if we take the special case of his argument in which the positive properties P are taken to be the properties that are true for every possible individual — sime

I don't see where that is implied in the argument.

P(ψ)≡¬N(ψ) — sime

If N is supposed to mean necessary existence, that is a rejection of axiom 5.

On the other hand:

Hm, good question!

D1 uses ≡, so I will say 3: "if and only if".

Wouldn't you rather be a European now than during the Protestant Reformation? — RogueAI

If DNA tests are to be believed, there are no Protestants in my genealogy, so I guess I would be the one doing the burning. That aside, yes.

As to music, this is sort of comical. I don't think it's possible to get any more sexually explicit than 2 Live Crew's hits like "Pop that Pussy," or something like Notorious BIG's "Unbelievable." White Zombie's 1995 hit single "More Human Than a Human," literally opens with a clip from a porno, and Nine Inch Nails 1994 hit "Closer" was all over the radio when I was growing up. At the very least, MTV's "The Jersey Shore," maxed us out on hedonistic degeneracy many years ago, lol. — Count Timothy von Icarus

We can bring up degenerate songs all the way back to the 1700s (do not look up "Mozart and shit"). The question is: were those songs being played in teens' parties back then? My knowledge of that is no. On the other hand, I know for a fact equally degenerate songs are being widely played pre-teen parties today.

Yes, you seem to be making that point quite well with the move to religious terrorism — Count Timothy von Icarus

Zeroes in on the very first graph as if the others aren't there

Not that it would matter, we know all of my graphs are correlated either way :^)

although this is generally explained by people being vastly more likely to report it than in prior decades — Count Timothy von Icarus

That is the unfalsifiable excuse people give. Were they braver, they would make the positive statement that "No, you were more likely to be r*ped 30 years ago in Paris than you are now!". Which is a statement that they would not be able to substantiate — lived experience and common sense would tell you before any statistics.

If, in S5, if god is possible then god is necessary, Gödel's ontological proof shows that god is not possible in S5. — Banno

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

If we reject S5 then the answer is "no" and all ontological arguments fail. — Michael

Understood.

4. It is not possible that there necessarily exists a God who is unique and performs miracles, or
5. It is not possible that there necessarily exists a God who is unique and does not perform miracles

Even though "God is unique and performs miracles" is not a contradiction, it might not be possibly necessary, and even though "God is unique and does not perform miracles" is not a contradiction, it might not be possibly necessary. — Michael

To me, this is circumvented by D1, defining God as having all positive properties. That way, performing miracles is a positive property (or not, whatever our choice is). All positive properties are possibly exemplified (T1). So, if performing miracles is a positive property:

"Is it possible that there necessarily exists a God who is unique and performs miracles?"

Yes.

"Is it possible that there necessarily exists a God who is unique and does not perform miracles?"

Since this "God" does not have the positive property of performing miracles, let's call it entity instead.

"Is it possible that there necessarily exists an entity who is unique and does not perform miracles?"

We don't know. The question meaningfully boils down to "is there a being that necessarily exists?". Now:

"Is it possible that there necessarily exists a entity who is unique and has every positive property except performing miracles?"

The answer to that seems to be yes, because necessary existence is a positive property. So, there would an infinite amount of lesser gods each having all positive properties except one, except two, and so on.

This seems to be the reply that Sobel gives (source #7):

Sobel (1987), playing Gaunilo to Godel's Anselm, showed the argument could be applied to prove more than one would want.

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. If there are n many positive properties (necessary existence being one of them), there necessarily are (n-1)! many beings; if n is infinite, there are infinitely many beings. This reminds me of modal collapse, which is implied by the argument put on the OP, and verified by computers that it does collapse.

To discuss the argument that does not imply modal collapse, we would have to discuss Anderson's and Fitting's, which I found be, at a first glance, impenetrable, especially when Fitting uses extensional properties rather than intensional (I don't know what the implication of that are and neither does Fitting by his own admission in his book).

Hey, calling cranks 'the crank' is my schtick. Please don't steal my act! — TonesInDeepFreeze

I would usually use "chauvinist" instead but the subject-individual doesn't qualify as such.

A quick look through his profile will show you are wasting your time.

What do you think of this rendition in English (1-6) of the argument https://thephilosophyforum.com/discussion/comment/913745 to show where the circularity is?

Attempts to reconstruct the homicide rate of medieval Oxford — Count Timothy von Icarus

Well, I have some graphs as well.









The graph for Italy is also conveniently cut off at a time when violence was peaking for political reasons:



Statistics are a tool to be abused by whoever uses them, distorted by whoever makes them.

Anybody who doesn't know what Bob means by moral decay is simply playing dumb. Stockholm, Paris, London, Rome, Brussels are unrecognisable from their 90s counterparts. The cities didn't change their buildings or streets, it is unrecognisably more dangerous. Music now is more obviously overtly sexual than ever, even the 2000s, where the sex was mostly in the undertones. Anybody who travels knows. Anybody who keeps up with mainstream music knows. That part of his thesis is undeniable from the standpoint he is looking at (society is in moral progression from the viewpoint of tolerance).

Violent crime is way down in Europe — Count Timothy von Icarus

That is hardly believable. And it is demonstrably false for national capitals. I'd bet that Western Europe 100 years ago —and sometimes I think even 500 years ago — was generally much safer than it is today when it comes to violent crime.

That society is in moral decline is a common illusion — Herg

A quick comparison of what clothing is acceptable today and 70 years ago, what sort of lyrics features in mainstream music, and all else shows otherwise. I wasn't around in the 60s, but I don't think children were being exposed to sexual content as extremely often as they are today.

Israelite religion was unique in that it broke from this conception but this conception is very ancient. — BitconnectCarlos

Well, Zoroastrianism is just as old if not older and has its own monotheistic creator God.

It's more to do that they are running the exact same playbook as they did with Trump back in 2016 but Britain-edition. The left-leaning press spent two years talking about how Putin and Trump colluded to take the election from Hillary — it was particularly favourable for them to run this lie when Trump technically lost the popular vote and won due to technicalities.

(p → ¬q) ↔ ¬(p → q):

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

Therefore (p → ¬q) ↔ ¬(p → q) is false

Jainism, btw, is not atheistic — BitconnectCarlos

I would say they are atheistic but spiritual. Labels aside, this is how the World History Encyclopaedia puts it:

It is a nontheistic religion in that it does not advocate a belief in a creator god but in higher beings (devas), which are mortal, and in the concept of karma directing one's present life and future incarnations; the devas have no power over a person, however, and are not sought for guidance or assistance in freeing one's self from karmic bondage. In Jainism, it is up to each individual to attain salvation – defined as release from the cycle of rebirth and death (samsara) - by adhering to a strict spiritual and ethical code of behavior.

For the connection between Jainism and Buddhism, you may be interested in this article https://human.libretexts.org/Bookshelves/History/World_History/Early_World_Civilizations_(Lumen)/06%3A_Early_Civilizations_in_the_Indian_Subcontinent/6.02%3A_Buddhism

Which is not-so-amenable to pure affirmation/negation. — tim wood

Correct.

You did not object to my rendering of it. — tim wood

I did. The logical rendering of A1 is as it is written in the image. Your rendering is invalid because it can entail contradictions.

Stop bullshitting and go solve the equation, insane crank.

A1 is an axiom, so it is not tautological, you won't get anything out of putting it in a proof checker.

The (p → ¬q) ↔ ¬(p → q) is invalid by the way, the left side is not the same as the right side.

Maybe I'm reading in too much. — tim wood

Yes, moral-aesthetic sense. What you quoted is me translating A2.

If the university believed that their press release was expired, they would retract it or publish a rectification. — Tarskian

It does not matter what the press says, especially when the researchers involved specifically say in their articles that the press has misrepresented their research several times. What matters is what I have quoted multiple times from the paper itself that says the exact contrary of your uneducated proselytising — wrong, from the several papers from different scholars that repeat over and over that Gödel's original axioms are inconsistent. Go send them an email and ask if Gödel's original axioms are consistent. They are not. You are wrong and you don't know what you are talking about.

How many times have you been kicked out of a meeting for exactly this reason?

So, tell us, when did you lose your job?

It wasn't the economy. We can all see what it really was.

It is actually pointless for you to look for a new job because history is simply going to repeat itself.

You'd better look for a job in which you don't have to interact with anyone, if a thing like that even exists. — Tarskian

Laughably pathetic attempt at a character attack. In the real world I do not have to deal with schizoid incompetents with delusions of grandeur like you babbling about things they are two degrees away from studying, no such issues follow.

You do not understand enough mathematics — Tarskian

Oh, really?

Go ahead and solve the following operation:

$\bigtriangledown \times (2 x y, 2 y z, 2 x z)$

Give the answer with the unit vectors specified, no parenthesis in the notation. On the left is the nabla operator, so we are clear.

Edit: The crank, despite online and active, hides when pressed to give an answer to an extremely basic vector calculus (an undergraduate subject for everyone in science) that one could do in one's head. That is all it takes to show the cranks claiming to know "mathematics" do not have surface knowledge of what they are babbling about.

I think "is there a God" is an obvious question to modern audiences, but it wasn't to the ancients. — BitconnectCarlos

Epicuros, despite believing in (pagan) gods, was an ancient Greek materialist (SEP, Sep 2021). U74, U75, and U76 fragments:
"the nature of existence is atoms and void"
"the nature of the whole universe is atoms and void"

they [Epicureans] held the gods to be immortal and indestructible (how this might work in a materialist universe remains unclear) — SEP

Ancient critics thought the Epicurean gods were a thin smoke-screen to hide Epicurus’ atheism, and difficulties with a literal interpretation of Epicurus’ sayings on the nature of the gods (for instance, it appears inconsistent with Epicurus’ atomic theory to hold that any compound body, even a god, could be immortal) have led some scholars to conjecture that Epicurus’ ‘gods’ are thought-constructs, and exist only in human minds as idealisations, i.e., the gods exist, but only as projections of what the most blessed life would be. — SEP

Many pantheists argue that physical conceptions are adequate to explain the entire cosmos. This is an ancient form of pantheism, found for example in the Stoics, for whom only bodies can be said to exist. [...] Such worldviews make no ontological commitments beyond those sanctioned by empirical science.
[...]
More specifically, God is identical with one of the two ungenerated and indestructible first principles (archai) of the universe. One principle is matter which they regard as utterly unqualified and inert. [...] The designing fire is likened to sperm or seed which contains the first principles or directions of all the things which will subsequently develop. — SEP

The Charvaka were an Indian philosophical school which was strictly materialistic, atheistic, and antidogmatic. They pitched against the Vedic religion and priests that "it could not be proven; it had to be accepted on faith and that faith was encouraged by a priestly class which was clearly benefiting from it at the expense of others" (WHE, Sep 2021). The Ajikiva too did not believe in a particular creator god.
Jainism, one of the oldest documented religions in the world, was actually a godless religion, believing in the holiness of the soul and higher (though mortal) beings.
In his Visuddhimagga, Theravada philosopher Buddhaghosa states "For there is no god Brahma. The maker of the conditioned world of rebirths. Happenings alone flow on. Conditioned by the coming together of causes.".

I cannot because the article is from 11 years ago. The "mistake" the article makes is not crucial for a news piece, but it is for the bullshit you are trying to push. Nonwithstanding, you are wrong and dishonest, completely ignorant of the context and work around Gödel's work, as it has been proven several times here — a crazy individual abusing mathematical and logical language in an attempt to put on make-up on whatever insanity it is you are devising next.

And so forth. I cannot tell if the form of the argument is valid: if I convert it to truth tables, it is not. And what is meant here by "exist." — tim wood

Ignore the schizophrenic above. He has been shown to be an ill-informed sophist in another thread several times. The argument as shown in the OP is verified as valid. You can't easily convert to truth tables.

what is meant by the words "God" (or "God-like") and "positive" — EricH

The definition is given in D1, and see the note in OP.

When we talk of properties naturally we are talking of things like big, small, nice, kind, smart, lazy, etc, not actions like winning this or that war. But let's say somehow "winning WW2" is a property. Is it a positive property or not? So far, we don't know. There are some ways to know if it is not a positive property, which are whether it necessarily implies or is implied by a not positive property, and whether it is contingently positive. So the doubt around a property being positive or not does not help us rejecting the axiom.

I agree with this. Gaunillon also said in his "Liber pro Insipiente" regarding the ontological argument that "there is nothing that may bring something from possibility to actuality".

http://www.ptta.pl/pef/haslaen/a/anselm.pdf

Winning WW2 was positive (presumably) — tim wood

That is not a property, is it?

I don't understand.

A1) What is "positive" and why not both? — tim wood

See note. If being all-knowing is positive, being not-all-knowing is not positive. Beautiful, not beautiful.

A2) How does that work? — tim wood

Everything that necessary follows from a positive property is also a positive property.

On A3, there is this from [3]:

And he might just maintain that the less evident axioms, for example that a conjunction of positive properties is positive, is an assumption which he adopts on grounds of mere plausibility and is entitled to accept until some incompatibility between clearly positive properties is discovered.

As a starting point, I'm guessing that failure to differentiate imaginary/fictional and real can lead to reification; that certainly holds elsewhere. — jorndoe

Anselmo did reply to Gaunillon by basically saying the latter misses the point. The perfect island may be thought of as non-existant, while God, which is exactly the greatest being, may not. On the other hand, if God is complex, we may think of him as having all the attributes he does, besides existence. Then however, Anselmo affirmed the doctrine of divine simplicity, so on that point the counter does not work.

On divine simplicity:

"The doctrine of Divine simplicity [quite nonsensical], according to which God is absolutely simple, has been out of favour for a while now in both Christian theology and philosophy. It is accused of being inconsistent with the doctrine of the Incarnation (Hughes 1989: 253–64), with that of the Trinity (Moreland and Craig 2003: 586) and of being incoherent in its own right (Plantinga 1980: 46–61)." — Collapsing the modal collapse argument: On an invalid argument against divine simplicity (Christopher Tomaszewski)

Though I am not convinced by C.T. that divine simplicity has been out of favour, especially because of the sources given.

https://news.sky.com/story/gravely-concerning-claims-of-russian-interference-in-general-election-to-spread-support-for-farages-reform-13161235?

Leftists will still fall for this, being tricked by the same playbook over and over.

Scott argued that Gödel's argument begs the question — which is to say it is circular. I had the same feeling when first reading the argument two years ago:

1 Being god-like is the essence of a god-like being
2 A god-like being has all positive properties
3 Being god-like implies having all positive properties
4 Necessary existence is a positive property
5 Being god-like implies having necessary existence
6 God exists because he has the property of necessary existence

We give a property to God (existence) before his existence is established. It reminds me of Descartes, simply defining God into existence. The reports on automated results however don't bring that up.

In fact, it is precisely at the present point in the argument that Scott's claim can be localized. Godel's assumption that the family of positive properties is closed under conjunction turns
out to be equivalent to the possibility of God's existence, a point also made in [SobOl]. We will see, later on, Godel's proof that God's existence is necessary, if possible, is correct. It is substantially different from that of Descartes, and has many points of intrinsic interest. What is curious is that the proof as a whole breaks down at precisely the same point as that of Descartes: God's possible existence is simply assumed, though in a disguised form. — [7]

Besides, "essence" here is used strangely. It does not mean "the thing that defines X" or "the thing without which X is not itself", but seems to be "the thing from which all other features of X sprawl". Perhaps it is due to being a translation from German.

More nonsense. I suggest you seek basic education so you don't have to abuse random internet links to appear smart.

So, according to you, what's wrong with this German report? — Tarskian

You are wrong and a news piece is not a reliable source.

Finding: The theorem prover LEO-II showed that the axioms and definitions in Gödel’s original proof script are inconsistent. This result was new to us.

Godel wrote his proof of God for the same reason as why he wrote all his other proofs: because he could. — Tarskian

His proof is not successful and he wrote it because he was a theist and believed in an afterlife.

Yes, but there is a secondary process ("entropy") that sabotages the main process ("preservation of energy"). — Tarskian

Entropy and energy are well-defined physical terms. They have nothing to do with the thread or what Tom Storm is talking about. Hence he not understanding.

Both answers turn out to be false (Russell's paradox).

Decidable propositions are (either true or false). One of both. Undecidable propositions can be (false and false) or (true and true). — Tarskian

Nonsense.

making sure the Democrats will lose — Benkei

Not so fast.

Yeah, he has dementia.

Edit: the press is actually pushing that Biden has a "stutter"? That is braindeadly funny.

Edit 2: Older but recent clip of Biden explaining he doesn't stutter https://x.com/cedrichohnstadt/status/1807232341644837112 he stuttered as a kid from nervousness of speaking publically. Obviously Biden does not have a speech disorder. People have never been around dementia patients, but now they also have never been around people who actually have pathological stuttering. Surprising lack of lived experience.

Constructivism is broader than intuitionism. Intuitionism is one form of constructivism. — TonesInDeepFreeze

Alright, so it was what I was thinking. Just confirming.

For example, Cantor's proof that there is no enumeration of the set of real numbers is accepted by constructivism — TonesInDeepFreeze

I am getting in halfway into the chat. Is "constructivism" here used in the context as related (not synonymous) to Brouwer's intuitionism, or something else?

Since this was in one of my browser tabs, I will make one last post.

NOTE: When I say OP, I am referring to the person I am talking to, not to the first poster of this thread.

As if it hadn't been proven that OP does not care about the discussion around Gödel's ontological proof, and only abuses it to prove "atheists are in denial", the source he himself quotes contradicts him.

It is true that it says:

i. The axioms (and definitions) are consistent. This was confirmed by Nitpick, which presented a simple model within a few seconds.

OP however still does not understand that we are talking about Gödel's original axioms — which are inconsistent. The fragment he quotes however is not talking about Gödel's original axioms. The very paper he quotes in fact includes a quote stating, again, that Gödel original axioms are inconsistent (he would know if he read (past tense) past page 6):

To study the consequences, we have replayed the experiments as reported above, but this time for the varied definition D2. Interestingly, the model finder Nitpick failed to report a model. To assess the situation, we subsequently tried to use the HOL theorem provers to prove the inconsistency of the modified set of axioms and definitions. To our surprise, the prover LEO-II indeed succeeded (in about 30 seconds) in doing so. We have both not been aware of this inconsistency. In fact, related comments in philosophy papers often classify Scott’s modification only as a ‘cosmetic’ change to what is often addressed as a minor oversight by Gödel.

d. Axiom A5 “Necessary existence is a positive property”, theorem T1 and Lemma 2 now imply falsehood.

If Gödel's axioms are inconsistent, it cannot be that Gödel provided a valid proof of a God-like being. The ones who did are those that display consistent axioms. Therefore, Gödel did not prove, "objectionably" or not, that there is a God-like being.

Once again, he is maliciously putting words into the mouths of serious scholars.

Furthermore, in the discussion of the paper, the scholars themselves say:

In philosophical circles, the debate is not yet settled and the allurement of ontological arguments seems far from fading.

However, the media writers are also to be blamed, because of their apparent interest in creating ‘headline stories’, and in copying, nitpicking and obfuscating text passages from each other instead of presenting unbiased, properly investigated and individually prepared information.

However, when the news subsequently made its way to the US, some intentionally (and very naively) obfuscated headlines appeared such as “Researchers say they used MacBook to prove Gödel’s God theorem” or “God exists, say Apple fanboy scientists”.

Moreover, there clearly are theologically and metaphysically relevant objections, including the modal collapse, which are not yet fully settled

There are consistent axiomatizations that non-trivially entail the necessary existence of a God-like being. As for any axiomatization, and not only those with a religious theme, it often remains a ’matter of faith’ to believe in the truth of the proposed axioms in the actual universe.

Our core contribution is a technological approach and machinery that, as has been well demonstrated here, can fruitfully support further logical investigations in this area

Extremely ironic for the sophist, to say the least.

OP does not address any of the contradictions I point out in his insipid posts. He zeroes in on one single point where he may be able to wiggle out and throw smoke screens and goes with it. He did not care at all to address the fact that Anderson himself, one of the people whose work he abuses, defended that the consistent form of the argument is refutable. He also does not care that Fitting's proof reformulates Gödel's argument to talk about extensional properties, while it is believed that Gödel had intensional properties in mind. He does not care about any of that because he does not argue in good-faith.

I'm afraid I couldn't follow your account of this. I'll have to take another look at it later on. But I'm not sure that the project of trying to articulate the Venn diagram is necessarily the best way to go. It may be constraining, rather than guiding, your thinking. — Ludwig V

It is the point of this thread as briefly stated in the OP itself https://thephilosophyforum.com/discussion/14855/metaphysically-impossible-but-logically-possible/p1

As to the issue with Venn diagrams, that is something that other users articulated too. Nevertheless, I think this stems from the definition of metaphysics we are going with. In some thread me and Josh had a short debate about it. If we see metaphysics as broadly synonymous with ontology, the Venn diagram linked there seems to be unproblematic: surely we agree that every physical possibility is also a logical possibility, so one encompasses the other; I think we can also agree that if something is ontologically possible, it is also logically possible, so one encompasses the other; using an etymological fallacy, metaphysics (ontology) is everything beyond physics, so metaphysical possibility encompasses physical possibility.

But it is mostly a musing of mine. There is a lot of talk about the spheres of possibility. I don't expect others to read it fully, but all I can do is recommend the following article: https://plato.stanford.edu/entries/modality-epistemology/ The beginning is the most important part of the article anyway.

Yes, but are the philosophers who want to make synthetic necessity among them? — Ludwig V

I don't get it. There is something missing in this phrase.

However, preserving those concepts doesn't seem to me particularly important. I would be quite happy to abandon all of them. — Ludwig V

I don't disagree, especially when names such as "logically-possible" seem to actually be conceptually/analytically-possible instead of anything to do with logic. The SEP article claims that the epistemology of possibility is the primordial issue at stake in issues such as mind-body dualism and the Berkeley's argument for Idealism. Though this could be true in a sense, I myself think that the issue is a semantic one and, if it is a metaphysical issue in any capacity, it is a derivative issue, not a primordial one — just like p-zombies is completely derivative from dualism/physicalism.

On the talk of necessity and contigency, I recently came across something interesting, "inus" conditions, where necessity and sufficiency blend:

Mackie has famously suggested that causes form a family of 'inus' conditions, where an inus condition is 'an insufficient but non-redundant part of an unnecessary but sufficient condition'.

At Biden's last physical, a cognitive test was not given. The doctors gave him a clean bill of health. It seems to me that the doctors didn't look for what they didn't want to find. If your loved one slurred their words and glitched out and fell down, you'd have the doc give them the test. That's why many think Jill's guilty of elder abuse. — fishfry

It is obvious for every neutral party. The world knows the president of Yankees has pathological cognitive decline. It is only those coping with their political affiliation that must deny it no matter what.

Everybody who has been around dementia patients will see what is going on. The patient's regress to a child-like state is symptomatic of dementia:



The occasional moments of lucidity are not, as some think, proof that Biden is fine. On the contrary. People in the earlier stages of Alzheimer's and dementia oscillate in their cognitive state, have moments of clarity to then relapse.

OP is another crank (like PL) hiding behind fancy mathematical and logical language to push his nonsense, this time the nonsense being religious proselytising, as can be seen from his other posts.