It seems to me that you must conclude that there is something more than just your thoughts. — Banno

Certainly more than my thoughts but possibly not more than my thoughts and experiences.

Novelty. We are sometimes surprised by things that are unexpected. How is this possible if all that there is, is already in one’s mind? — Banno

I can be surprised when I dream but it doesn’t follow that the things I dream about are “external” to my experience of them. So it’s not prima facie necessary that the same isn’t true of waking experience. It could be that dreams and waking experiences are two different modes of solipsistic existence.

Agreement . You and I sometimes agree as to what is the case. How is that possible unless there is something "external" to us both on which to agree? — Banno

It could be a shared hallucination. We’re both brains in a vat being fed the same misleading sensory inputs. Or it could be that you’re a figment of my imagination.

Error. We sometimes are wrong about how things are. How can this be possible if there is not a way that things are, independent of what we believe? — Banno

If solipsism is true but I believe that solipsism is false then my belief is in error. If solipsism and so mathematical antirealism are true then I still don’t know the square root of pi. Other minds and an external material world are not necessary to be wrong or ignorant.

Perhaps check out this article:

Epistemological Problems of Perception

The discussion in this thread, like all discussions, presupposes the existence of an "external" world in which the discussion is taking place... — Banno

Perhaps at the very least it presupposes that solipsism is false. It need not presuppose the existence of a material world (e.g. it allows for idealism), or that the world we experience is that material world (e.g. it allows for us being brains-in-a-vat).

But as philosophers we tend to want for something stronger than presuppositions, and so even solipsism is an open question.

There is no such a thing as "infinite" number. See this is an illusion, and source of the confusion.
Infinity is a property of motion or action, nothing to do with numbers. Infinite number means that you keep adding (or counting whatever) what you have been adding (or counting) to the existing number until halted by break signal (as can be demonstrated in computer programming).

A set containing 3 numbers can be made infinite, when it is in the counting Loop 1, 2, 3, 1, 2, 3 .... ∞ Therefore a term "infinite number" is a misnomer. I bet my bottom dollar that you will never find a number which is infinite, because it doesn't exist. If it did exist, then it is not an infinite number. — Corvus

Extended real number line

In mathematics, the extended real number system is obtained from the real number system ${R}$ by adding two infinity elements: +∞ and −∞, where the infinities are treated as actual numbers.

BREAKING
Special counsel says there is evidence Biden 'willfully retained and disclosed classified materials' but will not be charged
https://www.nbcnews.com/politics/joe-biden/special-counsel-says-evidence-biden-willfully-retained-disclosed-class-rcna96666 — RogueAI

The full quote, in the body, continues with:

but the evidence "does not establish Mr. Biden's guilt beyond a reasonable doubt."

Biden needs to drop out. There's no way around it. — RogueAI

Sure, after Trump.

But urgently, how do you write matrices and footnotes and equations here? — Lionino

https://thephilosophyforum.com/discussion/5224/mathjax-tutorial-typeset-logic-neatly-so-that-people-read-your-posts/p1

A question for mathematicians: looking at what I've done above, can this be written as a matrix like this?

$\begin{bmatrix}0.1 & 0.01 & 0.001 & \cdots \\ 0.2 & 0.02 & 0.002 & \cdots \\ 0.3 & 0.03 & 0.003 & \cdots\\\vdots & \vdots & \vdots & \vdots \\ 0.11 & 0.011 & 0.0011 & \cdots \\ 0.12 & 0.012 & 0.0012 & \cdots \\ 0.13 & 0.013 & 0.0013 & \cdots\\\vdots & \vdots & \vdots & \ddots\end{bmatrix}$

We can then say that $a_{m,n} = {m\over10^{n+\lfloor\log_{10}(m)\rfloor}}$?

Yes, there are an "infinite number" of infinite sets:

$\{0.1,\text{ }0.01,\text{ }0.001,\text{ }...\}\\\{0.2,\text{ }0.02,\text{ }0.002,\text{ }...\}\\\{0.3,\text{ }0.03,\text{ }0.003,\text{ }...\}\\...\\\{0.11,\text{ }0.011,\text{ }0.0011,\text{ }...\}\\\{0.12,\text{ }0.012,\text{ }0.0012,\text{ }...\}\\\{0.13,\text{ }0.013,\text{ }0.0013,\text{ }...\}\\...$

visual experiences are biological facts that arise under certain conditions of satisfaction — jkop

The epistemological problem of perception seeks to understand the relationship between visual experiences and the external world objects that such experiences are putatively of. Roughly speaking indirect realists claim that the relationship is only causal, whereas direct realists claim that the relationship is more than that.

For example, we mostly agree that we experience a red colour when electromagnetic radiation of a certain wavelength stimulates the sense receptors in our eyes, and that the wavelength of this electromagnetic radiation is influenced by the atomic structure of an external world object's surface.

What we don't agree on is whether or not it is correct – or even sensible – to say that this red colour is a property of that external world object. Indirect realists say that it isn't, whereas direct realists (or at least naive colour realists) say that it is.

Whether it's direct or not might not be a fruitful debate, because the way the term is understood is so diverse as to be hopelessly confusing. — Jamal

On that I agree.

I've tidied up my comment. Perhaps you could explain where you think I've gone wrong?

We adduce a sentence G that is is true (to be more precise, it is true in the standard model for the language of arithmetic) if and only if G is not provable in T.

Then we prove that G is not provable in T. — TonesInDeepFreeze

If all it proves is that every T has the true and unprovable sentence "this sentence is true and unprovable" then it seems vacuous.

Or does it prove that every T has a "natural" example of a true and unprovable sentence, like the strengthened finite Ramsey theorem in Peano arithmetic?

Of course, the particular problem here is really just linguistic — Jamal

I agree. This is the issue with the very meaning of the terms "direct" and "indirect". Each often seems to be defined as the inverse of the other, which is no definition at all.

Traditionally direct and indirect realism provide two competing answers to the epistemological problem of perception. The epistemological problem asks if we can trust our experiences to provide us with accurate information about the nature of external world objects. Direct realists conclude that we can and indirect realists conclude that we can't.

The usual way direct realists phrase their position is just to say that we perceive external world objects. But it doesn't follow from this that we can trust our experiences to provide us with accurate information about the nature of external world objects – unless they mean something very specific by perceiving external world objects.

So what meaning of perceiving external world objects would entail the direct realist's conclusion that we can trust our experiences to provide us with accurate information about the nature of external world objects?

My own take is that the properties of the experience – the look, the sound, the feel, the taste, the smell – must be properties of the external world objects. If they are then we can trust our experiences to provide us with accurate information about the nature of external world objects and if they aren't then we can't.

But what if someone were to say that the properties of the experience are not properties of the external world objects but that we are nonetheless perceiving external world objects? At the very least it seems to show that the usual dichotomy is an overly simplistic division. There should in fact be four options to consider:

1. We perceive external world objects and the properties of the experience are properties of the external world objects
2. We perceive external world objects and the properties of the experience are not properties of the external world objects
3. We do not perceive external world objects and the properties of the experience are properties of the external world objects
4. We do not perceive external world objects and the properties of the experience are not properties of the external world objects

We can perhaps dismiss (3) as a viable option, (1) I understand as naive realism, (4) I understand as indirect realism, but what of (2)?

(2) disagrees with the indirect realist's claim that we do not perceive external world objects but entails the indirect realist's conclusion that we cannot trust our experiences to provide us with accurate information about the nature of external world objects.

Is (2) direct or indirect realism, or something else?

Although I suspect that indirect realists will claim that we perceive external world objects if and only if the properties of the experience are properties of the external world objects, and so that (2) is a contradiction.

No, it doesn't. It is kind of like asking what physics has to say about if the sun suddenly wasn't there. Would Earth continue to orbit for 8 minutes or would it immediately commence a straight trajectory?
Another question: Does an infinite sheet of material (a meter-thick slab of concrete say) result in a uniform gravitational field?

Physics has nothing to say about either case since there is no way to describe what any of the above even means.

Luke is exploring a philosophical question about the implications of various philosophical models on the concept of time travel. The current model seems to be a sort of growing block model, which is full of contradictions, most of which have been left unexplored due to the slow pace of working through even the trivial bits. — noAxioms

Well, I think any reasonable philosophy needs to take into account the facts as we best understand them. According to General Relativity time is the fourth dimension of spacetime. Talking about "overwriting" the "timeline" is like talking about "overwriting" the "heightline" or the "widthline" or the "lengthline". It seems pretty nonsense.

What does it mean to "overwrite" a direction in space(time)?

What does it refer to then? — RogueAI

Nothing really. "Tell me the truth" just means "don't lie".

Let's use Sherlock Holmes as an example. Does Sherlock Holmes exist as an idea? — RogueAI

What does "Sherlock Holmes exists as an idea" mean? Does it mean "the idea of Sherlock Holmes exists"? And does this mean "we (can) imagine Sherlock Holmes"? I agree with this. But this does not entail that the name "Sherlock Holmes" refers to something that exists.

Like with the word "fact" your question abuses the ambiguity of language.

You're talking about fictional things: ghosts, Dracula, Sherlock Holmes, God, etc. Fictional things exist as ideas, otherwise, we wouldn't be able to intelligently talk about them. — RogueAI

If "ghosts" referred to something that exists then ipso facto ghosts exist. Ghosts don't exist. Therefore, "ghosts" doesn't refer to something that exists.

Also, if a lawyer tells a jury, "You'll discover what the truth is when the trial is done" he's not talking about something like a ghost, is he? — RogueAI

Like the noun "ghost", the noun "the truth" doesn't refer to something that exists.

Ghost can refer to an idea, which is a physical thing. — RogueAI

Ghosts don't exist. Therefore the word "ghosts" in the sentence "ghosts don't exist" doesn't refer to something that exists.

But a noun is always a person, place, thing, or idea. Those are all physical things, in the materialist ontology. If a word is correctly being used as a noun, it has to refer to some physical thing. — RogueAI

Did you see the next sentence of my comment (I can't remember if I edited it in after)?

"Ghost" is a noun. The existence of the noun "ghost" doesn't disprove materialism. Ghosts don't exist.

Under materialism, don't all nouns have to be physical? — RogueAI

Just because a word satisfies the grammatical role of being a noun isn't that it corresponds to some object that exists in the universe.

"Ghost" is a noun. The existence of the noun "ghost" doesn't disprove materialism. Ghosts don't exist.

Doesn't truth have to be a physical thing? — RogueAI

No. We just use the word "true" to describe a sentence that we understand as describing some feature of the world. There's no reason to treat "truth" as being some object that exists.

So let's do away with the word "true", like we did away with the word "fact".

Either a sentence describes some feature of the world or it doesn't.

Then you get X := NOT X — Brendan Golledge

Yes, that's how the sentence "this sentence is not true" is translated into symbolic logic.

Is "belonging to" a physical thing? They have to be, right? — RogueAI

Do they? I think this is where you're over-interpreting physicalism. Physicalism, as I understand it, is the position that everything that exists is a physical thing. Balls exist and are a physical thing. I exist and am a physical thing.

Belonging to isn't something that exists, and so isn't something that needs to be physical for physicalism to be correct. If A belongs to B then A is a physical thing and B is a physical thing. There are just two things involved.

The notion that the belonging to relationship between A and B must be some third physical thing that exists seems spurious. And the notion that the belonging to relationship between A and B is some non-physical mental thing that exists also seems spurious.

Whereas before the issue was with ambiguous language, the issue now seems to be with reifying verbs. You're giving too much metaphysical import to language.

I actually deleted that comment because I recognise that mountain height isn’t the best example. I think my previous comment about property is more pertinent.

I think that's a big problem for materialism. — RogueAI

Why? Is the below a big problem for materialism?

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 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?