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.

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. Unless, say, we could poll a bunch of mathematicians and ask them to assign a probability to the Riemann hypothesis being true. That would be one example I suppose. But I think that's credence (degree of belief) rather than probability (whatever exactly probability is).

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. — Ludwig V

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. So I don't see your point. Of course 1 has many different uses. Why is this nontrivial or interesting?

Applying numbers to objects in the solar system is one kind of language-game. Applying numbers to probabilities is quite another. — Ludwig V

It's another. It's not "quite" another. You seem to be saying that it's not only a different usage; but a super-different usage, if I'm understanding you. And it's not. It's just different.

In fact let me tell you what a probability is. It's just a real number between 0 and 1, inclusive. So it's the same real number one in the context of probability or anything else.

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. — Ludwig V

Yes ok. You don't have to suppose. Probabilities are additive. That is, if the events are independent (meaning that one is not dependent on the other) then you can add the probabilities. It's one of the axioms of probability. Or one of the consequences of the axioms, depending on how you state the axioms.

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. — Ludwig V

I see the point you are making but it doesn't seem right. If we roll a die the probability that it's either 1, 2, 3, 4, 5, or 6 is 1. There is no other possibility. In fact that's another one of the probability axioms: That the total probability of the entire event space is 1.

1 is conventionally used as the range of the outcomes. — Ludwig V

1 is a probability. 0 to 1, inclusive, is the range of probabilities.

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. — Ludwig V

Well, "evidence" is a term in the philosophy of probability, I suppose. But it's not a word in the formal mathematical theory of probability. In any event, I don't think that's right. Evidence can change the credence of an event -- your subjective degree of belief. But it doesn't change the probability.

I'm in way over my head on the philosophy of probability actually.

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. — Ludwig V

Well I certainly agree with you. I am not the one trying to apply probability theory to true/false propositions. @fdrake is doing that. I'm a bit baffled by the attempted connection.

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. — Ludwig V

Are you perhaps referring to credance, or the degree of belief? I can't really debate these issues, I know nothing about them. Truth in mathematics is binary. In real life, not so much. Also in intuitionist logic, where we reject the law of the excluded middle. That's another complication.

@fishfry There's one other point I would like to make, in the context of our previous discussion about time in mathematics. — Ludwig V

Uh-oh. Was all the preceding not for me? Probably wasn't since it's not about anything I can sensibly talk about. To me a proposition is true or false. That's the definition of a proposition.

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). — Ludwig V

Philosophical probability, I suppose. Mathematical probability has no time element in it. 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. No time involved.

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. — Ludwig V

The mathematics of probability is abstracted from all that. No time element.

This article gives the mathematical definition of probability.

https://en.wikipedia.org/wiki/Probability_axioms

You don't need to follow the symbology. The point is that time is not mentioned. Probability is a mathematical function that outputs a real number in the range [0, 1] and satisfies some rules.

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.

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...) — Ludwig V

Probability theory is abstract. Applied probability is applied.

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. — Ludwig V

I don't know why you have that hangup about probability 1. Probability 1 is just the probability of the entire event space. It's the claim that out of all the possible outcomes, one of them will occur. After all, in any situation, something must happen, even if we don't know what. The probability that something, anything at all will happen, is 1. That's one of the rules of probability in the Wiki article.

Ok. That will do. Maybe some of that is helpful. — Ludwig V

You have thought a lot more deeply about the real-world meaning of probability than I have. The math is just math, as in the article I linked. It's very mathy as you can see.

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. — Ludwig V

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

Unless, say, we could poll a bunch of mathematicians and ask them to assign a probability to the Riemann hypothesis being true. — fishfry

Yeah no I ain't assigning random variables to generic mathematical expressions.

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.

Yeah no I ain't assigning random variables to generic mathematical expressions. — fdrake

Ok. But you know in this case we can. We can interpret probability as credence, the subjective degree of belief, which is an epistemological claim rather than an ontological one. Pretty much any mathematician in that field would be glad to offer a number. Most believe it's true. I'd guess Riemann has better than a 90% credence among specialists.

With this interpretation, we free ourselves from having to give an account of what probability "is." We just talk about our own subjective degrees of belief. Sort of removes the mysticism from interpretations of probability.

This way we can reason mathematically about our beliefs, using the technical apparatus of abstract probability theory.

I'm just trying to interpret this question. About applying probabilities to predicates, I don't know anything about that. But I do think that people could "vote" on predicates, even in situations where you can never know the truth.

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. — Ludwig V

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.

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.

In math, a random variable is just a measurable function on a probability space; which defined as a measure space with total measure 1. It's all very technical and precise, and completely avoids all of the murky metaphysics of randomness. In that sense, my view of probability is not overloaded with philosophical interpretations. Whether that's good or bad I'm not sure. :-)

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

I feel like that's a poetic phrase to describe the fact that there's no time in math; that when we say 1 + 1 = 2. Works for me.

— Ludwig V

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. — Ludwig V

Yes. I confess I'm not sure what is the main thesis you and I are discussing. But clearly there are two meanings of probability:

* The formal, mathematical one; which doesn't even have a metaphysics. A probability is a mathematical gizmo that obeys some formal rules. Then we prove theorems about gizmos that obey those rules.

* 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.

But I do confess I don't remember what we are talking about :-)

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. — Ludwig V

I'm not entirely sure I followed that. I think if probabilities of 0 and 1 make you uncomfortable philosophically, by all means you should reject them, for all the reasons you've been explaining to me.

I don't know what is gained philosophically by my injecting the mathematical formalisms; because really, they don't even have anything to do with the way people think about probability. Perhaps the formalisms are irrelevant to your thoughts.

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

That was about the total probability being 1. Yes, that's a definition or an axiom, either one. It's a property that characterizes the universe of things that we're interested in when we use the word probability. On the one hand it's arbitrary. On the other hand, it provides tremendous logical clarity, an is amenable to mathematical techniques. Such is the power of mathematical abstraction. But, perhaps in the end, not relevant to your own thoughts on the subject. I can't tell.

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. — Ludwig V

Math does not react to those questions. Math can't even see those questions. A "random variable" is "a measurable function in a measure space[/i]. In math the word "random" doesn't mean anything at all. Math doesn't do meaning. That is the beauty of abstraction.

That's good news and bad news. The good news is that as a philosopher, you are free to think about randomness and probability any way you like, because math takes no position at all. And the bad news is that math takes no position at all! The rest of us have to figure out what it means.

What do you think?

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, — Ludwig V

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.

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!

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. — Ludwig V

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?

https://en.wikipedia.org/wiki/Posterior_probability

Posterior probability

https://en.wikipedia.org/wiki/Posterior_probability
Yes, and I once I realized that, I withdrew. Perhaps I wasn't clear enough.

Oh ok.

Most believe it's true. — fishfry

I'm still antsy about assigning a random variable to the truth of a theorem. How do you sample from mathematical theorems? What would it even mean for a mathematical theorem to be expected to be true 9 times out of 10? How do you put a sigma algebra on mathematics itself...

I'm still antsy about assigning a random variable to the truth of a theorem. How do you sample from mathematical theorems? What would it even mean for a mathematical theorem to be expected to be true 9 times out of 10? How do you put a sigma algebra on mathematics itself... — fdrake

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.

OR you ask each mathematician what is their subjective belief that it's true; and you average all those individual credences.

If I'm understanding your objection, the idea is to replace the idea of probability, with that of credence.

With probability, we have no idea what it "means" to say that a theorem might be 75% true. But with credence, we do. Even though the theorem itself must be either true or false; still we can each have a fractional "subjective degree of belief" that it's 75% likely to be true.

In this way we can apply the mathematical techniques of probability theory, sigma algebras and such, but without having to figure out what we even mean by probability. We go from the objective to the subjective. From ontology to epistemology. X may be true or it may be false. and no other outcomes are possible. Yet, I can still have a subjective belief, based on what I know, that it's 75% likely. It's just a guess, but it's objective. We ask everyone what they think.

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.

https://en.wikipedia.org/wiki/Credence_(statistics)

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.

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. — Ludwig V

Sometimes they are pretty much interchangeable and other times not. It depends on if it's an "if and only if" definition or not.

The axioms of group theory are the definition of group theory.

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

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

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. — Ludwig V

What table? Lost me on that.

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 don't know what you mean that a probability can be empty. A probability is a real number between 0 and 1 inclusive.

It depends whether you are a mathematician or a philosopher. — Ludwig V

Ok. So please remind me of what point we are trying to discuss.

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. — Ludwig V

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

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. — Ludwig V

Yes of course, no issues there.

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.

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. — Ludwig V

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?

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.) — Ludwig V

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.

I've lost the context of this. — Ludwig V

Me too, for sure.

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. — Ludwig V

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.

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. — Ludwig V

Why are you telling me this? I don't know what we are talking about.

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. — Ludwig V

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!

https://en.wikipedia.org/wiki/New_mysterianism

But I'm not sure why you mentioned this. The point was that the concept of credence lets us apply the mechanics of probability theory, without regard for the metaphysics. Because even though I don't know what's going on, I can have an opinion about it. And we can tally people's opinions to quantify their frequency.

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? — Ludwig V

No, not at all. Instead 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.

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. — Ludwig V

Ah. No. Not the point I'm making. 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.

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. — Ludwig V

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.

But I don't follow your point in bringing this up. And betters use credences! The odds are based on the credences of the betters, and NOT on any metaphysics of what is really going to happen. That's a good point. Gambling odds are based on collective credence, along with an attempt to judge "objective" reality. It's a bit of both.

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. — Ludwig V

Yes. That's why we aggregate everyone's subjective opinion and evaluation. These are situations whee nobody can know all the evidence. Like a murder mystery with only circumstantial evidence. We can't know for sure but we can use our best judgment and have a credence.

We started off talking about "probability - 1" and in order to understand that, we've explored the construction and meaning of the probability table. — Ludwig V

I don't know what you mean by 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. — Ludwig V

I've said nothing about Bayesian probability. I like credence because we can always have one, even when we can't know enough to assign a metaphysical probability.

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

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

But your idea about the nonexistence or vacuity of probability 1, that I don't follow.

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.

Even though the last post was 14 hours ago, the main page says the last post was 3 days ago. What the hell?
Anyway, spiral:

Check.

Ok, so not even an annexed file bumps it. Is the thread shadow banned?

Now 8 days ago.

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

You keep saying that. You have not yet articulated it in a way that makes me believe you are saying anything sensible.

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. — Ludwig V

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.

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. — Ludwig V

That's a tall order. 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?

The math of the everyday world is to be found in the grocery check-out lane and the baseball scores.

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? — Ludwig V

No, I think you obfuscated the point.

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.

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. — Ludwig V

Ok.

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. — Ludwig V

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

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? — Ludwig V

Well there's abstract and applied probability. I knew a grad student who got a Ph.D. in abstract probability and got a job as an actuary at an insurance company. The insurance companies know more about probability than anyone, it's their business. And bookies. Sports book operators know the theory and the practice.

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? — Ludwig V

I'm talking about credence, not Bayesian probability.

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.

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. — Ludwig V

Ok. Not disagreeing.

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. — Ludwig V

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.

As more news continues to come out, the Pennsylvania deal looks like an op. An operation. It is not as we are being told, and we will likely never be told. If it was some weirdo 20 year old kid with access to his father's gun, so be it. But the numerous incomprehensible malfeasances of the Secret Service raise many questions; and the Biden administration is actually stonewalling and slow-walking the case, raising even more suspicions. I'm not saying one thing or another, just that transparency and accountability are in short supply from the government this week.

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. — Ludwig V

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.

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

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. — Ludwig V

My sense is that he just didn't get it. That he was wrong, not just having a side. But I could be wrong too.

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. — Ludwig V

Yes agree. Science versus scientism. Science is using experiment and rationality to understand the world. Scientism is the belief that science is infallible, or that "trust the science" was ever anything other than an authoritarian political slogan. Covid lockdowns were scientism, not science. Science as a means of social control, not as a path to enlightenment.

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 — Ludwig V

Ok, list of events and their associated probabilities.

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.

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. — Ludwig V

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

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. — Ludwig V

Well, the prosaic applications of math to everyday life are not really what mathematicians do.

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. — Ludwig V

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

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

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.

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. — Ludwig V

Credence is not fantasy.

"Slightly right of centre" is about right. "typical collectivist leftist" sounds like slapping a conventional label on something without thinking about it very much. — Ludwig V

That was my three-word summary of everything I know about Starmer. I agree I haven't thought about him 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. — Ludwig V

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

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.

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. — Ludwig V

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.

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. — Ludwig V

LOL. My impression too.

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. — Ludwig V

Don't think I've heard that before, that the Constitution is the US analog of a hereditary monarch. Maybe there are some parallels.

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. — Ludwig V

I believe he said that "History shall be kind to me, for I shall write it."

I believe he said that in the context of WWII. Most of Chamberlain's bad reputation is due to Churchill. Chamberlain was actually a pretty good guy, and his appeasement of Hitler was both rational and very popular at the time. So I've read from some alternative views of history.

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.

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. — Ludwig V

Miscalculation or malevolence, take your pick.

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. — Ludwig V

Yes.

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

Ok.

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.

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 — Ludwig V

That makes perfect sense. I understand you now! Yes I was thinking of the empty set. Perhaps what you're describing I might call, "invalid," or an error condition in programming. In programming, an operation can succeed; or it can fail; or it can blow up entirely and throw an error condition.

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?

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?

Note that I introduced time into math, by imagining we're doing math on a slow computer!

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. — Ludwig V

Since you don't recommend the book I will not dispatch a clone to read it!

But surely, putting 1 + 1 into a computer and expecting to get back 2, is not an empty idea! I don't see that.

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 — Ludwig V

I took a MOOC in mathematical philosophy, and the prof showed us that "Snow is white" is true if snow is white. That was several years ago, and to this day I don't really get it.

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.

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

That was about something interesting but I forgot and didn't feel like tracing back :-)

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. — Ludwig V

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.

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. — Ludwig V

Yes, it would be the same game if you called the knight the frisbee.

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? — Ludwig V

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

But maybe I just didn't have the time to get a Ph.D. in quantum field theory in order to have any credence at all that there are quarks. I believe there are quarks, 100%. I believe in that particular science. But I would be hard pressed to lay out the mathematical theory. I don't know the evidence. I only know that if Sean Carroll tells me there are quarks, I believe him. Actually Veritasium has an awesome video on quarks, that's where I learned that mass comes from the binding energy that keeps the quarks from flying apart.

I believe what I just wrote. I have zero evidence for any of it. Binding energy is analogized by a rubber band, that's what I know about it.

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?

Here is my thesis. For every proposition P, I have a credence credence(P), whether I know the first thing about the topic or not. I think there's a 10 percent chance the Royals whacked Diana. I've seen enough hit man movies to know that when you die in a car crash, it might or might not have been an accident!

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!

Isn't having opinions about things that we know nothing about, one of the most human things we do?

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. — Ludwig V

The US government was up to its eyeballs in chicanery that would have shocked the naive America of the 50s and 60s. Assassinating foreign leaders. Interfering in foreign elections. Running sick mind control experiments. Business partners with the Mafia in plots to kill Castro. Controlling what the news media reported. I agree that just because they covered up the assassination, doesn't mean they did it. Doesn't mean they didn't, but doesn't mean they did. But under the law they are accessories after the fact, and just as legally accountable as the actual perpetrators.

Likewise this week. The Biden admin, Mayorkas and that clown Cheatle, are embarrassed at their gross incompetence on display. By the way I am not one that says Cheatle is a clown because she's female. I say she's a clown because she's an idiot. Whether she actually believed that nonsense about the sloped roof preventing an agent from being up there, she was stupid enough to say so in front of a camera. That's a firing offense for any bureaucrat. Because it totally destroys the public's trust.

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. — Ludwig V

It's a continuum, to be sure. Individual versus the collective.

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. — Ludwig V

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

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

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). — Ludwig V

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.

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. — Ludwig V

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.

I do not regard that as miscalculation. I regard that as evil, cynical calculation.

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. — Ludwig V

Well the recent batch of conservatives have been useless. May was terrible. Was Johnson next? Then Sunak? They're what we call RINOs, Republicans in Name Only. Squishy liberals with no convictions calling themselves conservatives. Well here's to Starmer, he's got his work cut out.

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

Is that right? Is there Churchill revisionism about?

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.

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. — Ludwig V

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.

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. — Ludwig V

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

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. — Ludwig V

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

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? — Ludwig V

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.

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. — Ludwig V

Right. Hence credence. I think you are agreeing with me. 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.

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? — Ludwig V

Sure.

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. — Ludwig V

Ok well I should terminate my own thread hijack about this subject. But a quick lookup showed that Ebola lockdowns were only in two regions. The covid lockdowns were virtually global and were not a good idea.

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. — Ludwig V

Some Europeans are getting restless, are they not?

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. — Ludwig V

Ok, I should look that up.

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

Yes I'd love to go back.

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. — Ludwig V

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

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.

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. — Ludwig V

Well ... letting the matter drop would be for the best. But ... can you explain to me how today being Sunday, the probability that yesterday was Saturday is anything other than 1?

I mean, suppose that you had to place a bet on the proposition. What do you think the odds should be?

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

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. — Ludwig V

Well, nothing is the WHOLE story. Life is complicated.

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

You have already stipulated to the opposite. You have, if I have understood you correctly, agreed that it's NICE if credence is influence by evidence; but sometimes there's not enough evidence or I'm not qualified to evaluate the evidence. Then I must NECESSARILY form a subjective degree of belief without benefit of evidence. It's your use of "should" that I object to. I could live with "preferable," but not "should."

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. — Ludwig V

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?

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. — Ludwig V

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?

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. — Ludwig V

In the US it was ugly. People lost their medical licenses for expressing scientific skepticism. Teachers, workers of all kinds lost their jobs. People lost friends. The mass formation, as some called it, was terrifying. For the first time I truly understood Nazi Germany. Excuse the argumentum ad Hitlerum. I saw how a society goes mad. I was immune by personality. I kept my head down, and since I'm not much involved in public society, I didn't have to risk anything. I just waited it out. But I'm wary of my fellow Americans now in a way I previously wasn't.

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. — Ludwig V

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.

Quite so. I forgot about the Lusitania. — Ludwig V

I saw a really good tv movie that cut between the action on board ship, on the German U-boat, and in the halls of the British admiralty. I read up a little afterward. A distinguished jurist was appointed to lead the inquiry. Afterward he called it, "a dirty business," and retired. They screwed the captain to cover up Admiralty complicity.

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 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. — Ludwig V

I don't see why not. If a bookmaker had to set odds on the proposition, he'd assign it as 1. Anyway let's agree to disagree.

That bet is money in the bank, so long as the odds show a profit. But who would take the other end of it? — Ludwig V

Nobody. That's why it's got probability zero!

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. — Ludwig V

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.

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. — Ludwig V

I better quit while I'm behind here.

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

Right. To account for situations where we can't possibly have any evidence, or know what's going on, but we have a subjective opinion and degree of belief anyway.

H'm. That's a new take on mathematics. — Ludwig V

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

https://plato.stanford.edu/entries/fictionalism-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? — Ludwig V

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.

https://en.wikipedia.org/wiki/Paraconsistent_logic

Anyway, you're not telling me that the axioms and definitions of probability theory are in some sense provisional, are you? — Ludwig V

Provisional. Explain what you mean by that word. They're seemingly sensible, but they immediately lead to anomalies like the famous non-measurable set and the Banach-Tarski paradox.

The probability axioms are highly useful and natural, but they bite.

https://en.wikipedia.org/wiki/Vitali_set

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.) — Ludwig V

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

I'm for nukes. Environmentally clean and abundant energy to run our world. Some of the eco-loons would have us living in grass huts. Of course THEY wouldn't live in grass huts. The rest of us would.

I see in England that they threw a few highwayblockers 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.

https://abcnews.go.com/International/wireStory/british-climate-protesters-plotted-highway-shutdown-record-harsh-112069763

Aren't you glad you asked :-)

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. — Ludwig V

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.

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.

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

Ok glad we got to the bottom of that!

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. — Ludwig V

Ok.

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. — Ludwig V

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

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. — Ludwig V

Oh you baited me about the eco-loons. 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.

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. — Ludwig V

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.

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. — Ludwig V

The ITER project had another setback. Nine more years delay, another five billion dollars over budget. Fusion would be nice if they can make it work. The fission waste is a problem, but you can't run the world on windmills.

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. — Ludwig V

I support free speech. Blocking roads is not speech.

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. — Ludwig V

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

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.

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

Sorry I mentioned it.

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. — Ludwig V

Oh please. He left as gracefully as Caesar did.

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. — Ludwig V

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

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. — Ludwig V

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

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. — Ludwig V

And the third world can suck eggs so that upscale liberal virtue signalers can feel good about themselves.

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? — Ludwig V

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.

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. — Ludwig V

her

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

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

https://www.cbsnews.com/boston/news/broken-wind-turbine-blade-atlantic-ocean-nantucket-massachusetts/

ps -- This just came in. 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.

https://www.thetimes.com/article/67d7c8f4-fbed-4ea1-94f3-252caa171723?shareToken=0b96051817d3dc87ee7ba226d3a18e34