At T₁ the ball is someone's property. At T₂ everybody dies. Nothing physical has changed about the ball but it is no longer someone's property.

At T₁ the ink markings are a true sentence. At T₂ everybody dies. Nothing physical has changed about the ink markings but they are no longer a true sentence.

There's certainly a sense in which we can say, of the above, that property and true sentences "cease to exist" if everybody dies, but there's also a sense in which the things which were property and were true sentences continue to exist even if everybody dies – they're just no longer property or true sentences.

Again, this is down to the ambiguity of language. Clear up the language and there's less of an issue.

Unless you want to argue that the concept of property disproves physicalism? I think that may over-interpret the physicalist's claim, but I'll leave it to a physicalist to comment on whether or not being someone's property is a physical state of affairs.

The encyclopedia is full of true sentences, even if all brains disappear, right? Is the randomly produced encyclopedia volume in the brainless universe also full of true sentences? — RogueAI

Well let's imagine a hypothetical physicalist:

1. In a brainless universe there are no true sentences; books simply contain ink printed on paper
2. Everything that exists in a brainless universe is a physical object (or process)

Is there a problem with this position?

My initial guess was that they would rule that a criminal conviction for insurrection would be required, but then I read that a criminal conviction has never been required for past cases where the clause was used to disqualify.

It would seem to me that the current court cases are the due process. Each court so far, when faced with the evidence on both sides, has ruled that Trump engaged in insurrection. The Supreme Court is now in a position to do the same.

So if they were to actually rule on the merits of the case rather than just delay, I suspect they will rule that there's insufficient evidence that Trump engaged in insurrection.

Right, I'm getting court cases mixed up. There's another one starting tomorrow about whether or not Trump can be removed from the ballot.

That seems a little wordy. Why wouldn't they just say that a science textbook has a lot of facts about the world? — RogueAI

Maybe they would, but they don't have to.

Or maybe they use the word "fact" to refer to both true sentences and the things that true sentences describe, and so whenever they say something about facts it is important to understand which meaning they are using at the time.

You're getting too confused by ambiguous language, so just forget the word "fact" entirely.

Physicalists claim that for all X the sentence "X exists" is true iff it describes some physical feature of the world, and that many of these physical features of the world would continue to exist even if intelligent life were to die out.

They're going to have to say that a science textbook is full of facts! How can it not be? — RogueAI

They can say that a science textbook is full of true sentences that refer to facts.

For my examples, fact = "true sentence" works fine. — RogueAI

Is that what the physicalist means by "fact"? Or do they mean the thing that a true sentence describes?

The physicalist says an encyclopedia volume is full of facts, right? — RogueAI

It's full of true sentences about mountains. It's not full of mountains.

Did the facts in the book disappear? — RogueAI

What do you mean by "fact"? Do you mean "true sentence" or do you mean the thing that a true sentence describes?

The timeline that would have existed if there were no time travel events gets overwritten by a timeline with a time travel event. — Luke

Does physics describe what the above even means?

So the physicalist has to claim that in a mindless -sorry!- brainless universe, facts still exist. That, to me, seems absurd, but the physicalist can say that an old Encyclopedia Brittanica book still contains facts, even if all the brains in the universe suddenly ceased to exist. — RogueAI

I think there's an element of ambiguity here. For some, the word "fact" means "true sentence". For others the word "fact" refers to the aspect of the world that true sentences correspond to.

So for some "it is raining" is a fact if it is true.
For others "it is raining" is true if it refers to a fact.

The physicalist who says that there are facts in a brainless universe is just saying that the world exists and has certain features even if there's nobody around to see them or talk about them.

And I'll add, arguing over whether or not a fact is a true sentence or the thing that true sentences refer to is a meaningless argument. Just so long as you make explicit what you mean by "fact", use it however you want.

My guess is that they delay it long enough that they can then declare it moot, allowing Trump to be a candidate, but not issuing an actual judgement on the issue.

Welfare is Unconstitutional:

The 10th amendment says, "The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people."

Nowhere in the constitution does it say that the government can take money from one person to give to another person for private use. — Brendan Golledge

Steward Machine Co. v. Davis

Steward Machine Company v. Davis, 301 U.S. 548 (1937), was a case in which the U.S. Supreme Court upheld the unemployment compensation provisions of the Social Security Act of 1935, which established the federal taxing structure that was designed to induce states to adopt laws for funding and payment of unemployment compensation.

Helvering v. Davis

Helvering v. Davis, 301 U.S. 619 (1937), was a decision by the U.S. Supreme Court that held that Social Security was constitutionally permissible as an exercise of the federal power to spend for the general welfare and so did not contravene the Tenth Amendment of the U.S. Constitution.

I don't think you can get away with any arbitrary definition. — Brendan Golledge

You seem to misunderstand what is happening here.

Take the English language sentence "this sentence is English". To better examine this we decide to translate it into symbolic logic. To do that we have to do something like the below:

S ≔ E(S)

Now take the English language sentence "this sentence is French". In symbolic logic this is:

S ≔ F(S)

Now take the English language sentence "this sentence is true". In symbolic logic this is:

S ≔ T(S)

Now take the English language sentence "this sentence is true and English". In symbolic logic this is:

S ≔ T(S) ∧ E(S)

Now take the English language sentence "this sentence is true and French". In symbolic logic this is:

S ≔ T(S) ∧ F(S)

Regardless of whether or not the right hand side is true, these are the accepted ways to translate an ordinary language (self-referential) sentence into symbolic logic.

See also here.

That's not Hilbert's paradox. There's no "magically doubling into 2 rooms" or anything like that. It's simply that whoever is in room 1 moves into room 2, and whoever is in room 2 moves into room 3, etc. In other words, each guest moves up a room. This leaves room 1 empty, ready for a new guest.

Michael said earlier that a definition is not truth apt. I can see how that would be the case if you defined an entirely new variable, such as Z <-> (X -> Y). However, since you are setting X equal to itself, you can do a truth table on it. — Brendan Golledge

These are two different sentences that you seem to be confusing:

1. X ≔ (X → Y)
2. X ↔ (X → Y)

In ordinary language, these mean:

1. "X" means "if X is true then Y is true"
2. X is true if and only if (if X is true then Y is true)

The angles in a true triangle add up to 180 degrees because that is the nature of Existence. — Philosopher19

What is this supposed to mean?

So all you're saying is that in Euclidean geometry the angles of a triangle add up to 180 degrees. And they do so because of the axioms of Euclidean geometry.

Imperfect triangles are imperfect by definition. I'm focused on absolutes. — Philosopher19

What do you mean by an "imperfect" triangle?

or the angles in a triangle add up to 180 degrees — Philosopher19

You should see non-Euclidean geometry where the angles in a triangle can be more or less than 180 degrees.

If definitions aren't subject to truth apt, then can I say, "Let 'X' mean a married bachelor," and that this sentence is not truth apt? — Brendan Golledge

The sentence isn't truth apt, but "married bachelor" is a contradiction.

But neither "if this sentence is true then I am 30 years old" nor "if this sentence is true then I am not 30 years old" is a contradiction, or at least not obviously so.

Is this statement false? If I've done the truth table right, then it means that the first line of the proof is wrong. — Brendan Golledge

The first line is a definition, not a premise, and so not truth apt. It is simply saying this:

Let "A" mean "if A is true then B is true".

What has not been shown to me is how this logically obliges us to view the set of all sets as contradictory. — Philosopher19

It doesn't. This is your misunderstanding. Russell's paradox only shows that the axiom schema of unrestricted comprehension leads to a contradiction, and so that naive set theory is inconsistent.

But the paper went on further to prove that if 6 is false, then 1 must also be false. So, it is a bad definition. — Brendan Golledge

It’s not that the definition is bad, it’s that when we apply the normal rules of logic to some self-referential sentences then we lead to a contradiction. It’s the paradox of all liar like sentences and there’s no agreed upon resolution.

If A is false, then B is not false. Given the definition of the sentence you are using, A is false (or meaningless) and B is true. — Brendan Golledge

Consider these sentences:

1. if this sentence is true then Germany borders China
2. if (2) is true then Germany borders China

Do you accept that (1) and (2) are materially equivalent?

If so then consider these sentences:

2. if (2) is true then Germany borders China
3. if (2) is true then Germany borders China

Do you accept that (2) and (3) are materially equivalent?

If so then (1) and (3) are materially equivalent.

As for your formal logic, I think I am confused about whether you are asserting logic or truth. For instance, I cant tell whether you mean, "if X is true, then Y is true" (I agree with this logic) or "X IS true, and therefore Y is true" (I disagree with this because I think X is either false or meaningless). — Brendan Golledge

Hopefully this is clearer:

1. X means if X is true then Y is true (definition)
2. If X is true then X is true (law of identity)
3. If X is true then if X is true then Y is true is true (switch in the definition of X given in (1))
4. If X is true then Y is true (from 3 by contraction)
5. X is true (switch out the definition of X given in (1))
6. Y (from 4 and 5)

Although one thing to consider is that A → B is equivalent to ¬B → ¬A, and so these are equivalent:

1. if this sentence is true then Germany borders China
2. if Germany does not border China then this sentence is not true

(2) appears to be a more complex version of the standard liar sentence.

When you say the axioms of naive set theory, are you referring to those notations that I asked you to put in clear language. — Philosopher19

Yes.

If so, it seems to me you left half way through trying to clarity on it. — Philosopher19

I'm not interested in teaching you mathematics. I am simply explaining to you that Russell proved that the axioms of naive set theory are inconsistent. That's it. It's not a debatable issue.

See Dunning–Kruger effect.

and that you cannot say x is bigger than y without some measurement/count involved to compare the sizes of the two. — Philosopher19

If you were a mathematician then you would know that this is false.

You're just in no position to argue against Cantor.

Can we establish set x as being bigger than set y without counting the number of items in x and y? If yes, how? — Philosopher19

Yes, we can establish set X as being "bigger" than set Y without counting the number of items in X and Y. We can establish this by using Cantor's diagonal argument. It is a well-accepted mathematical proof. If you were a mathematician you would understand it.

Again, 1 is contradictory. Put it in clear language as to why the contradictoriness of 1 obliges us to reject 2 or to view the set of all sets as contradictory. — Philosopher19

The axioms of naive set theory entail (1). Therefore, the axioms of naive set theory are inconsistent.

This is all Russell's paradox shows. Again, you're showing that you don't even understand the problem.

That is not an answer. — Philosopher19

It is an answer. You just don't understand it because you're not a mathematician.

disagreed that a and 2 are equivalent — Brendan Golledge

Two statements are materially equivalent if either both are true or both are false:

1. A if and only if B

If (1) is true then "A" and "B" are materially equivalent.

So, in the above case:

A) if this sentence is true then Germany borders China
B) if (A) is true then Germany borders China

If (B) is true then (A) is true. If (B) is false then (A) is false. Therefore, (A) and (B) are materially equivalent.

When you used formal logic, you didnt prove that x is true — Brendan Golledge

Are you referring to step 5? As it explains, it simply takes step 4 and replaces X → Y with X, which is allowed given the definition in step 1.

or that x->y is true — Brendan Golledge

Are you referring to step 4? As it explains, it follows from step 3 given the rule of contraction.
X → (X → Y) entails X → Y.

Can we establish set x as being bigger than set y without counting the number of items in x and y? If yes, how? — Philosopher19

Cantor's diagonal argument.

I've seen cantor's diagonal argument and the following objection applies to it: — Philosopher19

It doesn't. If you were a mathematician then you would understand it. Your question simply shows your ignorance of mathematics. You're really in no position to argue against Cantor.

This is where you show that you don't understand the problem.

Naive set theory accepts both the axiom of extensionality and the axiom schema of unrestricted comprehension.

The axiom schema of unrestricted comprehension entails that there is a set that only contains all sets that are not members of themselves (the Russell set). In conjunction with the axiom of extensionality this is a contradiction, and so naive set theory is shown to be inconsistent.

This is all Russell's paradox does.

In response to this, naive set theory had to be changed. Specifically, it had to reject the axiom schema of unrestricted comprehension.

ZFC replaces this axiom with two others; the axiom of regularity and the axiom of pairing. These axioms entail that no set is a member of itself, and so that there is no universal set.

NF restricts the axiom schema of comprehension to permit only stratifiable formulas. This does allow for a universal set.

It's not entirely clear what you're trying to argue. Is it that Russell's paradox doesn't prove naive set theory is inconsistent? Is it that ZFC allows for a universal set? You'd be wrong on both counts. Is it that NF is "better" than ZFC? I'm not entirely sure such a claim would make sense.

Or are you trying to argue that, independently of any set theory, a set that contains all sets that are not members of themselves is possible, therefore only set theories that allow for this are "correct"? That's putting the cart before the horse.

How would a difference in size be established between them when there is no counting involved? — Philosopher19

See Cantor's diagonal argument, which proved that there are higher-order cardinal numbers.

You've already admitted that you're not a mathematician, so it's strange that you think you know mathematics better than Cantor (and Russell).

Let A be the set of all integers.
Let B be the set of all positive integers.

Every member of B is also a member of A, but some members of A are not members of B (i.e. the negative integers).

B is a subset of A.
A is a superset of B.

1 is contradictory if you say set B only contains all sets that are not members of themselves. — Philosopher19

Yes, that's the premise. Let R be the set of all sets that are not members of themselves. This is the Russell set.

If R is not a member of itself then it is a member of itself. This is a contradiction. Therefore we must abandon the axiom schema of unrestricted comprehension.

ZFC replaces the axiom schema of unrestricted comprehension with the axiom of regularity and the axiom of pairing. These entail that no set is an element of itself, and so doesn't allow for a universal set.

Whereas NF restricts the axiom schema of comprehension by allowing only stratifiable formulas. This doesn't allow for a Russell set but does allow for a universal set.

There's really nothing to argue here. Russell's paradox is an undeniable proof that naive set theory is inconsistent. The "resolution" is to replace the problematic axiom with others, which is what has been done. ZFC does it one way, NF another way, and others in other ways.

Yes. Given the axiom schema of unrestricted comprehension there exists a set B whose members are sets that are not members of themselves.

This leads to a contradiction. If B is not a member of itself then it is a member of itself.

Therefore, we must reject the axiom schema of unrestricted comprehension (or the axiom of extensionality, but that would be far too problematic).

is predicate φ "A and B are equal if every member of A is a member of B and every member of B is a member of A"? If not, what is it? — Philosopher19

In Russell's paradox, $φ$ is "sets that are not members of themselves".

It says that A and B are equal if every member of A is a member of B and every member of B is a member of A.