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 non-trivial 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 non-trivial moral status could be one way of understanding what it is to have "moral value" or what is minimally required by "an adequate expression of respect for our value" so long as we are sentient. More ambitious arguments could replace 'non-trivial moral status' in what follows by something stronger, such as having the right to the equal consideration of one's interests, etc. But because the argument for veganism requires only that sentient non-human animals have non-trivial moral status, for arguments to be as convincing as possible to as many interlocutors as possible they should, like that below, focus only the grounds for non-trivial moral status. The argument below and its conclusion are entirely consistent with humans having greater moral status than sentient non-human animals, beyond the mere non-trivial moral status that it seeks to show sentient non-human animals to share with humans.

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

Where "a certain trait" is interpreted broadly so as to include sets of more particular traits, or having one of several more particular traits some of which may be sufficient but not necessary for non-trivial moral status. This premise is also consistent with some humans not having non-trivial moral status (e.g. brain-dead humans or human embryos).

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

If having the trait is the full explanation non-trivial moral status and why humans have it when they do, then possession of the trait must give non-trivial moral status to other beings that have the trait. 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 the traits 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 non-trivial moral status.

or equivalently

(P3) Sentient non-human animals have the trait that gives non-trivial 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 non-trivial moral status in humans and non-human animals.

Therefore

(C) Sentient non-human animals have non-trivial moral status

which, given what non-trivial 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 one's interlocutor that humans who have non-trivial moral status have that status in virtue of some trait that they possess - where again "the trait" can be a set of more particular traits or one of several more particular traits some of which may be sufficient but not necessary for non-trivial moral status. It is not necessary to specify what trait this is. But examples may include for example sentience, the potential for sentience, intellectual ability, moral agency, etc. Note that for this trait to be the full explanation of the non-trivial moral status of the humans who one's interlocutor thinks have non-trivial moral status (which may again exclude such humans as brain-dead humans or human embryos), the trait is going to have to be present in all but only all of these humans.

Premise 2

As most interlocutors will reject such arbitrary moral double standards once they clearly discern that they would be arbitrary moral double standards, it is unlikely that one would face much resistance on this premise.

What resistance might be faced can likely be dealt with by helping one's interlocutor to specify a more complex trait that she thinks confers non-trivial moral status consistent with both premise 1 and premise 2. This might involve some real clarification and change in view on the part of one's interlocutor. For instance, one's interlocutor might want to say something like "sentience gives humans non-trivial moral status, but it doesn't give non-human animals non-trivial moral status because no rational agents have implicitly made a contract to treat them as if they had non-trivial moral status." One could then ask one's interlocutor if she thinks that what fully explains the presence or absence of non-trivial moral status in humans - and all other entities as well - is that an entity has non-trivial moral status just in case and because it is either (i) a rational agent, or (ii) such that rational agents have contracted to treat it as if it has non-trivial moral status (and the humans who are rational agents have made a contract to treat sentient humans but not non-human animals as if they have non-trivial moral status). If so then one's interlocutor can accept premises 1 and 2 with this complex trait in mind. On the other hand, one's interlocutor might be hesitant to accept this view, on the grounds that she thinks non-rational but sentient (e.g. severely intellectually disabled) humans have non-trivial moral status independent of whether the rational agent humans have contracted to treat them as if they had it (making it wrong to kill or torture severely intellectually disabled humans even in societies that accepted this). If so then one can ask her why she thinks that these sentient humans have contract-independent non-trivial moral status but sentient non-human animals lack such status. In response she might say that the rational human agents owe it to the severely intellectually disabled humans to treat them as though they had non-trivial moral status because they are members of the same species. In this case she might, consistent with premises 1 and 2, accept as the moral-value conferring trait being either (i) a rational agent, or (ii) a member of a biological species (most? many? some?) members of which are rational agents.

Premise 3

If one can convince an interlocutor that sentience, or the potential for sentience, or something similar is the full explanation of what gives humans non-trivial moral status, then they must accept the premise, as sentient non-human animals possess these traits. A strategy to get people to agree that traits such as these are what grant humans non-trivial moral status is to consider traits commonly used as justifications for denying animals moral status or in our case non-trivial moral status, such as (low) intellectual ability, (absence of) moral agency etc.. Now if someone accepts P2 (rejects double standards), then they would also have to conclude that sentient humans who lack moral agency, have lesser intellectual abilities, etc., do not have moral status, or in our case non-trivial moral status, which they are unlikely to actually accept. The basic idea is that most differences that are used to morally devalue sentient animals can also be used to morally devalue some humans who one's interlocutor thinks (and continues upon reflection to think) have non-trivial moral status.

As suggested by the discussion of the defense of premise 2, there are some views against which more counter-argument is necessary, most commonly those that involve some version of speciesism, or the view that bare biological species membership is part of what gives an entity non-trivial moral status. The crudest such specisest view is simply that

The trait that grants humans moral status or non-trivial moral status is the trait of being human.

However, on reflection, most interlocutors will find such a view very implausible. Once one distinguishes bare biological species membership from things like having the intellectual abilities of typical human adults, it seems to be a very implausible or arbitrary basis for moral status - as implausible or arbitrary as the view that moral status is affected by other bare biological traits like sex (e.g. relative gamete size or X-Y chromosomal configuration) or race / ethnicity (e.g. superficial facial and skin morphology related to continent of recent ancestry). As Peter Singer puts the analogy in terms of implausiblity or arbitrariness between speciesism on the one hand and certain forms of racism and sexism on the other:

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 one's interlocutor 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 interlocutors, such as when presenting arguments to friends, family or strangers in the course of 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?

interlocutor : 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?

interlocutor : 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?

interlocutor : 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?

interlocutor : 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 not to treat x in the ways that consuming animal products treats non-human animals; or x has non-trivial moral status'

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