Another thing is that the scientific enterprise does not exist independently of "other phenomen[a] in the history of histories of human civilizations". Obviously, if the human civilization enters a decline (as a result of a global catastrophe, for example), its scientific pursuits will decline as well. Conversely, it is hard to conceive of science undergoing a decline in the midst of a burgeoning civilization.

Can you please address my first point then? — Caldwell

Your point - that science is cyclical - is just postulated out of nowhere. "[J]ust like any other phenomenon in the history of histories of human civilizations" - that's too broad and vague to even discuss.

You should go back and think about this some more.

https://www.google.com/search?q=When+were+clocks+used+for+the+first+time+in+science%3F

In reading a lot of this thread, it strikes me that the many competing theoretical physics models of how the Big Bang might have occured are not particularly useful for answering this question in the sense it is often asked.

Swerve and symmetry breaking as causal explanations don't get at the more essential question: why is there something rather than nothing? From whence all this matter and energy? Or, as important of a question, why does it behave the way it does?

It's unclear to me if physics can give us an answer on this. Physics is the study of relationships between physical forces, but how can it study why those relationships are what they are? — Count Timothy von Icarus

It is unclear to me how anything can give us the "ultimate" answer - one that cannot in turn be challenged with the same question: Why that and not something else or nothing at all?

What does it mean to explain something? We substitute an explanans for an explanandum, reduce what we want to explain to something that does not itself cry out for an explanation, at least in the current context. Something that we assume we already understand. But what could we already understand about a putative ultimate truth? Whence such understanding?

For people who find satisfaction in ultimate explanations, those explanations usually take the form of some religious or metaphysical story or method that appeals to them on some level. When they find something like that, they say to themselves: "Yeah, that sounds about right. I'll run with it." This sort of leap of faith is something that we practice all the time when dealing with minor questions and decisions, as well as matters of taste and preference - we call it intuition, confidence and such like. And that works out alright a lot of the time for practical everyday purposes. But such an approach seems to be incongruous with the sort of thoroughgoing skeptical inquiry that moves us to ask ultimate questions in the first place.

The problem with setting up the existence of matter and energy, or their fundemental behaviors as "brute facts," is twofold.

1. Many things we once considered brute facts have turned out to be explained by even more fundemental forces and particles. The onion keeps being peeled back. A lack of ability to progress in explanation does not mean there is no deeper explanation.

2. This answer is highly unsatisfactory, and explanations of theoretical models with varying levels of empirical support and claims of predictive power all amount to so much window dressing on "I don't know, it is what it is."

Of course, the entire question also seems to presuppose some sort of "God's Eye View" through which all truth corresponds to facts of being. I am not so sure this sort of correspondence epistemology actually makes any sense. On the one hand, it seems beset by the skepticism that has hung like a cloud over modern philosophy, "how can I be sure of anything except for my internal states," and on the other it takes a view of knowledge as somehow pure and ahistorical, when it appears that knowledge is more something that evolved and changes forms over time. — Count Timothy von Icarus

I would agree with this, for the most part. The conclusion that I would draw is not that we must strive towards something more fundamental and less contingent than some brute facts du jour. If there is a "God's Eye View" it is in any case epistemically inaccessible to us. So brute facts are all we have to work with. We just need to recognize them for what they are: contingent, mutable, subject to taste and temperament, and most of all, contextual. The explanations that we settle on depend on what sort of answer we are looking for in a given situation.

That's trivially easy. Premise "A is (im)moral" entails the conclusion "A is (im)moral". I don't see where that gets us.

what I mean by justified is that there are sufficient reasons to perform that action. For example, some people say that killing is wrong because you shouldn't kill other people. — Hello Human

That doesn't really clarify anything. What are sufficient reasons? Who makes the determination? If someones determines to do something upon deliberation, they judge there to be sufficient reasons for doing it. Or, to take a completely different tack, if something happened in a deterministic world at time T, you could say that any earlier or later state of the world contained within itself sufficient reasons for the that thing to happen at T.

I guess a climatology class for someone training in meteorology is like a cosmology class for someone training in orbital mechanics. Good to have for a well-rounded education, but not particularly useful for your future vocation.

Yeah, if there was a way to throttle a poster, limiting the number of comments and topics per day to, say, 10 and 1, then he would've been ok. No worse than the worst posters on the forum. But he was trashing up the forum like TheMadFool on drugs.

Just want to say thanks for your erudite and educational posts!

Warmed-over denialist garbage cribbed from notorious purveyors of science disinformation. Nothing to see here.

I thought Russell's point was that the notion of cause applies only to objects (“particular things”). If the universe is neither an object nor an abstraction produced by the mind, then what is it? — Amalac

But then we agree that the universe is not a thing or object, so that it doesn't exist in the same sense in which an apple exists (or would you say a quantifier exists?), and therefore there is no sense in applying the notion of cause to it as we would with an apple, no? — Amalac

Whether or not the universe can be thought of as an "object", what's important in this context is whether it is the sort of... thing that can stand in a causal relation to something else. It's not just a question of mereology either: an apple, or a basket of apples, can be put into a causal relation, no problem. But can the universe?

It's easier when the deficit angle is large - e.g. 90 degrees, as in the example given in the link above. If after making three right turns at a right angle you end up on the same spot where you started, there's no escaping the conclusion that you are living on a curved world!

Yes, you can detect intrinsic curvature on a sphere, even if it is not embedded in 3D space. Angles in a triangle won't sum up to 180 degrees.

http://www.thephysicsmill.com/2015/12/27/measuring-the-curvature-of-spacetime-with-the-geodetic-effect/

Well, I just don't see how we can tell whether the universe is a set in the same sense in which we are sets of atoms, or merely a set in the sense in which the set of all the objects in my table is a set. I'm just suggesting that to think the word universe refers to an object and not merely to a set may be a mistake. — Amalac

Are you saying that the universe is nothing more than an unstructured collection of items about which nothing can be said other than that they are distinct from each other? Because that is what insisting that the universe is nothing more than a "set" implies. If not, then where is the mistake? In referring to the universe as an "object"? OK, let's not refer to the universe as an "object". Where does that get us? We aren't any closer towards answering the question of whether we should expect the universe to have a cause.

In order to do that, we need to step back and ask what the notion of cause does apply to. And what sort of a notion is it? Is it an absolute metaphysical law? (Copleston apparently assumed there to be such a law; we know that Russell didn't share that view, but he didn't make that very explicit in this debate.)

If we suppose that the universe, defined as the sum total of all there is, isn't merely a set but also a thing (in the same sense in which an apple is a thing), then we could question Russell's claim, for why would the notion of cause not apply to the total then? — Amalac

You are generalizing Russell's objection into something much stronger (and as you point out, untenable) than what he intended. He merely denied Copleston's claim that the sum total of existents must have a cause. He didn't say that it cannot have a cause by virtue of being a collection. He did at one point say that the word "universe" had no meaning, which I thought was rather confusing. Perhaps where he was going with this was to say that the word "universe" has the function of a quantifier, rather than a proper noun, but he didn't get to develop that thought.

The thrust of Copleston's argument was in denying any brute facts of existence. Everything that exists contingently (whatever that means) must be entirely reducible to some other thing or things, and so on until you get to something that exists necessarily (whatever that means) and thus does not stand in need of a cause or a reason or an explanation (he used these terms interchangeably). And he wanted to apply that principle without restriction - a perilous undertaking. Recall how the unrestricted comprehension of predicates resulted in a set theory paradox that Russell had discovered earlier. Perhaps Russell was pushing in that direction when he offered this objection:

Well, I don't know. I mean, the explanation of one thing is another thing which makes the other thing dependent on yet another, and you have to grasp this sorry scheme of things entire to do what you want, and that we can't do. — Russell

There follows an exchange about whether the word "universe" is meaningful. But in the end, where Russell makes a stand is merely in denying that the principle of sufficient reason applies to the world as a whole.

But isn't it true that a “sum total” must be a class or set? — Amalac

The universe is a class or a set in the sense that these abstractions can be used to talk about the universe as the "sum total" of all there is, but not in the sense that that is all there is to say about the universe. As you rightly point out, classes and sets leave out relations between their members, such as causal relations, so they probably aren't the right sort of abstraction to use here.

I think a more productive approach is to ask what is meant by causes and reasons, to what sorts of things they apply, and where their expectation is warranted by our prior commitments. Copleston uses these notions very loosely throughout the debate. Russell had expressed strong skeptical opinions about things like "the law of causation," so one might have expected him to have pushed back more against the general premise. Nonetheless, the debate did eventually converge on that point, and there it ended.

Anyway, if I understand right through my sleep-addled brain, you're suggesting that it's not so much (as I was speculating) that maybe some law of preservation of free energy (/ some kind of equivalent symmetry) requires that more space and so energy be created to counteract the increase in entropy, but rather that the increase in space and so energy requires (or makes room for the possibility of) thermodynamic action to counteract the decrease in entropy. It's not things winding down that inflates space, but inflating space that keeps things wound up. — Pfhorrest

Just to add to what @Kenosha Kid said, entropy does not decrease when space expands. Rather, the ceiling of maximum entropy is lifted, so it has more room to grow. In the partitioned chamber example, before the partition was removed, each part of the chamber was at its maximum entropy. When the partition is removed, the configuration space is suddenly expanded, and so entropy can grow even further.

This is kind of how it looked 14 billion years ago, when the universe was a very uniform "particle soup." If not for expansion, it would've been at its maximum entropy already and nothing interesting would've happened.

I think the like score is unclear and misreading. Since likes are not offset by dislikes, the metric is cumulative, so it mixes several unrelated factors into one score: duration, frequency, plus whatever else induces likes. That whatever else is itself a mixed bag, in which post quality probably isn't even at the top. And yet "quality" is how the metric would often be interpreted.

The sun provides 37 Petawatts of energy, our global needs only amount to about 4, so there's plenty of energy there to provide all our needs. — Isaac

I wasn't closely following the debate with the crackpot, but these numbers jumped out at me.If our energy needs were on the order of 10% of all solar energy that reaches the surface, that would be a shockingly huge amount! But I think you made a mistake somewhere, perhaps conflating yearly and hourly rates or something like that. This wiki page gives a handy comparison table: Solar energy

Yearly solar fluxes & human consumption
Solar 3,850,000
Wind 2,250
Biomass potential ~200
Primary energy use 539
Electricity ~67

Energy given in Exajoule (EJ) = 10¹⁸ J = 278 TWh

LOL no, that was someone else. Pantagruel is all right.

My comments are about the ones I personally have interacted with including on here, which I qualified elsewhere. I admitted that the one's who don't proselytize are drowned out (in their silence) by what could well be an overly-vocal minority. — Pantagruel

So what you were trying to say was that all and only those atheists who are notorious for furiously proselytizing are notorious for furiously proselytizing. Very insightful, that.

Atheism isn't so much a logical argument as it is a social position. — Pantagruel

And why can't it be both? People with positions on all manner of things like to share them with other people, and even try to convince others to come to their side. So why is it not socially acceptable to be outspoken about atheism, of all things? Is it too shameful, too outrageous? It's especially funny to see someone complain about atheism being discussed on a philosophy board, where people come to discuss and argue about anything and everything, no matter how abstract or irrelevant. Methinks you are clutching your pearls too hard.

atheists are notorious for furiously proselytizing — Pantagruel

That's like saying "Americans are notorious for relentlessly shooting people in the street." The statement exposes your ignorant prejudice. There are billions of atheists in the world; entire countries that are largely atheist. Do you really imagine that all these masses of people are "furiously proselytizing" all the time?

So have any of you guys sobered up yet? I don't mind the like feature (it's almost invisible anyway), but I would much rather have the number of posts displayed under the member name than the number of likes. It's a more obvious and useful metric.

Yeah, but we only occupy a small part of one solar system as one species out of many. Independence means our existence isn't necessary for the rest to exist. That's quite different from cultural artifacts or human language, which clearly depend on us for existence. — Marchesk

So we need to explore what we mean by dependence (and the significance of any such dependence). The Anthropic Principle is one example where the usual direction of dependence is reversed: the world is/must be such as to accommodate the existence of humanity. The most far-reaching interpretation of this principle is explanatory. Why is the world such as it is? In part because our existence, which we take as given, puts various constraints on how the world could be.

A world without humanity would be somewhat like the kind of world we live in because the world was already here when we subsequently arrived to live in it. — Cuthbert

A world that was isn't the world that is though. Or if it be the same world, then it is the world with humanity in it.

I don't understand why John Locke was writing threads because he didn't write any replies to anyone's comments. This meant that he was not really involved in any dialogue or interaction on the forum. — Jack Cummins

He was not alone in this. There is this type of poster who are only interested in their own topics (if even that).

In the general, I take realist to mean the domain in question exists independent of humanity. Man is not the measure for things that are real, because they don't depend on us to exist. I think you would agree that the universe qualifies for being real, and that only solipsists seriously doubt that, although other positions would argue over what the world is, whether science provides us a somewhat accurate account, and to what extent we can know. — Marchesk

This sounds reasonable, but close scrutiny erodes the sense of understanding. What sort of independence are we talking about? A world without humanity wouldn't be the would in which we live, so the actual world depends on humanity at least in this sense. Is it mind-independence that we are after? That too is a slippery idea.

Concretizing the question may help: instead of asking about realism and anti-realism in general, consider some specific issue where controversy is more apparent.

This goes for your question as well, I think. Your point of departure were some writings on religious mysticism, which give the notion of "constructivism" a particular shape (I'll take your word for this). From there you decided to generalize that notion, but in the process of generalizing it lost most of its particulars and morphed into some vague notion of "anti-realism." That is to be expected.

Earlier I pointed you to another, somewhat more concrete example where several varieties of anti-realism are purported to be distinguished, and one of these varieties is also referred to as "constructivism" - which makes it at least notionally distinct from the broader concept. But generalizing from that example would probably run into the same issue, since not all subspecies would survive the process. What would be the generalized version of the error theory, for example?

I think that agnosticism is a better and more prudent position when it comes to the existence of God or a Diety then Atheism as per the above definition. The agnostic does not rule out the existence of God whereas the Atheist does. What are your thoughts ? — Deus

This doesn't tell us why you think agnosticism is better than atheism. If the underlined sentence is your reason, then I disagree. Depending on your epistemic situation (and I am not necessarily talking about gods here), it can be more reasonable to take a position, however tentatively, than to abstain from taking a position, or even renounce the possibility of any knowledge, as your suggested definition of agnosticism states.

If, while sitting in a chair, you announce that you have no idea whether there is a chair under you, and that moreover you cannot possibly know such a thing, anyone would think that you are out of your mind.

Thanks for this. What's the reference for Dummett?

My own takeaway so far is in alignment with that Crispin Wright quip: "realism about any topic" is kind of an oxymoron, since it means different things to different people in different contexts, and I am skeptical as to whether it means anything at all as a general concept. But more specific positions might be more robust.

You should probably tell us a bit more of where you are coming from with this query: where have you heard about "constructivism" and "anti-realism" respectively, what specifically have you read? "Vague" is right in the sense that there isn't a single accepted meaning for either term, and at least with respect to anti-realism, it is debatable whether it can even be nailed down to any coherent philosophical position. In the introduction to the SEP article on Moral Anti-Realism Richard Joyce includes this quip from Crispin Wright (which I like to cite, because it applies to so many topics): "[A] philosopher who asserts that she is a realist about theoretical science, for example, or ethics, has probably, for most philosophical audiences, accomplished little more than to clear her throat."

If you do a search for "constructivism," the most prominent results are from the fields of education and sociology (e.g. Review of constructivism and social constructivism), which is probably not quite what you had in mind.

A different kind of constructivism is Constructivism in Metaethics. If that is what you are asking about, then one obvious distinction between constructivism and anti-realism is that the latter refers to a much broader family of views than just metaethics (although seeing as you eventually settled on this forum, rather than Ethics, I am not so sure).

If you did have metaethics in mind, then from the SEP articles (Moral Anti-Realism and Constructivism in Metaethics) we can conclude that it is not even clear whether constructivism belongs to realism or anti-realism (but that may be seen as further evidence that the latter terms are not well-defined). At the very least, following the broad classification of the varieties of moral anti-realism from the first article, we can say that constructivism does not fall under either moral noncognivitism or the error theory.

So here's my (uneducated) crack at answering your question.

What I meant to say was that claiming that someone's arguments are vacuous because the person is an idiot, not sufficiently educated, right wing, an anti-semite, racist or whatever reason other than explaining what is wrong with their actual arguments, is no different than saying that someone is simply not worth listening to. Either way, that just is the ad hominem fallacy. — Janus

On the contrary, It's only a fallacy if your intention is to explain what is wrong with the argument. The way you phrased it here would be an ad hominem, because you are judging an argument on the basis of the character of the person who put it forward. If you decline to engage with the argument, then you cannot be committing a fallacy. You cannot break any rules if you aren't playing to begin with.

A line is 1D, a surface is 2D. Think of dimensionality as the number of independent coordinates that you need to locate a point in the domain. For example, if I wanted to locate a gap in the fence, I could say that the 6th plank from the left is missing. I would require two measurements to specify where a pants hole is located.

That's the main question I'm trying to get at - when is it reasonable to raise questions about something personal about someone as an argument. If someone were to say "Einstein was wrong about the speed of light," I think it would be reasonable for me to ask how the person is qualified to make that statement. — T Clark

If you bite, then you must put aside questions about qualifications and assess the argument on its own merit. But you don't have to bite - you could decide that giving a serious consideration to the argument isn't worth your time. Refusing to play doesn't break the rules of the game, since there is no rule that you must play.

What's the difference between saying that someone is not worth listening to, and saying that their arguments are vacuous, and thus refuted? — Janus

Saying that an argument is vacuous characterizes an argument, not a person, so this wouldn't be ad hominem.

Is it fair to call a gap in a number line a hole?

I think it has some similar problems to holes we see in the ground, except that it has the disadvantage of being yet even more abstract. At the very least with holes I can plant trees into them, fall into them, and so forth -- there's a causal interactive network. I'm not as confident when it comes to describing two-dimensional holes because it seems that for any series or function, if there is a hole in it, then that section is simply not defined or is said to not exist.

But perhaps we don't mean all the rest when we say "hole" and simply just mean this gap -- so that the natural number line is filled with holes (and if we can say the space between numbers exists, there would even be more hole than there are numbers) — Moliere

Yes, I think the primary concept of a hole is that of a gap, an absence in the middle of something. As such, we can very well think of holes in 2D or 1D. When we think of real, three-dimensional things, like a pair of pants or a fence for example, we can conceptualize them geometrically as surfaces or lines, wherein a hole will also assume an idealized 2D or 1D form in our mind.

A hole in the ground can be thought of as a gap in the surface (2D) or a missing volume of matter (3D), but when you are thinking about planting trees in it or falling to its bottom, you are shifting attention from the hole to the ground.

How would you answer creativesoul's charge of things not existing prior to conceptual schemes, then? — Moliere

To exist is to be the value of a variable
things exist before we give accounts of them — creativesoul

A specious charge. It comes for free with any definition:

"X is Y."

"Well, Y is a human concept. Are you saying that there were no X before anyone thought of Y?"

Quine's deflationary analysis of existence is a conceptual analysis, not a causal account of it, which would be an oxymoron anyway.

There are a number of common rhetorical moves, some of which are generally held to be fallacious - hence named fallacies. Nothing is wrong with the general concept.

As for ad hominem specifically, I agree that it very rarely turns up as a genuine fallacy in a discussion, and most charges of ad hominem come from people who think it's a fancy Latin for an insult.

If you said that bartricks was not worth listening to on account of him being an obnoxious dimwit, you would not committing an ad hominem fallacy - on the contrary, you would be very reasonable. You would be committing the fallacy if you said that batricks' argument was refuted on account of him being an obnoxious dimwit, but who ever does that?

EDIT: Also this leads to the deliciousiously abstract and totally silly but still interesting question: Are there such things as 2-dimensional holes? lol — Moliere

I won't dwell on donuts any more (never liked them anyway, or bagels for that matter), but I am a bit puzzled by this. Why not 2-dimensional holes? A hole in a plane, for example, would be 2D (or even 1D if it's just one point). Or did I misunderstand you?

At first I was uncertain about whether I'd posit that holes exist, but now I'm leaning towards the belief that holes exist. So, mostly, I think my thesis is just that holes exist, and I'm asking how you countenance that -- also, it's a question that gets at some of the popular topics 'round here without invoking the usual suspects ;)

I don't know if I'd say that it cannot be conceptualized that way... that's a bit more a priori than my approach has been so far. If the pacman example is wrong, consider the argument from predicates that I put towards Benkie here.

So my thesis is this: There exists a hole such that the hole is 0.17 km2, and it is in Kimberley.

And the question is: How's that work, on your view?

I pulled up some notional thoughts on Quine to jump from. What would you say about the existence of the hole? — Moliere

Well, one way out of the predication argument, for someone who doesn't want to admit holes into their ontology, would be to claim that any talk about a hole can be translated into talk about stuff (similarly to how, according to Russell, names can be eliminated by replacing them with definite descriptions). For instance, a hole in the ground can be described solely in terms of topography. (This is where you came in with your flat torus counterexample, but I don't think it works.)

This isn't wrong, but as I alluded to above, I take a looser, more pluralistic stance on ontology and am willing to go along with your/Quinean reasoning. Things exist by virtue of playing a role in our conceptual schemes. Or to put it a slightly different way, each thing exists within the context of those schemes in which it has a role to play - and that's good enough, as far as being and non-being are concerned.

(Interestingly, in solid state physics holes can be very active players indeed: they can pop in and out, move around, attract, repel, scatter and be scattered...)

I am skeptical of holes being a typographic feature, however, given the ability to represent a donut on a plane without a hole in a topologically identical manner. — Moliere

A torus in 3D is not topologically equivalent to a rectangle: you cannot continuously transform one into the other. In your demonstration you had to make cuts. You might as well "prove" that a solid rectangle has a hole in the middle... by taking scissors to it :)

In any case, finding one way to fail to detect a hole as a topological feature does not establish your general thesis, which I take to be that a hole cannot be conceptualized solely as a property of the entity that encompasses it. I think you are straining too hard to deny the obvious. Of course you can conceptualize holes in solid objects by focusing on the objects themselves, rather than the holes, and mathematics has the tools to do that precisely (if mathematical precision is what you are after), although it's a bit trickier than one might imagine, as simple topological criteria can detect some types of holes but miss others. A donut is an eminently holey object though: it's not even simply connected (unlike a shell, for example).

The question is not whether you can conceptualize holes that way, but whether you must, as a matter of principle. I don't think so, but then I have a loosey-goosey attitude towards metaphysics. Our language and our conceptual faculties are flexible and diverse; why should we dogmatically limit them? Must there be a fact of the matter about what holes Really Are (or Really Aren't)? In this case, the insistence that holes do not exist probably comes from seeing the world as a collection of self-sufficient individuals. Which is, admittedly, a handy concept that we employ in our everyday lives, mostly unconsciously. But it's not the only possibly concept, and sometimes not the best suited one.

Here is a historical case where a lab leak was passed off as a natural disaster. It took a regime change for the truth to come out: Soviets Once Denied a Deadly Anthrax Lab Leak. U.S. Scientists Backed the Story. (Open the link in incognito/private window if you run into a paywall.)

And that's the problem. Indeed there has been a conspiracy. The one where China wasn't open and truthful about the epidemic at the first place. — ssu

All that you describe here is a typical reaction to anything out of the ordinary in China. Assuming the prevailing natural origin hypothesis, this is exactly how you would expect authorities there to act. This is no evidence or even a cause for suspicion, one way or another. And all this has been known and documented, there haven't been any significant new revelations emerging lately.

As so many Republicans talk about the lab theory, the unfortunate will happen and this topic will irredeemably be made a US political partisanship issue. — ssu

Yes, unfortunately, everything about the pandemic has been highly politicized right from the start. And outside politics, you can see how the depressingly predictable dynamics unfolds: people get into arguments on- and offline, stake out positions, which then polarize and harden to the point where no evidence or reason has any chance of changing minds.

Apropos of the title and nothing else, just read this in an interview with a classics scholar Mary Beard:

I don’t know if this is novel to you, but in the last few years there has been a real resurgence of popular interest in Stoic philosophy — why’d you just roll your eyes? All to the good when people are interested in the ancient world, but this is one of the more mystifying bits of interest: clichéd self-help from a philosophy that, if you looked at it really hard, was nasty, fatalistic, bordering on fascist.

But what’s your hunch about why people are being drawn to Stoicism? What comes out in Marcus Aurelius particularly is rather clichéd thoughts: Never take a major decision when your mind is troubled. We can all agree with clichés like that. And they come with the rubber stamp of great antiquity because they were written by an emperor — an emperor who was about as brutal in massacring the enemy as Julius Caesar. But we tend to forget that side of him because he’s a bearded “philosopher.” It’s not very salutary to look at your Amazon ratings, but I always feel terribly pleased — though it doesn’t happen often — when I’m higher up than Marcus Aurelius. — Ancient Rome Will Never Get Old. Take It From Mary Beard. - NYT

:snicker:

(If you want to read the full interview and run into a paywall, open link in a private/incognito window. But this is the only bit that is relevant to Stoicism.)

Yes, the theorem itself, as you quoted it, does not mention truth. But from the theorem, we do go on to remark that the undecided sentence is true.

And the statement is neither true or false in the system on an even more fundamental basis than that it is undecided by the system: — TonesInDeepFreeze

There is an even more fundamental reason that the object-theory does not yield a determination of truth. That is that the object-language does not have a truth predicate. — TonesInDeepFreeze

But if we adhere to strict "truth=provability" principle, then the sentence is not true even in the metatheory, if it assigns truth to sentences subject to their provability in the object theory.

When we're talking about plain arithmetical truths, I don't know why we would have to go down the road of wondering about realism. I mean, non-realists still recognize the truth of arithmetical statements. — TonesInDeepFreeze

Anti-realists recognize arithmetical statements as true relative to particular mathematical theories, which are as fictitious as any other such theories. Realists view some mathematical systems, such as arithmetic, as representing an objective, mind-independent reality; for them the mathematical study of such systems can be likened to scientific research.

Again, I want to disclaim that this is a simplistic caricature, but here are some statements in the same spirit by mathematician G.H. Hardy:

Mathematical theorems are true or false; their truth or falsity is absolute and independent of our knowledge of them.

Pure mathematics... seems to me a rock on which all idealism founders: 317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way. — G.H. Hardy

(Quoted from another work of Torkel Franzen: "Provability and Truth" (1987))