◇∃xGx→∃xGx looks invalid. — Banno

Given the definition of “maximal greatness” as being necessarily “maximally excellent”, the argument is ◇□ ∃xGx→ □∃xGx.

It is possible that something is necessarily maximally excellent, therefore it necessary that something is maximally excellent.

I don’t know how accurate that website is at parsing modal logics, but my understanding is that modal ontological arguments are commonly accepted to be valid, and so opponents must challenge the premise(s).

https://plato.stanford.edu/entries/ontological-arguments/#PlaOntArg

The “victorious” modal ontological argument of Plantinga 1974 goes roughly as follows: Say that an entity possesses “maximal excellence” if and only if it is omnipotent, omniscient, and morally perfect. Say, further, that an entity possesses “maximal greatness” if and only if it possesses maximal excellence in every possible world—that is, if and only if it is necessarily existent and necessarily maximally excellent. Then consider the following argument:

There is a possible world in which there is an entity which possesses maximal greatness.
(Hence) There is an entity which possesses maximal greatness.

Under suitable assumptions about the nature of accessibility relations between possible worlds, this argument is valid: from it is possible that it is necessary that p, one can infer that it is necessary that p. Setting aside the possibility that one might challenge this widely accepted modal principle, it seems that opponents of the argument are bound to challenge the acceptability of the premise.

It's a false analogy. Vampires aren't non-contingent entities. — Hallucinogen

The greatest conceivable vampire is.

A vampire that exists is greater than a vampire that doesn’t exist.

A vampire that necessarily exists is greater than a vampire that non-necessarily exists.

Therefore, the greatest conceivable vampire is one that necessarily exists.

Replacing the word “vampire” with “intelligence” or “entity” or “thing” doesn’t change the logic.

But I was assuming that by "If there exists something which is TTWNGCBC", you meant the same thing as "If some X is TTWNGCBC," in the arguments you gave when you were previously attacking it. — Hallucinogen

Yes, they mean the same thing.

3 is not an axiom, just a definitional fact. 2. isn't necessary, I just left it there because you put it there. — Hallucinogen

Then the argument is invalid. To make your argument more precise:

1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. God is defined as TTWNGCBC
3. Therefore, God (necessarily) exists

It's still missing the premise that asserts that there exists something which is TTWNGCBC, which as you say is the very intent of the argument.

To make this clearer by analogy:

1. If there exists something which is the greatest conceivable vampire then this thing necessarily exists
2. Dracula is defined as the greatest conceivable vampire
3. Therefore, Dracula exists

The conclusion doesn't follow. I'd need as a premise that the greatest conceivable vampire exists.

I think the modal ontological argument is a much stronger target of discussion.

1. If God exists then it is necessary that God exists
2. It is possible that God exists
3. Therefore, it is possible that it is necessary that God exists
4. If it is possible that it is necessary that God exists then it is necessary that God exists
5. Therefore, it is necessary that God exists

In formal logic:

$\exists xGx\to\Box\exists xGx\\\Diamond\exists xGx\\\therefore\Diamond\Box\exists xGx\\\Diamond\Box\exists xGx\to\Box\exists xGx\\\therefore\Box\exists xGx$

1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. TTWNGCBC is God (or vice versa).
4. Therefore, God (necessarily) exists. — Hallucinogen

How does 2 differ from 3?

How so? — Hallucinogen

Because the conclusion doesn't follow. You would need an additional premise such as:

1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. There exists something which is TTWNGCBC
4. Therefore, God (necessarily) exists.

But 3) is an empirical claim that needs to be shown. It's not something that's true a priori.

The mistake the OP (and Anselm) makes is to derive 3) from 1), but that's a non sequitur.

3. in the above isn't in the original argument by the OP. They don't give the condition "if there exists God..." in the argument. It isn't necessary to include and I don't see a fallacy in the argument without it. All that is necessary is stating that God fits the definition of TTWNGCBC in some way, which the OP did in point 4. — Hallucinogen

Then the argument is:

1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. Therefore, God (necessarily) exists

Which again is invalid.

You're misunderstanding the logic. Look at existential quantification.

I'll be more explicit with my terms to make this clearer:

1. If there exists something which is TTWNGCBC then this thing necessarily exists
2. If there exists something which is TTWNGCBC then this thing is God
3. If there exists something which is God then this thing necessarily exists
4. Therefore, God (necessarily) exists

This is the fallacious argument that the OP has given.

It could go:

If some X is TTWNGCBC, then X necessarily exists
God is an X.
Therefore, God (necessarily) exists.

Not a non sequitur. — Hallucinogen

Then this begs the question, as the second premise just asserts that God exists.

No, the argument is "If some X is TTWNGCBC, then X necessarily exists". — Hallucinogen

If some X is TTWNGCBC then X necessarily exists
If some X is TTWNGCBC then X is God
If some X is God then X necessarily exists

Therefore, God (necessarily) exists

This is what the argument amounts to. The conclusion is a non sequitur.

1), 2), 3) is simplified to:

a) If some X is TTWNGCBC then X necessarily exists

Given 4), replace "TTWNGCBC" with "God":

b) If some X is God then X necessarily exists

Or in other words:

1. If God exists then God necessarily exists

Hence why the argument is just:

1. If God exists then God necessarily exists
2. Therefore, God (necessarily) exists

Clearly a non sequitur.

Libertarian free will remains a possibility. What's your point? — Metaphysician Undercover

That needs to be demonstrated. Disproving determinism isn’t sufficient.

John claims that humans can run at 30mph.

Jane claims that humans cannot run at 30mph because the fastest a human can run is 25mph.

Joe demonstrates that humans can run at 27.5mph.

Has Joe demonstrated that humans can run at 30mph? No.

John claims that humans can make free choices.

Jane claims that humans cannot make free choices because all actions are the deterministic consequence of some prior state.

Joe demonstrates that some actions are the indeterminate consequence of some prior state.

Has Joe demonstrated that humans can make free choices? No.

It's not difficult to understand an apple that is not sweet, or an apple that is not red - but an apple that does not exist? What is it? — Banno

I don't quite get the issue. We seem to understand what we mean when we ask whether or not ghosts or aliens or tachyons exist.

That’s fine. The point is that showing that determinism is false isn’t showing that free will is possible. The libertarian needs to explain what free will requires (e.g. an immaterial soul in your example) and that these requirements are possible.

Are you able to help me to expose the difference between these two conceptions of "free will" which are both incompatible with determinism? — Metaphysician Undercover

If our actions are the consequence of quantum indeterminacy then they are the result of random chance, not free choice.

Senate Republicans (except Murkowski and Collins) blocked the Equal Rights Amendment.

The Amendment:

Section 1. Equality of rights under the law shall not be denied or abridged by the United States or by any State on account of sex.

Section 2. The Congress shall have the power to enforce, by appropriate legislation, the provisions of this article.

Section 3. This amendment shall take effect two years after the date of ratification.

Then as an example, free will (according to the libertarian) is incompatible with both determinism and quantum indeterminacy. A demonstration that quantum indeterminacy is true is a demonstration that determinism is false, but not a demonstration that free will is possible. Free will requires that there is some third mechanism (e.g. agent-causation) for action, and the libertarian's task is to make sense of such a thing and show that such a thing is possible.

Why not? I think that if free will is inconsistent with determinism, then the demonstration that determinism is false is exactly what is required to demonstrate that free will is possible. — Metaphysician Undercover

It might be that free will is impossible if either determinism or some other X is true. A demonstration that determinism is false isn’t a demonstration that this other X is false, and so not a demonstration that free will is possible.

I would say that the Republican party has embraced a new vision of freedom that is defined overwhelmingly as negative freedom, i.e., freedom from constraint, particularly government constraint. — Count Timothy von Icarus

Unless it's drag shows or transgender health care or abortion or critical race theory.

1. That than which nothing greater can be conceived (TTWNGCBC) exists in thought.
2. It is greater to exist in thought and in actuality than to exist just in thought.
3. TTWNGCBC exists in actuality.
4. If TTWNGCBC exists in actuality, then God exists in actuality.
5. God exists in actuality — Epicero

One of these is true:

1. I conceive of [an entity which is all powerful and all knowing and exists] and this entity doesn't exist
2. I conceive of [an entity which is all powerful and all knowing and exists] and this entity exists

The thing conceived (as shown in brackets) is the same in both cases. Anselm's argument makes a fallacious reinterpretation of these as something like:

3. I conceive of [an entity which is all powerful and all knowing and exists and doesn't exist]
4. I conceive of [an entity which is all powerful and all knowing and exists and exists]

He then claims that because the thing conceived (as shown in brackets) in 4) is "greater" than in 3) then 2) must be true, which again is a fallacious reinterpretation.

1. If TTWNGCBC existed contingently, then there would be something greater than it (viz. a version of TTWNGCBC that existed necessarily).
2. Nothing is greater than TTWNGCBC.
3. Therefore, TTWNGCBC exists necessarily.
4. TTWNGCBC is God.
5. Therefore, God is necessarily existent. — Epicero

Your argument appears to be:

1. If God exists then God necessarily exists
2. Therefore, God (necessarily) exists

The conclusion doesn't follow.

Isn't this generally tautological? All unmarried men are bachelors is saying unmarried men are unmarried men. — Tom Storm

If "bachelor" means "unmarried man" then all bachelors are unmarried men.

"Bachelor" can mean "unmarried man", but it can also mean "man who has never been married" or "person with a first degree from a university" or "a young knight serving under another's banner".

The sentence "bachelors are unmarried men" doesn't specify which meaning of "bachelor" is being used, hence the need for the antecedent in the first sentence above.

Broadly, we may say that the doctrine of determinism entails that all the facts about the past together with the laws of nature uniquely determine the future. — Pierre-Normand

Does determinism allow for stochastic quantum mechanics?

In order to make sense of this, it is necessary to delve a little deeper into the arguments that make the contrary thesis seem compelling (and that Jaegwon Kim has formalized as a causal exclusion argument). And it is also necessary to elucidate with some care the notion of possibility that is at issue in Harry Frankfurt's principle of alternative possibilities (PAP). When both of those tasks have been accomplished, it becomes easier to see how an agent-causal libertarianism can be reconciled with merely physical determinism. As I said to SophistiCat, I intend to recruit GPT-4's assistance for rewriting my paper on this topic in order to improve its readability. — Pierre-Normand

I'll be interested in reading that when it's finished.

But until then, what do you make of unconscious determinants of free decisions in the human brain?

There has been a long controversy as to whether subjectively 'free' decisions are determined by brain activity ahead of time. We found that the outcome of a decision can be encoded in brain activity of prefrontal and parietal cortex up to 10 s before it enters awareness. This delay presumably reflects the operation of a network of high-level control areas that begin to prepare an upcoming decision long before it enters awareness.

Suppose you are being challenged to explain how you arrived at some belief, or formed some intention, after some episode of deliberation. The how question usually refers to the justification of your belief, or decision, and aims at probing the cogency and soundness of your justificatory argument. The probe, or challenge, can be conducted (as well as your defense) in complete abstraction of the underlying implementation of your cognitive abilities. — Pierre-Normand

Is this a difference that contradicts determinism?

If someone asks me how I beat some opponent at some computer game, I can describe it in such terms as predicting their moves, using attacks that they’re weak against, etc., or I can describe it as pressing the right buttons at the right times. Your approach to free will seems similar to the first kind of explanation and the determinist’s approach seems similar to the second kind of explanation. But they’re not at odds. They’re just different ways of talking.

So I would think that if you accept the underlying determinism then your position is compatibilist, not libertarian.

Is there a difference between these two sentences?

1. A triangle is a 3-sided shape
2. "Triangle" means "3-sided shape"

Obviously there's a use-mention distinction, but is that distinction relevant here?

1) would be considered an analytic sentence but wouldn't 2) be considered a synthetic sentence? And I think a case could be made that 1) and 2) mean mostly the same thing. Would it then follow that 1) is synthetic and that 2) is analytic? Or perhaps that the analytic/synthetic distinction isn't a significant one?

Or if 2) is in fact an analytic sentence, is it not also a posteriori? Something Kant considered a contradiction?

So we have a number of different sentences:

1. A triangle is a 3-sided polygon
2. "Triangle" means "3-sided polygon"
3. Joe Biden was elected the 46th President of the United States
4. It is raining

Some make a distinction between a priori truths (1), and a posteriori truths (2, 3, 4), and others make a distinction between constant truths (1, 3) and non-constant truths (2, 4).

Is there some significance to these distinctions?

What if I distinguish between truths about the weather and truths about things that aren't the weather?

Then what about a sentence such as "Joe Biden was elected the 46th President of the United States"?

The difference between such sentences is that in one the truth value of it can change such as the sky is blue. In others it remains constant and never changes such as all triangles have 3 sides. — invicta

Is there a difference between these two sentences?

1. A triangle is a 3-sided polygon
2. "Triangle" means "3-sided polygon"

The difference between such sentences is that in one the truth value of it can change such as the sky is blue. In others it remains constant and never changes such as all triangles have 3 sides. — invicta

Isn't that exactly what I said? Some sentences are always true and some aren't.

You claim that there is only one sort of truth, well I claim that there are two. Constant truth which never changes night or day and the variable type that changes the colour of the sky night or day. — invicta

Are you just saying that there are some sentences that are always true and some sentences that aren't?

So Chomsky's not wrong to say that there's no significant difference is he? — Isaac

He didn't say that. He said that there's no fundamental difference. And on that I think his recent remarks on the Republican party suggest that he's changed his mind.

It's an objective assessment of the number of people affected. — Isaac

You've just said that more people are affected by X than by Y. There's no "objective measure" for how many people must be affected by something for that thing to matter. I say it matters that Republicans are restricting abortion rights, and this policy is one area in which there is a significant difference between Republicans and Democrats.

Abortion policy is a complete irrelevance when it comes to the major issues civilisation faces. — Isaac

Well that's a very selfish outlook.

You just seem to be arguing that because the differences between Republicans and Democrats don't affect you then they're not significant. I disagree.

Wealth disparity isn't the only measure of the differences between political parties.

The latter are some actual laws and the former are, as yet, empty promises. — Isaac

They're not empty promises.

Blue states have been preparing to become abortion safe havens

So far in 2022, at least nine Democrat-controlled legislatures have passed legislation affirming that abortion is a legal right, protecting those who seek abortions and perform them, and expanding access to the procedure, sometimes using considerable public funding.

...

16 states and Washington, DC, have laws that protect abortion rights, as of May 1.

...

Other measures to protect abortion rights have passed at least one chamber in several states, but actually enacting them may be difficult. In Washington state, for instance, abortion rights are protected under the law, and lawmakers have considered an amendment that would enshrine abortion rights in the state constitution. But Democrats don’t have a supermajority in either chamber of the state legislature, and state law requires a two-thirds majority to put an amendment on the ballot.

Democrats are doing what they can to protect abortion rights, but where they don't have enough votes the Republicans' anti-abortion policy is a roadblock.

The argument was about how significant they are and I see no one addressing that beyond just declaring them to be. — Isaac

You don't see a significant difference between Democrats wanting to codify abortion rights in law and Republicans passing laws against abortion that don't even allow for exceptions for rape or incest, or when it's a pregnant 10 year old?

At least 11 US states – including Alabama, Oklahoma, Missouri, Arkansas and Texas – have passed legislation that bans abortion without any such exceptions. Where Republicans once believed that absolute bans were unpalatable and “toxic” with voters, the party’s legislators have now adopted the language once promoted by the most extreme anti-abortion activists in the country who say any such exceptions are “prejudice against children conceived in rape and incest”.

A pre-teen girl was denied abortion in the US state of Texas in a case that blatantly highlights the ill aftereffects of SCOTUS’ decision to scrap federal abortion rights. The 10-year-old, hailing from Ohio, was reported to be six weeks and three days pregnant, as reported by The Hill. According to Texas state law, females cannot get a fetus aborted after its cardiac activities begin, around six weeks.

As the OP mentions Chomsky's view in 2008, maybe it's worth considering his more recent view.

Chomsky: Republican Party 'most dangerous organisation on earth' (2017)

Noam Chomsky: The GOP Is a “Gang of Radical Sadists” (2021)

Noam Chomsky Says GOP 'Not a Political Party' but a 'Radical Insurgency' (2022)

I suspect he's changed his mind in 14 years.

So the measure of significance is "Michael says so"? — Isaac

No, I say so because there is a significant difference.

I think it would be childish to suggest that Chomsky literally meant that the two parties were identical in every way. He was obviously making the point that they weren't significantly different. So a counter-argument has to contain measures of significance, not merely the presence of differences. — Isaac

They're significantly different on welfare, healthcare, guns, abortion, and LGBT issues.