Revision as of 21:34, 17 December 2017

Note: This article is a work in progress

To jump to the proof of logical invalidity see Proof of Invalidity in First Order Logic

[DrSinger: I moved a load of stuff here (NTT to be revised), to be revised and added back in.]

Name The Trait, or #NameTheTrait is an argument for veganism formulated by vegan Youtuber Ask Yourself in 2015, and popularized during a series of Youtube debates in 2017 by Ask Yourself and Vegan Gains a vegan bodybuilder and Youtuber. Loosely speaking, NTT seeks to establish veganism from a personal belief in human moral value, similar to the well known argument from marginal cases (or Less Able Humans). Some street activists claim to have found the argument effective, when presented informally. However as we will see in this article, it is logically invalid, and Ask Yourself's attempts to make it valid have led to an alternative version of the argument that is question-begging. Furthermore, it is often combined with false claims such as "animal rights follow logically from human rights" which are defended with the use of invalid generalizations. These drawbacks can make the argument confusing and unconvincing. However the argument can be corrected by modifying its first premise to require human moral value to be based on a trait and by adding a premise that rejects double standards, preserving the original intention of the argument.

The formal, premise-conclusion presentation of #NameTheTrait is as follows:

Argument for animal moral value:
P1 - Humans are of moral value
P2 - There is no trait absent in animals which if absent in humans would cause us to deem ourselves valueless.
C - Therefore without establishing the absence of such a trait in animals, we contradict ourselves by deeming animals valueless
Argument for veganism from animal moral value:
P1 - Animals are of moral value.
P2 - There is no trait absent in animals which if absent in humans would cause us to consider anything short of non-exploitation to be an adequate expression of respect for human moral value.
C - Therefore without establishing the absence of such a trait in animals, we contradict ourselves by considering anything short of non-exploitation(veganism) to be an adequate expression of respect for animal moral value.

This article discusses the three primary issues with NTT. Firstly, it discusses its logical invalidity, and how its invalidity can create problems. Secondly, it discusses problems with the justifications used by Ask Yourself to defend the premises of the first, "for animal moral value" argument validity of the argument. And thirdly, the article discusses various problems with the second, less widely discussed "for veganism from animal moral value" argument, which suggests a potentially dubious, unclear, and rigid commitment to non-exploitation.

[Please put large comments on the talk page]

NTT's Invalidity

The Importance of logical validity

The main reason it helps to know whether an argument is logically valid is that it helps us to clarify if we have identified all of the substantive assumptions behind its conclusion. If we can see that an argument is valid, then we know that its conclusion follows from its premises simply because of their form, so we have identified and listed all of its substantive assumptions in its premises. If we can see that an argument is invalid, this helps us to know that it must be making further assumptions in order to be a good, rationally compelling argument. Knowing that an argument is making such assumptions, and determining what they are, can help us to understand why certain individuals may not find it compelling, and can spare us the confusion of failing to understand this. It can also put us in a better position to defend those assumptions forthrightly to those who might be inclined to challenge or fail initially to accept them.

As we will see below, NTT is invalid. Seeing why it is helps us to see how certain very plausible substantive assumptions can be added to its premises to make it valid. The making of these tacit assumptions by the presenter of NTT and the audience very likely explains why it is often a compelling argument. But as we will see below, the failure to acknowledge these assumptions can cause confusion, and inhibit a persuasive defense of its premises. As we will also see, the fact that to be compelling the argument must make such assumptions may help to dash certain hopes about the minimality of the argument’s assumptions (e.g. about the nature of value and ethics). Seeing that NTT is invalid will thus help us to appreciate the argument’s limits, and how other approaches may be helpful in defending the substantive ethical views that stand behind arguments like NTT.

Logical Validity

What it is for arguments to be logically valid and invalid is the following:

• Valid: No possible case has the premises all true and the conclusion false, due simply to the structure of the premises and the conclusion
• Invalid: Some possible case has the premises all true and the conclusion false, due simply to the structure of the premises and the conclusion

(This is not to be confused with sound which means an argument is both valid and its premises are true)

In other words, for an argument to be logically valid is for the truth of its conclusion to be guaranteed by the truth of its premises due to their logical form (or more specifically, the validity of an argument depends on the syntactic form of the argument, not the symantic meaning of the argument [1]). For instance, an argument of the form

(P1) If consuming animal products causes unnecessary suffering, then we should not consume animal products,

(P2) Consuming animal products causes unnecessary suffering,

Therefore, (C) we should not consume animal products

is logically valid. This is because it has the logical form:

(P1) If U then V

(P2) U

Therefore (C) V

Here, C follows from P1 and P2 simply due to their logical form, whatever the content of U and V may be (this particular way of a conclusion following from its logical form and that of the premises is known as "modus ponens" [2]).

This means that we should be able to change NTT, and so long as we preserve its logical form, it must remain valid (note: it would not have to remain sound). Hence the following must be valid if NTT is valid:

P1 - Humans are of moral value

P2 - There is no eye colour absent in cows which if absent in humans would cause us to deem ourselves valueless.

C - Therefore without establishing the absence of such an eye colour in cows, we contradict ourselves by deeming cows valueless

Which is clearly invalid as there is no premise to say moral value must be based on eye colour, likewise in NTT there is no premise to say moral value must be based on a trait. There is no special logical significance to the notion of a trait which means such a premise need not be stated.

One way to show an argument is invalid is to show a case where the logical form of the premises and conclusion of NTT allow the premises to be true and the conclusion to be false, such a case is referred to as a counterexample.

To see how to formally prove an argument is valid see Proving Formal Arguments (still a WIP).

Steel-manning NTT

Before proceeding we will rephrase the argument in the following way, to capture its essential reasoning

Part 1

(P1) All sentient humans have moral value

(P2) If an individual is a sentient nonhuman animal, then there is no trait absent the individual, which is such that, if the trait were absent in a sentient human, then the human would not have moral value

Therefore, (C) All sentient non-human animals have moral value

Part 2

(P1) All sentient non-human animals have moral value

(P2) If an individual is a sentient non-human animal, then there is no trait absent the individual, which is such that, if the trait were absent in a sentient human who has moral value, then we would not be morally required to not exploit the human

Therefore, (C) We are morally required to not exploit sentient non-human animals who have moral value

Summary of Issues

As we will see below, the reason NTT is logically invalid because its logical form allows for a counterexample in which sentient humans have moral value, sentient non-human animals that lacks moral value, and for all traits that sentient non-human animals lack, humans possess moral value with the traits removed. The reason we can pose such a counterexample is because there is nothing in the logical form of the argument that says moral value must be based on a trait (as is the case for the correction) nor is there anything to say humans lacking certain traits are animals (as is the case for the alternative interpretation).

Ask Yourself has argued that if one were to lose all of the traits that distinguish one from a non-human animal, then the resulting entity would be identical to that non-human animal, so P1 and P2 so interpreted [logically] entail C. The problem with this claim is that it presupposes something like the identity of indiscernibles: that if two entities have all of the same properties, then they must be the self-same object. This is a substantive metaphysical thesis, to which certain philosophers have objected (for discussion see [3]), so it must be added as an additional premise for the argument to be logically valid.

But as we will see below, the much greater problem with the argument so interpreted is that it has essentially no rational force. P2 so interpreted is essentially just asserting that beings with all and only the traits of sentient non-human animals have moral value. The argument thus offers little if any reason to change the mind of someone who does not already find this view plausible, and the defense of its premises offers no guidance on how to persuade such an individual, see how this version of the argument begs the question.

Proof of Invalidity in First Order Logic

In order to show the logical form of NTT, we will use what is known as First order logic. The sort of logic used to display the logical form of the argument above '(P1) If U then V; (P2) U; therefore, (C) V' is known as propositional logic, since it replaces full propositions flanking logical connectives like 'if...then', 'and' and 'or' with abstract symbols. First order logic goes inside the logical structure of propositions, and replaces predicates like 'is a sentient human' and 'is a sentient non-human animal' with abstract symbols. First order logic also considers variables for things to which those predicates are ascribed, and quantification over them (e.g. 'for all x, if x is a sentient human, then x has moral value'). It may be helpful to read the entry on logical connectives before reading the following sections.

Displaying the Logical Form of NTT in FOL

Symbols

• ∀ (for all)
• ⇒ (if, then; e.g. A ⇒ B means 'if A then B')
• ⇔ (if and only if; e.g. A ⇔ B means 'if A then B and if B then A')
• ¬ (negation i.e. not)
• ∃ (there exists)
• ∧ (and)
• ∨ (or)

Definitions

H(x) means 'x is a sentient human'

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

M(x) means 'x has moral value'

T(x) means 'x is a trait'

P(x,y) means 'x has y; e.g. if x is a sentient human and t is a trait, P(x,t) means 'human x has trait t', or 'a property of x is t'

RNE(x) means 'we a morally required to not exploit x'

Note we will also use the shorthand Hx to represent H(x), Px,y or Pxy to represent P(x,y) etc.

The Logical Form of Part 1 of NTT

(P1) ∀x ( Hx ⇒ Mx )

(P2) ∀x ( Ax ⇒ ¬∃t ( Tt ∧ ¬Pxt ∧ ∀y ( Hy ⇒ ( ¬Pyt ⇒ ¬My ) ) ) )

Therefore, (C) ∀x ( Ax ⇒ Mx )

In English

(P1) for all x, if x is a sentient human, then x has moral value

(P2) 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 moral value.

Therefore, (C) For all x, if x is a sentient non-human animal, then x has moral value

The Logical Form of Part 2 of NTT

(P1) ∀x ( Ax ⇒ Mx )

(P2) ∀x ( Ax ⇒ ¬∃t ( Tt ∧ ¬Pxt ∧ ∀y ( Hy ∧ My ⇒ ( ¬Pyt ⇒ ¬RNEy ) ) ) )

Therefore, (C) ∀x ( (Ax ∧ Mx) ⇒ RNEx )

In English:

(P1) For all x, if x is a sentient nonhuman animal, then x has moral value.

(P2) 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, and y has moral value, then if y lacks t, then we are not morally required to not exploit y.

Therefore (C) for all x, if x is a sentient non-human animal, and x has moral value, then we are morally required not to exploit x.

Showing NTT is Logically Invalid

The standard way of showing that an argument is invalid is to construct a counterexample, or a model, which is allowed by the logical form of the premises and the conclusion, in which the premises are true and the conclusion is false.Since Part 1 and Part 2 follow the same basic structure, we will only show a counterexample for Part 1.

Part 1 Counterexample

In the following counterexample, we will imagine a case in which, sentient humans have moral value, sentient non-human animals do not have moral value, and for all traits that sentient nonhuman animals lack, humans retain moral value with the trait removed.

In FOL

(E1) ∃x ( Hx ) ∧ ∀x ( Hx ⇒ ( Mx ∧ ¬Ax ∧ ¬Tx) )

(E2) ∃x ( Ax ) ∧ ∀x ( Ax ⇒ ( ¬Mx ∧ ¬Hx ∧ ¬Tx ∧ ( ∃y ( Hy ∧ ∀t (Tt ∧ ( ¬Pxt ⇒ ¬Pyt ) ) ) ) )

(E3) ∀x ( Tx ⇒ ( ¬Ax ∧ ¬Hx ∧ ¬ Mx) )

In English

(E1) there is a sentient human, and all sentient humans have moral value, are not sentient non-human animals, are not traits

(E2) there is a sentient non-human animal, and all sentient non-human animals do not have moral value, are not sentient humans, are not traits, and are such that there exists a human that lacks all the same traits as the non-human animal

(E3) all traits are not sentient non-human animals, are not sentient humans, and do not have moral value

Proving the Counterexample renders NTT invalid

If NTT is invalid, then the formula

( E1 ∧ E2 ∧ E3 ) ⇒ ( P1 ∧ P2 ∧ ¬C )

should be valid. That is to say, if NTT is invalid, and we have chosen our counterexample correctly, then if the counterexample is true, then the premises of NTT should be true and its conclusion false. We can check this using a logical proof generator, with the input

(\existsx (Hx) \land \forallx (Hx \to ( \negAx \land \negTx \landMx))) \land (\existsx (Ax) \land \forallx(Ax\to (\negHx \land \negTx \land \negMx\land( \existsy (Hy\land \forallt (\negPxt \to \negPyt)))))) \land (Tx\to( \negAx \land\negHx\land\negMx))\to(\forallx ( Hx \to Mx ) \land \forallx ( Ax \to \neg \existst ( Tt \land \neg Pxt \land ( \forally (Hy \to ( \neg Pyt \to \neg My ) ) ) ) ) \to\neg\forallx (Ax \to Mx))

which gives us valid. Hence we have demonstrated that NTT is invalid.

Checking the Validity Directly

We can also use the logical proof generator to directly show the argument is invalid by checking the formula

P1 ∧ P2 ⇒ C

We can do this with the input (for part 1)

(P1) \forallx (Hx \to Mx)

(P2) \forallx ( Ax \to \neg \exists t (Tt \land \neg Pxt \land ( \forally (Hy \to ( \neg Pyt \to \neg My ) ) ) ) )

(C) \forallx ( Ax \to Mx )

Or all together (P1 ∧ P2 ⇒ C)

\forallx ( Hx \to Mx ) \land \forallx ( Ax \to \neg \existst ( Tt \land \neg Pxt \land ( \forally (Hy \to ( \neg Pyt \to \neg My ) ) ) ) ) \to\forallx (Ax \to Mx)

which yields invalid. This is unlike the correction which gives valid.

The Alternative Interpretation of NTT

In the video to the right Ask Yourself explains his interpretation of NTT and why he believes it to be valid. The claim made is that, paraphrasing, all objects are constellations of traits, and that if the traits of the two objects are equalized, then the objects become the same object, and furthermore, to resist this is to deny the very first law of logic, which is the law of identity. This assumes a number of substantive metaphysical premises, which are outlined below:

Bundle Theory

The first claim, that objects are constellations of traits is not built into logic, it is a form of bundle theory which states :

Substances are in fact no more than bundles of properties conceived of as universals.[4]

This is a substantive metaphysical premise that needs to be stated if it's to be used as part of an argument. It's worth noting that the identity of indiscernibles would follow from such a premise, as correctly identified by Ask Yourself. This is one of the reasons why many philosophers have raised objections to such a premise.

Identity of Indescernibles

The claim that two objects with the same traits are the same object is a principle similar to the the identity of indiscernibles, which says: if for every property P, object x has P if and only if object y has P, then x is identical to y. Or in the notation of symbolic logic:

(∀P)(Px ⇔ Py) ⇒ x=y.

In the notation we have been using, this could be expressed as

∀x ∀y ∀t ( Px,t ⇔ Py,t ) ⇒ x = y)

(for all things x, y, and t, if x has t if and only if y has t, then x and y are the self-same thing. )

Or in that case that we are only considering traits, that may or may not refer to all properties, the principle would be expressed as

∀x ∀y ∀t ( Tt ∧ ( Px,t ⇔ Py,t ) ) ⇒ x = y)

i.e. for all things x, y, and t, if t is a trait, and x has t if and only if y has t, then x and y are the self-same thing.

The identity of indiscernibles is not simply a fact about the logical form of propositions or their components - it is instead a metaphysical thesis about the conditions under which entities are identical. Thus, an argument the conclusion of which follows only from its premises together with the identity of identity of indiscernibles in virtue of their logical form is not logically valid. To be logically valid, such an argument must include the statement of the identity of indiscernibles among its premises. In contrast, the law of identity, understood simply as 'x is identical to x for each x' or ∀x (x = x), is a fact about the logical form of the identity relation (so it does not need to be stated among the premises of an argument that involves propositions that employ the identity relation).

Alternative Version in FOL

With the addition of the identity of indiscernibles we can present a logically valid alternative version of NTT, as shown below:

(P1) ∀x ( Hx ⇒ Mx )

(P2) ∀x ( Ax ⇒ ( ∃y ( CPy ∧ My ∧ ∀t ( Tt ⇒ ( Px,t ⇔ Py,t ) ) ) ) )

(P3) ∀x ∀y ∀t ( ( Tt ∧ ( Px,t ⇔ Py,t ) ) ⇒ x = y)

Therefore (C) ∀x ( Ax ⇒ Mx )

In English

(P1) sentient humans are of moral value
(P2) for all sentient nonhuman animals there exists a counterpart to a sentient human that has moral value and has all the same traits as a sentient nonhuman animal
(P3) All things with the same traits are the same thing.
Therefore (C) Animals are of moral value

Here we have introduced the notion of a counterpart to a human, to mean a being that can take on all the traits of a non-human animal, and can become a sentient non-human animal.

This Alternative Version of NTT Begs the Question

With the addition of the identity of indiscernibles as P3, this alternative version of NTT becomes logically valid. However, the validity of this version of the argument comes at a very high price. The "counterparts" to sentient humans spoken of P2 are allowed to lack the essential properties of humans - like originating from human gametes - and to have the essential properties of non-human animals - like originating from bovine gametes. Hence, these "counterparts" need not be human, or us, at all. The only requirement of these entities is that they (i) have moral value, and (ii) have all and only the properties of sentient non-human animals. So in asserting that, for each sentient non-human animal, there is a "counterpart" that has moral value and has all and only the properties of the non-human animal, P2 is essentially just asserting that sentient beings with the properties of non-human animals have moral value. In doing so P2 assumes the substance of what the argument is supposed to prove, namely that sentient beings like non-human animals have moral value, thus rendering the argument question-begging.

To note how unconvincing this version of NTT really is, note that P1, about human moral value, really plays no role at all in deriving the conclusion of this version of NTT at all. The conclusion follows from simply P2, which asserts that for each sentient non-human animal, there is a being that has moral value and has all and only the same traits as the non-human animal, and P3, which entails that if the being with moral value has all and only the same traits as the non-human animal, then the being is identical to the non-human animal. But clearly, the argument that:

(P2) For each non-human animal, there is an entity with all and only the same traits that has moral value

(P3) If two entities have all and only the same traits, then they are the self-same entity

Therefore, (C) All non-human animals have moral value

is not a very compelling argument for the moral value of non-human animals at all. Anyone not inclined to accept the conclusion will have no more inclination at all to accept P2. Moreover, the structure of this version of the argument offers no guidance as to how to convince someone not inclined to accept the conclusion of the truth of the argument's premises, since it seems just as difficult to convince someone of the truth of P2 as to convince them of the truth of C directly.

Excluding Essential Properties

Based on the written version, P2 seems clearly to speak of traits that do not include essential properties and include only accidental properties. The distinction is that

An essential property of an object is a property that it must have [in order to count as the same object], while an accidental property of an object is one that it happens to have but that it could lack [and still count as the same object]. [5]

If the traits spoken of in P2 include only accidental properties, we are envisioning humans like oneself losing accidental properties that one has and non-human animals lack (like abstract reasoning ability, moral agency, etc.) and still retaining one’s status as oneself. The original written version of NTT seems to require this interpretation, since it says

"there are no traits absent in animals which if absent in humans would cause us to deem ourselves valueless,"

so the entities losing the traits are clearly supposed still to be us after losing them.

This interpretation of P2 as speaking only of accidental traits is not question begging. But it is is clearly invalid, as one could hold the view that we might call

Value Narcissism: one’s essential properties (or the essential properties of being human) are what give one moral value – or are such that, if one lost them, one would lose moral value.

A value narcissist could hold that although humans like oneself (or just oneself) have moral value, and one would retain this value if one lost the accidental properties that one has and sentient non-humans lack, non-human animals still lack moral value. They could thus accept P1 and P2 but reject C.

Some individuals faced with arguments for veganism like NTT may well be tempted to embrace something like value narcissism. For instance, in Ask Yourself's debates / discussions with the Warskis, Friend Ed, and Patty Politics, Ask Yourself's conversants seemed tempted to the view that being human (i.e. possessing the essential properties of a human) is necessary to have moral value - at least independent of other considerations like membership in a human community (the trait named by FriendEd). It is certainly true that Ask Yourself argued substantively against this view, although in doing so he unfortunately seemed to make invalid generalizations about the ways in which species membership might matter morally. But it seems quite possible that addition confusion in debates may stem from the fact that, on the natural interpretation of P2 as restricted to accidental traits, the argument simply invalidly overlooks the option of value narcissism, and makes it unclear how a substantive attack on the plausibility of value narcissism is needed for the argument to establish its conclusion.

Related Problems

False Claims

Ask Yourself proposes "veganism follows logically from universal human rights"

Proponents of NTT such as Ask Yourself claim that "veganism follows logically from universal (sentient) human rights" or that "(sentient nonhuman) animal rights follow logically from (sentient) human rights", which is false. For such a claim to be true human rights must logically entail animal rights, meaning the following must be true;

(P1) Sentient humans deserve rights

Therefore (C) Sentient nonhuman animals deserve rights.

Or in the notation we have been using.

∀x ( Hx ⇒ Rx ) ⊢ ∀x (Ax ⇒ Rx)

where ⊢ denotes logically entails and R(x) denotes x deserves rights.

Which is clearly invalid, since the following statements are not contradictory.

(i) Sentient humans deserve rights

(ii) Sentient nonhuman animals do not deserve rights

It's possible this is an ill-thought-out claim, not meant in a strict logical sense, used to promote the idea that veganism follows from logical consistency and a personal belief in human moral value. However such claims are likely to be taken in the strict logical sense, in which case, they are false and reflect poorly on veganism as a whole, particularly in the long-term.

Invalid Generalizations

Part of Ask Yourself's first response to criticisms from Philosophical Vegan

In defending P2 proponents of NTT often use invalid generalisations that take the form

If you reject being discriminated against for a certain reason then you contradict yourself by accepting it for someone else

i.e. the claim is that the following is a contradiction

1. It is wrong to discriminate against me for X reason
2. It is not wrong to discriminate against others for X reason

Such claims indicate double standards, not logical contradictions. For such statements to produce a logical contradiction, one statement would have do be the direct negation of the other (i.e. p ∧ ¬p). An example of this was during a series of debates with FriendEd, in which Ask Yourself claims the that FriendEd is contradicting himself by holding the following three statements.

1. It is wrong to kill humans because they are part of my group
2. It is not wrong to kill animals because they are not part of my group
3. It is wrong for someone to murder me because I am not part of their group

His reasoning is that by rejecting (3) you reject the justification group membership justifies killing/murder, in all cases, and as such you cannot deploy it in (1). This is incorrect, by rejecting (3), you only reject the statement

• It is wrong for someone to murder me because I am not part of their group

which does not logically entail rejecting the statement

• group membership justifies killing/murder

in all cases. Someone can reject the justification in one context (e.g. when applied to themselves) and deploy it in another context (e.g. when applied to animals), without contradicting themselves.

(1) & (2) would only create a contradiction if combined with either of the following two statements

• It is not wrong to kill humans because they are part of my group
• It is wrong to kill animals because they are not part of my group

In the notation of FOL the generalization being made takes the form

∀x ( Hx ⇒ ¬ Kx ) ⊢ ∀x ( ¬Kx )

where:
H(x) means x is human
K(x) means ok to kill x based on X justification
⊢ means logically entails

That is to say, for all x, if x is human then it is not okay to kill x based on some justification, entails for all x it is not okay to kill x based on the same justification. Which is incorrect, the statement cannot be generalized because it has been constrained to only apply to humans.

Problems with Part 2 of NTT

Commitment to Non-exploitation

Part 2 of the NTT argument requires a deontological commitment to non-exploitation as P2 states:

P2 - There is no trait absent in animals which if absent in humans would cause us to consider anything short of non-exploitation to be an adequate expression of respect for human moral value.

That is to say, to agree with P2 is to agree that exploitation of humans is always wrong. This is not an issue with the validity of the argument, but an issue with the soundness, as most people will be unwilling to agree with the premise, including Ask Yourself and Vegan Gains.

These issues have actually been problematic for Vegan Gains in debates (who has claimed to agree with NTT), when posed with questions such as

"Was exploitation involved in the production of your phone, if yes, why do you not boycott such products?",

his answer usually takes the form;

yes exploitation was involved, but I need them for my activism, income and youtube videos, and is not immoral for me to do so.

All of these are good reasons, however it shows that he does not consider the absolute of nothing short of non-exploitation to be an adequate expression for human moral value, as pragmatic considerations take precedence. And if pragmatic considerations take precedence, then it's an empirical cost-benefit analysis, and not an absolutist argument like this that is useful.

An example of this was during the Warski debate, in which, on the subject of technology Vegan Gains stated

"you can justify some amount of exploitation in that sort of area of your life"

Ask Yourself was Vegan Gains's partner in this debate and it's fair to say that he agreed. A similar issue arises when posed with questions such as "Do you avoid all things produced using animal products, or products that may contain trace animal products e.g. glues etc.?". Again the answer is no, and it that it is not immoral for me to do so. Which, similarly, means that he does not consider the absolute of 'non-exploitation' to be an adequate expression for animal moral value.

It's worth noting the definition of veganism used by most vegans, including Vegan Gains, is

'A philosophy and way of living which seeks to exclude—as far as is possible and practicable—all forms of exploitation of, and cruelty to, animals for food, clothing or any other purpose; and by extension, promotes the development and use of animal-free alternatives for the benefit of humans, animals and the environment. In dietary terms it denotes the practice of dispensing with all products derived wholly or partly from animals.'

which is not absolutist in nature.

Fans of Ask Yourself may think you can resolve such issues using the golden-rule, by answering yes to the question "would you accept the exploitation if you were the victim in these cases?". However this would not be relevant, as the argument as framed requires the absolute of non-exploitation.

Correction

It is possible to correct the NTT argument and preserve persuasive force by adding a premise that rejects double standards and 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.

In English

(P1) There exists a trait, such that, if an individual is a human then the individual has R if and only if they possess the trait

(only humans who possess a certain trait have R)

(P2) If humans have R if and only if they possess a certain trait, then all beings have R if an only if they possess the certain trait.

(rejection of double standards)

(P3) If an individual is a sentient nonhuman animal, then there is no trait absent in the individual, which if absent in a human, would cause the human to not have R.

or equivalently (without the negatives)

(P3) If an individual is a sentient nonhuman animal, then the trait that gives R to humans is present in the individual.

(sentient nonhuman animals possess this certain trait)

Therefore (C) Sentient nonhuman animals have R

(we are morally required to go vegan)

Where x has R means; we are moral required to not consume the products of x for food, in order to prevent harm to x.

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 (without the negatives)

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

Therefore (C) ∀x ( SNAx ⇒ Rx )

Proof of Validity

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.

Conclusion

As we have shown, there are numerous issues with the NTT argument, which can make it unconvincing and can cause it to reflect poorly on veganism as a whole, particularly when it is combined with false claims such as "veganism follows logically from human rights". Its merits can be summed up in the following question, one which activists who like NTT use;

Can you point to a difference between animals and humans that would justify treating humans same way if we were in their hooves?

Which is in essence, the golden rule. And if framing a question in this way makes people who otherwise wouldn't consider applying the golden rule to non-human animals do so, then that is all for the better. However when posed formally it should be posed in a way that is valid and convincing, like the correction.

Demonstrating the issues of arguments such as NTT helps to ensure vegans are using good arguments that will stand the test of time and reduce recidivism, as well as buys good will from carnists who may be encouraged to reconsider their beliefs that vegans are dishonest and take into consideration the good arguments for veganism and may move them to reducetarian practices.