DrSinger wrote: ↑Fri Dec 08, 2017 5:18 am
Margaret can you check over this
http://philosophicalvegan.com/wiki/index.php/NameTheTrait#Part_1_Counterexample
I am not sure if I have done the instantiation thing correctly, it is something I saw nightcell do
Unfortunately I don't think that those counterexamples quite work, because they don't have the right sort of existential import (sorry I didn't note this earlier). You can check this with your theorem prover, to see the conditional "IF (i), (ii), and (iii), THEN P1, P2, and Not C" is valid, and it appears it isn't:
Conjunction of P1 and P2 and not C:
(\forallx ( Hx \to Mx ) \land \forallx ( Ax \to \neg \existst ( Tt \land \neg Pxt \land ( \forally (Cy \to ( \neg Pyt \to \neg My ) ) ) ) )\land\neg(Ax \to Mx))
Conjunction of (i), (ii), and (iii):
(\forallx ( Hx \to Mx ) \land \forallt\forallx( Ax \land Tt \land ( Pxt \lor \negPxt) \to \negMx )\land\forallt\forallx( Cx \land Tt \land ( Pxt \lor \negPxt) \to Mx ))
IF the latter then the former:
(\forallx ( Hx \to Mx ) \land \forallt\forallx( Ax \land Tt \land ( Pxt \lor \negPxt) \to \negMx )\land\forallt\forallx( Cx \land Tt \land ( Pxt \lor \negPxt) \to Mx ))\to(\forallx ( Hx \to Mx ) \land \forallx ( Ax \to \neg \existst ( Tt \land \neg Pxt \land ( \forally (Cy \to ( \neg Pyt \to \neg My ) ) ) ) )\land\neg(Ax \to Mx))
As you can see, the countermodel had a completely empty domain.
I think that a really simple (but not completely irrelevant) countermodel to NTT part 1 would be one where:
There is exactly one sentient human; the set of sentient humans humans = {h}
There is exactly one sentient non-human animal; the set of sentient non-human animals = {a}
There is exactly one counterpart of a sentient human; the set of counterparts of sentient humans = {c}
There is exactly one (relevant) trait; the set of traits = {t}
The human and the counterpart have moral value and the non-human animal doesn't (nor does the trait!); the set of things with moral value = {h, c}
The human has the trait and the counterpart and the non-human (and the trait!) don't; the set of things that have t = {h}
You could if you like play around with generalizations of this, and check to see if the conditional (IF conjunction of features of counterexample, THEN P1, P2, & negation of C) is valid.
In order to actually specify a reasonably realistic counterexample like the above (which has existential import but doesn't require that the sets of the relevant things are ridiculously small), I think that you may have to say something like this (remember it's OK that counterparts aren't humans, even on the non-alternative interpretation, because humans are humans as they actually are and counterparts are humans as they could be under counterfactual circumstances):
(i) ∃x(Hx) ∧ ∀x(Hx⇒(¬Ax∧¬Tx∧¬Cx∧Mx))
(ii) ∃x(Ax) ∧ ∀x(Ax⇒(¬Hx∧¬Tx∧¬Cx∧¬Mx∧(∃y(Cy∧∀t(¬Pxt⇒¬Pyt))))
(iii) ∀x(Cx⇒(¬Ax∧¬Tx∧¬Hx∧Mx)
(iv) Tx⇒(¬Ax∧¬Hx∧¬Cx∧¬Mx)