Same issue with P14.

It is wrong to allow gratuitous suffering caused by food production practices
Gratuitous suffering caused by food production practices is preventable if and only if it is possible to adopt a vegan diet
Therefore a vegan diet ought to be adopted by all those who are in a position to adopt a vegan diet

It doesn't work as a syllogism so the material implication must be defended some other way.

If you want it to work as a syllogism then you need the following:

One ought make gratuitous suffering preventable iff one can make gratuitous suffering preventable
One makes gratuitous suffering preventable iff one adopts a vegan diet
Therefore one ought adopt a vegan diet iff one can adopt a vegan diet

Why didn't you include that explicitly in the argument in the first place? If your objective here is not to put an argument in what you know to be it's best formulation to scrutiny, but just some sort of test of our critical thinking skills, then I don't agree with your purpose here, and wish to take no further part. I don't feel like playing a game of 'spot the shortcomings in my knowingly inadequate argument'. — Sapientia

I submitted a stripped down version of a similar argument I prepared elsewhere for advice on a formal/logical issue, and so my intention was limited only to a formal analysis. In my estimation the full version was unnecessary for the purposes of the formal issue for which I wished to receive input. In that discussion issues of soundness arose, which prompted me to create this spin-off thread to address those issues. So as to encourage and not invalidate concerns already mentioned in the previous discussion I left the argument the same as the stripped down version presented in the logic section. You give me far too much credit, I don't presume to know much. Any shortcomings I had previously identified may have been given novel attention, including objections and solutions, by the very capable individuals on this forum.

It is wrong to allow gratuitous suffering caused by food production practices
Gratuitous suffering caused by food production practices is preventable if and only if it is possible to adopt a vegan diet
Therefore a vegan diet ought to be adopted by all those who are in a position to adopt a vegan diet — Michael

I added another term to the implication for the purpose of addressing this issue. I currently stands as:

i) It is wrong to allow gratuitous suffering caused by food production practices
ii) Gratuitous suffering caused by food production practices is preventable if and only if it is possible to adopt a vegan diet
iii) There are those who are in a position to adopt a vegan diet.

Therefore, a vegan diet ought to be adopted by those who are in a position to adopt a vegan diet.

Where, "there are those who are in a position to adopt a vegan diet" are specifically those agents that satisfy the conditions of the moral obligation contained in P1 (see P12 - C7)

The new P14 satisfies the conditions of the objection you raise in terms of the valid syllogism and material implication, which was missing in previous versions.

Well, soundness is what I addressed, but presenting a simplified version has predicably backfired, because one of my objections has already been resolved by details that were in the full version, but not in the simplified version that you presented here. And now you've brought at least three versions of the argument to my attention: the simplified version, the full version, and the revised version. Pick whichever version you think is strongest, disregard the others, and maybe I'll start again. Is this revised version the best current formulation that you've come up with or not? I don't want to waste my time going over old ground.

I added another term to the implication for the purpose of addressing this issue. I currently stands as:

i) It is wrong to allow gratuitous suffering caused by food production practices
ii) Gratuitous suffering caused by food production practices is preventable if and only if it is possible to adopt a vegan diet
iii) There are those who are in a position to adopt a vegan diet.

Therefore, a vegan diet ought to be adopted by those who are in a position to adopt a vegan diet. — Soylent

That still doesn't follow:

It is wrong to allow X
X is preventable iff Y is possible
Some can Y
Therefore those who can Y ought Y

Either the conclusion must be "those who can make Y possible ought make Y possible" or the second premise must be "X is preventable iff Y".

As I said before, if you want the first premise to be "one ought make gratuitous suffering preventable iff one can make gratuitous suffering preventable" and if you want as the conclusion "one ought adopt a vegan diet iff one can adopt a vegan diet" then you must have as the second premise "one makes gratuitous suffering preventable iff one adopts a vegan diet".

I've edited the OP to request that all comments are to respond to the revised (most current) version. That is the one I will be responding to and will not mention premises contained in any other versions unless they are contained in the revised version as well. As far as I can tell, the revised version is the strongest form of the argument I have ever conceived and there is no longer any conditions or information omitted.

It is wrong to allow X is logically equivalent to ought not X.
not X = Y
And some can Y (Z)

Therefore, ought Z

Yeah, maybe there's something still missing.

As I said before, if you want the first premise to be "one ought make gratuitous suffering preventable iff one can make gratuitous suffering preventable" and if you want as the conclusion "one ought adopt a vegan diet iff one can adopt a vegan diet" then you must have as the second premise "one makes gratuitous suffering preventable iff one adopts a vegan diet". — Michael

I don't know why I'm resisting this so much. Let me think on it a bit.

It is wrong to allow X is logically equivalent to ought not X. — Soylent

So "it is wrong to allow gratuitous suffering" is logically equivalent to "one ought not gratuitous suffering". Obviously that makes no sense. Previously I interpreted this as "one ought prevent gratuitous suffering" but you didn't like this one. Is "one ought make gratuitous suffering preventable" not the correct interpretation? If not then could you rephrase that first premise in a "one ought X" form (so that the conclusion "one ought Y" is properly derived).

not X = Y
And some can Y (Z)

Therefore, ought Z

But Y in "not X = Y" is "adopting a vegan diet is possible". So "some can Y" is "it is possible for some to adopt a vegan diet".

And if "Z" is "it is possible for some to adopt a vegan diet" then "one ought Z" is "one ought make it possible for some to adopt a vegan diet". Which is the conclusion I said follows and which differs from "one ought adopt a vegan diet".

So "it is wrong to allow gratuitous suffering" is logically equivalent to "one ought not gratuitous suffering". Obviously that makes no sense. Previously I interpreted this as "one ought prevent gratuitous suffering" but you didn't like this one. Is "one ought make gratuitous suffering preventable" not the correct interpretation? — Michael

The latter interpretation is preferable.

I was imprecise in my notation. The correct form is: It is wrong to X is logically equivalent to ought not X, and X is "allow gratuitous suffering" where "allow gratuitous suffering" means "to act in such a way so as to not make gratuitous suffering preventable".

Further versions of the argument may have to include some form of that, which might be best stated as your "one ought make gratuitous suffering preventable" as per your suggestion.

But Y in "not X = Y" is "adopting a vegan diet is possible". So "some can Y" is "it is possible for some to adopt a vegan diet".

And if "Z" is "it is possible for some to adopt a vegan diet" then "one ought Z" is "one ought make it possible for some to adopt a vegan diet". Which is the conclusion I said follows and which differs from "one ought adopt a vegan diet". — Michael

Let:
a = allow gratuitous suffering
b = it is possible for some agents to adopt a vegan diet
c = there are those who are in a position to adopt a vegan diet and those that are in a position to adopt of a vegan diet are those for whom it would be wrong to allow gratuitous suffering caused by food production practices
d = those who are in a position to adopt a vegan diet ought not allow gratuitous suffering caused by food production practices

If ¬Pa (= O¬a)
and ¬a = b
and c
then, d

Therefore, d.

Another step is still needed to get back to "ought adopt a vegan diet".

If ¬Pa (= O¬a)
and ¬a = b
and c
then, d — Soylent

You can't derive d if d isn't in the premises. Consider:

P1. A → B
P2. A
C1. C

Notice that it doesn't work.

Another step is still needed to get back to "ought adopt a vegan diet".

Yeah. And as I said above, you can only derive "adopt a vegan diet" if it appears somewhere in the premises. Specifically, you need "if one doesn't adopt a vegan diet then one allows gratuitous suffering". Then if one has an obligation to not allow gratuitous suffering then one has an obligation to adopt a vegan diet.

You can't derive d if d isn't in the premises. Consider:

P1. A → B
P2. A
C1. C — Michael

That's not the form though, it's:

P1 (A & B & C) → D
P2 A
P3 B
P4 C
C1 D

P14 If it is wrong to allow gratuitous suffering caused by food production practices and gratuitous suffering caused by food production practices is preventable if and only if it is possible for some agents to adopt a vegan diet, and there are those agents who are in a position to adopt a vegan diet, then a vegan diet ought to be adopted by all those who are in a position to adopt a vegan diet.
C6 It is wrong to allow gratuitous suffering caused by food production practices. (from P1, C2, C3, and C4)
P6 Gratuitous suffering caused by food production practices is preventable if and only if it is possible for some agents to adopt a vegan diet.
C7 There are those agents who are in a position to adopt a vegan diet. (from P12 and P13)

C8 A vegan diet ought to be adopted by all those who are in a position to adopt a vegan diet (from P6, C6, C7 and P14).

That's not the form though, it's:

P1 (A & B & C) → D
P2 A
P3 B
P4 C
C1 D — Soylent

And I'm questioning P1. What justifies the material implication? D certainly can't be derived from A, B, and C. So it must be something else.

I'm not sure I understand your objection. D is derived (entailed?) from A, B, and C as per modus ponens.

I'm not sure I understand your objection. D is derived (entailed?) from A, B, and C as per modus ponens. — Soylent

P1 isn't an example of modus ponens.

Using your example above, let A be "2 > 1", let B be "3 > 2", let C be "4 > 3", and let D be "5 > 6".

P1 (A ∧ B ∧ C) → D
P2 A
P3 B
P4 C
C1 D

So:

P1. If 2 > 1 and 3 > 2 and 4 > 3 then 5 > 6
P2. 2 > 1
P3. 3 > 2
P3. 4 > 3
C1. 5 > 6

Have I shown that 5 > 6?

Nooo......The entire argument is modus ponens. A premise need not be a self-contained argument. P1 is a hypothetical premise wherein the affirmation of D is supported by the affirmative conjuction of A, B and C (which were independently affirmed throughout the larger argument).

P1 is a hypothetical premise wherein the affirmation of D is supported by the affirmative conjuction of A, B and C (which were independently affirmed throughout the larger argument). — Soylent

And I'm questioning this hypothetical premise. I want you to justify this hypothetical premise. You can't use your argument to justify the premise if your argument depends on the premise. That's question-begging.

So forget the argument. Show me that P1 (or P14) is true.

For clarification, you're questioning the soundness and not validity; because it seemed to me that you were questioning the validity by questioning the form as you did here:

That's not the form though, it's:

P1 (A & B & C) → D
P2 A
P3 B
P4 C
C1 D — Soylent

And I'm questioning P1. What justifies the material implication? D certainly can't be derived from A, B, and C. So it must be something else. — Michael

And other comments regarding "valid syllogism".

For clarification, you're question the soundness and not validity — Soylent

I'm questioning the truth of P14, and so by extension the soundness of the argument. When I first asked you to defend P14 (when it was P9) you said that the material implication is defended as a deduction, but of course it isn't.

So you're still yet to show that P14 is true.

Using your example above, let A be "2 > 1", let B be "3 > 2", let C be "4 > 3", and let D be "5 > 6".

P1 (A ∧ B ∧ C) → D
P2 A
P3 B
P4 C
C1 D

So:

P1. If 2 > 1 and 3 > 2 and 4 > 3 then 5 > 6
P2. 2 > 1
P3. 3 > 2
P3. 4 > 3
C1. 5 > 6

Have I shown that 5 > 6? — Michael

Yes you have, by modus ponens.

If it's raining then circles are square
It's raining
Therefore, circles are square

Is a valid argument by modus ponens.

P1 may be false and so the argument is unsound, but nevertheless valid.
If you want me to justify the soundness of the premise then that's fine, but acting as if the argument is invalid is silly.

If you want me to justify the soundness of the premise then that's fine, but acting as if the argument is invalid is silly. — Soylent

I'm not acting as if the argument is invalid. I asked you to defend P14 (when it was P9). You said that the consequent is deduced from the antecedent. So I pointed out that if we take P14 as an argument then it fails.

So, again, I'd like you to defend the material implication in P14.

if we take P14 as an argument then it fails. — Michael

P14 is NOT an argument, it is a premise.

P14 is NOT and argument, it is a premise. — Soylent

And how do you defend that premise? How do you defend "(A ∧ B ∧ C) → D"? How do you defend "If it is wrong to allow gratuitous suffering caused by food production practices and gratuitous suffering caused by food production practices is preventable if and only if it is possible to adopt a vegan diet, and there are those who are in a position to adopt a vegan diet, then a vegan diet ought to be adopted by all those who are in a position to adopt a vegan diet."?

The point I have been making is that you cannot defend that premise by saying that D is deducible from A ∧ B ∧ C.

Side note: Looking back I see I've got my numbers wrong. It's P15. Is that a recent edit?

The same way one might defend other implications: analysis of terms, empirical observation, supportive arguments, faith or wishful thinking.

The same way one might defend other implications: analysis of terms, empirical observation, supportive arguments, faith or wishful thinking. — Soylent

You're being very difficult here.

Please defend premise 15.

Let:
a = allow gratuitous suffering caused by food production practices
b = it is possible for some agents to adopt a vegan diet
c = there are those who are in a position to adopt a vegan diet and those that are in a position to adopt a vegan diet are those for whom it would be wrong to allow gratuitous suffering caused by food production practices
d = those who are in a position to adopt a vegan diet ought not allow gratuitous suffering caused by food production practices the means to which is only by adopting a vegan diet

If ¬Pa (= O¬a)
and ¬a = b
and c
then, d

Therefore, d.

¬Pa is true by definition
b is true by empirical evidence
c is also true by empirical evidence
d follows from the transitive property applied to O¬a wherein ¬a = b and some b is c.

If ¬Pa (= O¬a)
and ¬a = b
and c
then, d — Soylent

You're just repeating the premise. I want you to defend the premise.

d follows from the transitive property applied to O¬a wherein ¬a = b and some b is c.

Notice how you're trying to defend the premise by treating it as a syllogism, saying that the consequent follows from the antecedent? As I've pointed out before, it's an invalid syllogism. D can't be deduced from A, B, and C.

I have no idea what you're looking for so until one of us figures out what the other is trying to say, we might be at an impasse.

Well, if I offered the following premise then what defence would you look for from me?

If London is the capital city of England then it is raining