People tend to think that 0.999 is a never ending sequence when in fact it's a converging series to 1.

I seem to think that the point being is to demonstrate the issue pictorially with a converging series. So, something is "reached", no?

In addition I see it of more use to talk about how fast or slow a convergence occurs.

Well think about whether 1/x converges for the set of all irrationals, as x goes to infinity. It doesn't. So, you have to consider whether some value is reached or is the limit, no?

What I mean is the typical notation for a Riemann sum of as n goes to infinity. So the implicit assumption is that you do reach a number, but as per calculus that amount of steps is reached once you instantiate an infinitesimal...

While I'm at it, you also don't have to "reach" 1 for 0.9...(9) for non-standard analysis and can instantiate a infinitesimal.

With that you were disregarding with instantiating infinity in a series sum that apparently converges to 1 for 0.9...(9)

It's just a Riemann sum, Tones, lol!

But, that's how it's usually phrased by others when thinking that you have to add an infinite amount of terms in a series, yes?

Actually, this is implied after an infinite amount of operations on a series. Like a Riemann sum.

Im somewhat unhappy with how the stoic inner calm and peace towards the world arises in my opinion. It seems to me that it's a difficult issue to talk about apathy.

Do you think that it's true that the stoic attains inner calm or peace through apathy? Is this a natural unavoidable attitude? Is apathy and attitude towards life worth displaying in your opinion?

The more I try to metaphilsophically analyze myself, the greater the impression of mine is that I have fallen into a general sense of apathy towards life itself. The most prominent concerns of a philosopher, being concerned with the 'good' and how one should go about it are not so prominent features of a life concerned with it, and are rather set aside for not going about attaining it with zest or haste. Namely the dictums of treating one's day as if it were your last, seem pretentious through a deeper desire to be free from all excessive wants or even needs in one's life.

Thus, I am forced to conclude that the Cynic was right after all in his or her practicality and efficiency at attaining what one would or can call an inner sense of peace with the world.

Is this something the reader finds worthy of commenting in the positive or negative? What are your thoughts?

I think I see what your getting at information-wise, yet to parametrize for units you would need some operation other than in silicone to estimate a value for a unit of complexity, no?

Otherwise the example of qubits is sufficient to demonstrate the issue?

Sorry I can only reference Shor's algorithm as an example of what I am saying, and it ain't that much.

It sort of strikes me as odd that the only physical units to determine complexity in mathematical computations would be quantum computers with qubits... What do you think?

That was a treat watching. Thanks.

Sorry, but, he made 9 phone calls to the DOJ about turning over the election and handing him the victory. He may or may not have dementia; but, it strikes as some kind of needless spin so he can turn out superior because that what he believes he is, when the issue was about not his superiority; but, the votes of Americans.

? — Baden

Trump would like to spin anything in what he does and somehow come out superior. But, the dementia seems to show when he tried to spin the 2020 elections.

You can't spin elections, can you?

As far as I know, Euclid made mathematics a shared game with his Elements. Much of which was expressed as propositions.

Another round of international silence.

Thank God he's not a neo-con.

Philosophy as therapy and all that. It's all Wittgenstein.

Wittgenstein

Things in engineering are usually defined as sometimes overdetermined or positively redundant, in practice.

Epistemic closure of mathematics or its inability being used in practice doesn't prohibit a computer from modelling a bridge, and neither does it not prohibit an engineer from making redundancy measures to keep a boat afloat after hitting an iceberg, by compartmentalizing the ship.

IE, if relations don't have an ontological existence in the world, Santa Claus only exists in the mind. But if relations do have an ontological existence in the world, then Santa Claus exists in the world. — RussellA

I think it's really anti-Frege at this point with Santa Claus and psychologism, no?

As in more detail, that relations can be represented symbolically or in manner and form; but, for the person that is Santa Claus, doesn't exist...

Does that make sense?

It's a wise parent who knows just how to answer children depending upon the age and sophistication of the child.

Some answers are, in themselves, things of beauty. A friend of mine from years past was asked by his young son, "Daddy, how high is the sky?" His answer; "Exactly 50 feet higher than the top of the rainbow." — Torus34

Of course, the sky is very high. But, it's interesting that you invoke ordinary language in the discussion. I seem to think that in ordinary language, Santa or Pegasus have some realm of ontological residency, to sound a little strange.

But, it doesn't strike me as odd to say that when treating an utterance such as:

Where does Santa Claus live?

with the response being:

At the North Pole.

As being devoid of any truth, no?

Perhaps this is what Wittgenstein was talking about in para 58 of Philosophical Investigations, where I think he is saying that a name such as "Santa Claus" is part of the language game, not an ontological part of the world. — RussellA

It's not enough to state that they are part of a language game, in my opinion. I believe that they should be stated for what they are in terms of where they existentially reside. The process of determining their commitment as ontological entities seems important to say as clear as possible, that they are a fiction.

So, the next question is, what's the problem with treating them as fictions...? None?

Yet, even if Pegasus and Santa Claus don't exist ontologically, we can go to a shopping mall during Christmas and say "that person" is Santa Claus. Well, not exactly. Likewise, we can point to a statue of Pegasus and say "that is Pegasus", but again, not really. These are representations, in the everyday use of the word, of our fictitious ideas.

It is a complicated topic. — Manuel

I'm not sure it's that complicated. It's elucidating that you say that certain features or pictorial objects can stand for or represent a name, such as, Pegasus or Santa Claus...

Does this not necessitate the use of language towards the descriptions of these fictions or literary figures in apparent reality?

Of course, if a child were to ask the following;

'Where is Santa Claus?'
'At the North Pole, of course, my child!'

, then, nothing further can be said, than what was told was a lie. So, there's an ontological commitment once treated as a statement or proposition, that can be elucidated when treating these fictitious entities as non-existent or truth apt.

If we really want to take this seriously, then we simply state the ontological "area"/"region"/"place" where they exist as fictitious entities or literary figures, no? I see this as a necessary condition when talking about things such as Pegasus or Santa Claus, no?

I just wanted to thank @Fooloso4 for his comments in this thread.

"Stuff", because the content makes a difference. — Banno

Is it that anti-realism applies to ethics and aesthetics because we seek to make the world as we say, while realism applies to ontology and epistemology because we seek to make what we say fit the world — Banno

So, it's content that makes up stuff, yes? But, then we have facts and some kind of coherentism in how they can find their use in language, yes?

In my view, if not overly simplistic, it comes down to a pragmatic understanding of how epistemic criteria or even what you describe as content determine use. I think, that makes sense.

And an abstract concept conceived in the mind is not the same as a visually perceptible object created by the imagination. — Apollodorus

Is this noesis?

My gut feeling is that although philosophy does not set out to be disruptive, it is pretty much guaranteed to do so if you take it seriously - at the very least, to use Kant's worn out phrase, you'll awaken from a dogmatic slumber. — Tom Storm

Why is that true? It seems almost like a sine qua non, no?

Plato's philosophers, after all, were to be trained for the express purpose of serving the people. — Apollodorus

Much how like teachers arise nowadays.

It is so mind boggling how smart Plato was.

Similarly, the task of Plato's philosophers is to distance themselves from everyday life in order to see things in a different light (the light of the Good) after which they return to society to enlighten their fellow citizens. — Apollodorus

This raises an interesting question as to whether a philosopher or philosophers have any duty towards their fellow citizens. What do you think?

My sympathy is always with the folk in the cave. Why would you leave when things are predictable and familiar? There is no great psychological benefit to be found in disruptions and upheavals. Further, most of us are not looking for truth or deliverance, we are looking for safety. — Tom Storm

Yes... It is an issue to think that philosophy can hold any safety in challenging questions and truths. People do value safety in higher regard.

Also, I don't think philosophy asks for disruptions and upheavals. It's just the task of the philosopher to question.

Most people don't react positively to their idea of reality being rattled. They'd rather live in the comfort of their own illusions than to confront them. That is why. — Tzeentch

I see. I have experienced something similar to this idea of the truth that one holds can be subject to scrutiny and be challenged. It's tiresome offer a while but is the bread and butter of philosophy.

The Western liberal tradition is profoundly hostile to the Platonic 'doctrines of illumination'. — Wayfarer

Yes, that's an interesting topic one can go on about for quite a while. While the Medieval scholastics and other clergy so viciously appropriated Plato's Cave along with even the Bible, I don't believe that one can argue otherwise that the metaphor has not been treated fairly. After all, it wasn't religion that should be doing the liberating from the cave, which it has come to pass as what actually has transpired throughout time.

It's the task of liberal philosophy to make the world a safe space for the individual, grounded firmly in a naturalism which sees h. sapiens as simply another species, albeit a very clever one. Homo Faber. — Wayfarer

I can't help but notice that this is the Aristotelian interpretation of a guiding telos. Is that true or off mark?

Did you free yourself from your shackles? If so, how did you do it? If not, what seems to prevent you from unshackling yourself? — Bitter Crank

I read Ayn Rand, obviously and she helped or taught me to shrug them off. At least that's what she learned from Aristotle, no?

No, but more seriously...

But to back up, is Plato's cave real--is it a valid metaphor of our world? Are people figuratively chained to the wall and capable of viewing only shaky flickering shadows on a wall? — Bitter Crank

Well, your looking at a wall of text, no? Perhaps even something more interesting than what's happening on the TV? All things considered, the strength of the metaphor has been echoed throughout time for some 2500 years, so there's some psychological reason if not literary interest in how it was phrased. I heard Plato was a really smart guy.

The opposite is a very attractive -- that we know reality; that we are not stuck with flickering shadows of reality. Workers of the world, unite! You have nothing to lose by your chains (and a world to gain)! — Bitter Crank

Certain truths are inconvenient to display nowadays than mention. Yes, it seems true. The power of mathematics, being Plato's main interest at the Academy with geometry still hold true. Thinking aloud, Is this really all about education? Don't we have enough educated people today with so little to offer in terms of the liberation one can find in one's self from the tyranny of reality of one's own ill psychology?

Was Plato himself free of the cave? He may have had the insight that what he saw of flickering shadows was not reality, but did HE know reality? I suppose he thought he did. Forms schmormes. — Bitter Crank

I think his influence has the appeal that he was in some sense free. He had something to offer to the world that made it a better place.

Maybe we should just burn philosophy's libraries. Smash its statuary; close down philosophy departments. Fire the faculty. Slam the door shut on 2500 years of rehashing stories like The Cave. — Bitter Crank

Supposedly, no. I think education is important. But, the recent threads about stupidity and climate change, and science denial mean that were still sitting in some figurative cave...

I have no idea what it meant to a then native speaker. — tim wood

I mean, over time the Greek nous, has come to mean, at least philosophically, as mind or intellect.

In use it refers to or implies much of what a mind might do or contain.

I am unaware of any reference in Ancient Greek to anything like modern intelligence. And subject to correction, I don't think there are any. — tim wood

As, I said, over time some sort of reification occured and is modernly associated with intelligence, no?

Unfortunately, the same can’t be said for Wittgenstein, and I think this moralism is implied in his work. — Joshs

At least for the early Wittgenstein it was everything outside the domain of propositional analysis.

I also do want to mention Searle in how he carries out the moral issue from the perspective of law and order in/of a society. Not just the individual and their conception of morality.