Pentagon ran secret anti-vax campaign to undermine China during pandemic — Tzeentch

Just thegreatsatanthings :sparkle: :hearts:

a=0.3333333
10a=3.3333333
9a=3
a=3/9
a=1/3
1/3 = 0.33333

b = 0.12121212
100b=12.12121212
99b=12
b=12/99
12/99=0.121212

One could argue that the equality does not hold, or that 1/3 does not equal 0.333...

There is
a=0.999...,
10a=9.999...,
10a-a=9,
9a=9,
a=1 therefore 0.999...=1

Of course, one could (with undesired consequences) reject the first two steps of this proof.

There is also the sum of an infinite geometric progression of term a = 9*10^(-n):

0.999 = 0.9 + 0.09 + 0.009 +...
= 0.9/(1-0.1) = 0.9/0.9 = 1

Then again, one could reject that the equation for the sum applies. The equation of the infinite sum relies on the notion of limit, and it is the notion of limit that is at play on the 0.999... debate.

The argument that 0.999... only approximates 1 has grounding in formal mathematics. In the 1960's, a mathematician, Abraham Robinson, developed nonstandard analysis (Keisler, 1976). In contrast to standard analysis, which is what we normally teach in K-16 classrooms, nonstandard analysis posits the existence of infinitely small numbers (infinitesimals) and has no need for limits. In fact, until Balzano formalized the concept of limits, computing derivatives relied on the use of infinitesimals and related objects that Newton called "fluxions" (Burton, 2007). These initially shaky foundations for Calculus prompted the following whimsical remark from fellow Englishman, Bishop George Berkeley: "And what are these fluxions? ... May we not call them ghosts of departed quantities?" (p. 525). Robinson's work provided a solid foundation for infinitesimals that Newton lacked, by extending the field of real numbers to include an uncountably infinite collection of infinitesimals (Keisler, 1976). This foundation (nonstandard analysis) requires that we treat infinite numbers like real numbers that can be added and multiplied. Nonstandard analysis provides a sound basis for treating infinitesimals like real numbers and for rejecting equality of 0.999... and 1 (Katz & Katz, 2010). However, we will see that it also contradicts accepted concepts, such as the Archimedean property — https://files.eric.ed.gov/fulltext/EJ961516.pdf

Mind you that this article is not written by experts.

I am considered a ultra-high net worth individual. What about you? — Tarskian

You write like someone who is on welfare. The words "ultra-high net worth" have never come out of the mouth of a rich person.

Vector calculus was not a subject in my degree. It is of absolutely no use in operations research. — Tarskian

Yeah, I would imagine that someone in "operations research" does not know basic calculus or can't even go to an online calculator to plug it in like any high schooler would.

Post-grads are people who don't make money and who will never make money. I don't want to be compared to them. — Tarskian

The supposedly pious believer turns out to be a degenerate who needs to lie to online strangers about his Calvinistic god: money. Not shocking.

I became stinking rich from writing code that deals with elliptic-curve cryptography (ECDSA) at a point at which no university even taught it. — Tarskian

No, you didn't. Good job confessing your economic status, which no one is interested in or asked about, by compensating.

By the way, how much money have you already made from vector calculus? — Tarskian

Vector calculus is essential for the operation of the machine you use to write uneducated nonsense on.

Furthermore, vector calculus has nothing to do with the foundations of mathematics. — Tarskian

No shit.

Seriously, you are more stupid than you think. — Tarskian

Did you win many pizza coupons at the "operations research" department, SEAsia sexpat?

As a European myself — Tarskian

:lol: :lol: :lol:

For a relatively short time, atheism allows to increase national income. — Tarskian

No, it doesn't.

Instead of investing in producing the next generation, they have to import it from people who did. — Tarskian

There is no meaningful correlation between religiosity and birth rates. Atheist Czechia has much higher birth rates than deeply religious Spain, Greece, and Italy.



Any other malformed idea of yours that you want me to educate you about?

You fail to understand the discussion about non-standard models of arithmetic. — Tarskian

There is nothing to understand. You are writing gibberish about free will and Gödel.

Parts of model theory are my personal interest. It is my hobby. I am semi-retired. I can royally afford to spend my days reading up on what I like. Of course, I did not waste my time on additional degrees. Why would I? — Tarskian

This is the same script run by the clinically online on welfare everytime they are pressed about their non-existant qualifications.

By the way, I am not interested in vector calculus. — Tarskian

The crank cannot solve a simple mental computation that every single person in science and technology learns in their undergrad. And yet he insists that he understands things that would only be taught to people in mathematics post-grad.

No one who seriously studies foundations of mathematics is ignorant of nabla and the cross product operator — it is like solving quadratic equations and not knowing how to calculate the area of a triangle. Unserious crank rambling nonsense about a field he hasn't been introduced to.

Everybody agrees that mathematics applies to the physical world, but nominalists will broadly say that 2+2=4 is not about the world, so it is not true of it. — Lionino

That is the advantage of platonism over nominalism on the matter of the application of mathematics. Each different nominalist program for mathematics will have a different solution for it — Azzouni's solution being deflationary (dissolving the issue).

I personally think the issue is misguided.

Again, complete gibberish. Gödel has nothing to do with multiverses.

Go ahead and solve the following operation:

▽×(2xy,2yz,2xz) — Lionino

Let's see if that post-grad talk about math is backed by undergrad knowledge.

If it isn't, then it means that there is more than one universe that interprets the same theory. The existence of inexplicable truths such as free will therefore implies that our universe is part of a multiverse. — Tarskian

Complete gibberish.

western civilization — Tarskian

Another episode of Yankees trying to lump themselves in with Europe by pretending a shared "civilisation".

Unlike religion, atheism is known to be a dangerous, society-terminating form of bullshit. — Tarskian

Statistically false by all acounts. The less religious a country is the better it is doing.

Mind coming from matter is indeed miraculous, and also embarrassing to scientists recently.
https://www.scientificamerican.com/article/a-25-year-old-bet-about-consciousness-has-finally-been-settled/

I predict more scientists losing more bets to philosophers. Ditch the whole "matter" thing entirely. There is no matter. It's all mental stuff. — RogueAI

This piece, one of the worst written I've read all year, does not support your text around it. On the contrary even.

If mathematics applies to the physical world, surely it is true of it? — Ludwig V

Everybody agrees that mathematics applies to the physical world, but nominalists will broadly say that 2+2=4 is not about the world, so it is not true of it.

The Engineers of Prometheus, pictured in page 12, are God(s) according to the redefinition proposed. However, nobody thinks the Engineers are gods, they are highly intelligent extraterrestrial creatures who created human beings — metaphorical usages of the word "god" nonwithstanding. That is not therefore how the word is used. It is not just a refinement but a redefinition, as the set of individuals defined by each, the traditional and proposed, don't overlap.
The redefinition therefore is wrong and would be refused by any lexicographer.
This is not a matter of metaphysics or theology, it is a matter of language.

Ever hear of pantheism? — Pantagruel

In common speech, it is silly atheism dressing up with the robes of changing the definitions of "God" and "universe" — the former which you are doing. If you are talking about Spinoza's God, it is the first motor, where the lines between natural and supernatural blur. I will challenge you once again to bring up an academic. Note that Spinoza's God is quite in line with Cambridge's definition.

This is a complete non-sequitur. I said that the description of the being(s) that I provided did not preclude them being consistently identified with the being(s) that conformed to the Cambridge definition that you supplied. — Pantagruel

Of course, the "highest form of consciousness" does not preclude being a spirit that controls reality. "Being a banana" does not preclude from "being 5 feet long". Yet, being 5 feet long and being a banana are not the same thing. Your definition and the accepted definition of God are not the same thing, they often don't overlap, like banana and being 5 feet long, therefore your definition is wrong. This is not a "non sequitur" (incorrectly used and hyphenated), or a false analogy, it is a perfectly descriptive analogy of your complaint.

Nevertheless, you say "the main defining feature of of a god is...". "Main defining feature" of something is exactly a definition, your definition of god is wrong, as the dictionary and any attentive English-speaker will confirm. When someone is learning English, no one teaches "God" the way you think of it, they teach it as it is in the dictionary.

Which isn't to say the Cambridge definition is authoritative, because it isn't. — Pantagruel

The Cambridge definition gives a good definition of what people mean by the word 'God'. You can complain about authority as you give the ability to communicate with fellow English-speakers.

who denies the validity of the concept. — Pantagruel

Most atheists don't deny the validity of god, just don't believe in its materiality. Your comment that atheists should not comment on god is ridiculous. Mathematicians prove theorems by showing its opposite is impossible. They don't believe in the opposite and yet they are working with it. Some physicists who work with relativity and the theory behind white holes, with string theory don't commit to the idea that those structures actually exist. Many philosophers who work with ontological proofs of God don't actually believe in god or in the effectivity of ontological proofs.
Your comment is plainly absurd and sophomoric.

You also should not comment on God, as what you understand by the word "God" is completely distinct from what God actually means. You don't necessarily believe in God as what the word actually, otherwise this discussion wouldn't be happening.

That is probably why western negativity towards Islam disturbs me so much. — Tarskian

The reason is probably because you have not read European history and don't keep up with modern European politics.

Sorry, that's just plain ridiculous. — Pantagruel

Ok, I challenge you to bring up any academic citing (not mentioning) another academic using the word "God" in a way that is not supernatural.

This doesn't in any way shape or form contradict the generalized description I provided. — Pantagruel

The definition of mathematics doesn't contradict the definition of banana, and yet the two are not the same thing.

So why should the concept of god not likewise be amenable to...refinement? — Pantagruel

Not slightly the point of what you are quoting there, but Spinoza and neoplatonists refined the concept of God. What you are doing is not refining a concept but changing the meaning of a word completely. In any case, everybody is free to reject your definition, so they can stay atheists.

If you claim not to believe in atoms, you are certainly the last person that someone should talk to who is interested in developing a theory of atoms. — Pantagruel

Unintentional denial of the scientific method and proofs by contradiction right here.

How big of an imbecile does one have to be to really believe the US President “runs the country”? — Mikie

Preparing the rhetorical environment for "Who cares if the president is a disabled vegetable? There are many people in executive functions besides just the president!!".

AI already surpassed the average person in that it runs on a much more interesting and unpredictable script — the similarity is that both are soulless automatons.

So when you use the appropriate sense of the "world", and say that realism is true of the world, you are saying that realism is true of some parts of the world - the abstract parts? — Ludwig V

In the case of platonism, yes. In the case of immanent realism, it would be true of some (physical) parts of the world. Now, a finer distinction: in the case of psychologism/conceptualism, true about our minds (so mathematics would reduce, prima facie, to psychology if psychologism is true).

Since they are both true in the abstract world, but not simultaneously in the physical world, would it not be helpful to add that explanation? — Ludwig V

I don't know about neaty gritty details of platonistic matemathics — if mathematics is true of the physical world too or rather only applies to it —, if such shenanigans are even developed that deeply, but Euclidean geometry applies to a car going from the theater to the restaurant (the surface of the city is flat), non-Euclidean to an airplane going around the Earth (spherical geometry) or things interacting in space-time (hyperbolic geometry).

So under these axioms, in S5, every possible positive property is exemplified in at least one being, meaning that necessarily there are innumerably many beings — every possible being with a certain set of positive properties necessarily exists. — Lionino

Trying to put this in logical terms, I think it would be ∀φ[□∃xφ(x)]. From source [3]:

It would seem to even follow that there are near-perfect, but defective, demi-gods and all matter of other theologically repugnant entities. Gaunilo concluded, reasonably enough, that something must be wrong with the argument.

What academy are you referring to? — Pantagruel

The one that academics are part of.

The main defining feature of a "god" is having abilities which transcend human understanding — Pantagruel

Cambridge dictionary seems to disagree:

a spirit or being believed to control some part of the universe or life and often worshipped for doing so, or something that represents this spirit or being:

In any case, that is not a defining feature because it is nonsense. Our modern ability to solve differential equations in our head transcends the human understanding of Bronze Age Europeans, and yet we are not gods.

If you are going to set yourself up as presenting an authoritative definition of "god," I would think that advertising yourself as an atheist isn't the most credible first step.

Let's face it. Atheists, by their own declaration, are really only qualified to speak about what god is not. — Pantagruel

The epistemic stand of a person has zero bearing on whether they are qualified to define something or not. In fact, nobody is qualified to define anything, there is no such thing as a private language, the definitions are given to us by the society around us. Whether someone is qualified to redefine a word depends on whether they are an authority in the field that that jargon belongs to.

If that seems reasonable to you. — Pantagruel

Just checking for consistency.



Is the above a God for you? In the universe of Ridley Scott's Alien (which wasn't even supposed to be an Alien movie but alas), going off your definition, the answer should be yes. Yet, nobody in the academy, when discussing philosophy or theology, has the above in mind when talking about God. Redefining words to mean something completely different from what they do is not interesting. There are non-flawed definitions of "God" that don't entail talking about the above.

You edited your comment. I think I see the confusion. I thought you were referring to lines 3 and 4 of this post. But I guess you were talking about this.

For the record, I don't think the criticism, in the post you referred to, is successful. I developed why in my post last page.

I have as much right as the next person to flesh out the concept of God in whatever ways make the most sense to me. — Pantagruel

Do you then grant that I have all the rights to flesh out the concept of God as the banana that I will eat in 15 minutes before leaving for the gym?

It is not from S5 but from Gödel's definitions. When you go to D3 in the OP, NE(x) is basically the exemplification of all properties of x, so ◊∃x(P(x)∧NE(x)) ↔ ◊□∃xP(x) where NE is necessary existence and P is all positive properties except necessary existence.

If you assume the conceptualization entails the non-existence of the thing then perhaps it is the conceptualization that is flawed — Pantagruel

If the conceptualisation of something is flawed because it entails contradiction, what people have in mind is demonstrably false and what can exist is something other than what people have in mind. Assigning this or that label to this or that conceptualisation doesn't change the facts about the world (up yours, Early Wittgenstein).

Also, you have a modal operator after a quantifier. I don't think S5 can do anything more with that than to regard the quantified formula as just a sentence letter, so S5 sees pEx(nPx) as just pQ. — TonesInDeepFreeze

If it is worth something, ◇∃x(□Px) → □∃x(Px) is valid in S5.

I missed these posts.

Perhaps I misunderstood. What then? — fishfry

The objects that constitute both Euclidean and non-Euclidean (the unending many of them) spaces are abstract and both exist. Those objects may be applied in our scientific theories because a description of these objects can also describe some phenomenons in the real world. The problem is how do we get knowledge of these objects, if they are not physical? That is Benecerraf's problem.

If both of these are true, then we need to be very careful about what we mean by "the world". There is an application that takes "the world" to exist in space and time. — Ludwig V

This is not one of those cases. The world here is meant by everything that is not created by the mind (realism X anti-realism), not just what is located in space-time (physicalism).

It seems to me you are thoroughly confused.

The fact that posters decided to pile on a premise that the thread rests on rather than the thread itself is the posters' fault, not OP's.

For example https://thephilosophyforum.com/discussion/15250/if-existence-is-good-what-is-the-morality-of-life starts by setting a premise and establishing that the thread is not the place to discuss that premise. The first reply to that thread is in fact praising it for the way it was set up and "making the boundaries of the discussion clear". I think the boundaries of this thread were clear, Leontiskos thinks so too.

The book comment applies to every thread here that puts forward a thesis. It is silly.

Te encantaría leer a Austin, sin duda. :smile: — javi2541997

No dudo que me encantaría leer los libros de cualquier filósofo, pero la vida es curta, y aun me resta mucho para leer.

Treating and debating ethics, or meta-ethics, with the minutia and precision that metaphysics needs, ends up in what has to be the most boring and unconclusive discussions.

This anxiety seem to stem from some sort of mind-body dualism. "Why am I in this body and not another?". As soon as we accept that our mind is exactly the consequence of the body, and I could not have possibly been born into the body of a bee or cow because the "I" is exactly determined by the body, the anxiety vanishes.

My post doesn't say anything that other replies here haven't said in other ways.

:up:

So if your definition of God is that God is the highest form of consciousness, then God by definition does exist. — Pantagruel

Anything can exist as soon as we arbitrarily and unilaterally change the definition of "anything". But what we get is not informative, it is a tautology.

P. Q. ¬(p → q):
0. 0. 0
0. 1. 0
1. 0. 1
1. 1. 0

P. Q. (p → ¬q)
0. 0. 1
0. 1. 1
1. 0. 1
1. 1. 0 — Lionino

The first table by the way is a NOR gate with an inverted P, and the second table a NAND gate. Physically different.

Ok

Your transition to from 3 to 4 is basically ◊∃x(P(x)∧NE(x)) ↔ ◊□∃xP(x).
Your reply to Leontiskos fights with the definition of God including necessary existence or not. I don't think it has to include it. As you said:

Imagine that some intelligent, all powerful, all knowing, creator of the universe actually does exist, but that because it doesn't necessarily exist then we refuse to call it God, as if the name we give it is what matters. — Michael

I don't see any issues because, differently from others, for me your 3 and 4 are equivalent. Once we establish ◊∃x(P(x)∧NE(x)), we can then claim ◊□∃xP(x). The issue with this transition, as I pointed, is that it invites a Gaunillon counter-argument:

So, there would an infinite amount of lesser gods each having all positive properties except one, except two, and so on. — Lionino

The proof we are discussing is Gödel's proof. From what I've read, epistemic modality has nothing to do with the proof, the proof uses S5. On the contrary, Gödel is trying to prove exactly something it is clear we have no clue about.

what the operators are supposed to mean ('◊' and '□') — Leontiskos

Many-worlds semantics.

But then:

Otávio Bueno and Scott Shalkowski (2015) adopt modalism about modality. They maintain that there is no reductive analysis of modality in terms of non-modal facts or properties. For arguably one cannot reduce the truth of “It is possible that P ” to “It is true in some world, w, that P” without wondering whether or not w itself is possible or impossible. — SEP

and as soon as they try to nail them down other logicians will disagree — Leontiskos

Such is the life of the philosophuck.

Presumably Godel is making the same sort of error, equivocating on "possibility." — Leontiskos

That would be out of scope just like discussing whether S5 obtains or whether existence is a predicate. We can make a thread for ontological arguments in general.

Some points.

I have seen elsewhere that some think that D1 is basically Zermelo-Russell's paradox. I would say it doesn’t imply the paradox. The set of all sets argument is paradoxical precisely because it’s universal. D1 however is restrictive, “all positive properties” isn’t the same as “all properties”. Having all of something isn’t an issue, an all-colourful being can be defined as “having all colours”, such a being is not only possible but also exist in real life. Stars emit all frequencies in the visible light spectrum.

Then that, for A3 to be valid, D1 cannot yield paradoxes (violation of LNC). I would say it doesn’t end up in paradox because of A1 — it makes sure that no positive properties conflict with each other. For example, being colourless is the denial of being colourful, only one of those is positive. Being transparent ←→ being colourless, therefore being transparent is also the denial of being colourful (this example ties in with A2).

All we are left with is the claim that it is possibly necessary that there exists an X such that X is all powerful, is all knowing, etc. — Michael

The claim that ◊□∃xP(x) where P is every positive property besides necessary existence.

The claim comes T1 and D1. A God possesses all positive properties. Positive properties are possibly exemplified. Then we have C. Being that necessary existence is a positive property, and it is possibly exemplified, we end up with ◊□∃xG(x). Your argument seems to be that, to take advantage of S5, for ◊□p ⊢ p, we must pull the predicate NE out of the variable, so we end up with ◊□∃xP(x) where P is every positive property except necessary existence, and since necessary existence has been pulled out, we don't know whether ◊□∃xP(x) is true. Is that right?

Yes, the graph presented also goes against my intuition. Though, I think the graph applies to the States only, so then the results aren't all that shocking.

Well, that is the contention over the argument, innit. Some folks will insist that it proves God is necessary in S5. — Lionino

I guess that is what is meant by

Hence, if it is not necessary that there is a god, then there is no god. This by way of setting out what is at stake for the theist - it's all or nothing. — Banno