This is still hardly a problem though, namely because of Leibniz's Law: there are predicates true of a set that are not true of its members. For instance, consider cardinality. The set {a, b, c} would be truly predicated of having the cardinality of 3, though none of its members have a cardinality of 3 — Kuro

I address something like that here. The set of both metals weighs 3g but none of its members weigh 3g. It doesn't then follow that we should treat the existence of this set as being additional to the existence of each of its members, else the total weight of things which exist would be 6g, which is false in this example.

I have a piece of metal that weighs 1g and a piece of metal that weighs 2g. So the collection of metal weighs 3g. This is the only metal that exists.

What is the total weight of all the metal that exists? 3g or 6g? Obviously 3g. You don't add the weight of the collection to the weight of its parts. So you can't say that the collection exists in addition to each of its parts. Unless you want to be a Platonist and say that the collection exists as some abstract, weightless object, which I think is absurd. — Michael

Well, physical properties like weight reflect the subsuming nature of a collection: a collection doesn't add weight additional to the weights of its parts; it subsumes their weights. — litewave

And the same when it comes to counting the things that exist. The existence of the collection subsumes the existence of its parts. Either you count the collection and say that 1 thing exists, and weighs 3g, or you count its parts and say that 2 things exist, and collectively weigh 3g. You can't count both the collection and its parts and say that 3 things exist, else you then have to say that they collectively weigh 6g.

Since the collection is not identical to any of the coins, it is a different object than any of the coins. — litewave

It's not identical to any one of the coins but it is identical to both of the coins. So you're duplicating entities when you count both coins individually in addition to the collection as a whole. This post really makes this point clear.

"Sum" is just a different name for "collection". If the collection is an object that is not identical to any of its parts then it is a different object than any of its parts - simple, isn't it? The collection is an object in addition to its parts. You dismiss this object because it coincides with the parts but it is something else than any of the parts. — litewave

A collection of two coins has two parts; each of the coins. I am saying that the existence of the collection is identical to the existence of each of the coins; you're saying that it's additional to the existence of each of the coins. So you're saying that the existence of a collection of two parts is additional to the existence of its two parts. That's nonsense.

The existence of a collection of two parts is identical to the existence of its two parts. That's common sense.

Here's another argument:

I have a piece of metal that weighs 1g and a piece of metal that weighs 2g. So the collection of metal weighs 3g. This is the only metal that exists.

What is the total weight of all the metal that exists? 3g or 6g? Obviously 3g. You don't add the weight of the collection to the weight of its parts. So you can't say that the collection exists in addition to each of its parts. Unless you want to be a Platonist and say that the collection exists as some abstract, weightless object, which I think is absurd.

A coin collection is a set that means more that a number of individual coins as the collective can be related in many different ways compared to treating the coins as unrelated units. The sum becomes more than its parts. — universeness

In terms of function or use or conception, sure. But it terms of counting the number of things that exist, no.

I notice the set theorists on TPF are keeping their distance from this thread. :cool: — jgill

Is it even a matter of set theory? Seems to me that it's more to do with the philosophy of mathematics: mathematical realism or anti-realism? I'm clearly on the side of anti-realism.

But if a collection is an object, what is it identical to? It is obviously not identical to any of its parts. — litewave

It's identical to the sum of its parts. If you say that the collection exists in addition to each of its parts then you count each of its parts twice; once when counting the parts themselves and once when counting the collection. This really is such a simple point, I don't understand the objection.

No, it's not, you made two references to the same object. — universeness

And referring to a collection of coins refers to each of the coins in the collection. So you refer to the same coins twice when you say that the collection exists and each coin exists.

That depends on your mode of speaking. You can talk about a collection as being a single object if you want, but you can't then say that because the collection is a single object and because each of its members is a single object then there are three objects. That would be like saying Joe Biden exists and the President of the United States exists, therefore at least two people exist, which is an invalid inference.

If you don't have the collection in addition to each of the two coins, what is the collection then? — litewave

The collection is the two coins. You either think and talk about them as being two coins or you think and talk about them as being a collection of coins. They're different modes of speaking.

You also have the collection of the two coins, which is a third collection (the two coins being the first two collections); it's just a different kind of collection and it is not a coin. — litewave

You don't have the collection in addition to each of the two coins. It's really a very simple point, what's hard to understand?

If the parts exist, their collection necessarily exists too. There can be no parts without their collection and there can be no collection of parts without the parts. The parts and their collection are connected by necessity. — litewave

There are just all possible (logically consistent/self-identical) collections, from the empty ones to infinitely large ones. After all, what would be the difference between a possible collection and a "real" collection? — litewave

The point being made is that if I have two coins then it's not the case that I have the first coin and I have the second coin and I have a pair of coins, such that I can be said to have 3 things. Either I say that I have the first coin and I have the second coin or I say that I have a pair of coins.

That a pair of coins exist just is that the first and the second coin exist. The mistake made is to treat the existence of the pair of coins as being distinct from the existence of the first and of the second coin.

The first is a 1973 decision by the Justice Department's Office of Legal Counsel stating that a sitting president cannot be indicted. For that reason, Mueller said, charging Trump with a federal crime "is unconstitutional."

A federal judge addressed this memo a while back.

Judge tosses Trump's lawsuit to keep his taxes secret

Marrero’s most dramatic conclusion, however, may be his charged swipe at the Justice Department’s legal guidance that a president cannot be indicted while in office.

“The court is not persuaded that it should accord weight and legal force the president ascribes to the DOJ memos,” Marrero wrote.

He noted that the argument a sitting president cannot be indicted often relies entirely on these memos, which don’t carry the force of law or legal precedent.

"[T]he theory has gained a certain degree of axiomatic acceptance ... as though their conclusion were inscribed on constitutional tablets so-etched by the Supreme Court,” he said.

It might be DOJ policy not to indict a President, but that's all.

It could be documents about Chad for all you know. — NOS4A2

I don't think Chad has any nuclear capabilities. The document is likely to be regarding one of the nuclear powers.

Now it’s about a different country’s national security. — NOS4A2

This is one document amongst many, many more. That same report also says:

Among the 100-plus classified documents taken in August, some were marked “HCS,” a category of highly classified government information that refers to “HUMINT Control Systems,” which are systems used to protect intelligence gathered from secret human sources, according to a court filing.

We just don't know the details of these documents (obviously). We'll know more about the national security risk after the intelligence agencies have completed their damage assessment (assuming the results will be made public).

Either way, I wasn’t talking about you. — NOS4A2

Then who were you talking about? The news agencies reporting on the matter? Because, again, the original report specified that it wasn't clear whether or not it was concerning the United States or foreign nations.

But if you want to go ahead and say that other posters here were jumping the gun, then go ahead, but it seems like you're trying to deflect attention away from the fact that Trump was illegally in possession of, and insecurely storing, at least one document related to the defence and nuclear capabilities of some other nation. That's a huge deal. Your attempts to try to defend Trump and make it out to be some Democrat/FBI-led political hoax or whatever is absolutely ridiculous.

You also said this, linking to a report alleging the Trump administration was sharing nuclear tech with Saudi Arabia. — NOS4A2

Because I didn't rule out that it was about U.S. weapons. But neither did I say that it was about U.S. weapons. I'm actually capable of nuance.

We’re now going to pretend that we haven’t been speaking about US nuclear documents this whole time? — NOS4A2

I haven't. I don't know about you. You make a habit of misrepresenting whatever anyone else is saying. This is what I quoted in my original post on the matter:

FBI searched Trump’s home for classified material about nuclear weapons: report

FBI agents searched for classified material about nuclear weapons, among other items, when they served a warrant at former President Donald Trump’s home in Florida earlier this week, the Washington Post reported Thursday night.

Citing sources familiar with the investigation, the Post reported that government officials were deeply concerned that the nuclear documents believed to be stored at Trump’s Mar-a-Lago residence could fall into the wrong hands.

Separately, the New York Times reported the documents were related to some of the most highly classified U.S. programs, and that officials feared they were vulnerable to be stolen from Trump’s home by foreign adversaries.

The Post said their sources did not give details about the nuclear documents, such as whether it involved U.S. weapons or those of foreign countries.

Sensitive information about U.S. nuclear weapons is usually restricted to a small number of government officials, the Post reported, noting that material about U.S. weapons could be an intelligence coup for adversaries, and that other nations could see classified U.S. information about their nuclear programs as a threat.

First it was nuclear documents, now it’s a document describing a foreign government’s military defenses. — NOS4A2

"[A] foreign government's military defenses, including its nuclear capabilities."

The original report saying:

Classified documents relating to nuclear weapons were among the items FBI agents sought in a search of former president Donald Trump’s Florida residence on Monday, according to people familiar with the investigation.

...

They did not offer additional details about what type of information the agents were seeking, including whether it involved weapons belonging to the United States or some other nation.

So what sands have shifted? It seems to me that the new report simply confirms that they found what they were reportedly looking for, and clarifies that the documents were related to some other nation.

Material on foreign nation’s nuclear capabilities seized at Trump’s Mar-a-Lago

A document describing a foreign government’s military defenses, including its nuclear capabilities, was found by FBI agents who searched former president Donald Trump’s Mar-a-Lago residence and private club last month, according to people familiar with the matter, underscoring concerns among U.S. intelligence officials about classified material stashed in the Florida property.

Reification does not target merely the existence of abstract entities, otherwise it's simply another name for the philosophical position of nominalism — Kuro

But nominalism is the position that abstract objects don't exist?

Reification deals with treating abstract entities concretely — Kuro

Maybe I'm being imprecise. I usually think of reification as taking a realist approach to abstractions, and so would include Platonism, not just as saying that abstract entities are "concrete" (which I assume by this you mean "physical"?). But I'll try to be more precise in future if this is a misuse of the term.

You're confusing singletons with just the elements. x, {x}, {{x}}... so on are all not identical with each other, and for instance the singleton set {x} is a member of the powerset but not the set, whose member would be x. — Kuro

I think this is just an issue of terminology. The point I'm making is that if we have a red ball and a green ball and a blue ball, then even though we can consider them in various configurations, e.g. (1) a red ball and a green ball, (2) a red ball and a blue ball, (3) a green ball and a blue ball, etc., it's not the case that there are multiple balls of each colour, and it's not the case that each configuration is a distinct entity in its own right, additional to the red ball, the green ball, and the blue ball. That realist interpretation of sets (what I think of as reification) is, I believe, mistaken.

The existence of the set {red ball, green ball}, if anything, is the existence of the red ball and the existence of the green ball. It's something of a category mistake to treat them as separate (à la Ryle's example in The Concept of Mind of the person who, after being shown the various colleges of Oxford University, asks where the actual University is).

Are you not reading what I'm saying? Sets don't exist as abstract, Platonic entities, distinct from and additional to their constituent parts.

An apple, for example, isn't an abstract, Platonic entity, distinct from and additional to the atoms that constitute it. It's not the case that the atoms exist and the apple exists, but rather the existence of the atoms is the existence of the apple.

If the constituent parts are there, then their collections are automatically there too. — litewave

Not as abstract, Platonic entities, distinct from and additional to their constituent parts.

The existence of each member of a set is the existence of that set.

If a red apple and a green apple exist then I wouldn't say that three things exist: it’s not the case that a red apple exists and a green apple exists and the abstract, Platonic set of both apples exists.

We've been taking as a starting point "snow is white" is true iff p and then discussing p, whereas I think we should instead take as a starting point snow is white iff q and then discuss q.

Snow is white iff snow appears white, or
Snow is white iff snow reflects all wavelengths of light, or
Snow is white iff snow has a mind-independent sui generis property of whiteness

We can then bring this back to truth-predication by understanding that if "p" is true iff p and if p iff q then "p" is true iff q.

"Snow is white" is true iff snow appears white, or
"Snow is white" is true iff snow reflects all wavelengths of light, or
"Snow is white" is true iff snow has a mind-independent sui generis property of whiteness — Michael

I wonder if this helps us address the redundancy view.

1. "'Snow is white' is true" means "snow is white"
2. "Snow is white" means "snow reflects all wavelengths of light"¹
3. Therefore, "'snow is white' is true" means "snow reflects all wavelengths of light"¹

If (2) is true but (3) is false then (1) is false, and the redundancy view refuted.

Or perhaps (2) is false, and that even if snow is white iff snow reflects all wavelengths of light, "snow is white" doesn't mean "snow reflects all wavelengths of light", in which case there is still the issue of explaining what "is white" means. Although perhaps that's a topic for another discussion.

¹ Replace with whichever "snow is white" means "q" is correct

Tarski was certainly critical of modern correspondence formulations, but also said that "One speaks sometimes of the correspondence theory of truth as the theory based on the classical conception.": — Andrew M

He also says, preceding that, "Nonetheless, it is my feeling that the new formulations,
when analyzed more closely, prove to be less clear and unequivocal than the one put forward by Aristotle."

I guess this is why nobody can agree on whether he was a correspondence theorist or not. Ironically he's less clear and unequivocal than we'd like.

Right, so this is an issue of reification. Some people think of a set as being some abstract, Platonic entity that "exists" in some sense, distinct from its members? I'm not a mathematician but that just strikes me as nonsense.

But the cardinality of P(E) can only be greater than E's if there exists elements in P(E) that are not members of E. — Kuro

That's not true. The power set includes repeated members. Taken from the Wikipedia article:

If S is the set {x, y, z}, then all the subsets of S are

• {}
• {x}
• {y}
• {z}
• {x, y}
• {x, z}
• {y, z}
• {x, y, z}

and hence the power set of S is {{}, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}

x, y, and z are repeated.

Right, but q could become an endless string of proposals for the necessary conditions of "truth", as we're already experiencing in this thread anyway. — Metaphysician Undercover

Well that's true of any "X is Y iff Z" so I don't understand that objection.

I just think saying something like "Snow is white" is true iff snow reflects all wavelengths of light is more meaningful than saying something like "Snow is white" is true iff snow is white and so might help us better understand the concept of truth.

Or maybe it will lead us to the redundancy view that truth-predication is vacuous, even if a grammatically useful tool (e.g. so that we can say such things as "what you say is true").

Sure, but if we remove "true" from the equation, then we are off topic of the thread, which is a discussion of truth. — Metaphysician Undercover

Refresh the page, I’ve made an edit.

I don't think it makes a difference.

How isn't it just a more substantial account of p? — bongo fury

Because "p" is true iff p. Therefore a substantial account of p is a substantial account of "p" is true.

We've been taking as a starting point "snow is white" is true iff p and then discussing p, whereas I think we should instead take as a starting point snow is white iff q and then discuss q.

Snow is white iff snow appears white, or
Snow is white iff snow reflects all wavelengths of light, or
Snow is white iff snow has a mind-independent sui generis property of whiteness, etc.

We can then bring this back to truth-predication by understanding that if "p" is true iff p and if p iff q then "p" is true iff q.

"Snow is white" is true iff snow appears white, or
"Snow is white" is true iff snow reflects all wavelengths of light, or
"Snow is white" is true iff snow has a mind-independent sui generis property of whiteness, etc.

Yes, Tarski endorsed the correspondence theory of truth. — Andrew M

I believe there isn't much agreement amongst philosophers on that. Tarski himself says in The Semantic Conception of Truth:

We should like our definition to do justice to the intuitions which adhere to the classical Aristotelian conception of truth-intuitions which find their expression in the well-known words of Aristotle's Metaphysics:

To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, or of what is not that it is not, is true.

If we wished to adapt ourselves to modern philosophical terminology, we could perhaps express this conception by means of the familiar formula:

The truth of a sentence consists in its agreement with (or correspondence to) reality.

(For a theory of truth which is to be based upon the latter formulation the term "correspondence theory" has been suggested.)

If, on the other hand, we should decide to extend the popular usage of the term "designate" by applying it not only to names, but also to sentences, and if we agreed to speak of the designate of sentences as "states of affairs," we could possibly use for the same purpose the following phrase:

A sentence is true if it designates an existing state of affairs.

However, all these formulations can lead to various misunderstandings, for none of them is sufficiently precise and clear (though this applies much less to the original Aristotelian formulation than to either of the others); at any rate, none of them can be considered a satisfactory definition of truth. It is up to us to look for a more precise expression of our intuitions.

...

As far as my own opinion is concerned, I do not have any doubts that our formulation does conform to the intuitive content of that of Aristotle. I am less certain regarding the later formulations of the classical conception, for they are very vague indeed.

So it seems to me at least that he doesn't endorse the correspondence theory but does endorse the Aristotelian theory, which he thinks of as different.

You do know that nuclear codes change between administration. Might you at least clarify that they our outdated and useless nuclear codes? — NOS4A2

When have I ever said anything about nuclear codes?

All of it, it turns out, was misinformation and propaganda. — NOS4A2

I didn't realise you knew what was taken and what was missing.

You believed and tried to sell the idea Trump was selling nuclear codes to Saudi Arabia, perhaps without knowing they change the nuclear codes from administration to administration. — NOS4A2

No I didn't. I referenced a news article that said that the FBI was searching for classified material about nuclear weapons, a Congressional report that said that the Trump administration was trying to transfer sensitive nuclear technology to Saudi Arabia, and then wondered what it would mean if the FBI failed to find what they were looking for, suggesting as a hypothetical that Trump could have sold the information to Saudi Arabia.

My actual quote being "Jesus. Imagine they don't find them. What if Trump sold them to Saudi Arabia."

Nowhere did I say that I believed that Trump tried to sell nuclear codes.

https://thephilosophyforum.com/discussion/comment/728295

You employ propaganda in order to combat propaganda. — NOS4A2

I employ facts. But nice of you to admit that I am indeed combatting propaganda.

Now compare Biden's speech with Trump's recent rally:

... this election is a referendum on the corruption and extremism of Joe Biden and the radical Democrat party.

If you want to stop this destruction of America, you must vote Republican you gotta get out

...

He's an enemy of the state, you know that? The enemy of the state is him and the group that control him, which is circling around him, 'Do this. do that Joe, you're going to do this Joe."

...

The FBI and the Justice Department have become vicious monsters. controlled by radical left scoundrels lawyers and the media who tell them what to do—you people right there—and when to do it.


...

Before our very eyes, our beloved country is being taken over by the very people who turned democracies into dictatorships and into ultimately, ruination.

...

Think of this, think how bad they are, think how evil they are.

...

But this battle is not about me. This is a struggle for the very fate of our republic. Our movement is fighting against a corrupt group of unelected tyrants who believe they can wield absolute power over you, with the help of a willing and very corrupt media.

They think the deep state, not the citizens should be the true masters of this country.

...

We have to smash the grip of his vile and vindictive political class. We have to clean house in Washington, D.C. and we have to restore government for the people.

If we do not, our republic and, indeed, our country will be destroyed and we will never be able to do what is called a comeback. You won't be able to do it. It'll never come back again.

...

The 2020 election was rigged, and now our country is being destroyed by people who got into office through cheating and through fraud.

...

Under a Democrat, all the streets of our great cities are drenched in the blood of innocent victims.

...

The Radical Left Democrat Party is not, in my opinion, a 50 percent party within our country. They're against God, guns, oil, law enforcement, voter ID, tax cuts, regulation cuts, the Constitution and they're against our founding fathers. But other than that, actually, they're quite good. The way they win is to cheat in elections. I really believe that. How can you be against all of those things and for some of the things that therefore and be considered a 50/50 party? I don't believe it.

They cheat like hell on elections all over the country, and they're really good at it.

...

Together we are standing up against some of the most menacing forces, entrenched interests and vicious opponents our people have ever seen. Despite great outside dangers, our greatest threat remains the sick, sinister and evil people from within our own country. But no matter how big or powerful the corrupt radical left Democrats are—and they are corrupt and they are powerful. We have to make them much less powerful.

No anti-Trump analysis of Biden’s’ words is going to convince me otherwise. — NOS4A2

That much is clear. I don't respond to you to because I think I'll finally get through to you. I know you're a lost cause. I respond to you to for the sake of others, combatting your rhetoric/misinformation/propaganda.

There is some evidence Biden knew and even signed off on it.

https://nypost.com/2022/08/23/biden-called-in-fbi-to-look-at-classified-trump-documents/ — NOS4A2

You're referring to this?

The May 10 missive by Acting Archivist Debra Steidel Wall to Trump attorney Evan Corcoran — published late Monday by JustTheNews — confirms that the White House counsel’s office, “affirming a request from the Department of Justice supported by an FBI letterhead memorandum,” asked the National Archives on April 11 to “provide the FBI access to the 15 boxes for its review within seven days.”

The White House asking the National Archives in April to give access to the FBI to the boxes returned In January is evidence that Biden knew and signed off on the search warrant issued in August? You really are reaching.

I'm referring to the Facebook stuff and the whistleblower reports. — NOS4A2

FBI responds to Mark Zuckerberg's claims on Joe Rogan show about Hunter Biden's laptop

Zuckerberg said that while the FBI didn't specifically name the New York Post article about Hunter Biden, it "fit the pattern" of what the FBI warned about.

He defended the agency, calling it a "legitimate institution," which prompted him to take the warning seriously.

The story was allowed to remain on Facebook, but with limited exposure.

In a statement, the FBI said it routinely provides entities of potential threat information, but it "cannot ask, or direct, companies to take action on information received.

Meta responded via Twitter saying quote, "the FBI shared general warnings about foreign interference, nothing specific about Hunter Biden."

Now he is ramping up his rhetoric, treating his opponents like domestic terrorists. — NOS4A2

You sure like to engage in your own rhetoric. This is what he said:

Donald Trump and the MAGA Republicans represent an extremism that threatens the very foundations of our Republic.

Now, I want to be very clear, very clear up front. Not every Republican, not even the majority of Republicans, are MAGA Republicans. Not every Republican embraces their extreme ideology. I know, because I’ve been able to work with these mainstream Republicans.

...

And here, in my view, is what is true: MAGA Republicans do not respect the Constitution. They do not believe in the rule of law. They do not recognize the will of the people. They refuse to accept the results of a free election, and they’re working right now as I speak in state after state to give power to decide elections in America to partisans and cronies, empowering election deniers to undermine democracy itself.

MAGA forces are determined to take this country backwards, backwards to an America where there is no right to choose, no right to privacy, no right to contraception, no right to marry who you love. They promote authoritarian leaders, and they fanned the flames of political violence that are a threat to our personal rights, to the pursuit of justice, to the rule of law, to the very soul of this country.

So, no, he isn't treating his opponents like domestic terrorists. He's saying that a specific subset of his opponents are trying to undermine the principles of democracy and restrict personal rights.

He has already sent his goons to rifle through Trump’s documents, perhaps worried what sort of info Trump had on him. — NOS4A2

There is no evidence that he directed the search, and no evidence that he even knew about it beforehand. And they weren't there to search Trump's documents but to search for the Government's documents which Trump was illegally retaining. And you're inventing a motivation.

Since we now know the FBI was working to suppress info that would reflect badly on Biden — NOS4A2

If you're referring to the Facebook stuff, they just warned them to be on the lookout for Russian propaganda. It was Facebook that made the decision about which specific stories to suppress.