral status or in our case R, such as (low) intelligence, moral agency etc. Now if someone accepts P2 (rejects double standards), then they would also have to conclude that humans who lack moral agency, (low) intelligence etc. do not have moral status, or in our case R, which they are unlikely to actually accept. The basic idea is that, most differences that are used to devalue sentient animals morally, can also be used to devalue some humans morally.

Though there are some exceptions, which require a different counterargument, most commonly the view of speciesism, which in the case of humans would hold

The trait that grants humans moral status or R, is the that of being human

Which is to give humans special consideration simply on the basis of being human. Analogies can be made between speciesism and other forms of discrimination, such as racism, something which Peter Singer has done;

the racist violates the principle of equality by giving greater weight to the interests of members of his own race, when there is a clash between their interests and the interests of those of another race. Similarly the speciesist allows the interests of his own species to override the greater interests of members of other species. The pattern is the same in each case. (Singer 1974: 108) [1]

Comparisons of this sort are likely to compel people to look toward other traits on which to base moral status.

Informal Presentation

In the case of making informal arguments, which rely on implicit agreements and assumptions between opponents, such as when presenting arguments to friends, family or street activism etc. it is not necessary to present the argument in full detail. One way to present the argument, which is used by activists, is the following:

vegan : Can you name a trait present or absent in animals that justifies treating them the way we do?

opponent : moral agency, (low) intelligence etc.

vegan : What about humans who lack moral agency or have (low) intelligence etc. such as the mentally disabled and infants, would it be justified to treat them in this way?

opponent : That's different, they are not human.

vegan : Do you think simply being human grants humans special consideration? Isn't that a lot like other forms of discrimination, like being white is what grants whites special consideration?

opponent : Yes I suppose it is.

vegan : Personally, I believe it's the capacity to experience well-being, happiness, and suffering (sentience) that gives a being moral status, and means we shouldn't harm them for our taste pleasure. Would you agree with that?

opponent : Yes, I suppose I would. Perhaps going vegan would be the right thing to do.

In First Order Logic

Definitions

H(x) means 'x is a human'

SNA(x) means 'x is a sentient non-human animal'

R(x) means 'we are moral required to not consume the products of x for food, in order to prevent harm to x'

T(x) means 'x is a trait'

P(x,y) means 'x has y'

In First Order Logic

(P1) ∃t ( Tt ∧ ∀x ( Hx ⇒ ( Rx ⇔ Pxt ) ) )

(P2) ∀t ( Tt ∧ ( ∀x ( Hx ⇒ ( Rx ⇔ Pxt ) ) ⇒ ∀x ( Rx ⇔ Pxt ) ) )

(P3) ∀x( SNAx ⇒ ¬∃t ( Tt ∧ ¬Pxt ∧ ∀y ( Hy ⇒ ( ¬Pyt ⇒ ¬Ry ) ) ) )

or equivalently

(P3) ∀x( SNAx ⇒ ∀t ( Tt ∧ ∀y ( Hy ⇒ ( Ry ⇒ Pyt ) ) ⇒ Pxt ) )

Therefore (C) ∀x ( SNAx ⇒ Rx )

Direct Translation

(P1) there exists t, such that t is a trait, and for all x, if x is a human, then x has R, if and only if x has t

(P2) for all t, t is a trait, and if for all x, if x is a human, then x has R if and only if x has t, then for all x, x has R if and only if x has t

(P3) for all x, if x is a sentient nonhuman animal, then there does not exist t, such that, t is a trait and, x lacks t, and for all y, if y is a human, then if y lacks t, then y does not have R

or equivalently

(P3) for all x, if x is a sentient non-human animal, then for all t, if t is a trait, and, for all y, if y is a sentient human, then, if y has R then y has t, then x has t

Therefore (C) for all x, if x is a sentient nonhuman animal then x has R

Proof of Validity

Logical Proof Generator

We can show this is valid argument by using a logical proof generator, to prove the formula

P1 ∧ P2 ∧ P3 ⇒ C

with the input

(P1) \existst ( Tt \land \forallx (Hx \to ( Rx \leftrightarrow Pxt ) ) )

(P2) \forallt (Tt \land ( \forallx (Hx \to ( Rx \leftrightarrow Pxt ) ) \to \forallx ( Rx \leftrightarrow Pxt ) ) )

(P3) \forallx ( Ax \to \neg \existst ( Tt \land \negPxt \land( \forally (Hy \to ( \negPyt \to \negRy ) ) ) ) )

or equivalently

(P3) \forallx( Ax \to \forallt ( Tt \land \forally ( Hy \to ( Ry \to Pyt ) ) \to Pxt ) )

(C) \forallx ( Ax \to Rx )

Or all together (P1 ∧ P2 ∧ P3 ⇒ C)

\existst ( Tt \land \forallx (Hx \to (Rx \leftrightarrow Pxt ) ) ) \land \forallt ( Tt \land ( \forallx (Hx \to ( Rx \leftrightarrow Pxt)) \to \forallx (Rx \leftrightarrow Pxt))) \land \forallx (Ax \to \neg \existst (Tt \land \negPxt \land (\forally (Hy \to ( \negPyt \to \negRy))))) \to \forallx ( Ax \to Rx )

which yields valid

Note that without the modification of premise 1 to require human moral value to be based on trait, and the addition of the premise to forbid double standards, the argument would not be even close to valid, which is the case for the original NTT formulation.

Natural Deduction

First we will prove the following to make our proof simpler:

∀x( SNAx ⇒ ¬∃t ( Tt ∧ ¬Pxt ∧ ∀y ( Hy ⇒ ( ¬Pyt ⇒ ¬Ry ) ) ) ) ⇔ ∀x( SNAx ⇒ ∀t ( Tt ∧ ∀y ( Hy ⇒ ( Ry ⇒ Pyt ) ) ⇒ Pxt ) )

Starting with the left-hand-side (LHS)

LHS	⇔ ∀x( SNAx ⇒ ¬∃t ( Tt ∧ ¬Pxt ∧ ∀y ( Hy ⇒ ( ¬Pyt ⇒ ¬Ry ) ) ) )
	⇔ ∀x( SNAx ⇒ ∀t ¬( Tt ∧ ¬Pxt ∧ ∀y ( Hy ⇒ ( ¬Pyt ⇒ ¬Ry ) ) ) )	(¬∃x Px) ⇔ (∀x ¬Px)
	⇔ ∀x( SNAx ⇒ ∀t( Tt ∧ ¬Pxt ⇒ ¬∀y ( Hy ⇒ ( ¬Pyt ⇒ ¬Ry ) ) ) )	¬(p∧q) ⇔ (p⇒¬q)
	⇔ ∀x( SNAx ⇒ ∀t( Tt ∧ ¬Pxt ⇒ ¬∀y ( Hy ⇒ ( Ry ⇒ Pyt ) ) ) )	(p⇒q) ⇔ (¬q⇒¬p)
	⇔ ∀x( SNAx ⇒ ∀t( Tt ∧ ∀y ( Hy ⇒ ( Ry ⇒ Pyt ) ) ⇒ Pxt) )	(p⇒q) ⇔ (¬q⇒¬p)
	⇔ RHS

Hence we have shown the equivalency.

Now we can prove the validity of the argument using natural deduction.

Natural Deduction Proof of Validity

1	∃t ( Tt ∧ ∀x ( Hx ⇒ ( Rx ⇔ Pxt ) ) )	assumption (P1)
2	∀t ( Tt ∧ ( ∀x ( Hx ⇒ ( Rx ⇔ Pxt ) ) ⇒ ∀x ( Rx ⇔ Pxt ) ) )	assumption (P2)
3	∀x( SNAx ⇒ ∀t ( Tt ∧ ∀y ( Hy ⇒ ( Ry ⇒ Pyt ) ) ⇒ Pxt ) )	assumption (P3)
4	Ts ∧ ∀x ( Hx ⇒ ( Rx ⇔ Pxs ) )	existential elimination	1
5	Ts ∧ ( Ha ⇒ ( Ra ⇔ Pas ) )	universal elimination	4
6	Ts ∧ ( ( Ha ⇒ ( Ra ⇔ Pas ) ) ⇒ ( Rb ⇔ Pbs ) )	universal elimination	2
7	SNAb ⇒ ( Ts ∧ ( Ha ⇒ ( Ra ⇒ Pas ) ) ⇒ Pbs )	universal elimination	3
8	¬ ( SNAb ∧ ¬ ( Ts ∧ ( Ha ⇒ ( Ra ⇒ Pas ) ) ⇒ Pbs ) )	( p ⇒ q ) ⇔ ¬( p ∧ ¬q )	7
9	¬ ( SNAb ∧ ¬ ¬( Ts ∧ ( Ha ⇒ ( Ra ⇒ Pas ) ) ∧ ¬ Pbs ) )	(p ⇒ q) ⇔ ¬(p ∧ ¬q)	8
10	¬ ( SNAb ∧ ( Ts ∧ ( Ha ⇒ ( Ra ⇒ Pas ) ) ∧ ¬ Pbs ) )	negation elimination	9
11	¬ ( SNAb ∧ ¬ Pbs ∧ ( Ts ∧ ( Ha ⇒ ( Ra ⇒ Pas ) ) ) )	∧ commutivity	10
12	SNAb ∧ ¬ Pbs ⇒ ¬ ( Ts ∧ ( Ha ⇒ ( Ra ⇒ Pas ) ) )	¬( p ∧ q) = (p ⇒ ¬q)	11
13	¬ (SNAb ⇒ Pbs) ⇒ ¬ ( Ts ∧ ( Ha ⇒ ( Ra ⇒ Pas ) ) )	¬(p ⇒ q) ⇔ (p ∧ ¬q)	12
14	( Ts ∧ ( Ha ⇒ ( Ra ⇒ Pas ) ) ) ⇒ (SNAb ⇒ Pbs)	(¬p ⇒ ¬q) ⇔ (q ⇒ p)	13
15	Ts ∧ ¬( Ha ∧ ¬ ( Ra ⇔ Pas ) )	(p⇒q) ⇔ ¬(p∧¬q)	5
16	Ts ∧ ¬( Ha ∧ ¬ ( (Ra ⇒ Pas) ∧ (Pas ⇒ Ra) ) )	biconditional elimination	15
17	Ts ∧ ¬ ( Ha ∧ (¬ (Ra ⇒ Pas) ∨ ¬(Pas ⇒ Ra) ) )	¬(p ∧ q) = ¬p ∨ ¬q	16
18	Ts ∧ ¬ ( (Ha ∧ ¬ (Ra ⇒ Pas) ) ∨ (Ha ∧ ¬( Pas ⇒ Ra ) ) )	p ∧ (q ∨ r ) = (p ∧ q) ∨ (p ∧ r)	17
19	Ts ∧ ¬ (Ha ∧ ¬ (Ra ⇒ Pas) ) ∧ ¬ (Ha ∧ ¬( Pas ⇒ Ra ) )	¬ (p ∨ q) = (¬p ∧ ¬q)	18
20	Ts ∧ (Ha ⇒ (Ra ⇒ Pas)) ∧ (Ha ⇒ (Pas ⇒ Ra) )	( p ⇒ q ) ⇔ ¬ ( p ∧ ¬q )	19
21	Ts ∧ (Ha ⇒ (Ra ⇒ Pas))	∧ elimination	20
22	SNAb ⇒ Pbs	Modus Ponens	14, 21
23	Rb ⇔ Pbs	Modus Ponens	6, 5
24	(Rb ⇒ Pbs) ∧ (Pbs ⇒ Rb)	biconditional elimination	23
25	Pbs ⇒ Rb	∧ elimination	24
26	SNAb ⇒ Rb	transitivity	22, 25
27	∀x (SNAx ⇒ Rx)	universal introduction (C)	26