I'm afraid that this isn't sufficiently restrictive or explanatory. If by 'possible' you mean metaphysically possible, then, no, there can be arguments where it's metaphysically impossible for the premises to be true and the conclusion false, but the argument isn't logically valid. So for example '(P1) this cup contains water; therefore (C) This cup contains H20' is such that there is no metaphysically possible world where the premise is true and the conclusion is false, but it isn't logically valid; it has the logical form 'W(c) |- H(c)', and that simply isn't logically valid. Even if by 'possible' you mean conceptually possible, then, still, no, there can be arguments where it's conceptually impossible for the premises to be true and the conclusion false, but the argument isn't logically valid. So for example '(P1) John is a bachelor; therefore (C) John is male' is such that there is no conceptually possible world where the premise is true and the conclusion is false, but it too isn't logically valid: it has the logical form 'B(j) |- M(j)', and that simply isn't logically valid. It's only if by 'possible' you simply mean (in a narrower sense than conceptual possibility) logically possible that it's true that an argument is valid iff it's impossible for the premises to be true and the conclusion false: but then we haven't explained what narrow sense of logical possibility is.=== Logical Validity ===
Validity and invalidity for logical arguments are defined as follows: <br>
*'''Valid''': No possible case has the premises all true and the conclusion false
*'''Invalid''': Some possible case has the premises all true and the conclusion false
I think that this is HIGHLY relevant to NTT, because the ethical premises in NTT may be necessarily true, and Isaac has recently tried making it valid by invoking the bundle theory and / or the identity of indiscernibles, which if true are necessarily true. So if we agree with the premises we may think that there's no metaphysically possible world in which the premises are true and the conclusion is false. But that doesn't make it logically valid. All of the confusion is coming from Isaac et al saying that if the premises are true then the conclusion has to be true. Well, sure, in some sense of 'has to', because the suppressed premises may have to be true. But that doesn't make it logically valid - the conclusion doesn't follow from the premises simply in virtue of the logical form of the conclusion and the premises.
I beg you to let me replace this with the following explanation of logical validity, which I assume we all recall from formal logic, and with which I believe I have some success explaining to some people what we're talking about and why Isaac's claims don't address it:
"What it is for an argument to be logically valid is for the truth of its conclusion to be guaranteed by the truth of its premises simply in virtue of the logical form (or syntactic structure of the content) of the premises and the conclusion. 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 (sentential) logical form:
(P1) If U then V
(P2) U
Therefore (C) V
Here, C follows from P1 and P2 simply from this abstract logical form whatever the specific 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").
In the following sections we will prove that NTT is not logically valid - that is, the truth of its conclusion is not guaranteed by the truth of its premises simply in virtue of the logical form of the premises and its conclusion. (To show this requires not only looking at its sentential logical form, like that in the above argument, which replaces whole sentences flanking logical connectives like 'if...then', 'and' and 'or' with abstract symbols, but looking at its predicate-logical form, which replaces the predicates within these sentences with abstract symbols, and quantification over entities that can have the properties signified by those predicates, like 'for all x' and 'for some x', as will be seen below)."
I also beg you to let me put this at the outset of the section on showing that NTT isn't logically valid so people who have no background in any of this understand WTF we mean by 'logically valid' and WTF we are talking about, since Isaac et al are using 'valid' in a colloquial way to mean 'if the premises are true then the conclusion has to be true / we rationally ought to agree with the conclusion" (which isn't logical validity, because e.g., it could be that if the premises are true then we rationally ought to believe that the conclusion is true because we rationally ought to believe that a suppressed premise is also true).
More generally, about the invalidity section: It seems to me that there’s a lot of great stuff in here, but I'm worried that it's difficult for many members of our audience to access, and some of it might be more elaborate than we need in order to make the basic points. Some points about how I understand our audience:
(1) Very few if any members of our intended audience have any philosophical background, and I think that most will not have any mathematical background either. We want this to be accessible to all vegan advocates who are interested in this issue, including people who understand themselves as being helped by it in their street activism (as Banana Warrior Princess has discussed).
(2) Most of our readers don’t have forever to get to the main points and aren’t as interested in every possible twist and turn as we are: I think they need a quick punchline.
(3) People need a clear explanation of what’s going on with its invalidity before worrying about any of the confusions that have arisen in discussions with Isaac. The exception would be cases where the confusions are natural and can alert us to the importance of making helpful distinctions – for instance about what we mean by ‘logically valid’ (I like this was of designating it, but we still need to explain what it means, as above). This is important not only to avoid confusing people by layering Isaac drama on top of the various elements of the argument's invalidity, but to avoid this thing coming across as a biased hit-piece. We’ve seen how unhelpful defensiveness and intellectual one-upmanship is when practiced by Isaac; I think that it’s critical to engage in strategic communication and be good role models by rising above the sniping and offering clear, professional explanations that address the merits and demerits of arguments, not the merits and demerits of individuals.
So what I’d recommend is trying to have as simple and clear main narrative as possible, which presupposes as little background as possible, and which considers a maximally charitable interpretation of the argument as possible, and then move some of the other stuff to (i) a technical appendix with all of the things that need to be done to get to the most charitable interpretation, and also (ii) a section or entry on objections / replies / confusions - which I think should perhaps replace (at least in name) our page on Isaac; instead of a page on Isaac, why don't we have one that includes the various things Isaac has said in trying to defend the argument’s validity and how these don’t work?
I think that we should also foreshadow why anyone should care about logical validity instead of looser relation. I think that I’ve been able to convince at least one of Isaac’s subs that we’re talking about a technical sense different from what Isaac means when he talks about ‘valid’ or ‘consistent’. This young gentleman’s subsequent reaction was exactly what I anticipated it would be; it was in essence “OK, so why the fuck should I care about that? Why the fuck should I care about some pedantic, technical distinctions made by stuffy professional philosophers?” Indeed, I think that the burden of proof is on us to explain this all to them. Young people these days are refreshingly culturally libertarian: they’re not going to take something on your say so or authority unless you give them a good reason for it. Unsubstantiated assertions like “these are the standards for formal arguments” simply aren’t going to cut it. I believe that, because no one has explained to the uninitiated why on earth they should care about logical validity per se, there is an impression that people on here are just fetishistically complaining that NTT doesn’t meet certain aesthetically pleasing formal conditions – or even worse, trying to make Isaac and his subs look stupid or ignorant simply for not having the technical background that we have, and are deliberately using terms in ways that he doesn’t understand without explaining them to him simply to lord it over him. I’m certainly not saying that any of this is true, but it is something we need to dispel if we’re going to communicate effectively and strategically.
I think that we thus need to explain why anyone should care about whether an argument is logically valid vs. rationally compelling in some looser sense, and it is this. It helps us clarify if we have identified all of the substantive assumptions behind a conclusion so that it follows formally (when it is logically valid), or (if it isn’t logically valid) what the additional substantive assumptions are (even if very plausible and widely accepted), so we can know that we’re actually making those assumptions (in this case contra some of what Isaac has suggested), not cause confusion or look stupid by not admitting that we are making them, and be in a position to defend those assumptions forthrightly.
