That may well be true. Most people choose the news that suits them.

Modern affairs and lived experience are telling me that people are broadly still sheep that need herding. — Lionino

That's odd. Many people think that trying to organize people is like trying to organize ferrets - very difficult and any organization you do achieve rapidly disintegrates. That fits better with my lived experience. But maybe you live in a different world from me.

Ok. Well I'm all talked out here. I think we've long forgotten the topic. — fishfry

Let's agree to disagree. Sorry I brought it up. No wait, you brought it up and I let you bait me for a while. — fishfry

I agree. But I would like a better mutual understanding before we move on. I don't know for sure about you, but my comments were intended to provoke a reply, but only in the interests of a discussion. I thought you were doing the same. I didn't realize that you thought I was baiting you, which is a different kettle of fish. So I apologize.

Sorry I mentioned it. — fishfry

I wasn't complaining that you did. In fact, in our disagreement, the vagueness of meaning enables a diagnosis of what we disagree about, so it was actually useful. (I'm not sure whether the same applies to the concept of metaphysics.)

Oh please. He left as gracefully as Caesar did. — fishfry

Quite so. I'm afraid I was guilty of irony, which is always dangerous. His inability to recognize when the game is up is not particularly unusual. I can think of other examples.

The Dem hysteria that started on election night of 2016 has been extremely damaging to the country. — fishfry

I agree with you that the hysteria around everything is very damaging. But I think both sides are to blame. Each side thinks that it can win by escalating the emotional temperature; the media feeds on that and joins in. The question who started it is a good one - unless the answer is to be used as a weapon of further escalation.
But neither side is really to blame. There can be little doubt that a large part of the problem is systemic - the whole set-up encourages escalation and the desire to win, rather than compromise. Again, it's not unique to the US. It's not difficult to think of other examples.

Well toss a can of soup on a painting then. You lost me here. — fishfry

Couple of soup throwers were convicted, they're going to jail. So never mind on the soup. Looks like England has had enough of the eco-loons. — fishfry

At least they threw tomato soup, which is easier to clean than pain. — Ludwig V

I see from the reports that the soup did actually damage the paint of the frame, so I was wrong about that.

Responding to those protests with outrage and attempts to suppress is exactly what they want - to attract attention and controversy. Difficult as it may be, the only thing that would persuade them to stop is ignoring them. But it is also important to reward them when they do the right thing, there should be a reasonable response to civilized and legal protests.
Failure to recognize when one is being baited is very common and failure to deal with it rationally - by not rising to the bait - frequently underlies escalation.

Did you hear about that windmill that fell apart, closing a beach during the height of tourist season? Fiberglass shards everywhere. — fishfry

I'm not sure what you expect me to say. It's definitely a bad thing. Needs to be checked out and any problems resolved - and any parties who haven't been doing their job properly held to account.

But does it show that wind farms should be abolished? I don't think so. The fact that so many people dislike them is much more relevant and it's right to be cautious about setting them up. Off-shore farms seem to be more acceptable, so it's better to be content with them. (There's the question of bird strikes as well, though I've heard that they may have found a solution to that.) I think it's unlikely that that on-shore farms can be a major contributor to the project of finding renewable sources of energy. For on-shore generation, solar farms may be more appropriate.

Fictionalism is a useful point of view. Avoids having to defend what math "means." — fishfry

Yes, Meaning is as ill-defined as metaphysics. It's usually easier not to mention it.

I hope things don't get too much worse. At the moment nobody knows if we have a president. — fishfry

It is ironical that his most Presidential act has been not to stand for his second term. He'll be a lame duck until January, but that's normal. I expect the system will survive.
There's a paradox about democracy which "of the people, for the people, by the people" misses. It is crucial that the people who lose the election accept the result. That means that the process has to be very carefully organized so that there's as little excuse for contesting it as possible. So the events in January 2021 are a concern. I've also heard that some Trump supporters have said that they will refuse to accept the result if they lose; (I assume they will accept it if they win!). That's absurd. It puts Trump in the same territory as Putin and Xi Jinping. Bluntly, hypocrites.

I support free speech. Blocking roads is not speech. — fishfry

The people who were jailed were convicted under existing laws. The new law is an opportunistic grab by those who want to ensure that free speech is allowed, so long as it cannot be heard. It's a difficult balance to strike. My complaint about those protests is that they were too effective because they produced more opposition without taking their campaign forward. Protest needs to attract attention - especially media attention, of course - without creating more opposition for the cause.

The fission waste is a problem, but you can't run the world on windmills. — fishfry

Probably not. There's also solar panels, hydro-electric, tidal, wave, and volcanic. Still, it's pretty clear that lots of batteries will be needed. China has quietly cornered the market in the rare earths that are needed for them. Now, that's a sensible way to approach the issues. The rest of us will have to pay their prices or find alternatives.

We'll all toil in the windmill factories? I think I better quit while I'm behind here. Eco hysteria is a luxury belief. Green policy hurt third world is one random link I found. — fishfry

There are two distinct problems. One is enabling as many people as possible to find decent jobs. That's a problem anyway. The other is enabling people whose jobs are phasing out to find alternative employment. That's more difficult. There have been many cases in the past (like phasing out coal) which have not been well managed. But it doesn't seem impossible. At least we could try harder.
It quite likely that third world countries will suffer more. There's a lot of talk about providing additional help to them. That seems like a no-brainer, since unless they join in it will be hard to restore stability. But, curiously, it seems to be very difficult to make progress. Why? Who could possibly be opposing that?
Does your link compare the damage to third world countries with the damage that will be caused by climate change? Or perhaps with the damage caused by existing free trade treaties?

I'm all for clean air and water. I'm also for modern civilization. The point is to strike a sensible balance, not to throw tomato soup on paintings. — fishfry

Clean air means less carbon dioxide and methane. Clean water means less plastic. Amongst other things.
Sensible balance is good. But big corporations always end up defending their shareholders' interests and fail in the end. They just waste time and money.
At least they threw tomato soup, which is easier to clean than pain. Paint has been used in the past for similar escapades. It can be cleaned off, but it is much more difficult to do so.

True. I would say that communication just generalizes language. — Apustimelogist

I wouldn't disagree with that. But, having thought about it, I want to emphasize the multifarious uses of language, many, but not all, of which involve communication in one form or another.

Similarly, what an animal communicates about is different to their actual perceptual/cognitive/physical engagement with what they are communicating about. — Apustimelogist

I'm really sorry, but I can't get my head around what you're saying here. Could you break it down for me?

What are we communicating to ourselves? — Lionino

It's a good question and I agree that communication with others and with oneself (insofar as it happens) are different.
Two different examples of communication with oneself. I make a shopping list, to communicate with my future self so's I don't forget anything. When I have gathered some of the items, I may recite the list to myself, looking at or laying my hand on, each item as I name it, so as to make sure I don't forget anything.
When I get my receipt, with each item listed, I may keep it so's I can communicate with the manager or someone at home if there is a dispute.

This is likely true. Maybe the best path is to merge the most valuable ideals. Don’t confine yourself to one set of concepts. — Igitur

That's a good recommendation. One should be sensitive to differences as well as similarities.
I think you'll find common elements, but also incommensurable ones and incompatible ones. Ideally such ideals should be tailored to one's practical and social environment?
There is much in common across the Abrahamic religions, for example, but also quite serious differences. The Tao Te Ching, however, seems to me to be almost completely incommensurable with Christianity, though I'm sure that others will disagree with me.

Language isn’t simply a tool that we use to access concepts , in its very instantiation it uses us to transform the sense of our concepts and percepts by enacting them in the world. — Joshs

I agree. Concepts do not exist independently of language in some separate platonic reality, in which concepts exist passively waiting to have a label slapped on them so that they can be thought. Understanding language gives us concepts in terms of which we can think about various things, and so our thinking is structured by them.

For Merleau-Ponty, perception is ‘languaged’, but this cannot be understood in terms of a split between thinking and communicating. — Joshs

Yes, the concepts of our language actually structure our perception.

To think and perceive is to communicate with oneself by way of the world. — Joshs

The idea of communicating with oneself is a bit awkward, isn't it? There are examples of thinking that one might call communicating with oneself - reminding oneself, exhorting oneself and so on. But I think there are also cases of thinking that are working out a problem, organizing one's thoughts and so forth. Those are not communicating with oneself or anyone else, but doing a different kind of job.

It needs to be said, as frequently as possible that the uses of language are multifarious. They are not confined to the communication of truths. I don't think it is possible to get a real understanding of language without taking that into account.

I suspect you'll come to find, e.g., that the ideal Christian is quite different from the ideal Jew and that different religions contain different visions for humanity. — BitconnectCarlos

That's very likely true. A comparative - and dispassionate - study would be very interesting.
But it also seems to me that we might also find that certain traits of human character might find recognizably similar expression in each religion - or at least those that are big enough to have internal divisions or sects. The most obvious example is fundamentalism, which seems to me to be instantly recognizable in all the major religions.

Hmmm. "No action." As a bit of a gambler back in the day, I understand that!! Probabilities 0 and 1 are no action. Not a valid bet! So I can sort of relate to your point. — fishfry

I'll settle for that. It's a very marginal point, anyway.

I better quit while I'm behind here. — fishfry

Both this argument and the one about evidence are actually aimed at the same point. Once you have introduced probability as an interpretation/application of the formal function, it is very difficult to ignore reality - metaphysics.

Clear, with some study. And consistent, well we often can't even prove our axioms are consistent. Nobody knows for sure if the axioms of set theory are consistent.
And paraconsistent logic is a thing these days. Logic in which we can allow a certain well-controlled amount of contraction. — fishfry

Yes, all true.

Fictionalism. It's all fake. But interesting and useful, so why not do it anyway and enjoy it. — fishfry

I have read about this, but didn't realize that's what you meant. It's an interesting take on the idea that we construct mathematics - and some other things as well. However, if it is fiction, it is not the same kind of fiction as literary fiction. However, fake means pretending to be something you are not. Neither is doing that.

I think the eco-loons are self-centered virtue signalers. — fishfry

I'm sure that many of them - especially the loonies - are virtue signallers. It doesn't follow that they all are. There is a real issue here.

Every time you make energy production harder you starve a few hundred thousand third-worlders to death. The Green agenda is starting to crack in Europe. We all like clean water and air, but destroying our economy in the name of "the planet" is suicidal and cruel. The billionaires flying their private jets to climate conferences give the game away. The Obamas own beach front property in two states. They must not be too worried about the seal level rising. — fishfry

There's a line of thought in eco circles that accepts that the world will not be able to make the changes quickly enough to make much difference. I think that's right. The thing is, the disruption and costs of serious climate change will be greater than the costs of changing now. If we could change now, and do it right, the disruption could be kept to a minimum. There'll be lots of work in the new industries.

I'm for nukes. Environmentally clean and abundant energy to run our world. — fishfry

Fusion could do it, and it seems to be getting closer. Fission leaves waste. There used to be a lot of concern about what to do with it. I think the plan now is to bury it and leave it alone - for 100,000 years. You can't say those guys are not ambitious.

I see in England that they threw a few highway-blockers in prison for 4-5 years. Did you see the story? A good start, I say. And the next time some trust fund vandal glues their hands to a museum floor, just leave them there. — fishfry

Don't worry. The last Government passed a new law, restricting free speech to ensure that all protest can easily be ignored. I doubt that the new Government will prioritize repealing it. The people who've been imprisoned will become martyrs - and the whole thing will escalate.

Is the Biden coup getting much play where you are? He published a letter saying he's dropping out of the race. But there's no video or photos of him signing the letter, and he hasn't been seen for five days. I have no doubt the global competition is taking note. The leader of the free world is the victim of a coup by his own political party. — fishfry

Oh, yes, it's all over the media. From here, it seems that the chaos will continue and spread. I don't think it will end with the election, either.

We don't need language to think about things. — Apustimelogist

No, that's obviously true. I suppose there are questions about what's going on. But you could also say that you don't need language to communicate. Animals can do that as well. Then there's the question whether animal communication systems count as language, or what the limits of language without words are. Hence the temptation to posit a "language of thought" - "mentalese". (This was mentioned by someone earlier in the thread.) But without some empirical evidence, I don't think there's any useful mileage in speculation. Chomsky doesn't help.
Thought a Chomskian universal language wouldn't be private. Nor are animal languages. I'm not sure about this.

I agree with holding to the metaphor — Moliere

There's no harm in pushing a metaphor as far as it will go. But it is to be expected that it will break down sooner or later. I didn't quite follow the last half of your post.

I am not sure if that arrogance is universal. Wittgenstein had quite the temper. — Lionino

I wouldn't disagree ssewith you about either arrogance or bad temper. But I think a certain level of arrogance, or at least self-confidence, is necessary to do philosophy at all.
Don't all philosophies see their tradition through their own interpretations. Isn't that built in to the whole business of reading and understanding philosophy?
Yet I agree that the criticisms of analytic philosophy that you mention are appropriate.

To me I don't see the inherent distinction between a public language and a private one other than only one person uses it. So to me it is a counterexample to the private language used by only — Apustimelogist

Yes. Wittgenstein isn't very clear about defining his target. But that may be because he wants to target all the varieties of dualism, and doesn't want to tie himself down to any specific varieties.

that language is meaningless without the need for the communication of inaccessible information, whether that communication being with other people or yourself. — Apustimelogist

It depends on your definition of inaccessible. The only thing I'm clear about is that he intends "logically" inaccessible. I don't know about communication with myself. I find "mental notes" very unreliable.

Language is primarily a tool for communication rather than thought — Apustimelogist

I wouldn't fight over the question of priority. That it has multiple uses is not in question, I think.

Isn't the rule following paradox, which philosophers still debate to this day, solved by the way the language center of the brain is uniform for many newborn children? I don't see how else one would solve the rule following paradox. — Shawn

It might be. But I take his point to be logical, so the expectation would be that the sceptical arguments would still apply - unless you could take "This is what I do" to be identifiable with a brain state. Don't forget that the brain is very plastic, so we may well find a great deal of variation in the ways they work. I can't see that they are likely to work in the same way that our computers work.

Maybe that is a naïve point, but, since rats and other languageless animals are known to be able to perform mental simulations, doesn't that show in a straightforward manner that language is not necessary for thought? — Lionino

A lot depends on what you mean by language. But I wouldn't be dogmatic. It could be sufficient without being necessary and it could enable kinds of thinking that are not available to other modes. "Thinking" is a very flexible concept.

Anonymous moral advice is the best, actually. — Tarskian

I can see that. The confessional is a possible example - except, of course, are priests independent? It depends on how you rate their religion.

My preference would be for someone I trust and not too close for a discussion.

It is the same for other types of advice, such as investment advice or relationship advice. They won't tell you the truth if they simply can't. — Tarskian

There's no escape from the responsibility of deciding who to ask and, in the end, what to do.

analytics cut themselves off from most pre-analytic philosophy, did everything "in-house" which entailed a lot of reinventing of the wheel in ways that look horribly philistine and only appeal to a very specific niche of people who like goofy decontextualized thought experiments, [...] — Lionino

I like that. Though some analytics don't cut themselves off from their tradition, but re-interpret it into their own language. Mind you, a lot of all that has gone on throughout philosophy, hasn't it? It just means that analytic philosophy is less special than it thinks it is. But then, every new philosophical approach thinks that. It's all very confusing.

Thanks for the clip. There's a lot in it that doesn't easily come out in prose.

Does it matter what the primary function of religious thinking is? — Igitur

It depends what you mean by primary, and the point of view.

Assuming you care about religious truth, values, or community, you would probably also attempt to practice religions — Igitur

I think you understate this. Religion is not merely about truth, but about how to live. The practice is the point, really. The truth is just there to give a basis for the practice. That's why Bhuddhism, Stoicism, etc. all figure in this discussion.

[H]istory amply shows, imo, that 'religion' is required only (or at least mostly) for herding sheep, prophets making profits and sanguinary propitiating/martyring/scapegoating. — 180 Proof

Yes, also for all of that. If religion is primarily how I am to live, others will use it for their purposes. So will I. If religion is primarily about social control (manipulation), I will demand of it that it tells me how to live.

It's curious to me that in Ancient Greece, one can discern two different social roles for religion. One is to justify the power structure. The other is to give a resource - an ally - to those who don't have power. One can see how both would be useful even though they seem contradictory. We can see both tendencies in the churches to-day.

I suspect that the primary overall social role of religion is to enable some unity in communities much larger that the "natural" one, which appears to be about 150 people. The major religions all arose at about the same time as big cities. I don't think that's an accident.

This seems like the most important thing to respond to, the idea that it is unreasonable to try out so many sects of religions. — Igitur

Yes. That's why it is perfectly reasonable to go for satisficing rather than maximizing. In other words, something that is good enough, rather than something that is perfect. (Your suggestion of looking at popular brands is close to this.) In addition, I am bound to start from where I am, that is, by evaluating the religions available in the community I happen to be born in. There's no reason to look further afield if I can manage with what is nearest to me. I don't know that objective absolute truth is the most important criterion. Something that's near enough will do.

b) The moral advice or ruling must enjoy consensus amongst independently judging scholars. These scholars must not be on someone's "payroll". — Tarskian

That's perfectly reasonable. Except that the ideal is impractical. Everyone has to make their living somehow. Independence is a mirage. We have to settle for an independent mind, which is not impossible, though difficult - and requires courage.

Right, but you see the problem here right? How does any individual ever know that they are properly chastising someone for following a rule wrong? Per Wittgenstein, they can't be sure that they ever understand a rule. — Count Timothy von Icarus

There is no criterion beyond agreement between us. So if I am understood and understand, everything is in order. (It's not a question of chastisement, really. Either communication works, or it doesn't). It is also true that communication can and frequently does, break down, for one reason or another. But, again, the point is that there are ways of restoring it and even ways of coping with failures.

Imo the private language argument is about showing that when you have no external enforcement of these criteria, any kind of stable foundation for word meaning evaporates... — Apustimelogist

I agree with that.

The counterexample introduces the same kind of practical enforcement as the social case and so it doesn't contradict the point being made imo. — Apustimelogist

Yes. But I thought that was one of Wittgenstein's points. Because you said it was a counter-example, I thought that you were saying that because we can write notes to ourselves (which we clearly can), Wittgenstein was wrong. I regularly write notes to myself and they work perfectly well. But Wittgenstein's point is not that we need to be validated every time we follow a rule - that's absurd - but that we need validation sometimes - a practice of validation - , so that there is agreement about how to apply the rule.

I think this is reinforced by the observation that at the social level, social rules tend to drift, almost without anyone noticing. Language drifts, patterns of behaviour change, but there is general agreement, so communication doesn't break down. (Though in practice, of course, social unity is only partial, so the drift is more complicated than that.)

So I think we agree, and I'm sorry for my confusion.

But ... can you explain to me how today being Sunday, the probability that yesterday was Saturday is anything other than 1? — fishfry

I'm not saying that if to-day is Sunday, the probability that yesterday was Saturday is anything other than 1. Of course not. I'm saying that because today is Sunday, probability doesn't apply to the proposition that yesterday was Saturday.
(Yes, I'm writing this on Monday, but it is simpler to pretend that it is Sunday for the sake of simplifying the discussion.)

If you were a betting man, what would you bet that today being Sunday, that yesterday was Saturday? What is your credence for that proposition? How should a bookmaker set the odds? — fishfry

That bet is money in the bank, so long as the odds show a profit. But who would take the other end of it? I suppose you might find a taker who would give you your money back. But that would be an empty ritual. There's a good reason why bookies close their books when the race is over.
More politely, where there is no risk, there is no bet.

That is, if today is Sunday, what is your credence that yesterday was Saturday? — fishfry

Ah, this is a different can of worms. "Credence" is degree of belief, isn't it? And belief concedes the possibility of falsehood. So that makes sense.
But when there is no possibility of falsehood, we do not speak of belief; we speak of knowledge. So if you assign a credence to "Yesterday was Saturday", you are allowing the possibility that it wasn't. But if you assign a credence of 1, you are excluding that possibility.
In my book, credence doesn't apply.

I agree that it feels tidier to express the outcome by saying P(outcome) = 1.

I could live with "preferable," but not "should." — fishfry

I think "preferable" is better than "should". I'm happy with that.

Don't you like fiction? Do you have the same complaints about the novel Moby Dick ("He tasks me. He heaps me.") and the game of chess; one a work of fiction, and the other a meaningless formal game with entirely made-up rules? — fishfry

H'm. That's a new take on mathematics. I can understand the idea that axioms and definitions can be posited in a spirit of exploration. The point in that case is to work out the implications of certain ideas. But the axioms and definitions, even if they are, in some sense, provisional, need to be clear and consistent, don't they? Anyway, you're not telling me that the axioms and definitions of probability theory are in some sense provisional, are you?

Immigration is an issue on both sides of the pond. Liberty versus top-down control. The wokesters versus the people who never voted for the woke policies. The double standard of justice, a kid jailed fo making bicycle marks on a Pride crosswalk, while Antifa defaces statues. Don't get me started. LOL. — fishfry

It looks as if I have got you started. There are real and serious issues at stake in these disagreements. (You didn't mention climate change.) The biggest problem is that the parties have given up listening to each other. Meanwhile, Putin and Xi Jinping with Kim Jong Un and Ali Khameini are calculating that the West is so divided that they can re-make the world in their own image. There's a serious need for some waking up on all sides. Perhaps one day, the threat will be so great that we'll be forced to recognize that the things that we share are more important than the things we disagree about. I hope we don't wake up too late.

I’m picturing Woody Allen trying out Christianity by eating Wonder bread with mayo in Hannah and her Sisters. — Joshs

I guess I can get this gist of the joke from the general context. I don't remember much about the movie. Was that an actual scene, or something that you imagined?
But it makes a point, doesn't it?
Doesn't Woody find meaning through watching a Marx brothers movie? Perhaps we should wait and see what happens to us by accident.

High level functions, like language processing and production, reach down into lower level functions and color them, and everything ends up very interconnected. — Count Timothy von Icarus

Quite so. Nature and nurture are so intertwined that we should be very cautious about what distinctions we want to make.
It is even possible, isn't it, that when we decode the brain, we may find that the structure of thought mirrors the structure of the language we speak - and I do not mean any universal grammar, but the grammar of specific languages.
I'm may be naive, but I've always thought of thought as talking to oneself, like reading to oneself silently. It may be that language not only helps us to get our thought in order, but enables us to do so. I've encountered people who tell me that they can think in visual images.

I would take the private language to be at its strongest when it is a straightforward rejection of Cartesian absolute privacy. There are always outward signs of any "inner" experience. — Count Timothy von Icarus

I agree with that - whole-heartedly. But, coming back to philosophy after a long break, it seems clear to me that the philosophical context has changed.
There's a group of arguments dating back to the last century (which is not so long in philosophy) that I think of as neo-dualist. They seem to ignore the PLA, but nonetheless not so easily refuted by it. Bats, Mary's room, philosophical zombies. Not to mention the advances in neurology.

This jives with a broadly enactivist view. — Count Timothy von Icarus

Yes. I'll sign up to that.

If a stronger formulation is taken, e.g. that private rule following is impossible because of the possibility of unknown error — Count Timothy von Icarus

That's not quite how I take it, though I admit that W says much that looks as if that's what it's about. I would argue that the real point is that there is nothing that would count as error. There's no distinction between right and wrong, which means that "right" and "wrong" have no application to a private rule. Which makes it difficult to explain what the force of the rule is.

this seems to actually follow on for social rule following too, — Count Timothy von Icarus

Well, I would accept that if there is social agreement on how a rule applies in a new situation, that's how it applies. Rules of etiquette, for example. Linguistic rules.

So, with the lion, it seems clear we should know what "please bring more zebra steaks sir," means if the lion says it. However, there also seems to be a sense in which the lion's inner experience, which corresponds to outward signs, is more hidden from us because we do not share the same "form of life." Yet per the topic of this thread, I do think mammals might be said to share some sort of "form of life;" we can recognize each other's emotional states decently after all. — Count Timothy von Icarus

Quite so. The lion is, perhaps, not a typical example. Our interaction with lions is, perhaps, a bit limited. I'm sure you know that there are many other cases where we can already distinguish what many in the field are happy to call linguistic behaviour - even in bees.

And this seems true for any thought to me. — Count Timothy von Icarus

I wouldn't disagree with that.

In theory, it seems possible that given enough observations we might be able to determine to some degree "what a person is thinking about." But then the person's body is itself a sign of inner changes, which of course Wittgenstein seems to suggest. The body is just an imperfect sign in this respect, in part because we have a useful capacity for deception. — Count Timothy von Icarus

There's no doubt that looking at it more closely shows a much closer relationship between body and mind than traditional dualism would want to recognize.

This is in line with Augustinian semiotics. The body is sacramental, an outward sign of inner/higher realities. — Count Timothy von Icarus

I'm not sure that I understand this. But if you are saying that the Augustinian view that W seems to posit as his target has a bit more to be said for it than is usually recognized, I'll agree with you. It must be right that we learn language by observing and imitating the people around us. It's the focus on names that's the big issue.
Higher/lower realities are a bit mysterious to me. They're all equally real, after all.

Given this, it would make sense to pick popular religions and try them out, learning as much as you can, and giving each a chance to display their truth to you. When you find a religion you think contains truth, you practice it but remain skeptical, still searching other religions for more/more relevant truths. — Igitur

I'm puzzled about what you mean by trying religions out. You must mean more than going through some motions - something closer to taking them seriously. But the only ideas even close to religious that I've been able to take seriously (since I abandoned the church I was brought up in) don't require taking seriously the idea of a God or gods. Pascal seems to think that it is possible to do something like trying Christianity out, but he believes that I will end up believing it. I think he may be right; at least, it is a possible outcome. So even "acting as if" Christianity is true requires at least accepting that adopting it would be a good thing.
Then there's the issue of which variety of each religion one is to try out. It's simply not practical to think of trying out all the sects of Christianity or any of the others.
Religions do seem to think that certain altered states of consciousness. Granting their almost irresistible appeal, it seem to me obvious that they need to prove their worth in the mundane world, in which all religions need to exist. And I'm not convinced that their worth goes beyond that of a holiday - which is not negligible, but is far from the scope of anything I would consider a worth-while religion.
Trying things out is entirely reasonable. But surely, there needs to be some preliminary investigation and assessment of what is worth trying out.

We should go back to agreeing to disagree, since your understanding of probability 1 is contrary to, well, everyone else's. Is this a standard philosophical view? IMO you are choosing to confuse yourself about something very simple. — fishfry

Fair enough. We're obviously not going to reach agreement. For what it's worth, my diagnosis is that we disagree about the boundaries of the relevant context. For you, the assignment of 1 to the probability of an outcome which has actually occurred, is sufficiently defined by the context of probability theory. For me, it isn't.
I'm perfectly happy with our agreement (?) that it can be described as empty. That bothers me, but not you.

There's no meaning in symbols. That was the thesis. Mine and Searle's, at any rate. — fishfry

I can understand, roughly, why you (plural) believe that and there's a sense in which I agree. I just don't think it is the whole story.

Then you agree with my point. Credence could be influenced by evidence but need not be. — fishfry

Yes, I do. But I also think that credence should be influenced by evidence.

They might have little or no evidence themselves. Credence is just what people believe, evidence or not. If you redefine evidence as "what my friends believe," that way lies mob rule. — fishfry

Careful.

We should go back to agreeing to disagree, since your understanding of probability 1 is contrary to, well, everyone else's. Is this a standard philosophical view? IMO you are choosing to confuse yourself about something very simple. — fishfry

I hope you weren't just appealing to a vote. But if you mean that I should take more seriously the opinion of others who can be expected to know what they are talking about, then your question is valid. My view is not at all standard. That doesn't bother me. What does bother me is that the orthodox view is comprehensible and so not irrational. I'll have to reconsider.

Credence is a nice concept because we can apply the rules of probability to it, but we needn't know anything about the world to have subjective beliefs. — fishfry

Yes, I can see that. If you'll forgive me, I think that mathematicians and especially logicians tend to be to keen to get to the formalization and too quick to move from setting up the formalization to exploring it. I get stuck on the question what the value is of beliefs that have no connection with the world. To believe something is to believe that it is true.

The covid lockdowns were virtually global and were not a good idea. — fishfry

I agree with that. I went looking for the UN policy statement about this, but couldn't find it. But I did find a string of warnings about the dangers. Whatever went on in the US, disagreement was not suppressed everywhere.

Some Europeans are getting restless, are they not? — fishfry

Certainly. Their problems are different, but nonetheless based on their history. Like the Brexiteers, they want to have their cake and eat it. The difference is that their ambivalence is the question of Russia. The problem exists, but less acutely, for the whole of the mainland. Geography is inescapable, even in these times.

He all but fired the torpedo himself at the Lusitania to get the US into WWI. The Admiralty records are sealed to this day. — fishfry

Quite so. I forgot about the Lusitania.

Yes, I have thought before that a.nice counterexample to Wittgenstein's private language argument is someone writing a note to themself to remind them to do something in the future, a scenario that requires someone to enforce some relationship between words and things in the world for the sake of reminding themselves. — Apustimelogist

I'm afraid few decent philosophical arguments can easily be refuted by counter-example. Someone else can read the note, so it doesn't count as private language - even if it's in cipher.

Obviously, Wittgenstein was not a cognitivist (there are hints at it, yes); but, rather an early behaviorist at the time, influenced by Russell's own thoughts about psychology. — Shawn

There's a lot that makes him look like a behaviourist, because his target is what we might now call qualia. But what form of behaviourism does he sign up to? He doesn't use any of the appropriate language - stimulus/response, for example. (Even though the example of pain is wide open to that kind of model.) If he was a verificationist, it would not be unreasonable to read behaviourism into what he says. But he is equivocal.

Asking whether and how a proposition can be verified is only a special form of the question “How do you mean?” The answer is a contribution to the grammar of the proposition — Phil. Inv. 353

A contribution, not an answer.

I imagine coming to understand extraterrestrial or synthetic lifeforms capable of language would end up being a good deal more difficult than learning a new human language, although perhaps not impossible. — Count Timothy von Icarus

I guess the first problem is how we might come to understand that an extra-terrestrial or synthetic form was alive. We would have to apply the idea of a common humanity in a new context. We can do that, but I don't think we can work out the answer in advance.
I think it is helpful to look at what has been involved in decoding unknown scripts, starting with how we recognize that particular marks are a script, as opposed to a natural phenomenon or a decoration. It all depends on the assumption of a common humanity. But that won't apply to decoding the human brain. How that might apply in those circumstances is really not at all clear.

In the context of him analyzing a debate: debates turn on fixed points, and foundations are below those fixed points: a hinge can be replaced, but the foundations take time to change. — Moliere

Yes, that's true. But both have their uses in a building. Whether the same proposition can be a hinge and a foundation is hard to say. We could perhaps say that the same proposition might be used as a hinge in one context and a foundation in another. But not, I think, at the same time. Case studies would be interesting.

I'm being too poetic for the conversation. I'd take your or anyone elses reading over mine -- just some silly thoughts that came to mind. — Moliere

I didn't think your comment was silly. And we are discussing metaphors.

That makes perfect sense. I understand you now! Yes I was thinking of the empty set. — fishfry

:smile:

A tautology that doesn't assert anything is kind of a dead end in the reality tree, if I may wax poetic. If we're processing it, it's an error. It doesn't have any meaning.
Is that about right? — fishfry

Yes.

But anyway, mathematicians are trained to get used to empty objects. There's the empty set, and the empty topological space, and so forth. You get used to accepting vacuous arguments. So I don't see empty ideas as a problem. An empty idea is still and idea. The empty set is a set. — fishfry

Empty sets, etc., are defined in a context, which assigns a use to them (though perhaps not a meaning!). So that's different. The criticism is directed against ideas or uses that are not in a context that gives a use to them.

But if that -- then I still don't get it! Probability 1 says that something is certain to happen. If I add 1 plus 1, I am certain to get 2. If we have a slow computer, we put in 1 plus 1 today, and we are certain, with probability 1, that the computer will output 2 tomorrow. What's wrong with that? — fishfry

Quite so. I'll overlook the intrusion of time. My point is different.
The use of "probability=1" is defined in the context of the table (function), that is, in context where a range of possible outcomes is given, one of which will turn out to be the outcome. Outside that context, it's use is not defined. Or rather, its use is defined as "= true". That is quite different from "probability (A v B vC..) = 1" meaning "the total of the probabilities of A v B v C... is 1", that is, its use in defining the range of the probabilities of the outcomes. So it serves no purpose, apart from confusing me.

When the knight is captured it doesn't feel good or bad. The player may feel good or bad. I'm back to the Chinese room. Searle says the room doesn't know what any of the Chinese sentences mean. So if you agree meaning is in the mind, that's what I believe also. — fishfry

Meaning is a slippery word. One might want to object that the meaning of the word "table" is an object in the world. But we make the words and we use them.

I say that it is NICE if my credence is based on some evidence. Maybe I put some work into forming my opinion. — fishfry

I would put it stronger, but it is true that credence is not necessarily based on conclusive evidence, and may be not be based on evidence at all.

I hope I'm making my point. We are all obliged to place high credences on many things that we can't possibly have the slightest idea about. The electric grid will be up tomorrow. How the hell do I know? Did I personally inspect every faulty transformer that's about to blow, and take down half the county with it? — fishfry

You're right. Most of what we know, we know at second hand. If we had to prove everything ourselves from scratch, we would be very limited. Standing on the shoulders of giants and even midgets is essential. Philosophers like to brush that aside and only pursue the gold standard. There shouldn't be any problem about assigning a credence to what we are told by others. I would count it as evidence. Why not?

Point being that I have a credence, which I found by simply thinking about it for a moment, about a situation in which I can't possibly know the first thing, and actually I haven't looked into it much. So I know nothing. But I have an opinion! — fishfry

Quite so. We react instantaneously and without conscious thought to most of what's going on around us. We would never keep up if we had to sit down and reason everything out.

But, if I've got any sense, I will give more credence to credences assigned by someone who knows what they're talking about over credences assigned by someone who doesn't. That's reasonable, surely?

I would say at the least, that many of the authoritarian types in our society took advantage of the situation, in a manner not supported by the science. And anyone who pointed that out, was cancelled, had their career ruined, their jobs or professional licenses taken away. — fishfry

Well, the opposition in the UK were certainly not silenced. Their voices were heard throughout. The problem is that without an estimate of what would have happened without lockdowns, we have no way of assessing their success. It's has always been regularly used with Ebola outbreaks, so it must have its uses. But those incidents have been relatively contained. I think the scope and duration of the COVID lockdowns was the problem.

I don't like the idea of giving up national sovereignty to such an undemocratic institution as the EP. "Brussels" has become a pejorative and not just the name of a city. — fishfry

It's not that simple. Every time you sign a treaty, you give up some sovereignty. It's a question of balance - quid pro quo.

That last bit I didn't know anything about, the Northern Irish. — fishfry

It's long and peculiar story. There'll be lots of stuff on the internet if you want to look it up. The problem was that it needed free access to both UK and Republic markets. While both were in the EU, it wasn't a problem. But when the UK left, it was not possible for them to continue free trade with both and yet could not give up either. It was obviously insoluble from the beginning, but nobody bothered until the reality hit.
They seem to be reasonably satisfied with the most recent arrangements, but they are a bit of a lash-up.

I went on a business trip to Cork once, it was so lovely. — fishfry

I'll bet. It's a very beautiful place. The whole island is - outside Belfast.

Is that right? Is there Churchill revisionism about? — fishfry

Well, there's always been a counter-narrative. The left wing have never liked him. There was the Sidney Street siege, Gallipoli, the famine in Assam in 1943, and pet research projects that wasted a lot of money and it took a lot of persuading to get him to accept the invasion of France. No financial scandal that I know of, which makes a nice change. I think most people accept he made a critical difference in WW2.

I think it does challenge foundationalism, which is why Lee Braver named his book on Wittgenstein and Heidegger ‘Groundless Grounds’. — Joshs

As it happens, I'm in the middle of reading this. However, I was hoping to find something that questioned the need for bedrock assumptions. I was also commenting on this metaphor. Wittgenstein seldom relies on just one metaphor. I like the river-bed much better. Nonetheless, if I ask myself what the river-bed is founded on, I find myself confronted with the planet earth. No bedrock there.

That's how I understand them: "hinges" are almost too mechanical for foundations: and in a way hinges can only be placed upon structures build on foundations... hrm. The up-down metaphor — Moliere

I think he presents the hinge metaphor in the context of analysing a debate - elaborating the idea that the debate turns on a fixed point. I would assume that this only applies to the context of the debate, and that what was a hinge may become a bone of contention in another context.

In his own metaphorical terms, I think when Wittgenstein says that his spade is turned when he hits the bedrock of "forms of life," many would simply suggest that he buy himself a shovel or a pick axe. — Count Timothy von Icarus

Well, even the expanded metaphor makes a good point. Foundations need to be in a different category from what is founded. More logic doesn't give you the foundations of logic and so forth. However, I do agree that the "bedrock" metaphor doesn't challenge foundationalism itself, and that's always puzzled me. The radical issue is whether foundations are always necessary. After all, it turned out that there are no foundations of the planet.

If our culture and language impact brain development in early childhood, there is not just an abstract difference between individuals of different cultures, but a physical one. — Lionino

But even that accepts that we are the product of our environment as well as our genes, and so undermines one form of essentialism. However, if I embed myself in second culture, that will affect what got embedded with my first culture and change that. The brain continues to change and develop throughout life.

Wittgensteinians often make claims that are the opposite of "common sense." For example, the claim that a man who washes ashore on desert Island loses his ability to make and follow rules, but then regains this capacity when a second person washes ashore later. Obviously, a great many Wittgensteinians (as well as people generally) find this to be somewhat absurd. — Count Timothy von Icarus

Does Wittgenstein appeal to common sense? He certainly relies on our intuitions, since we are expected to think things our for ourselves, but that's not the same thing, is it?
That claim is indeed absurd. Robinson Crusoe didn't forget everything he learnt when he washed ashore. On the contrary, he continued to embody the culture he came ashore with. No doubt, as he continues alone, he is very likely to adapt and develop what he has learnt and may move away from the starting-point without being aware of the fact. (In the fiction, Defoe ensures that doesn't happen.)

That's one way of framing it in the "Tarzan Versus Crusoe," discussion at least, but there is also the idea that Crusoe cannot make new rules so long as he is alone, and any continued rule following can only be judged by an absent community. — Count Timothy von Icarus

That's not wrong. But it is likely that after enough time, his rescuers will find deviations and adaptations in his way of life.

Unless some "tribe" (a favorite thought example of Wittgenstein) is in possession of the truth itself and the rest itself, we are dealing with opinions and beliefs held at that time and place to be true. The truth is, we are not in possession of the whole of the immutable truth. Throughout history human beings have held things to be true that turn out not to be. This is not something to be solves by attacks on the truth of relativism so understood. — Fooloso4

There's a lot of scary rhetoric about relativism. But it seems to me the greatest danger is precisely believing that one is in possession of the absolute truth and therefore does not need to compromise. That has serious real-world consequences.

all of Wittgenstein's complaints about "philosophers using language wrong," can be waved away by simply claiming that Wittgenstein is not privy to the language game used by these philosophers. Perhaps being a metaphysician, a Thomist, etc. are all discrete "forms of life?" — Count Timothy von Icarus

You're not wrong. I would rather say "discrete language-games" or, in the case of religion and science "discrete practices". But there's always the common ground of human life to appeal to. After all, if we can agree that we disagree, we must have something in common. Mapping that is always a useful first step.
That confidence - that there are rights and wrongs about how to use language - seems to me to be something of a hangover from the Tractatus. But his practice seems to have been different. Anscombe's story about why it looked as if the sun goes round the earth indicates a rather different practice.

Nevertheless when people use Wittgenstein's ideas, they have to interface with other arguments. Perhaps you can do that solely in his terms, but honestly trying to do it equitably makes it very difficult for Wittgenstein. Which is a weakness of his, rather than of philosophy. — fdrake

Quite so. In fact, if you want to engage in debate, you need to meet on common ground, and starting from a Wittgensteinian position is unlikely to do that.

Despite the theories about forms of life, I do not think it is vague unless one treats it as a theory. He has no theory about forms of life, he is simply pointing beyond language as something existing in and of itself to our being in the world and all that entails conceptually and practically. The boundaries between one way of life and another or one practice and another are not fixed and immutable. — Fooloso4

I agree with that. I prefer to think of those notions as ways of approaching problems, needing to be adapted to apply to specific situations, rather than doctrines or protocols.

We can agree to disagree, but I don't understand why you think probability 1 is "empty." — fishfry

This is a bit embarrassing. I was using a bit of philosophical jargon, which seems to be out of date. You must have been wondering how empty sets were relevant. The expression derived from the logical positivists who classified tautologies as empty or trivial because, although they are not false, they do not assert anything. For them, proper, non-empty, statements were those that could be verified or falsified. The idea is used in Peter Unger's book Empty Ideas

Unger’s argument is that thinkers used to put forward arguments whereby “if what they said was true then reality was one way. If it was untrue then it was another way .... They were sticking their necks out.”

See Review of Unger "Empty Ideas (I don't recommend the book. For all that the review talks about philosophy being fun, which I approve of, this book is hard going for rather small rewards.) I don't agree with this application of the argument, but the idea can be useful.

Some examples may help.
1) An obvious case is "This sentence is true".
2) If I assert that snow is white, it is empty for me to assert in addition that I believe that snow is white.
3) Tarski's redundancy theory of truth (which, in case you don't know, is popular among philosophers) says that "snow is white" is true iff snow is white.
4) The probability of p = 1 iff p is true iff p

Law of unintended consequences is a rule of general life too, right? — fishfry

Yes. But I thought that unintended consequences were events in the empirical world.

I don't see why. The importance to some people of the world chess championship is not inherent in the rules of chess. Symbolic systems have no meaning in them. It's the people who supply meaning. — fishfry

We're using "meaning" in slightly different ways. The paradigm case of a symbolic system for me is language, and that has meaning - if it didn't, it wouldn't be a symbolic system. A symbol is created by setting up rules for the use of an arbitrary character or object. So the rules of chess set up rules for the use of the various elements of the game. I'm inclined to say that establishes the meaning of the symbolic characters within the game, and I would agree that that meaning is "in the minds of" the players and spectators.
I also agree with you that the significance of the game (e.g. its interpretation as a war game, suggested by the names of some of the pieces, or the value attached to titles like "grandmaster") is not established by the rules of the game. So there are layers of meaning (or significance), depending on context.

Credence is not fantasy. — fishfry

Yes, I'm agreeing with you. But I want to distinguish between the two by saying that credence should be based on evidence or at least plausibility and that fantasy has neither of those. That's all. How else would one separate them?

The security incompetence is of a degree that invites suspicions of complicity. Just as in the JFK assassination, where the Secret Service was likewise grossly incompetent. Biden has other problems this week. Rumor has it he's dropping out of the race this weekend. But that might just be spin from his enemies (in his own party) leaking to the press to weaken him. — fishfry

Yes, I remember the JFK story. I was once, briefly, an auditor (annual accounts for companies and other institutions). They drummed into me that when something was wrong, cock-up was more likely than conspiracy. But that doesn't prevent suspicions.

Well if he's not free-market he's a collectivist! Generally speaking. — fishfry

The days of dogmatic nationalization of the means of production are long gone. Nowadays, at least in the UK, it's a pragmatic issue and we have a number of half-way houses and regulators for specific areas.
But isn't the free market a collective social institution? One of the basic functions of the state is to supervise and enforce contracts, and the companies and other collectives that operate in the market are themselves collective institutions - and they aren't accountable to voters.

I did hear that he wants "closer cooperation with Brussels," meaning that he'll be yet another British PM stabbing Brexit in the back. I think it might have had a chance to produce good results if the politicians had respected the will of the people. — fishfry

There was a lot of back-stabbing in the aftermath of the referendum. It was not pretty. But I don't think any of the Prime Ministers intended that. Brexiteers told everyone that the EU could be adjusted to suit what they wanted. The EU were reluctant to do so - and why should they? It's not as if public opinion in
the EU thought Brexit was a good idea. Brexiteers labelled any compromise as "stabbing Brexit in the back"; it seems they didn't grasp what negotiation is all about. The only people who were stabbed in the back were the Northern Irish who were thrown under a bus by Boris Johnson.
I voted remain, but had serious doubts about the ultimate EU project ("ever closer union"). Europhiles didn't pay enough attention to the longer-term history of the UK (since, say, 1700).

Miscalculation or malevolence, take your pick. — fishfry

Forgive me, but I can't think of anyone, malevolent or not, who actually benefited from the lockdowns apart from the vulnerable groups - older people, people with health issues. I plump for miscalculation, in spite of the UN warnings, so by British politicians.

Interesting that after the war, the British people showed Churchill their appreciation by voting him and his party out of office at the first opportunity. — fishfry

Yes. The conservatives thought they could go back to the way things were before the war. The voters wanted a fresh start. They got it - even the conservatives had to accept the new ways. It took them 50 years to unpick it and they're still not done.

I believe he (sc. Churchill) said that "History shall be kind to me, for I shall write it." — fishfry

Well, people were kind to him for quite a long time. But that's changing now.

Well I'm cycled out on this I think. At the end of most of the convos I'm in. I could let this go soon. — fishfry

I don't think I have any more to say about probability = 1. So let's agree to disagree. I think I understand at least where and why we disagree. I'm sorry I can't make myself clear to you.

That's a tall order (sc. the relationship between the purely mathematical abstractions in the context of what I'll call the everyday world). You mean differential geometry, the super-abstract geometry of Riemann, applied to general relativity? Or the math of quantum field theory? Or do you mean something far more prosaic? — fishfry

If I were qualified to tackle those areas, I would take them on. But I know better than to talk about them without a reasonably thorough understanding of them - which I don't have. I have to settle for the prosaic. Which matters too, I think.

Since the context of the use of the concept has changed, the meaning of the original concepts may or may not have changed, but may well be seen differently. Does that help?
— Ludwig V
No, I think you obfuscated the point. — fishfry

I can see why you think that. But I'm fascinated by the fact that we can posit some relatively simple rules and draw such startling and unexpected conclusions from them. How is that possible? For you, that's your home, but for me it is foreign - and confusing - territory.

I said there is no meaning in math. That when we manipulate symbols according to rules, there is no meaning that's part of the formal game. But of course "in the back of our minds," we do know what it all means. We have some every day experience in mind, even though that has no bearing on the symbology we write down. — fishfry

To me, that's paradoxical. But, from another perspective, very helpful.

You're the pro, so when I say metaphysics it just means, "What's really true about ultimate reality." Or something like that. — fishfry

That's good enough for this discussion.

The metaphysics is that when we say, "The probability of rain is 25%," we're making a statement about the REAL WORLD. When I say that "My credence it will rain is 25%," I am making a factual, verifiable statement about my subjective state of mind. I don't need to know anything about the real world, though I do base my credence on the available evidence. Clouds in the sky, for example. But in credence, I'm not making a claim about the world. I'm making a claim about my own subjective degree of belief. — fishfry

OK. It's just that a link to the real world (whatever that is) is what makes the difference between something interesting and useful and a fantasy.

Maybe that's all there is.
— Ludwig
Ok. Not disagreeing. — fishfry

For me, the formal representations in decision theory do have the prospect of articulating our decisions more precisely and enabling us to make more coherent and better balanced decisions.

I read Spiked Online (https://www.spiked-online.com/) as my main source of British politics. They're slightly right of center. I gather Starmer is a typical collectivist leftist, but that the so-called "conservatives" mucked up their own charter so badly they deserved to go. Maybe he's a better guy than I've heard. — fishfry

"Slightly right of centre" is about right. "typical collectivist leftist" sounds like slapping a conventional label on something without thinking about it very much. So it's very likely that he is better than you've heard. Most of the British media is right wing, so most of what was written was, essentially, political. (Perhaps the most significant thing about our election is that the normally right wing press abandoned the Conservative party. That's not happened since Blair got elected in 1997.) You have to realize that our right wing political people have no hesitation about government action when it suits them; but they often disguise it so they don't have to take responsibility for the outcome. Starmer's programme is very moderate and addresses areas where almost everybody agrees that existing, supposedly free market, structures have completely failed to deliver.

I'm not saying one thing or another, just that transparency and accountability are in short supply from the government this week. — fishfry

I'm not surprised. It's clear that there was a major screw-up on the security front. So the Government was bound to take some flak. So it went in to self-protection mode. All Governments do that. It doesn't usually work very well. It seems likely to reinforce Trump's lead in the election stakes. Biden must surely wish it had not happened.

Is Charlie someone's idea of a philosopher king? Poor guy, his entire role in life from the time he's a child is wait for his mum to die, then she turns out to have great genes and lives till 96. And a year later the poor guy gets a serious cancer. Feel bad for him. I always like Liz, she was a very great lady. — fishfry

I also feel sorry for Charlie. He's never been comfortable in his role. No, he's nobody's idea of a philosopher-king. He's there to be the unity that ties us all together, despite our disagreements and whatever happens in politics. Simply by existing. A philosopher-king would be completely unsuited to the role. It needs someone who doesn't think. He does, though not very well. That's one big reason why he's not suited to the role. But he will do his best, and I'm sure it will serve. In the US, that role was served by the Constitution. That seems to have become a political and legal football too, which really does not help.

Winston Churchill said that the greatest argument against democracy was a five minute conversation with the average voter. I believe that! — fishfry

He did, and he's right. But the full quote is:-

Many forms of Government have been tried, and will be tried in this world of sin and woe. No one pretends that democracy is perfect or all-wise. Indeed it has been said that democracy is the worst form of Government except for all those other forms that have been tried from time to time. — House of Commons, 11 November 1947

He also said: -

My idea of it (sc. democracy) is that the plain, humble, common man, just the ordinary man who keeps a wife and family, who goes off to fight for his country when it is in trouble, goes to the poll at the appropriate time, and puts his cross on the ballot paper showing the candidate he wishes to be elected to Parliament—that he is the foundation of democracy.
And it is also essential to this foundation that this man or woman should do this without fear, and without any form of intimidation or victimization. He marks his ballot paper in strict secrecy, and then elected representatives together decide what government, or even in times of stress, what form of government they wish to have in their country. If that is democracy, I salute it. I espouse it. I would work for it. — House of Commons, 8 December 1944

Great man. But his record before WW2 was, let's say, mixed.

Covid lockdowns were scientism, not science. Science as a means of social control, not as a path to enlightenment. — fishfry

Covid wasn't dangerous enough. When people realized that it wasn't the plague or Ebola or HIV, they felt, not unreasonably that the risks and benefits were not sufficient. They were misapplied as a result of a political miscalculation. IMO.
The problem got serious in the two world wars 100 years ago. It was very successful in developing new weapons - arguably, it was a major factor in winning them. And, then, of course, "science" got taken up by institutions that were not capable of grasping what it was all about and misused in the service of other interests.

Ok, list of events and their associated probabilities. — fishfry

I wish I had thought of that. But I do think the layout is significant. But I think that's over.

Please do not hesitate to make several arguments at once. Thank you in advance for your insights! — LFranc

1 Singer doesn't ask himself what "needs" and he doesn't distinguish between relative and absolute poverty. (There may be stuff about this that I'm not aware of, but I very much doubt there's anything definitive.) Singer's "argument" is grossly exaggerated and seems more like a slogan than a proper argument. When you get in to the detail, it's obvious that things are not anything like as clear-cut as his rhetoric. Charity has its place in life, but this isn't it.

2 The argument, as we can see, and as every charity knows, is almost completely ineffective. Everybody (most people, many people) feel guilty for a while and then either works out a defence or just forgets it. This is not what motivates people.

3

So my conclusion for this topic is -- we don't have an answer. Nothing. Rien. Morality is a chore. — L'éléphant

A moral argument that presents morality as a duty and a chore has missed the point of morality - or at least the point of charity. It should not be about lecturing and bullying people. Not only is it counter-productive, but it leaves out love (prioritizing the welfare of some people over others) and compassion, which, if not patronizing, is the only proper motivation for charity. (There's a much better idea than Singer's in Indian philosophy - that the opportunity to give is a privilege and the we should thank the people that we give to rather than expect them to thank us. Whether it is more effective than Singer's is debatable, but still I prefer it to Singer's hectoring.)

However, there are other considerations here.

A Justice. The benefit of society is that we are stronger and better together. If resources are not shared, especially in times of trouble, there is no point to it and in extremis society does break down - so everybody suffers. That's not well defined, and you can always dismiss it as envy, but there are powerful motivators at work here. (Neither communism nor capitalism). (This comes under the heading of requirements for a society to function, which may or may not count as morality. But whatever its name, it matters).

B Enlightened self-interest. It isn't just those are homeless who benefit from help. We all do, because we don't have pictures of misery lining the streets we walk down, we don't have so much thieving and robbery, we don't have hungry mobs rioting and looting and so on. Helping an alcoholic get their life under control does not just benefit the alcoholic, but also the rest of us. It's not grand morality, but it is an effective motivator.

Probability = 1

P(X=1|X+1=2). Where X is a random variable. That'll give you probability 1.
— — fdrake

Yes ok, a true proposition has prob 1 and a false one 0. I don't see how intermediate probabilities could apply. — fishfry

We are very close here. However, I take the fact that intermediate probabilities don't apply to mean that in a context where intermediate probabilities don't apply, "probability = 1" is empty.
— Ludwig V
I was building on his point and your reply. We have somewhat different opinions. I'm not sure that anything important hangs on it, so perhaps we should leave it at that.

MATHEMATICS

You keep trying to frame this discussion in terms of speech acts. I'm not sure what point you are making. — fishfry

Applications are always at the historical origin of every abstract theory. Not specific to probability. — fishfry

I'm interested in the relationship between the purely mathematical abstractions in the context of what I'll call the everyday world. I'm not trying to undermine the concept of mathematics in any way.

I'm not saying there's no meaning in math. I'm saying that the math itself doesn't refer to its meaning when we're doing the formalizations. The meaning is not to be found in the math, but rather in the minds of those who do or use the math. Is that better? — fishfry

Yes. Not perfect, but better. I understand meaning to be the use of a symbol, in the context of related symbols. So I would say that pure mathematics does have a meaning, defined by the interacting concepts in play. When the interpretations and applications come into play, we have a new context. Since the context of the use of the concept has changed, the meaning of the original concepts may or may not have changed, but may well be seen differently. Does that help?

But I do think that interpretations and applications are not an optional add-ons to an abstract system.
— Ludwig V
They are not optional add-ons. So they are mandatory add-ons? Or not add-ons at all? Didn't understand that. — fishfry

That's a very good question. What I said was not quite right. I refer you to what I said about meaning and use above.

Right. Well that's the beauty (or the flaw I suppose) of mathematical abstraction. Mathematicians just think a probability distribution is a particular kind of function on a probability space. There is no meaning or metaphysics. — fishfry

Well, I've explained what I mean by meaning. I hope that meets the case. But I'm not at all clear what you mean by metaphysics. I would hope that nothing that I say is metaphysical, but the word is so badly defined that I might have erred unwittingly.

POSTERIOR PROBABILITY

Posterior probability. Updating your probability with new information. Of course once something has happened, the probability is 1 that it happened. But then the probability is 1, so it makes sense to say that, right? — fishfry

I read the Wikipedia article. The context seems to be Bayesian probability, which is a different kettle of fish. It's not, if I understand you right, about the basic mathematical function, but about the inputs to the function, so we're talking about an application, right?

I'm saying we can substitute credence for probability, so that we can apply the techniques of probability without being burdened by metaphysics. I didn't say it was more true, only more workable. A pragmatic shift in view. — fishfry

The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood via an application of Bayes' rule. From an epistemological perspective, the posterior probability contains everything there is to know about an uncertain proposition (such as a scientific hypothesis, or parameter values), given prior knowledge and a mathematical model describing the observations available at a particular time. After the arrival of new information, the current posterior probability may serve as the prior in another round of Bayesian updating. — Wikipedia

OK. It's a small point, but wouldn't be clearer to say and more consistent with the timelessness of mathematical functions, to say that when new information becomes available, a new probability is established, which is substituted for the old one? I think that's compatible with what Wikipedia says.
Bayesian probability is a scenario, or posits a scenario. There's nothing wrong with that. Traditional probability does the same thing with its reliance on gambling scenarios. You're right that it is not a question of truth or falsity, but of enabling us to apply an existing concept in a new way - and one that is particularly interesting in view of the fact that we do ask about the probability of single cases.
I don't see the metaphysics in standard versions of probability. Can you explain?

BAYES

Yes ok. If a baseball hitter has a batting average of .250, we would say he has a 1/4 chance of getting a hit on his next at bat. But of course this is absurd, the specifics of his next at bat are subject to all kinds of variables, how he's feeling, how the pitcher's feeling, the humidity and temperature of the air, etc. — fishfry

This way of articulating chance or probability depends on a "frequentist" concept of probability. One can then understand what the probability means as a phenomenon over a number of cases. But that makes it difficult to see how it applies to a single case. I guess a way of making it concrete is to see it is a question of the odds on a bet. That'll work for insurance and precautions in general, and in planning to take account of possible eventualities. But that only has application in the context of balancing risk and reward - decision theory. Maybe that's all there is.

MISCELLANEOUS

Well I'm concurrently dabbling in the political threads in the Lounge, so this all seems like light recreation by comparison. — fishfry

Yes. Public/political life - the "state of the world" - has all the ghastly fascination of watching a shipwreck. I expect you know that there's been a change of government in the UK. Suddenly I found myself unreasonably optimistic. Well, until I heard about the events in Pennsylvania.

... we ask a hundred million people in the street to vote on how we should run our society! I believe it was Socrates who distrusted democracy. "In Plato's Republic, Socrates depicts democracy as nearly the worst form of rule: though superior to tyranny, it is inferior to every other political arrangement." So says Wiki. We can certainly see his point. — fishfry

Yes. If you expect the democratic vote to determine policy, you are going to come unstuck. Whether it was Socrates or Plato who rejected democracy is underdetermined and likely always will be. Small correction. The view in the Republic is that democracy will always turn into tyranny, because demagogues will take over and establish themselves. Say no more. The thing is, Plato blocks a proper discussion of the issues by positing someone who gets the answers right. But sometimes there is neither right nor wrong and sometimes actual people get things wrong. So his appeal to the philosopher-kings avoids the real issues. Popper says that the vital thing about democracy is that you can get rid of the ruler when they screw up.
Well, perhaps one can quote the old saying that those who do not understand history are doomed to repeat it.

I know that whereof I cannot speak, thereof I must put a sock in it. That's as far as my knowledge of Wittgy goes. Also, that he thoroughly misunderstood Cantor's diagonal argument. I seem to recall that. — fishfry

Yes, that bit of the Tractatus is much misunderstood. There are suspicions that he was flat wrong, but that would be heresy. He is, perhaps, a rather specialist taste. Yes, his interpretation of Cantor and Godel is vigorously contested. I have the impression, however, that almost everything about those two is contested. I'm not taking sides yet.

I'm a new mysterian. I don't think we're going to know. We can't know any more than an ant on a leaf in on a tree in a forest can know about the world as we understand it. But the ant knows warm from cool, what to eat and what eats it. It has a metaphysics! — fishfry

H'm. Metaphysics again. Ants know what they need to know. There's a concept of the "lived world" that's quite useful in cases like this. Sure, whether you call it a metaphysics or a lived world, we have one too.
But there's a difference. We contemplate Euclid's geometry and start wondering whether the parallel postulate is really necessary. Next thing you know, whole new worlds have opened up. Or Mercator realizes that conventional maps are all wrong and works out how to project a spherical surface into two dimensions. So something new happens. We can do this in a generation or two, whereas evolution can take a very long time indeed.
We'll never know everything because we'll always find new things to know.
There are too many people around who think that science has the answer to everything or can discover the answer to anything. That view is overblown and we do need a more tempered attitude to it.

I haven't explained what I mean by a probability table. I meant something like this. (Forgive my primitive graphics)
Probability
{E(1) v E(2)} 1
Possible outcome E(1) 0.5
Possible outcome E(2) 0.5
not{E(1) v E(2)} 0

When the outcome is known, all that is required is a foot-note - "The outcome was <E(1) v E(2)>" - nothing more.

This is one of those times a def is an ax and vice versa. You can say probability is the study of measurable spaces with total measure 1; or you can say that this property is one of the axioms of a probability space. It's the same thing, really. — fishfry

Yes, I get that. In the sense that we've discussed, it is a speech act either way. However, axioms and definitions are not the same kinds of speech act. I expect there's a mathematical explanation of the difference. But they are both setting up the system (function?) - preparatory. So they are both different from the statements you make when you start exploring the system, whether proving theorems or applying it.

Posterior probability. Updating your probability with new information. Of course once something has happened, the probability is 1 that it happened. But then the probability is 1, so it makes sense to say that, right? — fishfry

This is a different speech act, even though it may be the same sentence. The context is different.

The point, or my point anyway is that the mathematical theory of probability is entirely abstracted from any meaning or interpretation or philosophy of "probability" that anyone has ever had. — fishfry

So what does it mean to update the table? Are you correcting it, or changing it, or what? It seems like something that happens in time. You might be constructing a new table, I suppose.

But then the probability is 1, so it makes sense to say that, right? — fishfry

In a way, yes.

P(X=1|X+1=2). Where X is a random variable. That'll give you probability 1.
— fdrake
Yes ok, a true proposition has prob 1 and a false one 0. I don't see how intermediate probabilities could apply. — fishfry

We are very close here. However, I take the fact that intermediate probabilities don't apply to mean that in a context where intermediate probabilities don't apply, "probability = 1" is empty.

In that sense, my view of probability is not overloaded with philosophical interpretations. Whether that's good or bad I'm not sure. — fishfry

.
It depends whether you are a mathematician or a philosopher.

Perhaps the formalisms are irrelevant to your thoughts. — fishfry

Hardly irrelevant. I think I understand your point about abstract systems and I am interested in interpreting or applying the abstract formal system; but that begins with the system.
However, I can't help remembering that Pascal was interested in helping his gambling friends, so the application drove the construction of the theory. In the same way, counting and measuring drove the construction of the numbers - not that I would reduce either probability theory or numbers to their origins.
But I do think that interpretations and applications are not an optional add-ons to an abstract system.

Math doesn't do meaning. That is the beauty of abstraction. — fishfry

Yes, I get that. There are even some beautiful arguments in philosophy. I'm sometimes tempted to think that the beauty is the meaning. I would, sometimes, even go so far as to agree with Keats' "‘Beauty is truth, truth beauty,—that is all/Ye know on earth, and all ye need to know." But only if all the philosophers are safely corralled elsewhere.

I'm not a normal philosopher, with a fixed (dogmatic, finalized) doctrine. I'm exploring, with a view, if I'm successful (and I rarely am), I'll be able to understand how these concepts are related and maybe even construct some sort of map or model of them. (I'm heavily influenced by Wittgenstein, I'm afraid, though I'm incapable of imitating him. But that is why I don't do metaphysics.)

All the real world usages of probability, from games of chance to the insurance industry. The way people think about all these correlations actually being causations, somehow. The way philosophers try to think about causality. — fishfry

I've lost the context of this. I do hate the way that some people talk of chance and probability as if they were causes. Most philosophers (after their first year or two) will jump on that very firmly and, yes, the conventional doctrines about causation have little to recommend them. As for real world applications, they are derived from the mathematics, but heavily adapted. For one thing, they don't atually assign probabilities, but estimate them, and buffer them with likelihoods and confidence intervals. Almost a different concept, linked to the mathematics by the "frequentist" approach.
Probability is the main way that we try to limit uncertainty, find some order in the chaos.

When pressed, I believe there must be something universal in all this. If it's just random, that's too nihilistic for me to bear. That would be my philosophy of God, which I never thought of that way before. Thanks for the example! — fishfry

You're welcome. I agree that there is something universal here. It is the faith that there is order to be found in the chaos we confront in our lives. Some people think that is a truth about the world, but I'm not at all sure it is that. The evidence points both ways. However, chaos is worse than anything. We will do anything, think anything, to achieve some way of organizing the world. Probability is not ideal, but it is better than nothing.

Credence, or subjective degree of belief. You ask 10,000 specialists in analytic number theory whether they think the Riemann hypothesis is true. You take the percentage of yesses out of the total to be the credence of the group. — fishfry

If you think about why you select specialists to ask, you will see that your are not escaping from the serious difficulties about achieving knowledge, in particular, the fact that conclusive proof of anything is very hard to achieve (not impossible, I would say, but still difficult). We have to weigh one argument against another, one piece of evidence against another, and there seem to be few guidelines about how to do that. Eliciting the consensus of those who are competent is one way of doing that - although far from certain. Asking 10,000 random people in the street what credence they have in the Riemann hypothesis won't help much, will it?

Better clarify that. Everyone's personal opinion is subjective, that's the beauty of the concept of credence. But the FACT that 75% of them think X and 25% think not-X, that's objective. So we can use the rules of probability without having to do metaphysics. — fishfry

Oh, I agree that there is a fact there. The question is what it's value is and that takes us back to the evidence.
So - the great virtue of Bayesian probability is that it will give you a probability for a single case, which neither mathematical nor empirical probability can do. I still have a problem, because we normally express a probability in terms of the number of times it can be expected to show up in a sequence of trials. But that limitation, strictly speaking, means that its application to a single case, which we very often want to know, is extremely murky. Expressing it in terms of making bets helps.

Even though we can't know probability of God; every single person in the world can assign that proposition a credence. That's why I'm big on credence. It takes the metaphysics out of probability. We aren't studying anything "out there," we are only studying our own subjective degrees of belief. — fishfry

But each of those people, if they are rational, will be assigning their credence on the basis of the evidence. But in this case, and many others, the issue is what counts as evidence and how much weight should be placed upon it.

We started off talking about "probability - 1" and in order to understand that, we've explored the construction and meaning of the probability table. I think that was all constructive, but we've got as far as we can with it. Now we are talking about Bayesian probability and what credence is.

I know that I can be a bit relentless. If I'm boring or annoying you, please tell me and I'll shut up.

Calculus or analysis is the perfect example of us getting the math right without any concrete foundational reasoning just why it is so. — ssu

Oh dear! That's a real can of worms, isn't it? Some philosophers would argue that the engineers have got it right. Perhaps it is best to start with the foundation of philosophy - a question. "What do you mean by a foundation?" But I do know that some mathematicians regard philosophers in much the same light as they regard engineers. Still, it's all great fun and often elegant and beautiful; I don't want t be a grinch.

All of these sets are of finished "actual infinity", not the potential infinity as the Greeks thought. — ssu

Yes. I remember. I don't think I ever replied properly. I can see why those definitions might seem reasonable. But it seems better to me to say that "potential", "actual" and "complete" have no application here. On the other hand, I can see that there are real problems here, so I'm not sure that these labels matter very much. Do they solve any problems?

To my reasoning it doesn't. And both Leibniz and Newton could simply discard them too with similar logic. — ssu

The trouble is that, like plastic, if you discard them, they just come back to haunt you. Perhaps Berkeley had a point. Perhaps the concept of incommensurability could help here?

Writing x^2 means x². A bit lazy to use this way of writing the equation. — ssu

Thanks. One has to do something when one doesn't have the keyboard for the symbolism. Handwriting is much more flexible.

Yet using the diagonalization method we get also many other very interesting theorems and proofs and also paradoxes, which in my opinion are no accident. — ssu

I didn't realize that argument was so powerful.

“They are neither finite Quantities nor Quantities infinitely small, nor yet nothing. May we not call them the Ghosts of departed Quantities?

He was a great wit. I'm still trying to make up my mind whether he was a great philosopher or a complete charlatan - even possibly both. This comment is typical. It is very sharp, very pointed. But the calculus is embedded in our science and technology.

I just wanted to describe the seemingly paradoxical nature of the infinitesimals. — ssu

Yes, I see. You can remove an infinitesimal amount from a finite amount, and it doesn't make any difference - or does it?

Set theory gives us the actual infinity — ssu

What do you mean by "actual infinity"?

I'm afraid I don't know what "^" means. But the paradox in the concept of the infinitesimal - that it both is and is not equal to zero - Is not difficult to grasp - and I realize that that's what the concept of limits is about. (But the idea of a limited infinity is, let's say, a bit counter-intuitive.)

Zeno's least eating dog has to eat something, but then if let's say eats from Platons dog 1, then the food hasn't decreased! — ssu

I don't get this. There's enough food for all the dogs, so why does it have to take some from Plato's dog? If it does, then of course the amount of food for Plato's dog has decreased, but the food supply is infinite, so the amount of food available overall hasn't decreased. What's the problem?

Well, in my view mathematics is elegant and beautiful. And it should be logical and at least consistent. If you have paradoxes, then likely your starting premises or axioms are wrong. Now a perfect candidate just what is the mistake we do is that we start from counting numbers and assume that everything in the logical system derives from this.
And if someone says that everything has been done, that everything in ZFC works and it is perfect, I think we might have something more to know about the foundations of mathematics than we know today. — ssu

Right from the beginning, 2,500 years ago, people have been thinking that everything has been done and is perfect. But then they found the irrationality of sqrt(2) and pi. A paradox is not necessarily just a problem. Perhaps It's an opportunity. Oh dear, what a cliche!

This simply goes back to in the story of Plato's rejection of Zeno's most eating dog, just in a different form. — ssu

Believe it or not, I can see that.

This is why idea of infinitesimals is rejected in standard analysis. — ssu

I'm a bit confused about infinitesimals. Are they infinitely small? Does that mean that each one is equal to 0 i.e. is dimensionless? Is that why they can't be used in calculations? (I thought that Newton used them in calculus and Leibniz took exception.)

In fact you yourself brought up an old thread of four years ago, which is topic sometimes even banned in the net as it can permeate a nonsensical discussion. — ssu

Well, actually, someone else mentioned it. I misunderstood what it is about and off we go. Once I realized it was about the sum of an infinite sequence, I withdrew, with some embarrassment. But I've learnt some interesting snippets.

That's always a good solution to a difficulty - slap a name on it and keep moving forward. Sometimes mathematicians remind me of lawyers.
— Ludwig V
Unfortunately... yes. — ssu

There is another way, mentioned in the video. Just relax and live with your paradox. It's like a swamp. You don't have to drain it. You can map it and avoid it. Perhaps I just lack the basic understanding of logic.

That the total probability of the entire event space is 1. — fishfry

Yes. Is that a definition or an axiom? Whatever it is, it isn't just another assignment of a probability because it enables the actual assignments to the outcomes to be made. But I don't see that anything is wrong with representing them as percentages, in which case the probability of the entire event space is 100. Meteorologists seem to be very fond of this.

A probability measure is a function from some event space to the set of real numbers between 0 and 1, inclusive, satisfying some additional rules. That's it. — fishfry

Timeless present? It looks like it. In which case it is what I'm looking for.

Now particular applications of probability often involve real life, temporal events, such as tomorrow's weather or the next card dealt from a deck. The underlying theory is abstracted from that. — fishfry

Yes. Most of the discussions I get involved in are at the applied level. But I have seen some posts that are completely abstract. So I think I understand what "event space" means. It is a metaphor to describe a formulation that doesn't identify actual outcomes, but only gives, for example, E(1), E(2)... - variables whose domain is events. In particular applications, that domain is limited by, for example, the rules of the game. That's not a complaint - just an observation.

The probability that something, anything at all will happen, is 1. — fishfry

Yes. But the mathematical table you draw up doesn't change when it does happen. Assigning a probability to the outcome that happened isn't a change to the table, but just a misleading (to me, anyway) way of saying "this is the outcome that happened (and these are the outcomes that didn't happen)". The table doesn't apply any more.

The probability that something, anything at all will happen, is 1. That's one of the rules of probability in the Wiki article. — fishfry

Yes. It's a rule, not an assignment of a probability.

It's the philosophical contexts that I don't know much about. — fishfry

Yes. To be honest, the value, throughout our dialogue, is the opportunity for me to see how mathematics reacts to these questions. So the difference is the point. I'm very grateful to you for the opportunity.

To be honest, the use of "probability=1" is so widespread that it seems absurd to speak as if it should be banned. So far as I can see, it doesn't create any problems in mathematics. But in the rough-and-tumble of philosophy, it's a different matter. People asking what the probability is of God existing,

P(X=1|X+1=2). Where X is a random variable. That'll give you probability 1.
— @fdrake
Yes ok, a true proposition has prob 1 and a false one 0. I don't see how intermediate probabilities could apply. — fishfry

Neither do I. But given that intermediate probabilities don't apply, I would say that probability in this case doesn't apply. Probability theory has no traction. Perhaps that's too strong. So I'll settle for a philosopher's solution. Philosophers have (at least) two ways of describing statements like this - "trivial" or "empty".
But now consider "There is one star in the solar system". Given that there is just one star in the solar system, intermediate probabilities don't apply. So assigning a probability of 1 is trivial or empty.
But, once I have won the lottery, intermediate probabilities don't apply.

Earlier you said there was something off about using 1 as a probability and that .999... = 1. But that's two uses of the same number 1. — fishfry

Yes, and I once I realized that, I withdrew. Perhaps I wasn't clear enough.

And here's then the problem: not only Plato started from counting, but even today Set Theory starts from counting too with the Peano Arithmetic. — https://en.wikipedia.org/wiki/Class_(set_theory)ssu

I see your point.
I don't quite get that "fork" argument. The notation using lower case beta for a member of the set and upper case beta for the set is confusing, and I think there's a typo in the statement of the paradox. But I know better than to challenge an accepted mathematical result.
Wikipedia defines proper classes as "entities that are not members of another entity."
That's always a good solution to a difficulty - slap a name on it and keep moving forward. Sometimes mathematicians remind me of lawyers. That's what happened with sqrt2 etc. Also when defining the limits of infinite sequences.

Can you know or compute C, if you know both A and B? No, if A and B are as above, then only thing you know is that C can be a natural number 6 or 7 or 8 or larger. It might be six, but then it might be three googol also. — ssu

Yes. I always thought that was the point. Why should everything have a definite, computable result? Stating the range of a result is not pointless.

I apologize for this post. I'm just flailing around. Actually, I'm still not sure where the best place to begin is.

This is about categories or conceptual families or language-games and the importance of context and use. I won't try to give a general characterization of this. I think it will help more if I focus on something specific.

As an example, what's the probability of X+1=4 given that X=3? Probability 1. — fdrake

and
quote="fdrake;916313"]The probability that 2+2=4 doesn't make too much sense.[/quote]
What fdrake is saying (I think) is that probability is inapplicable without a context of argument and evidence and has much to be said for it.

I've never seen probabilities assigned to mathematical facts like that. Not sure what it means. — fishfry

Neither am I. But if probability=1 and true=1, then fdrake's conclusion follows.

1 is a probability and 1 is the number of stars in our solar system. — fishfry

These are different uses of "1", in different contexts (language-games).
(Iadded this later, to try and clarify). Compare a traditional example:- "John came home in disgrace, a flood of tears and a wrecked car." "In" is ambiguous, because "disgrace", "flood of tears", and "wrecked car" are different kinds of thing, are pieces of different language-games and "in" is polymorphous and has different senses, or uses" in each of them. That's the theme of this whole argument.
Applying numbers to objects in the solar system is one kind of language-game. Applying numbers to probabilities is quite another. Actually, there are (at least) two ways of using numbers in the context of probabilities. There are 6 probabilities (I prefer "possibilities" or "outcomes" as less confusing) when throwing a die, each of which can be assigned a probability of 1/6, and if the 6 comes up we can, I suppose, assign a probability of 1 to that outcome.

So I would prefer to say that probability is not applicable to either 2+2=4 or (x=3)&(x+1=4). Why? Because there are no other possibilities. Probability of a specific outcome is only meaningful if there is a range of possible outcomes. 1 is conventionally used as the range of the outcomes. Assigning a probability to one outcome and then to another without outside that context is meaningless. 1 isn't counting or measuring anything - it's just the basket (range) within which we measure the probabilities (in relation to the evidence and if there is no evidence, then equally to all). (fdrake is right to emphasize the role of evidence - especially in the context of Bayesian probability) We use 100 as a basket in other contexts when it suits us. In the case of the die, P(1v2v3v4v5v6)=1 is just reasserting the rules.

In the case of truth, the language-game that provides the context is different. In a sense, when we assign 1 to truth, it is not a number at all. We can equally well use "T" or a tick if it suits us. This reflects the point that "true" is one of a binary pair. Probability isn't. I want to say that probability and truth are different language-games.

But that would be too quick, because they are related. Probability is what we retreat to when we cannot achieve truth, one might say. There are others - "exaggerated", "inaccurate", "vague", "certain", "distorted", "certain". I would be quite happy to say that truth is not binary, but multi-faceted; the language game of truth has more than two pieces - probability is just one of them. Probability itself has more pieces than are usually recognized. In the context of empirical probability, we find ourselves confronted with "likelihood" and "confidence" and, sometimes, "certainty" and, of course, in the context of Bayesian probability, "credence" - "degree of belief" turns up from time to time, as well.

@fishfry There's one other point I would like to make, in the context of our previous discussion about time in mathematics. Given that, probability is a bit of a problem, because it seems to me that it has time, or at least change, built in to it. (I have seen it said that probability is inherently about the future). We build the table around the outcome, in the context of a thought-experiment such as tossing coins or throwing dice or drawing cards lotteries or roulette wheels. (I expect you know that Pascal built the theory around a desire to help his gambing friends) We expect an outcome, when everything changes. Time isn't essential. The outcome could be unknown, for example. Even if it is known, we can pretend that we don't know it. But there is an expectation of change, without which probability makes no sense. So the timeless present does not describe what is going on here.

One could regard probability theory as applied mathematics, but probability isn't a prediction. Probability statements are neither confirmed nor refuted by the actual outcome. (That's not quite black and white, because we do use deviations from probability predictions as evidence that something is wrong. But still...)

I prefer to say, however, that the probability table does not change when the outcome is known. It describes a situation and that description is correct even after the outcome is known - it just doesn't apply any longer. So probability = 1 doesn't really apply.

Ok. That will do. Maybe some of that is helpful.

Full disclosure - I haven't formally studied probability either, any more than I've studied mathematics. But I have discussed both and thought about both a good deal, in various philosophical contexts.

This is why I argue that with infinite you cannot start counting. This also shows why 1+ ∞ = ∞ and ∞ + ∞ = ∞. — ssu

That's exactly what I have been trying to say all along! :smile:

I am the one who apologises for derailing the topic in an inconsistent scenario — javi2541997

I don't think you have derailed anything. If there's any derailing going on, it's me that's doing it.

Just think of a finite line you draw and put at the start zero and in the end — ssu

You can do that, but it's very misleading. It suggests that an infinite line is just a very long line. That's wrong. The best way I can think of is to draw your line and put your ∞ or ω at the end of it, but remember that those symbols mean that the line goes on forever - it has no end. That's why we always just write down the first few elements of the sequence and then ... or "and so on". That's not just an abbreviation or laziness or lack of time. It's telling you that the sequence has no end.

The whole story is about the problem of definition that math has. And for the Grand Order you refer to, there is the Well Ordering Theorem. — ssu

I don't know about all those theorems. I know I should, but I had a deprived education.
But what strikes me about your Grand Oder is that the only fixed point you have is Plato's dog. It is the only possible origin for the ordering of the dogs that eat more than Plato's dog, in which case we have to call it dog 0. But it is also the only possible origin for the ordering of the dogs that eat less than Plato's dog. We can call it Dog 0 or Dog 1, but either way, it won't look much like a single order from the dogs that eat less to the dogs that eat more.
The short version of this is that you have to start both sequences from a point in the middle of the line.