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| − | As discussed in the main entry on [[NameTheTrait|#NameTheTrait]], the formal, premise-conclusion presentation of #NameTheTrait in English is as follows:
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| − | Argument for animal moral value:
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| − | P1 - Humans are of moral value
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| − | P2 - There is no trait absent in animals which if absent in humans would cause us to deem ourselves valueless.
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| − | C - Therefore without establishing the absence of such a trait in animals, we contradict ourselves by deeming animals valueless
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| − | Argument for veganism from animal moral value:
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| − | P1 - Animals are of moral value.
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| − | 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.
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| − | 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.
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| − | In the [[NameTheTrait#Summary_of_Issues:_Steel-Manning_and_Interpreting_NTT|summary of issues]] section of the [[NameTheTrait|main entry]], we presented the following steel-manned version of the argument in order to discuss its logical form:
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| − | :(P1) All sentient humans (or even just you) have moral value<br>
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| − | :(P2) There is no trait absent in sentient non-human animals which is such that, if the trait were absent in sentient humans (or you), then they would be not have moral value.<br>
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| − | :Therefore, (C) All sentient non-human animals have moral value<br>
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| − | In the [[NameTheTrait#Displaying_the_Logical_Form_of_Part_1_of_NTT_in_FOL|Displaying the Logical Form]] section of the [[NameTheTrait|main entry]], we presented the following version of the argument in FOL (here in English with the specific meanings of the predicates and relations):
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| − | (P1) for all x, if x is a sentient human, then x has moral value<br>
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| − | (P2) It is not the case that there exists a thing, t, such that t is a trait; and for all x, if x is a sentient non-human animal, then x does not have t; and for all y, if y is a counterpart of a sentient human, and y does not have t, then it is not the case that y has moral value<br>
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| − | Therefore, (C) For all x, if x is a sentient non-human animal, then x has moral value<br>
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| − | This entry discusses the considerations that go into this steel-manned version presented in the [[NameTheTrait|main entry]].
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| − | ===We / Ourselves===
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| − | The above formalization deals with two issues regarding the use of "us/ourselves" (See [[#Existential_Meaning|existential meaning]]).
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| − | #If we consider the product of the human without the trait to be a human, then P2 is rendered vacuously true (see proof below). This is due to the fact that P1 implies a human can never be valueless, so that in P2 there can never be a trait that if absent in humans would cause humans to be valueless.
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| − | #Thus to steel-man P2, we '''must''' consider the being that remains after removing the trait to '''no longer be human'''. When Isaac uses hypothetical situations (such as what if your brain is transferred to a computer, would it be ok to kill you? etc. ), we are no longer talking about a human anymore. So we can just admit that "us" is the product of whatever is left after removing the trait.
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| − | It's worth noting that there is nothing in the argument that forbids applying completely different moral standards to the set of humans than to the set of (nonhuman) animals. And this is the essence of why NTT fails as a formal argument, and requires additional moral universalist premises in order to be logically valid.
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| − | Note : It is up to Isaac or any other supporter of the argument to demonstrate that C follows from the premises or that the negation of C leads to a contradiction. Additionally it is also preferable to have the deduction system clearly specified. Until this has been demonstrated, the argument should not be taken as valid.
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| − | === P2 is vacuously true if "us/ourselves" represents humans ===
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| − | In the above translation we are steel-manning P2 of the original argument by not requiring 'us/ourselves' to be human. Since P2 becomes vacuously true if the 'us/ourselves' represents humans (see below).
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| − | P2 would have the following form if "us" represents humans :
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| − | P2:⇔ ¬ ( ∃t: ( ∀x: A(x) ⇒ t ∉ T(x) ) ∧ ( ∀y: H(y) ⇒ ( t ∈ T(y) ∧ ( ∀q: ( T(q) = T(y) \ { t } ) ∧ H(q) ⇒ ¬ M(q) ) )
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| − | Note the addition of "∧H(q)" in the last part of the sentence. The sentence has the form ¬(A ∧ (B ⇒ C ∧ (D⇒ E))) with :
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| − | * A :⇔ ∃t: ( ∀x: A(x) ⇒ t ∉ T(x) )
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| − | * B :⇔ ∀y: H(y)
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| − | * C :⇔ t ∈ T(y)
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| − | * D :⇔ ( T(q) = T(y) \ { t } ) ∧ H(q)
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| − | * E :⇔ ¬ M(q)
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| − | # Now in D we can instantiate q to be a human. D⇒ E take the form "true => false" for a trait of our choosing and using P1. This makes D⇒ E False, which in turn makes C ∧ (D⇒ E) False.
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| − | # We apply the same trick in B ⇒ C ∧ (D⇒ E) by instantiating y to be human, which makes B ⇒ C ∧ (D⇒ E) False.
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| − | # Then by conjunction A ∧ (B ⇒ C ∧ (D⇒ E)) is False.
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| − | # Applying the last negation make the whole sentence True.
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| − | Since the choice of trait and human instance is arbitrary, the statement is vacuously True, meaning it can't be False in any structure that fulfils our mentioned predicates.<br>
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| − | And if P2 is vacuously true, then P2 can be removed with no effect on the argument, which simply leaves<br>
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| − | P1:⇔ ∀x: H(x) ⇒ M(x)<br>
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| − | C:⇔ ∀x: A(x) ⇒ M(x)<br>
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| − | i.e. <br>
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| − | P1: Humans are of moral value <br>
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| − | C: Animals are of moral value <br>
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| − | An obvious non sequitur.
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| − | === P2 is vacuously true if humans are considered to be in the set of animals ===
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| − | If we allow the definition of trait to be so broad that it includes the trait of 'being part of the set of humans', and we allow for this 'trait' to not be absent in animals (i.e. to be present in animals), then P2 becomes vacuously true. This is because it would imply there can be animal which is human i.e. ∃x:(A(x) ∧ H(x)) (there exists an x that is both human and animal). Subsequently there would be no trait that can satisfy both being absent in all animals and present in all humans. i.e. there is no 't' that can satisfy both '∀x: A(x) ⇒ t ∉ T(x)' and '∀y: H(y) ⇒ t ∈ T(y)'<br>
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| − | This leaves us with a negated series of conjunctions of which at least one conjunction will be false. This makes the series of conjunctions false, and the negation true, hence P2 becomes vacuously true. <br>
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| − | This is not an issue introduced by the FOL translation, it is present in the original argument itself by the requirement that the trait can be absent of humans, which of course 'being human' cannot. <br>
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| − | To show this more formally, we can define the trait of 'being part of the set of humans' to be 'h' with, <br>
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| − | ∀x: (H(x) ⇔ h ∈ T(x))
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| − | i.e. for all x if x is human then x possesses the trait of being human, and if x possesses the trait of being human then x is human <br>
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| − | Now the statement 'h is absent in humans' would be <br>
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| − | ∀x: (H(x) ⇒ h ∉ T(x)) <br>
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| − | which of course would be false, by the definition. <br>
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| − | Note we could provide a very similar proof that P2 is vacuously true if 'moral value is allowed to be a trait' since by P1, it is also something a human cannot lack.
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| − | === Separating humans and nonhuman animals ===
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| − | To avoid the above scenario we must change P2 such that we are now talking about humans and nonhuman animals (which is arguably implicit from the way Isaac presents his argument).
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| − | P2:⇔ ¬ ( ∃t: ( ∀x: (A(x) ∧ ¬H(x)) ⇒ t ∉ T(x) ) ∧ ( ∀y: H(y) ⇒ ( t ∈ T(y) ∧ ( ∀q: ( T(q) = T(y) \ { t } ) ⇒ ¬ M(q) ) )
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| − | note the addition of '∧ ¬H(x)'. Now by P1, we know that the only trait that if present in animals (or if not absent in animals), that would give animals moral value, is the trait of 'being human', which is not possible here. This is because for a nonhuman to possess the trait 'human' the statement <br>
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| − | ∃x(¬ H(x) ∧ h ∈ H(x) ) <br>
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| − | Must be true. But it of course is false because ∀x: (h ∈ T(x) ⇔ H(x)) <br>
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| − | Hence there is nothing in P2 to give all animals the trait 'human' nor is there anything to give animals moral value, so the argument is a non sequitur.
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| − | === All Humans ===
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| − | P1 only says humans have moral value (implicitly all humans), not that only some humans do.
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| − | <blockquote>P1 - Humans are of moral value.</blockquote>
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| − | Human may range from vegetative states to a fertilized egg, and for "conservatives" who believe those have intrinsic value there's common disagreement that violent criminals have moral value (still human).<br>
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| − | This in itself seems to contradict the notion of a value giving trait other than the arbitrary "human" status.<br>
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| − | If you want value to be based on another trait, your first premise can't make that impossible.<br>
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| − | Isaac has permitted that other premises be substituted in for P1 (such as "I am of moral value") and maintained that the same conclusions can be reached. This premise is easy enough to correct, although the argument still fails even when limited to personal moral value.
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