OK, maybe you don't realize that its unpleasant when someone implies that your posts rely on uncharitable interpretations and that it comes across condescending when you then post a link to the principle of charity. — shmik

I've been posting links to the principle of charity (as well as certain fallacies) the first time I mention it on a thread for ten years. It's a habit at this point, and this is the first complaint I've ever received about it. But if all this has been about me hurting your feelings, then I apologize. I never meant to do so.

To which you didn't reply. — shmik

Not directly. I chose to write up the entire argument in propositional calculus instead as that seemed the most direct way to prove my point that the argument is valid. My indirect reply can be seen in how I represented P6 in that rendition: A <=> H (where A = "some gratuitous suffering is preventable" and H = "it is possible to adopt a vegan diet"). The preventable gratuitous suffering referenced in my abbreviation is that caused by food production practices, so this gives us "gratuitous suffering caused by food production practices is preventable if and only if it is possible to adopt a vegan diet."

But again, "some" follows from "all." If all x ought to P, then x1 ought to P. — Postmodern Beatnik

I'm not sure. Consider:

X ought be saved iff X can be saved.
X can be saved iff all Ys donate.
Therefore all Ys ought to donate.

But if one Y doesn't donate then no other Y ought to donate because their donations cannot save X. So each Ys obligation to donate is dependent on every other Y donating.

X ought be saved iff X can be saved.
X can be saved iff all Ys donate.
Therefore, all Ys ought to donate.
Therefore some Ys ought to donate. — Michael

This is the claim. It follows that if all Ys have an obligation, then some Ys have an obligation. It doesn't do to argue that the argument is invalid (it's not) or unsound (it may not be) because some Ys do not fulfill the obligation, it just means that some are immoral and need to do better to fulfill an obligation that all Ys logically have.

No, because if one person doesn't donate then the others donating won't save X, and donating was only obligatory on the premise that it would save X.

Consider:

Donating is obligatory iff it will save X.
If one person doesn't donate then X cannot be saved.
Therefore if one person doesn't donate then the others are not obligated to donate.

Donating is obligatory iff it will save X.
If one person doesn't donate then X cannot be saved.
Therefore if one person doesn't donate then the others are not obligated to donate. — Michael

That argument isn't even close to being valid.

Where in the argument is the conclusion contained?

Of course it's valid. Perhaps this variation will make it clearer:

I am obligated to donate if my donation will help towards saving X.
If you don't also donate then my donation will not help towards saving X.
Therefore if you don't also donate then I am not obligated to donate.

Or let's imagine that two pilots are obligated to fly a plane. If one refuses (or becomes unable) is the other obligated to fly the plane alone, despite the fact that two are required and he'd crash without aid? No. The refusal (or inability) of the first pilot relieves the second of his obligation.

It's not a variation, it's an entirely new argument. But this argument is invalid because it denies the antecedent (note: this is likely a pedantic comment and possibly just an typographical oversight):

If my donation will help towards saving X, then I am obligated to donate (rearranged first premise to be in logical form)
If you don't donate, then my donation will not help towards saving X.
You don't donate
My donation will not help towards saving X
Therefore, I am not obligated to donate.

But this argument is invalid because it denies the antecedent (note: this is likely a pedantic comment and possibly just an typographical oversight): — Soylent

Yes, I meant iff rather than if.

your pilot example misses the point. It changes the obligation in the shift from all to some.

The obligation is this:

If two pilots are present, then all pilots would be obligated to fly.

It follows that from that obligation that;

If two pilots are present, then some pilots would be obligated to fly.

You can't deny the antecedent to deny the consequent, because the obligation in both cases only holds as long the as the antecedent is affirmed (i.e., two pilots are present). If some pilots are not obligated to fly, it must be that the antecedent condition has not been satisfied, but that also holds for all pilots since that was the obligation that allowed us to say some are obligated. Some necessarily follows from all.

Michael your pilot example misses the point. It changes the obligation in the shift from all to some.

The obligation is this:

If two pilots are present, then all pilots would be obligated to fly.

It follows that from that obligation that;

If two pilots are present, then some pilots would be obligated to fly. — Soylent

That doesn't work. In the example two pilots are present; it's just that one refuses to fly. Is the other obligated to fly alone (despite it being a futile suicide)? No. So what's the alternative phrasing? "If two pilots agree to fly then all pilots would be obligated to fly"? But then, of course, their obligation to fly is dependent on them agreeing to fly which doesn't quite seem right, does it?

I'm not sure. — Michael

Well, your uncertainty notwithstanding, it's still a basic fact of logic.

Consider:

X ought be saved iff X can be saved.
X can be saved iff all Ys donate.
Therefore all Ys ought to donate. — Michael

This argument is invalid.

But if one Y doesn't donate then no other Y ought to donate because their donations cannot save X. So each Y's obligation to donate is dependent on every other Y donating. — Michael

I have already dealt with cases like this above. They are not counterexamples to the rule because they are not cases where it is simultaneously the case that all X ought to P and not the case that some X ought to P. Instead, they are cases where x₁ ought to P iff x₂–x_n actually P. At best, the obligation of x₁ in such cases is to show up prepared to donate (and to donate iff x₂–x_n show up).

(I have also suggested that the argument in the OP is best understood as not involving such contingent responsibilities.)

Consider:

X ought be saved iff X can be saved.
X can be saved iff all Ys donate.
Therefore all Ys ought to donate.
— Michael

This argument is invalid. — Postmodern Beatnik

Yes, you're right. This is what I meant:

All Ys ought to save X.
X can be saved iff all Ys donate.
Therefore all Ys ought to donate.

They are not counterexamples to the rule because they are not cases where it is simultaneously the case that all X ought to P and not the case that some X ought to P. Instead, they are cases where x1 ought to P iff x2–xn actually P. At best, the obligation of x1 in such cases is to show up prepared to donate (and to donate iff x2–xn show up).

If all of these 11 players make a full football team then do some of these 11 players make a full football team? No, because a full football team requires 11 players.

So I think a distinction needs to be made between "the set of people S is X" and "each member of the set of people S are X". The former assigns X to the set as a whole and not to a subset, whereas the latter assigns X to each member of the set and so also to a subset.

With respect to the OP, is C5 to be understood as "the set of people who can adopt a vegan diet ought adopt a vegan diet" or as "each member of the set of people who can adopt a vegan diet ought adopt a vegan diet"?

(I have also suggested that the argument in the OP is best understood as not involving such contingent responsibilities.)

But if the prevention of gratuitous suffering depends on contingent responsibilities (i.e. that a sufficient number of people adopt a vegan diet) then the obligation to adopt a vegan diet depends on contingent responsibilities. If one person can't make a difference then you can't conclude that so-and-so ought to adopt a vegan diet even though nobody else will. I think that was @shmik's point.

A solution to this would be to argue that one ought do that which if done by enough people would prevent gratuitous suffering.

All Ys ought to save X.
X can be saved iff all Ys donate.
Therefore all Ys ought to donate. — Michael

Okay, but what's the problem here? If the premises are true, then the conclusion is true. But if you think the conclusion is false, then you ought to reject one of the premises. That's why it's quixotic to go up against the rule: if it's not the case that some S are P, it's not the case that all S are P.

If all of these 11 players make a full football team then do some of these 11 players make a full football team? — Michael

It depends on whether you mean "all" in the logical sense or not. If you really mean that each player makes a football team (which is what it means in the language of logic to say that all of these 11 players make a full football team), then it would follow that some of these 11 players make a full football team. We would have a valid—but unsound—argument. But what you actually mean is "the combination of these 11 players makes a full football team," which does not involve the logical "all" and therefore does not entail the logical "some." Surely you know this, so surely you realize that this attempt at a counterexample is fatuous.

So I think a distinction needs to be made between "the set of people S is X" and "each member of the set of people S are X". — Michael

I've already made this point myself, so I'm not sure how this constitutes a response to anything I've said.

With respect to the OP, is C5 to be understood as "the set of people who can adopt a vegan diet ought adopt a vegan diet" or as "each member of the set of people who can adopt a vegan diet ought adopt a vegan diet"? — Michael

The latter. This is clearer if one bears in mind the revisions I suggested—and Soylent accepted—early on in the thread (which transformed C5 into "a vegan diet ought to be adopted by all who are in a position to do so").

But if the prevention of gratuitous suffering depends on contingent responsibilities (i.e. that a sufficient number of people adopt a vegan diet) then the obligation to adopt a vegan diet depends on contingent responsibilities. — Michael

But my point here, where the topic is validity, has been that the argument does not make the obligation contingent. And my point elsewhere has been that the argument should not make the obligation contingent. In order to succeed, the argument needs to be framed in terms of individual duties. And the most charitable way of reading the argument requires us to understand it as doing exactly that. So the objection is irrelevant. It basically says, "if we change the argument in such-and-such a way, it's invalid!" But of course, any argument can be made invalid if we're allowed to fiddle with the premises however we like.

Hey @Michael yeh pretty much all your posts were along the same lines as what I was arguing.

Maybe things would be hurried along somewhat if we can agree that all the sentences bellow mean the same thing.

I'm not sure. Consider: — Michael

I agree that some follows from all generally. — shmik

It depends on whether you mean "all" in the logical sense or not. — Postmodern Beatnik

@Postmodern Beatnik
We all agree that: All birds can fly -> some birds can fly.
Neither me nor Michael are arguing that this is not the case. The examples we are presenting are not meant to be counter examples to this. They are meant to be analogous to Soylents argument. So when you say that the examples have errors you are just agreeing with the point.

The problem comes when speaking about the elements of the set and the set itself. As in Michaels example:

All Ys ought to save X.
Each element of the set Y ought to save X

X can be saved iff all Ys donate.
X can be saved iff the entire set Y donate

Therefore all Ys ought to donate.
Therefore the entire set Y ought to donate

Therefore some Ys ought to donate. — Michael

As mentioned this is problematic and it's not meant to be a counter example to some following from all. It's meant to be analogous to a version of the argument which from looking at Soylents posts, he upholds, even though you yourself think the version is problematic. The problem of switching between talking about the set X and talking about the elements of the set i.e the set of all natural numbers is infinitely large does not imply that some of the natural numbers are infinitely large.

So I think a distinction needs to be made between "the set of people S is X" and "each member of the set of people S are X". — Michael

I've already made this point myself, so I'm not sure how this constitutes a response to anything I've said. — Postmodern Beatnik

Because this is the motivation behind the discussion against Soylents version of the argument. Again, you are fighting an invisible battle to prove that all -> some while we are speaking about the distinction between the set and the members of the set.

@Postmodern Beatnik
Just for extra clarity, if you look back on the thread after this quote:

But the choice is not between reading P6 as meaning "by everyone" or "just by one person." If the reading is "by anyone who is in a position to," as I suggested, that is going to be a very large number of people. So the fact that you cannot change your local supermarket's buying patterns alone is irrelevant. And if it were true that a vegan diet ought to be adopted by anyone who is in a position to do so, then it wouldn't matter whether or not other people will in fact do so. All that would matter is whether or not any given individual was in a position to adopt a vegan diet.

Read the responses to this as if I had interpreted it to be maintaining a version of the argument. The version that used the incorrect move from speaking about the set as a whole to speaking about the elements.
Then when you said all implies some, I took that as you reaffirming that incorrect version.
Maybe then you'll see why people have responded to you by bringing up this issue, and get a different picture of how the thread progressed.

Okay, but what's the problem here? If the premises are true, then the conclusion is true. But if you think the conclusion is false, then you ought to reject one of the premises. That's why it's quixotic to go up against the rule: if it's not the case that some S are P, it's not the case that all S are P. — Postmodern Beatnik

The issue is that if one Y refuses to donate then this relieves the others of their obligation to donate because their donations alone cannot save X, and their donations were only obligatory on the premise that it would save X.

But what you actually mean is "the combination of these 11 players makes a full football team," which does not involve the logical "all" and therefore does not entail the logical "some." Surely you know this, so surely you realize that this attempt at a counterexample is fatuous.

The point is that P6 needs to be more specific in light of this. Is it saying that gratuitous suffering caused by food production practices is preventable if and only if a vegan diet is adopted by the combination of those who are in a position to adopt one, or is it saying for each person who is in a position to adopt a vegan diet, gratuitous suffering caused by food production practices is preventable if and only if that person adopts one?

The latter. This is clearer if one bears in mind the revisions I suggested—and Soylent accepted—early on in the thread (which transformed C5 into "a vegan diet ought to be adopted by all who are in a position to do so")

...

But my point here, where the topic is validity, has been that the argument does not make the obligation contingent. And my point elsewhere has been that the argument should not make the obligation contingent. In order to succeed, the argument needs to be framed in terms of individual duties. And the most charitable way of reading the argument requires us to understand it as doing exactly that. So the objection is irrelevant. It basically says, "if we change the argument in such-and-such a way, it's invalid!" But of course, any argument can be made invalid if we're allowed to fiddle with the premises however we like.

Then for the obligation to be framed in terms of individual duty it must be the case that an individual can prevent gratuitous suffering by adopting a vegan diet. The argument must be something along the lines of:

If I can prevent gratuitous suffering caused by food production by adopting a vegan diet then I ought to adopt a vegan diet.
I can prevent gratuitous suffering caused by food production by adopting a vegan diet.
Therefore I ought to adopt a vegan diet.

But as you said to @shmik earlier, "So the fact that you cannot change your local supermarket's buying patterns alone is irrelevant." Except it isn't irrelevant. If I can't change my local supermarket's buying patterns alone then the second premise above fails.

The current argument seems to be saying something like "the combination of these people ought to adopt a vegan diet because gratuitous suffering caused by food production is preventable if and only if the combination of these people adopt a vegan diet (and one is obligated to prevent gratuitous suffering), therefore this individual ought to adopt a vegan diet" which is analogous to "the combination of these players makes a full football team ... therefore this individual makes a full football team".

Neither me nor Michael are arguing that this is not the case. — shmik

Then the two of you shouldn't have presented your comments as objections. If I point out that "all" entails "some" and you guys respond with some version of "no, it doesn't," then the logical force of your response is a denial of the claim that "all" entails "some."

The examples we are presenting are not meant to be counter examples to this. They are meant to be analogous to Soylent's argument. — shmik

But as I have pointed out several times, Soylent's argument is not committed to anything like what you and Michael have accused it of, particularly after my suggested revisions were accepted. So if the examples were meant to be analogous to anything in the argument, they have failed at that.

So when you say that the examples have errors you are just agreeing with the point. — shmik

Except the main error I am pointing out is that they aren't analogous to anything in the argument. I can agree that the sun rises in the east while continuing to maintain that this has nothing to do with whether or not Socrates is a man.

It's meant to be analogous to a version of the argument which from looking at Soylents posts, he upholds, even though you yourself think the version is problematic. — shmik

Well, Soylent is free to correct me if I am wrong, but I don't think the proper interpretation of his posts has him committed to "if the set {x, y, z} is S, then x is S, y is S, and z is S." I think he has been saying the same thing as me, albeit in different terms: "if all x's are S, then x₁ is S, x₂ is S, x₃ is S..."

(So how about it, @Soylent? Which do you mean?)

But in any case, I have only been defending the logical validity of the argument with my suggested revisions. No one, even Soylent seems to have ever thought that the original version presented in the OP was free of problems.

Again, you are fighting an invisible battle to prove that all -> some while we are speaking about the distinction between the set and the members of the set. — shmik

For one, I'm not trying to prove it. I have no need to prove it. It has long been proven, and I am just pointing it out that fact to two people who have denied it (whether they meant to or not). For another, I'm pretty sure the "battle" isn't invisible. I can see it, you and Michael must be able to see it in order to respond, and I suspect anyone else reading the thread can see it as well. And finally, if you and Michael have been trying to talk about the distinction between the set and the members of the set, then you have done an incredibly bad job of it. I made the same point at the outset of the discussion, and you've both been directing your objections at me. Moreover, you've been presenting those objections as responses to my statement of the logical fact that "all" entails "some." Only now has either of you come out with what you were supposedly saying all along. It's like putting the blank space on a tape at the beginning instead of at the end.

Read the responses to this as if I had interpreted it to be maintaining a version of the argument. The version that used the incorrect move from speaking about the set as a whole to speaking about the elements.
Then when you said all implies some, I took that as you reaffirming that incorrect version.
Maybe then you'll see why people have responded to you by bringing up this issue, and get a different picture of how the thread progressed. — shmik

I understand how your error came about. I just don't understand why you are so keen to defend it.

The issue is that if one Y refuses to donate then this relieves the others of their obligation to donate because their donations alone cannot save X, and their donations were only obligatory on the premise that it would save X. — Michael

Which means it was never true that all Ys ought to save X. So again, the argument is unsound. And more importantly, it is not analogous to anything that has been argued here.

The point is that P6 needs to be more specific in light of this. — Michael

What both you and shmik seem to have missed is that P6 is one of the premises that was modified right away. You keep going after the version in the OP, missing the point that the version found there was discarded ages ago. The revised P6 says "gratuitous suffering caused by food production practices is preventable if and only if it is possible to adopt a vegan diet." The explicit statement of who is to be adopting a vegan diet then comes up in the revised P9 (and then the revised C5).

But as you said to shmik earlier, "So the fact that you cannot change your local supermarket's buying patterns alone is irrelevant." Except it isn't irrelevant. If I can't change my local supermarket's buying patterns alone then the second premise above fails. — Michael

Context matters, Michael. The point of that comment was that changing your supermarket's buying patterns isn't the only way to reduce or eliminate one's contribution to gratuitous suffering, therefore the fact that you cannot change your local supermarket's buying patterns alone is irrelevant. Nice try, though.

The current argument seems to be saying something like "the combination of these people ought to adopt a vegan diet because gratuitous suffering caused by food production is preventable if and only if the combination of these people adopt a vegan diet (and one is obligated to prevent gratuitous suffering) — Michael

And my point has been that it doesn't say this, no matter how many people want to misread it that way.

Since this seems to be so confusing for some people, here is the revised version of the argument:

P1 If any gratuitous suffering is preventable and known, then it is wrong to allow said gratuitous suffering.
P2 If some nonhuman animals are sentient and food production practices would constitute gratuitous suffering in humans, then food production practices constitute gratuitous suffering in some nonhuman animals.
P3 Some nonhuman animals are sentient.
P4 Food production practices would constitute gratuitous suffering in humans.
C1 Food production practices constitute gratuitous suffering in some nonhuman animals. (from P2, P3 and P4)
P5 If food production practices constitute gratuitous suffering in some nonhuman animals, then we know of some gratuitous suffering.
C2 We know of some gratuitous suffering. (from C1 and P5)
P6 Gratuitous suffering caused by food production practices is preventable if and only if it is possible to adopt a vegan diet.
P7 If it is possible to adopt a vegan diet, then gratuitous suffering caused by food production practices is preventable.
P8 It is possible to adopt a vegan diet.
C3 Gratuitous suffering caused by food production practices is preventable. (from P6, P7 and P8)
C4 It is wrong to allow gratuitous suffering caused by food production practices. (from P1, C2 and C3)
P9 If it is wrong to allow gratuitous suffering caused by food production practices and gratuitous suffering caused by food productions practices is preventable if and only if it is possible to adopt a vegan diet, then a vegan diet ought to be adopted by all who are in a position to do so.
C5 A vegan diet ought to be adopted by all who are in a position to do so. (from P6, C4 and P9)


And here it is (again) schematized in propositional calculus:

Let:
A = some gratuitous suffering is preventable
B = some gratuitous suffering is known
C = it is wrong for someone in a position to prevent gratuitous suffering to allow it
D = some nonhuman animals are sentient
E = food production practices would constitute gratuitous suffering in humans
G = food production practices constitute gratuitous suffering in non-human animals
H = it is possible to adopt a vegan diet
I = a vegan diet ought to be adopted by all who are in a position to adopt it

Argument:
P1. (A & B) --> C
P2. (D & E) --> G
P3. D
P4. E
C1. G
P5. G --> B
C2. B
P6. A <=> H
P7. H --> A
P8. H
C3. A
C4. C
P9. (C & (A <=> H)) --> I
C5. I

Since the topic of this thread is the validity of the argument, I would like to know where the invalid move is made in this schematization.

The revised P6 says "gratuitous suffering caused by food production practices is preventable if and only if it is possible to adopt a vegan diet." — Postmodern Beatnik

Shouldn't that read "gratuitous suffering caused by food production practices is prevented if and only if a vegan diet is adopted"?

Furthermore, this is still unclear, and my point still stands. Is it that gratuitous suffering is prevented if and only if everyone adopts a vegan diet? Then if one person doesn't then the others can't prevent gratuitous suffering by adopting a vegan diet, and so they have no obligation to adopt a vegan diet. Or is it that for each person gratuitous suffering is prevented if and only if that person adopts a vegan diet? Then if we accept that I can't prevent gratuitous suffering by adopting a vegan diet then I have no obligation to adopt a vegan diet.

If you want to frame the obligation in terms of individuals then you have to frame the justification in terms of individuals. So I think the argument needs to be like this:

P1. ∀x: C(P(x)) → O(P(x))
P2. ∀x: P(x) ↔ V(x)
C1. ∀x: C(V(x)) → O(V(x))

Which is to be read as:

For any person, if that person can prevent gratuitous suffering then that person ought prevent gratuitous suffering.
For any person, that person prevents gratuitous suffering if and only if that person adopts a vegan diet.
For any person, if that person can adopt a vegan diet then that person ought adopt a vegan diet.

C5 in the OP's (revised) argument seems to be the same as C1 in the above argument, but is P6 in the OP's (revised) argument the same as P2 in the above?

Which means it was never true that all Ys ought to save X. So again, the argument is unsound. And more importantly, it is not analogous to anything that has been argued here.

It was (and still is) true that all Ys ought to save X. It's just that donating won't save X unless all Ys donate. If my obligation to donate is dependent on it saving X, and if my donation saving X is dependent on others donating, then my obligation to donate is dependent on others donating.

And so by analogy, it was (and still is) true that all people ought to prevent gratuitous suffering. It's just that adopting a vegan diet won't prevent gratuitous suffering unless all (or enough) people adopt a vegan diet. If my obligation to adopt a vegan diet is dependent on it preventing gratuitous suffering, and if my adoption of a vegan diet preventing gratuitous suffering is dependent on others adopting a vegan diet, then my obligation to adopt a vegan diet is dependent on others adopting a vegan diet.

Before I say another word, have you actually taken the time to read the thread and notice the various clarifications that have been given along the way? Because so far, it seems like you have not. Furthermore, do you have any response to this post? Because if not, then it seems like you don't a leg to stand on as far of the topic of this thread—the logical validity of the argument—is concerned.

Because if not, then it seems like you don't a leg to stand on as far of the topic of this thread—the logical validity of the argument—is concerned. — Postmodern Beaknik

But I wasn't addressing the logical validity of the argument. I was addressing your exchange with @shmik on the ambiguity of the argument, specifically regarding whether or not something which is true of all X is also true of some X, and how such a thing might entail that one's obligation is dependent on what others do (as explained in the last two paragraphs of my last post).

My concern is with P8, which strikes me as an out of place assumption but I can't quite articulate the problem. Does anyone have any insight and/or solutions? Does that premise render the argument circular or is it ok to have an assumption like that in the argument for the purposes of validity? I'm not invested in the argument, I drew it up quickly just as an interesting exercise.

P1 If any gratuitous suffering is preventable and known , it is wrong to allow said gratuitous suffering.
P2 If some nonhuman animals are sentient and food production practices would constitute gratuitous suffering in humans, then food production practices constitute gratuitous suffering in some nonhuman animals.*
P3 Some nonhuman animals are sentient.
P4 Food production practices would constitute gratuitous suffering in humans.
C1 Food production practices constitute gratuitous suffering in some nonhuman animals. (from P2, P3 and P4)
P5 If food production practices constitute gratuitous suffering in some nonhuman animals, we know of some gratuitous suffering.
C2 We know of some gratuitous suffering. (from C1 and P5)
P6 Gratuitous suffering caused by food production practices is preventable if and only if a vegan diet is adopted.*
P7 If a vegan diet is adopted, gratuitous suffering caused by food production practices is preventable.
P8 A vegan diet is adopted.* — Soylent

I'm somewhat puzzled why you think this is a problem, since you have set aside any discussion about the validity of the premises.
It seems to me perfectly easy to me to construct false or contestable premises to draw ridiculous or dubious conclusions.
eg.
1 Jews are evil
2 Evil must be destroyed
3 Therefore Jews must be destroyed.

You could even shorten your argument to remove reference to humans, by simply claiming that animals can suffer and that suffering is to be avoided at all costs.

You could also attack the entire argument on what it ignores; the gratuitous suffering caused to humans by the fact that a universal vegan diet would deprive the world of domesticated animals, and the loss of the pleasure of thousands of gourmet recipes that involve meat, and admit to no substitute.