7 ) Then anything relevant to X cannot be relevant to any philosophical claim. — fdrake

Why would this follow?

If they move any further to the left, they would just be centrist or maybe center-right. They would not be left in any European country. — Manuel

"If the Democrats move left they would only be centrist in Europe, therefore such a move would not make them left."

The U.S. is not Europe. This is not a good argument.

I disagree that Trump has moderated alot of his positions. In fact he seems to be moving to the extremes on issues like immigration (where he wants mass deportations) — Mr Bee

"Majority of Americans support mass deportations" (CBS).

and trade (where he wants to impose a global tariff on all goods) — Mr Bee

Trump's love of tariffs is idiosyncratic from all political angles, true. But because of that it is not polarizing in any partisan manner.

The only area where he's moderated is on abortion and social security but apart from that he's a standard Republican and governed like one in his first term. — Mr Bee

Abortion, social security, IVF, LGBT... Trump is also moving the party towards non-interventionism. RFK and Gabbard are former Democrats, to name two within his administration.

The Democrat platform isn't the problem since it remains popular (while Trump's ironically enough isn't) but Democrats aren't able to sell it as well as Trump is able to sell himself which goes back to the main problem I see for Democrats. — Mr Bee

This seems backwards to me. Trump's public persona was a liability in this election, not a boon. The Democrat platform was bad enough to strongly neutralize that liability. I am amazed at how completely it was neutralized.

Losing to Trump twice after barely eeking out a win in 2020 when they ran their "safe" candidate should be a clear sign that what they're doing isn't working. — Mr Bee

So what needs to change if "the platform isn't the problem"? A more impressive candidate and a focus on the policy proposals? I am not sure what golden policy proposals the Democrats are supposed to have in their back pocket.

By "truth" I mean to refer to people who are honest and who value, care about, truth and honesty. — tim wood

By "truth" you mean people who care about truth?

I'd say an OP which cares about truth would have a more truthful first sentence. :grin:

A ) If X is a subdomain of Y, then studying Y is studying X. — fdrake

I'm not opposed to that, but what I said was the opposite.

it leaves unexamined how context would need to distribute over the nesting of contexts — fdrake

I don't think I've left that nearly as unexamined as you have. You seem to be committed to your same implicit claim that there is no contextless 'context', or no "context of contexts." Why think such a thing?

- It's not a subset, it's a ratio (Latin).

We could study a deer according to its totality, and we could study a deer according to its aspect of movability, and we could study a deer according to its aspect of longevity. The two latter studies are co-implicative with the former. When we study the movability of Deer we are being informed about the totality of Deer, even though our object is not the totality of Deer.

The analogy of course limps given the sui generis character of being.

Similarly if "philosophy" in @J's sense has to do with logic, or thinking qua thinking, or justification qua justification, or explanation qua explanation, then any contextualized instance of logic/thinking/justification/explanation will implicate philosophy. When a biologist makes an argument about the digestive system of deer, the philosopher is not barred from the argument in the way that an astronomer is. The philosopher's input cannot be a priori excluded, and this is because he deals with the "context of contexts."

Why though? — fdrake

Why does the study of being qua motion (physics) implicate the study of being qua being (metaphysics)? Because motion is a kind of being.

I am putting philosophy and metaphysics together. Really there is an analogy. We are talking about philosophy in terms of justification or inquiry, and in that sense it is the justificatory "context of contexts" that parallels metaphysics' foundational character.

So if we put it in @J's terms, where philosophy is fundamentally bound up with thinking, we would say that the art of thinking qua thinking is implicated in every contextual form of justification, given that justification is a form of thinking. I would call this "thinking qua thinking" logic, which is the art of discursive reasoning. Thus whenever we operate in some justificatory context, we are presumably implicating ourselves in logic; and logic pervades all justificatory contexts as water pervades the ocean, not as a foundation underlies a house. There are strong commonalities between philosophy, metaphysics, and logic.

- :up:

How do you argue that the convergence goes to philosophy without already arguing that philosophy interrogates the context of all contexts. — fdrake

I see this as fairly simple. There is a context of all contexts and that which pertains to it is what we call "philosophy."

contexts tend to relate to each other even if they are distinct (but have fuzzy boundaries) — fdrake

You are relying on a very linear justificatory scheme, where the boundaries aren't overly fuzzy. Classically the boundary of philosophy or metaphysics is not fuzzy, it is non-existent. The context of contexts is not a linear terminus that is hermetically sealed. It is encompassing.

If at the end of our cogitating, all we have is the Q recursion as our "termination in philosophy," that’s not much of a result. The problem is how to shape it into something more significant, something actually about the nature of philosophy as a pursuit of wisdom, or at least knowledge. — J

Why isn't it "much of a result"? Is there some argument other than, "Because it's inevitable?" Because I don't see why an inevitable justificatory aspect must be unimportant. I actually think the inevitability of philosophy is largely what makes it important. Philosophy is necessarily unavoidable, and that is why it is important.

There is a sui generis aspect of philosophy here given the way it is being defined. Instead of defining it according to its principles and object—as we do with other sciences—philosophy is being defined as the study pertaining to the "context of contexts," to use fdrake's language. Or for Aristotle, "The study of being qua being." Philosophy or metaphysics is not limited in the way that every other science is limited. It is not contextualized; it is not bound by a priori principles or presuppositions.

Aristotle's depiction is instructive. Sciences other than philosophy/metaphysics study being under some aspect other than being. For example, physics is the study of being qua movement. But the study of being qua being will be implicated in every other study of being (qua X). Thus philosophy does not stand merely as a linear foundation, but rather as a porous and encompassing ocean for all aquatic life.

- :up:

The elites navigated the 2008 financial crisis extraordinarily well, but the "morality card" has now been overplayed and the broader political movement has become trapped in oppressor-oppressed quicksand.

Deduction should allow you to pass, by valid inference, from what you know to what you did not know. Yes?

In mathematics, these elements are well-defined. What do we know? What has been proven. How do we generate new knowledge? By formal proof.

Neither of these elements are so well-defined outside mathematics (and formal logic, of course). There is no criterion for what counts as knowledge, and probably cannot be. And that defect cannot be made up by cleverness in how we make inferences.

I see no reason to question the traditional view. "Our reasonings concerning matters of fact are merely probable," as the man said. There is deduction in math and logic; everyone else has to make do with induction, abduction, probability. — Srap Tasmaner

Are you claiming that knowledge does not exist outside mathematics? I don't see why "the elements being less well-defined" results in any serious problem here. This comes back to the Meno question I have posed to you elsewhere. One could answer that question by denying that knowledge exists.

Deduction should allow you to pass, by valid inference, from what you know to what you did not know. Yes? — Srap Tasmaner

Sure, and haven't we achieved that with Billy?

I was referring to a situation such as the one involving the neo-Freudian. He attempts to short-circuit philosophical discourse by explaining it in terms of his discipline, abandoning any philosophical vocabulary about reasons, arguments, or truth. Another example might be a theological coup, in which someone insists on translating all talk of reasons, truth, etc., into a discussion of the speaker's salvation status (i.e., "You're only saying that because you're saved/damned"). It's a kind of ad hominem argument, but more general and potentially sweeping because it claims to invalidate not only a particular argument but all the premises of philosophical discourse. Many positivist/ordinary-language attacks on metaphysics also have this same characteristic, I think. And I'm claiming they can all be answered with more philosophy. — J

Okay. In that case I agree with you that, "...the starting point of philosophy is in fact the realization that its inquiries cannot be brought to an end by absorption into another discipline" ().

And I would say that these cases like the neo-Freudian rely on philosophical thinking to debunk philosophical discourse, and therefore result in a kind of performative contradiction. Thus philosophy could here be considered "highest" because it does not require these sorts of performative contradictions and rational gaps/incoherence.

The solution isn't that hard, it really isn't. However I worry that the problem isn't that the Dems are incompetent but that they're incompetent by design. It's not like there weren't opportunities these past few election cycles, but the party always made sure that the candidate that was nominated was the candidate that wouldn't rock the boat. — Mr Bee

The parties are in disarray. 2016 saw two populists make waves, Trump and Sanders. If I recall, when Sanders was checked by the powers of the DNC, 4/10 Sanders voters moved to Trump. Of the two populist hijackings of 2016, one worked and one didn't, and the effects were predictable. The Democrats paid a price in votes and palatable candidates, and the Republicans paid a price in policy. There is pressure to reshape the two parties. For the Republicans the reshaping is already well underway; for the Democrats it looks inevitable.

But Trump moderated the conservatism of the Republicans and he now holds the center. So I don't agree that "the solution isn't hard" for the Democrats. Concede to Trump and adopt the same core positions? Move left and abandon the center? Oddly, the Democrats find themselves in a strange pickle just 8 years after Obama left office. Their only grievous mistake was running Clinton in 2016.* I don't think they would've won the election any other way in 2020, given Sanders' head start. (Cue the Bernie Bros' protestations...)

* And perhaps letting Sanders run as a Democrat in 2020. But they did not want to risk him running as an independent.

Yes, that's an important distinction. I think the problem I'm proposing in the OP is more about termination than justification. Self-reflection -- that is, the ability of philosophical discourse to always reply with more questions that can only be answered philosophically -- is literally interminable. That's the aspect that I said cannot be brought to an end, and that many philosophers regard as evidence of something important and special about such discourse. — J

Yes, I think we are on the same page. I was thinking of that as justification, but as your post indicates, if an answer to an inquiry cannot be definitively justified then that inquiry cannot come to a term (or be terminated). Similarly, an answer which cannot be satisfactorily/definitively justified for a community cannot be terminated/concluded by that community. The history of philosophy shows that even where agreement and termination occurred, it did not occur universally (cf. Holmes' dissent in Abrams, "...time has upset many fighting faiths...").

I suppose I am wondering what you meant when you talked about an inquiry being, "brought to an end by absorption into another discipline."

This is going to sound paradoxical, but perhaps the starting point of philosophy is in fact the realization that its inquiries cannot be brought to an end by absorption into another discipline. — J

Sure, but isn't it that there is no end because there are no presuppositions? If an inquiry requires support and presuppositions are the ultimate supports, then an inquiry without presuppositions cannot ultimately be brought to an end in any obvious way.

But one could speak about "bringing an inquiry to an end" via justification or via termination. I am thinking about justification, where an answer to a question is definitively justified.

This is similar to our exchange here about the uniqueness of metaphysics.

Clearly we couldn't know that reflection is endless until we'd discovered it to be so, which is a process in time, but having learned this, we can posit that feature as the feature which makes philosophy unique... — J

I think we could know this "a priori." That given the principles at stake, philosophical investigation can have no concrete end.

Is it left-leaning to ban homophobia, transphobia and racism? — Christoffer

It is left-leaning to simply assume that something is homophobic, transphobic, or racist, which is precisely what you are doing in failing to address the arguments at hand. The left is exceedingly accustomed to using these labels to shut down speech and debate.

(Is "presuppositionaless-ness" translated from the German? :wink: ) — J

:lol:

Oh, I didn't realize that's what you meant. — J

I see it more as an aside, since your OP is not centered on this topic. My first post only touched on it in my first two sentences.

I was referring merely to the "gotcha" aspect, where any questioning of philosophy becomes yet more philosophy. Do you think this has to do with the lack of presuppositions? I'd like to hear more about that. — J

I don't know if this answers your question, but I see the presuppositionaless-ness of philosophy as substantive because it represents one of the basic reasons why philosophy is so difficult and so useful. It is what gives philosophy an undeniable sovereignty. Other disciplines have fairly clear starting points, but not philosophy. Other disciplines have a fairly clear Overton window, but not philosophy. ...Or at least, much less so with philosophy.

But I don't want to distract from the more central topic of the OP, which seems to be, "Is philosophy 'highest' in some way beyond having no presuppositions?"

Americans just absolutely hate the establishment. And they hate to be told what to think especially by the liberal elite. — ssu

Yep. And this has become built-in to culture in a remarkable way. I think of movies like The Matrix. The odd thing is that the DNC hasn't at all figured this out. They depend on superficial cultural currents to overcome deeper cultural currents.

- Right, but I am uncomfortable with viewing the presuppositionaless-ness of philosophy as "an argumentative trick." There is something substantive about the uniquely presuppositionaless discipline. I find that aspect of philosophy interesting and important, albeit inevitable. So we could ask whether there is something more without denigrating that aspect.

The support relation is also notoriously tricky to formalize (given a world full of non-black non-ravens), so there's a lot to say about that. For us, there is logic woven into it though:

"Billy's not at work today."
"How do you know?"
"I saw him at the pharmacy, waiting for a prescription."

It goes without saying that Billy can't be in two places at once. Is that a question of logic or physics (or even biology)? What's more, the story of why Billy isn't at work should cross paths with the story of how I know he isn't. ("What were you doing at the pharmacy?")

As attached as I've become, in a dilettante-ish way, to the centrality of probability, I'm beginning to suspect a good story (or "narrative" as Isaac would have said) is what we are really looking for. — Srap Tasmaner

Good post. I may have fallen too far behind in this thread, but I don't think we have to choose between logic and physics to explain such an argument. Physics provides us with a particular kind of logic which makes the argument sound.

I want to say that "flows from" or validity in logic is a specific kind of inferential relation and justification. Your story about Billy fulfills that inferential relation, albeit with some tacit premises.

Well, the thing is, deducibility is for math and not much else. — Srap Tasmaner

But why? Given the explanation, can we deduce that Billy is not at work?

I agree that the consequence relation ("follows from") is hard to formalize. Or rather, I think it is impossible to formalize.

(Feel free to ignore this post if the thread has moved too far away from it.)

I hear you,but one has to read the room. — Swanty

Right, and Lionino would have probably returned and said something even more provocative, which is why it isn't worthwhile to defend. Or like says, there are probably more provocative things that have already been deleted.

- Yep. :up:

I think Lionino could be defended. After all, an inflammatory style is not against the rules on TPF. I think Lionino had a way of highlighting a left-leaning bias on the forum. At the same time, I don't expect a forum to be perfectly objective, and TPF is better than most. What is needed though, is a clear line so that the bias has a measure of transparency. We conservatives are accustomed to wrestling with one hand tied behind our back in progressive spaces, but clear guidelines are helpful in setting expectations.

(I messaged Lionino 2 months ago encouraging him not to get impatient. I think he made a choice to flirt with being banned.)

- Hard to say. Presumably it is the set of ideas that spread internationally after George Floyd's death, ideas which are centered on a narrative of racist police along with the repudiation of police forces (on those grounds) and a generally revolutionary attitude. It would not be surprising if this was felt most keenly in Lionino's France.

What one never hears is that the story is much more complicated, as indicated by things like Liz Collin's "The Fall of Minneapolis" and Radley Balko's response. Glenn Loury and John McWhorter have discussed this issue at some length (link).

But Lionino couldn't control himself, and I will miss him. — javi2541997

Yep. I think he wanted to be banned.

But he was ultimately being anti-U.S., which is curious. He complained that "Burgerland" (the U.S.) exports "georgefloydism" and "sodomy," and this was construed as racism and homophobia. Is it racist to oppose the exporting of "georgefloydism" and homophobic to oppose the exporting of "sodomy" (LGBTQ+ agenda)? Certainly not in the U.S. In the U.S. this would be seen as an ideological claim, not a factual claim. In fact there are many Black people in the U.S. (and particularly Minneapolis) who oppose everything about the George Floyd movement, and there are even LGBTQ+ individuals who oppose the overt exportation and inculcation of that agenda.

But Lionino decided to use TPF as a place to come when he was angry, as opposed to a place to avoid when he was angry. That makes all the difference.

Interesting thread. Philosophy could be called highest because it is without presuppositions. But could it be called highest for a more substantive reason?

You seem to want to say that philosophy has to do with thinking qua thinking, and that if all being can be thought, then philosophy has a relation to all being in a way that other disciplines do not. That seems right. Or we might say that there is no thinking or knowledge that is non-philosophical. Philosophy itself has no presuppositions, and every act of thinking has philosophical presuppositions.

So, why is it that Republicans in the US just dominate the airwaves and internet social media sites? I mean Mark Zuckerberg was grilled pretty badly after Russia interfered with the 2016 elections. Now, Elon Musk with X.com has likely interfered with this election cycle. One can wonder how much of a ego-trip these rich billionaires had or have had.

So, is it the case that it is just the ultra-wealthy and elite supporting their own candidates? — Shawn

Left = legacy media = $$. Right = grassroots media & free speech. Do a quick search on the fundraising and spending numbers from the left and the right in the last election. That Trump won big despite having less money and less favorable press completely undermines your silly thesis.

(Of course, the far-left is largely excluded from the wealth and power of the center-left. It is an uneasy alliance.)

What you're after is a more robust relationship between premises and conclusions, something more like grasping why it being the case that P, in the real world, brings about Q being the case, in the real world, and then just representing that as 'P ⇒ Q' or whatever. Not just a matter of truth-values, but of an intimate connection between the conditions that 'P' and 'Q' are used to represent. Yes? — Srap Tasmaner

...And I want to say that an argument is supposed to answer the "why" of a conclusion. Inferential argumentation is an explanation for a proposition/conclusion. Validity is one aspect of the goodness of such an explanation.

Similar to what I said earlier about the genus of discourse, some arguments are apparently neither valid nor invalid:

Now the question arises: is it invalid? I don't claim that. — Leontiskos

Probably they are not "arguments" at all.

To give another example using Srap's color idea:

• Everything which is not white contains pigment
• Numbers are not white
• Therefore, numbers contain pigment

That is the sort of thing that is occurring when one tries to claim that any argument with inconsistent premises is trivially valid. The domain of discourse when speaking about validity is arguments, and arguments do not contain premises that are known to be inconsistent. Some arguments have premises that are inconsistent but are not known to be inconsistent, and that is where reductio comes in. Are these latter kind truly arguments? Not in any perfect or ideal sense, but they are in the sense that the arguer believes the premises to be consistent.

Well, what do we say here ― leaving aside whether color exclusion is a tenable example? What you're after is a more robust relationship between premises and conclusions, something more like grasping why it being the case that P, in the real world, brings about Q being the case, in the real world, and then just representing that as 'P ⇒ Q' or whatever. Not just a matter of truth-values, but of an intimate connection between the conditions that 'P' and 'Q' are used to represent. Yes? — Srap Tasmaner

These are interesting topics that Aristotle also takes up, but I don't think I'm being overly greedy in what I desire. I am not requiring a special kind of aitia/account/explanation. Here is what I said above:

Validity is a relationship between premises and conclusion. This is what I say is the common interpretation of your sources on validity:

1. Assume all the premises are true
2. See if it is inferentially possible to make the conclusion false, given the true premises
3. If it is not possible, then the argument is valid

...

...validity is an inferential relationship between premises and conclusion. — Leontiskos

As Enderton notes, validity is about deducibility. It is not merely about truth values. It is about the inferential relationship between premises and conclusion. In order to show that Q follows from P, we have to show how Q is correctly inferred from P, and we need to have evidence that ~Q cannot also be inferred from P.

A key contention of mine is that I am representing the notion of validity in formal logic better than Tones is. I don't even need to advert to real-world cases, like that of color. Even within propositional logic itself, validity has to do with "follows from" and deducibility.

- Yeah, you're giving me flashbacks to Flannel's thread.

TL;DR. If you think of the material conditional as a containment relation, its behavior makes sense. — Srap Tasmaner

That was a really interesting post, and it presents an interesting attempt to bridge propositional logic and real-world reasoning. I am reading Burnyeat on Aristotle's Enthymeme, which is closely related to your discussion of George. Unfortunately I've already spent too much time on TPF today, so I am not going to say a whole lot more.

My take on material implication:

Material implication is the way it is for much the same reason that humans are the way they are given Epimetheus' mistake. When the logic gods got around to fashioning material implication they basically said, "Well if the antecedent is true and the consequent is true then obviously the implication is true, and if the antecedent is true and the consequent is false then obviously the implication is false, but what happens in the other cases?" "Shit! We only have 'true' and 'false' to work with! I guess we just call it 'true'...?" "Yeah, we certainly can't call it 'false'."

I haven't thought about this problem in some time, but last time I did I decided that calling the vacuous cases of the material conditional 'true' is like dross. In a tertiary logic perhaps they would be neither true nor false, but in a binary logic they must be either true or false, and given the nature of modus ponens and modus tollens 'true' works much better. It's a bit of a convenient fiction. This is not to say that there aren't inherent problems with trying to cast implication as truth-functional, but it seems to me that an additional problem is the bivalence of the paradigm. — Leontiskos

The purpose of material implication is inferences like modus ponens and modus tollens. Degenerative uses are improper. The consequence relation can appropriate the material conditional without any risk of degenerative use (at least until you do the weird stuff Tones is doing, in which case the risks are re-introduced).

See also:

...Soon after this, Frege expresses frustration that 28 years after he introduced the material conditional mathematicians and logicians continue to resist it as something bizarre! — Leontiskos

When a formalist takes up logic, they neglect its teleological character, and when logic has no teleological character there can be no degenerative or non-degenerative uses. That is the problem, methinks.

To be sure, one might use disjunctive syllogism to prove that B is A from the contradiction, but that doesn't make the form of the above valid. — Count Timothy von Icarus

Yes, that's my point.

Tones thinks it is valid by definition, because any argument with inconsistent premises is (trivially) valid.

Now the question arises: is it invalid? I don't claim that.

But surely we don't want to claim that the fallacy of exclusive premises is true just in cases it is possible for its premises to be true. — Count Timothy von Icarus

Not sure what you mean by this.

- Interesting, but it doesn't adjudicate the question. I don't expect the question to be adjudicated on these sorts of grounds (and Tones involves himself in petitio principii when he claims that his sources favor his interpretation). The sources I cited include a notion of "follows from," which obviously excludes Tones' approach of relying on the degenerative case of the material conditional. When A is false (A→B) is true, but B does not follow from A.

- What does footnote 11 say? Because the whole dispute rides on that single word, "whenever."

"There are a number[11] of people voting for me for President on Tuesday — Srap Tasmaner

I affirm that it is valid by any of these considerations:

(1) Apply the definition of 'valid argument'. — TonesInDeepFreeze

And that is the option we are talking about, nitpicker.

From the post you sidestepped:

Your interpretation is mistaken because validity is an inferential relationship between premises and conclusion. You would establish an inferential relationship without examining the inferential structure and relations. To say, "The premises are contradictory, therefore an inferential relationship between premises and conclusion holds," is to establish an inferential relationship without recourse to inferential relations. — Leontiskos

- Good post. This is a very broad and pervasive topic that perhaps deserves its own thread someday.

In natural deduction systems, if you assume A and then eventually derive B, you may discharge the assumption by writing 'A → B'; this is just the introduction rule for →, and it is exactly the same as the '→' that might appear in a premise. — Srap Tasmaner

This is a source of the disagreement. I don't disagree that you can "discharge" the consequence in that way, but it avoids the crucial matter of the degenerative case of the material conditional, and this is precisely what Tones wants to rely upon. It seems to me that the only reason people tend to substitute consequence with → is because arguments de facto exclude the degenerative case that Tones wants to re-introduce. An argument is a teleological act that aims at legitimate validity, not degenerative validity. Validity in logic is desirable, not undesirable.

You're giving a different reason for why it's valid versus Tones. — frank

Yep. :up:

Lots of people are not paying attention to the differentiation of arguments for why the OP might be valid. Three options have been given: modus ponens, explosion, and the definition of validity. TonesInDeepFreeze's is the latter... — Leontiskos

- Can you spell out your point for me? It looks to me like a good example of why a sentence is different from an argument. I don't think it is possible to translate your point into an argument, is it? If I am right, that's in part because the material conditional and the consequence relation do not operate in the same way, particularly when the antecedent contains a conjunction in that way.

This whole thing is an unwieldy topic in general. For example, can premise (1) of the OP be assigned a true value? And can both premises of the OP be assigned a true value? I suspect that the answers to these questions go beyond the purview of standard propositional logic, and creep into the space of Frege's judgment stroke. So it's not even obvious that Tones is right when he says that the premises of the OP cannot both be assigned a true value, although I have no real dog in that fight.

Another one:

"a major topic in the study of deductive logic is validity. This is a
relationship between a set of sentences and another sentence; this relationship holds whenever it
is logically impossible for there to be a situation in which all the sentences in the first set are true
and the other sentence false." [bold added]

https://logiclx.humnet.ucla.edu/Logic/Documents/CORE/LogicText%20Chap%200%20Aug%202013.pdf — TonesInDeepFreeze

The idea that it is a relationship already excludes your reading. If a relationship between A and B must be established, then one must know something about both A and B. Yet you think that merely knowing something about A—that it is inconsistent—proves validity. If an isolated fact about A proved validity then validity would not be a relationship between A (premises) and B (conclusion). This is another source that excludes your view. The other (single-sentence) sources you presented favor my view but do not exclude your tendentious view. — Leontiskos

. . .The validity relation is a relation in the ordinary formal sense of a set of ordered pairs. That is distinct from any of the ordered pairs themself. — TonesInDeepFreeze

Validity is a relationship between premises and conclusion. This is what I say is the common interpretation of your sources on validity:

1. Assume all the premises are true
2. See if it is inferentially possible to make the conclusion false, given the true premises
3. If it is not possible, then the argument is valid

Your interpretation changes the ordering of the conjunction and condition, and probably also the nature of the condition. You want to say that if we cannot assume that all the premises are true (on pain of contradiction), then the argument is valid by default. There is no need to look at the inferential structure.

Your interpretation is mistaken because validity is an inferential relationship between premises and conclusion. You would establish an inferential relationship without examining the inferential structure and relations. To say, "The premises are contradictory, therefore an inferential relationship between premises and conclusion holds," is to establish an inferential relationship without recourse to inferential relations.

I mentioned it several posts back, but it seems possible to have an invalid argument with necessarily false premises. — Count Timothy von Icarus

I agree, but Tones is talking about assignment or inconsistency, not necessary falseness. A (formal-propositional) contradiction is necessarily false, but not everything that is necessarily false is a (formal-propositional) contradiction.

"All triangles are not three-sided shapes," is necessarily false, it is contradictory, but it is not contradictory in the formal-propositional sense. I think this goes somewhat to my edit about levels of modality. Your earlier post about the relevance of matter and form within abstract fields like mathematics also gets at this point. See:

Edit:

This is a matter of different modal levels, so to speak, or different domains or levels of impossibility. Tones is committing a metabasis eis allo genos. He is committing a category error where the genus of discourse is not being respected. Contingent falsity, necessary falsity, and contradictoriness are three different forms of denial or impossibility. The definition of validity that Tones favors is dealing in the first category, not the second or third. The domain of discourse for such a definition assumes that the premises are consistent. It does not envision itself as including the degenerate case where an argument is made valid by an absurd combination of premises. An "argument" is not made valid by being nonsense. — Leontiskos

The OP's question was not about ordinary English at all. — Srap Tasmaner

Tones is interpreting English-language definitions of validity according to the material conditional, not merely the OP. He himself now recognizes this:

And, yes, the equivalence is per the material conditional. — TonesInDeepFreeze

Edit:

And now explicitly:

English as a meta-language regarding formal logic. In that meta-language, 'if then' is taken in the sense of the material conditional. — TonesInDeepFreeze

He thinks the consequence relation of logic (∴) is the material conditional, such that a contradictory set of premises automatically makes an argument valid, irrespective of any explosive argumentation within the argument.