What would be the implications if we would say for any given argument under all values of the antecedent the conclusion may not result in a logical contradiction or the argument will be deemed invalid? — Benkei

This goes back to my pedantry comments. I can't see how it could matter if we designated a name for that special class of modus ponens described in the OP, where it is structurally consistent with modus ponens but is logically inconsistent. This thread strikes me as more of a primer in formal logic nomenclature than in logic qua logic.

If I woke up with amnesia or hallucinating I was Jesus, with no accurate Hanover memory, I'm still Hanover.

Isn't this just a Ship of Theseus question?

Most - I think all - lies are soluble in appropriate analysis. — tim wood

An example: I was speaking to a Russian woman who's been in the US for decades. Her recollection of the "Miracle on Ice" when the US won the Olympic gold in hockey was that the Soviet team was paid off. She said there was no way a top rated professional team could lose to amatuers. She said for the right money, they'd have had sex with each other (her words).

What fit my narrative was freedom over oppression and that Americans can win if they just believe. What fit her narrative was that her team was superior but her nation was corrupt. I hadn't thought about it before, but who knows what actually happened? We have no evidence of cheating, so I go with the US version, but my guess is that Russians rolled their eyes at the result while the US cheered.

And so if I'm as entrenched in US culture as Trumpians are in Trump culture, I can't imagine things being other than they appear. Does this give rise to conspiracies? Of course it does, but that's what breeds this post truth thing.

In the Truth Era, I wonder how much truth there was, or were we just more accepting due to homogenuity of ideology.

Cite some representative samples of my "unclear" "jargon laden style and weird grammatically abbreviated sentences". Thanks. — 180 Proof

Just playing.

But we've never trusted Russian elections or Iranian news. We've never agreed upon basic facts with our enemies. My question is whether the change is in what we take to be Truth as opposed to who our enemies are now. We find our enemies next door now, when we used to have to go far.

Isn't distrust just a symptom of polarization of viewpoints as opposed to something new?

What I know of Taylor appears in your quote, so feel free to fill in the details of what I don't know.

How is Taylor not consistent with Cartesianism? Taylor says we cannot offer a meaningful description of the human condition without describing our drivers for moral behavior. To be sure, our desire for morality and appreciation of it is unique among the other creatures in the world, or, if not truly unique, hyper developed comparatively. For that reason, I'd agree with Taylor regarding the idea we must analyze morality if we want to analyze people.

What I don't see though is why I could not be a Cartesian and fully agree with Taylor. Cartesian dualism posits a mind that has a free will that is subject to moral evaluation. Wouldn't Descartes agree with Taylor's assessment of the significance of understanding morality if one wanted to understand humanity then?

Per Descartes, if the self is defined as having free will, and it is through this free will that morality arises, then to understand the self would require an understanding of morality, and this would be in agreement with Taylor, true?

I wonder though how much Truth there was in the Truth Era as opposed up our current Post Truth Era. How much of is it that we just don't have a unified worldview and therefore we lack a subjectively consistent perspective?

Did the US and USSR.agree on the facts? Do Israel and Hamas agree on the facts? Do the Southern Baptists and atheists agree on the facts?

That is, is the Post Truth era really just a Post Common Ideology Era? We're used to people far away disagreeing with us on basic facts, but isn't a substantial part of this change just caused by our no longer agreeing with our neighbors?

From my perspective, the prior Trump election wasn't stolen. The arguments otherwise (which I hear among the educated where I live) are completely idiotic. But does the US Constitution really say anything about abortion? Are transsexuals truly women? Did Harris really have a chance like we were told? Not from your perspective, but what is the Truth?

Why do the murky areas of Truth always seem to land consistently with Ideology?

This isn't to dispense with the idea that there is Truth, but it is to suggest we've always found Truth/God on our side. We're just frustrated because we don't worship a common god.

But that's policy, not identity. But then you go on to say people voted because of their identity as republicans. It could be both of course, but you seem to be inconsistent as to which you consider more causal. — bert1

I think you read where I said that people vote Republican because they are Republican to suggest it's just a matter of party identity. There may be some of that, but that's not really what I meant. I meant they are Republican because they believe in Republican ideology.

Just like the reason Christians (for example) go to church. They go because they're Christian, meaning they believe in Christianity, not just because it's their team.

I get how you read what I said as you did, but it's not what I meant.

This poll tells us what the left believes the right believes.

If the right told you the only reason you voted for Harris was because you didn't like Trump and because all you wanted was a woman, how might you respond? I think you'd say you voted Democrat because you are Democrat.

A Trump vote was anti-woke, pro police, pro immigration control, pro reduced taxes, pro reduced regulation, pro Israel, pro life, pro drilling for oil, among other things.

Believe it or not, over 50% of the population voted Republican because they are Republican.

Mine was funny. Yours is disturbing.

If you awoke with your brain in a different body, and you were a hot girl, I'd be all over that.

Now we're even with the disturbing posts.

This scenario isn't that far fetched actually as this video analysis shows. It's only a few minutes and worth a watch, particularly at around 1:40.

Is this not why it's an extrovert's world?

How do we approach Betty Sue, that most intimidating creature? Do we walk right up to her and speak our heart? Never!

We have our friend send a note, or today we text, or maybe we set up an entire online meeting system where we can interact with her picture. If we do decide to directly approach, we drink a few pints to be sure our inhibitions are weakened.

And this is good to a point. Friendship groups like this one get formed, even marriages. But the other side is that friends meet up to do nothing but stare at their phones. People can't walk down the street without bumping into each other as they check their messages. Bodies in the wild, minds far away.

We're the addict who learned to cure our social limitations only to no longer know how to socially interact without our crutch. We have forgotten we evolved doing this in an entirely different way for 1000s of years. Successfully.

That's ambiguous. It could mean two things: — TonesInDeepFreeze

You make a valid point.

(C) and (D) are WRONG (see below). — TonesInDeepFreeze

I appreciate the deep analysis, but can you just draw me some Venn diagram circles with 1, 2, 3, and 4s on them and then I can see what can be what? It's easier on my visual brain.

We're actually debating what terms each of us can make up and the best terms that would describe whatever we're trying to say. I'll defer to yours with my backwards name and provide myself a translator so we can speak the same language. In truth, I think we largely follow what each other are saying at this point.

What I mean by "incoherent" is that which is "expressed in an incomprehensible or confusing way; unclear." @Michael's rendition of what "incoherent" might look like includes gibberish, which is a new additon to this conversation, so it might require an entirely different term. We could then start inserting such non-linguistic items such as the smell of lilac and that weird feeling of deja vu in as premises. Everyone loves a good emoji as well, so that could go in there too.

In any event, "Gloobelfooble" could indeed be a statement, inasmuch as A can be statement and Q can be a statement.

If Gloobelfooble, then Q
Gloobelfooble
Q

You're claiming the statement "that's a valid conclusion" is a category error because conclusions can't be valid or not valid, but only true or false. It'd be like asking what kind of document my cat is, for example.

The statement "that's a valid conclusion" does make sense, so I would think a listener who hears that would realize immediately that the person speaking isn't using the term "valid" as a term of art, but must mean something else.

But regardless of how you get there, the conclusion "arguments can be both valid and invalid" is false. — Michael

Can we say the conclusion is valid or do we reserve the term "valid" only to argument forms and not to conclusions?

No 3 is a 4 because no argument can be both valid and invalid. — Michael

I get that, but a 3 permits explosion, which can force anything anywhere.

Then all 3s imply that 3 is a 4.

It's not raining and it's raining therefore it's not raining.. So yeah, it's "incoherent" in that its premises are inconsistent. — Michael

Accepting that definition of "incoherent," we can then say we have (1) valid and coherent arguments and (2) valid and incoherent arguments.

We can also have (3) valid and sound arguments and (4) valid and unsound arguments.

Would you agree that:

A. All 3s are 1s, but not all 1s are 3s?
B. All 2s are 4s, but not all 4s are 2s.
C. No 1s or 3s are 4s or 2s.
D. No 4s or 2s are 1 or 3s.

(Venn diagram is: 3 is a circle within the 1 circle and 2 is a circle within a 4 circle).

The OP is a 2, but not all 2s are a 4, so just calling it valid but unsound doesn't capture its special class.

Maybe we should could call 2s a "NotAristotle" after the creator of this thread. Or, is there already another name for 2s.

Disagreement with what I've said here?

Candidly, there can't be any sensible doubt that the argument in the OP is valid for formal propositional logic. So in order for those who claim it is invalid to be correct, there must be more than one form of validity, and hence logical pluralism follows. — Banno

That is true, but shouldn't there be a distinction not just between "valid but not sound" but also between "valid but incoherent"?

For example:

If P then not Q
P
not Q

This is valid. It is sound if P and ~ Q are true. Unsound if not.
If P and Q are the same thing such that:

If P then not P
P
Not P

This is valid and not sound, but also not coherent.

As in, "If I went to the store, I did not go to the store, and I went to the store, so I did not go to the store." That is valid, but meaningless. I have no idea what you did, whether you went to the store, didn't go to the store, and I can't understand how your going to the store made you not go to the store."

And that was the debate for 20 pages I suppose. The pluralism might not be over "validity" if you wish to protect that term to only reference formal structure, but perhaps over soundness if you want to speak of what synthetically is false versus what is analytically false.

This conversation is pedantic and legalistic if I'm understanding it correctly. We all can agree with what truth tables show and what logic dictates, but the battle might be over terms, but I might misunderstand because that was the extent of my disagreement.

The incoherently true statement is also distinct from the vacuously true statement. As in, "if Tokyo is in Spain, then the Eiffel Tower is in Bolivia." There the antecedent cannot ever be satisfied, so it can never be true, but it's impediment to truth is due to a synthetic falsehood, but that's unlike the OP where the antecedent is premised to be false.

I'll let you guys better explain it to me if I've misunderstood this, but the contradiction and the incoherence that follows is what trips this issue up to me at least.

Yeah but it probably won't beat places like China and India given how much more lax their regulations are. Those are the countries they need to compete with. — Mr Bee

I'm not supporting Trump here, but I'm just going through his policies. What you bring up here is why he wishes to impose tarriffs. He's using his bully power to limit trade with a nation that needs it, which will weaken them. If they locate other markets in Europe, I would expect tarriffs in Europe. And so what would then happen is that someone takes out a calculator and realizes the better way to make money is not to create their economic policies from moral theories, but instead to maximize profits.

Has he suggested decreasing defense spending before? It sounds like he will just continue the status quo of the US being the biggest spender on defense by far. I think it appeals to his tough guy persona. — Mr Bee

This is the whole thing about him wanting to force NATO nations to pay for their own defense. He's threatening Europe with insecurity by underfunding NATO unless European nations better foot the bill. This fits his "everything is a deal" persona.

There's only so much more drilling that can be done to reduce oil prices (contrary to what some on the right say the Biden administration is overseeing record production right now). Also contrary to what Trump says, there is little correlation between the price of other goods the price of oil and gas. — Mr Bee

I'm not getting into the weeds of what causes what because I don't know enough about it. I can say that fuel costs are an important part of everyone's budget and they've increased. Sam's Club sells gas at like 10 cents cheaper per gallon and cars are up and down the street to save the $2.00 on a tank. It's part of inflation control.

This is in Europe's interest, though. Relying on other countries for defense is nothing other than giving up one's sovereignty. This is exactly why I view Europe as little more than Uncle Sam's vassals. — Tzeentch

Sure, but the price one pays for a defense results in the loss of other things, like public healthcare, losses in revenues from business regulation and all sorts of things.

The EU should decouple from the US, and instead seek engagement with continental powers like China. — Tzeentch

Yeah, great idea. Work with China. Let me know how that works out. Know who loves Trump? The Vietnamese and Vietnamese Americans. Know why? They hate China, just like he does. That is, a nation that was devastated by the US has aligned itself with the US instead of China because it needs protection from China. Think that one through.

If you're in any way geopolitically conscious, you will keep the US very far from your door. — Tzeentch

If you're Iran that's probably true.

1. As the U.S. scales back on environmental regulations, the EU could solidify its global leadership in climate action. This moment could further the European Green Deal and enhance the EU's position as a hub for green technology innovation and investment. By strengthening partnerships with like-minded regions (e.g., Canada, Japan), the EU could lead a coalition to tackle climate change and attract global investors focused on sustainability.

2. The EU could also capitalize on a more protectionist U.S. approach by attracting foreign investors looking for stable markets.

3. The EU can leverage its more stable stance to exert greater influence in institutions like the UN, WHO, and WTO. By doing so, the EU could shape international policy in ways that align with its standards on trade, human rights, and environmental protection.

4. Given Trump's prior skepticism toward NATO and multilateral security, the EU could take a stronger stance on European defense and autonomy. This might involve further funding for the European Defence Fund and strengthening PESCO (Permanent Structured Cooperation).

5. Policies may lead to a U.S. shift away from renewable energy production, possibly leading to increased oil and gas prices. The EU may want to fast-track its transition to renewables to mitigate potential price shocks and reduce reliance on external energy sources, especially in a time of political instability. — Benkei

1. The US economy will boom under this plan, as global change regulations are expensive. The US will outproduce the EU and will attract places like Canada and Japan to engage in business with them. It is doubtful those nations will prioritize the ethics of global resource management over reduced prices.

2. The US isn't as much protectionist as it is narcissist. It doesn't think it can live by itself. It thinks it's the only one that matters because it's better than everyone else. Particularly under Trump, he's willing to do business with anyone under his terms. Whatever foreign investors the EU acquires are subject to US interests because a deal that disrupts US interests will have negative consequences as the US tries to eliminate the disruption. This isn't to say the US will prevail in any and all competitive efforts against it, but I don't think it's reasonable to think a competive response wouldn't be forthcoming.

3. Those organizations are paper tigers without US support. If you can't get US buy in, they become debate clubs.

4. This is exactly what Trump is trying to motivate. He's trying to save on defense costs by pushing it back on Europe.

5. A shift toward more drilling will reduce oil prices and forestall climate friendly alternatives like electric cars and the like, which many Americans have no interest in anyway. Any drop in cost of living, even if temporary, will make Trump very popular because inflation of basic needs (like fuel, housing, and food) have risen drastically recently.

The solution is for the EU and its many nations is to figure out how to work closely with the US in order to function together harmoniously. You guys are going to have to deal with the devil. I can deal with having to deal with the devil since its the devil my fellow Americans and I created, but for you, wow, that must really suck. You were just sitting there eating your sandwich and this lands on your plate.

The average American doesn't want to be ruled by a woman. I never expected their sexism to be that severe. — javi2541997

You can't say it's because she's black because Obama was in office two terms, so if you can't call the average American racist, you've still got misogyny to argue.

Who'd have thunk Trump's election theft routine was a successful reelection strategy? The man thinks outside the box.

Trump Wins!

Since you weren't going to call it, I got to do it.

This is the NYT election predictor based on the current info. https://www.nytimes.com/interactive/2024/11/05/us/elections/results-president-forecast-needle.html#

It shows 78% chance Trump wins.

Is a software licence in a natural language or in a formal language? — Banno

I speak from the Anglo legal perspective, particularly American. Ambiguity in contracts feeds an industry, and even should there be clarity, ambiguity will be argued because the value of one's claim or obligation will be greatly affected by what the word means.

But in the law, we have a whole system to decide what things mean. And they mean what the person or people authorized to say it means.

But Americans like risk, so we keep things vague and subject to argument. Trials and hearings have the element of surprise, so compromises become of great value. We over pay sometimes just for certainty.

What this has to do with logic is that any argument goes so long as it's colorable. And this sparks creativity if you enjoy such chaos.

So how do you know what's what? You rely upon past decisions, and the art of the analogy and the ability to distinguish comes into play. Such is the significance of precedent. That we've been wrong for 100 years might hold more sway than a rigorous reevaluation. If you can't have clarity from the past, you'd have it nowhere.

Persuasion is the skill of the lawyer. Sometimes that has to with other than being strictly right. But what is "right" anyway?

Nice. Much appreciated.

I don't know what you mean. Example? — TonesInDeepFreeze

https://en.wikipedia.org/wiki/Proof_by_contradiction

Why would I? Every argument is its own thing. If the conclusion deductively follows from the premises then the argument is valid — Michael

Checking the validity of one argument using another is done all the time.

You say that because you're not linking your first argument to your second. That is, I consider Argument 1 to be "an interpretation" of Argument 2, not as two seperate arguments. This is one argument with 2 conclusions, both Q and ~Q. The premises must be true because they are taken as givens. Given P1 and P2, both Q and not Q are implied. The conclusion can be shown to be false by analysis of the same premises.

This is just what the word "valid" means. I think you think it means something else. — Michael

This is what "valid" means: "An argument is valid if there is no interpretation in which all the premises are true and the conclusion is false."

It is raining
It is not raining
George Washington is made of rakes

Per our definition, this argument is not valid becasue all the premises are true and that conclusion is false because you also indicated:

It is raining
It is not raining
George Washington is not made of rakes

I fully understand that the conclusion is also true, so there's that, but that's the nonsense of contradictions. That is, these arguments both meet and do not meet the definition of "valid."

I don't quite understand what you're trying to say here. — Michael

I'm saying that if you can interpret the same argument and obtain contradictory conclusions, then the argument is not "valid" under this definition of "valid":

"An argument is valid if there is no interpretation in which all the premises are true and the conclusion is false."

If we interpret it under my first iteration, we receive the conclusion ~P.
If we interpret under my second iteration, we receive the conclusion P.

We therefore have an "interpretation" in which all the premises of #1 are true and the conclusion is shown to be false via interpretation #2.

2. An argument is valid if there is no interpretation in which all the premises are true and the conclusion is false. — Michael

It depends on the length to which we "interpret" an argument and how you interpret "interpret."

P1. P->~P
P2. P
Conclusion: ~P

can be interpreted as:

1. ~P (P1, which is equivalent to ~P v ~P)
2. P (P2)
3. ~P v P (1, 2, this is correct as either v or &)
4. P - > P (3)
Conclusion: P (2,4 )

These two arguments are interpretations of each other because they maintain truth throughout based upon the premises provided.

Interpreting the same argument, we arrive at contradictory conclusions, which violates the definition of "valid."

This is the explosion issue. Everything follows from a contradiction. The question of validity versus soundness doesn't typically contemplate the contradiction, but it instead contemplates synthetic falsity of contingent premises yet valid logical structure (e.g. All cats can fly, I have a cat, my cat flies, valid but unsound because cats don't fly versus If all cats can fly then all cats can't fly, I have a cat, my cat can't fly.).

I'll put this to rest if someone can find an article outside our blabbing that actually considers the issue of the "validity" of the OP.

In this case, there is no interpretation in which all the premises are true. — TonesInDeepFreeze

A premise is defined as an analytic truth. It cannot be false, regardless of its synthetic falsity. If C means "Cows bark," it is irrelevant if they don't for the purposes of formal logic.

My point is simply that if you have an analytically false premise (meaning it cannot be true in any world), it fails to meet the definition of "premise."

An argument without premises is not a syllogism.

That is to say, accepting what you've argued as true, the OP is not a valid argument because it's not an argument at all.

A premise is an assumed truth.

Alright, so you're substituting the conclusion of the OP from A to A &~A, which can simply be represented by an F, for false.

Back to my truth by negation maneuver then.

The opposite of (A & ~ A) is (A v ~ A), which is a tautology

So, if I can prove from the OP that (A v ~ A) flows, then the argument is invalid because I would have shown F is T.

P1. A -> ~ A
P2. A

1. A&~A (1,2)
2. ~A (1)
3. ~A v A ( 2 disjunctive introduction)

Still not valid, considering the contradiction allows me to prove anything I want, even that T is F.

Yes, I do see the issue of identity versus inference, but that is solved by superfluous logical machinations and becomes a pedantic exercise to maintain the distinction between "identity" and "inference."

For example:

P1. A -> ~A
P2. . A

1. ~A (1,2 m.p.)
2. ~ A v A ( 1 and disjunctive introduction)
Therefore:. A (P2, 2 negation of ~ A)

Note I've not just reasserted P2 in my conclusion, but I've logically deduced that since not A could not be true based upon A being a given premise, by elimination, A must be true.

I'm sure there are more convoluted ways to go about it, but does that satisfy your objection?

You can't deny that A is a conclusion because it is proven by the second premise, which is also A.

To deny A flows from the premises makes the curious argument that a premise has been eliminated by other premises.

In any event, premise 1 is reducible to ~A, so when you couple that with the second premise of A, you then can claim "A and ~A," allowing you to prove whatever you want.

Premise A & ~ A

Inferences:
:
A
~ A
A v C (cows bark)
~A
Therefore C

and so on and on

The argument:

1. A -> ~A
A
therefore ~A
valid

Another argument:

2. A -> ~A
A
therefore A
valid — TonesInDeepFreeze

If under #1, I assume A (the negation of the conclusion) and I prove A from that (as is shown under #2), then I've proven invalidity by negation because I've shown my negation is true.