Isn't Possibly P also ~▢P? — Luke

Should probably add that ◇P is consistent both with ▢P and with ~▢P.

With marbles, that's to say that there being at least one red marble in the set is consistent with all the marbles in the set being red, and with not all the marbles in the set being red (but at least one is).

~▢P by itself just says 'not all', P is not true of everything in the domain. Might not be true of anything.

There's definitely a limited pot of stuff and labour, and at the end of the day, that's what things like wealth and value are for. — Isaac

In the abstract, maybe? But practically there are two issues: first, it's not the total at a given moment that matters, but what's available, what's controllable, and that changes; second, we have credit, and the future is a long time, even at a discount.

Ownership is always about power. — Isaac

There's an old Carl Sandburg poem: guy tells a tramp to get off his land, the tramp asks what makes it his, guy says he got it from his father — where'd he get it? Got it from his father. Where'd he get it? Well, he fought for it. Alright then, I'll fight you for it.

I own my phone here because I have the power to do what I want with it uncontested and you don't. — Isaac

Hmmm. That sounds like right not power, but power is ever so slippery, and we don't want to confuse it with capacity or force. We both have the capacity to doom scroll on your phone, but only you have the right to, and I'm obliged to respect that right. You're saying further that there is some entity (perhaps yourself and some of your friends who work out, perhaps cops and courts, perhaps just the vocal disapproval of surrounding citizens) with the capacity to force me to respect your right, so rights come down to power in that sense, and thus property as well.

That's as may be, but how does it help us?

So in taking a European-type possession, the British stole something because they took away power. — Isaac

I mean, I'm getting the rhetorical effect there, but you've talked yourself into a circle: now power — the guarantor of property — is itself a possession that can be stolen. What would underwrite possession of power, since it can't be power? Is it going to be right after all?

(I hope it doesn't seem like I'm nitpicking here — I think this is the most productive disagreement we've ever had. You take care of the forest, and I'll look after the trees.)

Maybe the extent to which wealth is the basis of a society is the extent to which that society defines itself by in-groups/out-group distinctions, such that "I own..." has real meaning, whereas for societies where out-groups are rarely even encountered, wealth might be less relevant as there's not much meaning to "we own..." if there's no-one that excludes from those rights. — Isaac

I think that tracks. No anthropologist here, but we tend to name isolated societies for the word in their language that just means "people" right? But from my studies in college (wonderful lefty anthropologist who taught us from a book called Europe and the People Without History) and my son sharing what he's learned from Graeber and Wengrow's The Dawn of Everything, population contact goes back as far as you want to go. The isolated tribe in a state of nature is mostly myth.

So the story of property is the story of power is the story of in-group/out-group. The first use of power is the denial of some land use by an out-group. With such a social technology available, a group within a group could deny the rest of the group use of something, claiming ownership the other members of the group are bound at spear-point to respect.

Now if that's the story, then the Europeans are just another out-group, and rather than being denied use of land and resources, they have the capacity to deny those already here such use. Seems like more of the same, not a break with history. The difference may be qualitative though, if the Europeans have a much more comprehensive conception of use and what exclusive rights they're inclined to enforce.

This starts to look a bit Hobbesian, or Trumpian, or even Hitlerian — it's always the struggle for power, everyone's a crook it's just that Europeans were better at it.

That's not where we want to end up is it?

Would be nice to cast a fond glance back toward where we started, with the nature of employment, the connection between risk and profit, all that. It's not that far at all, if it's all power struggle all the time, but I'm not convinced. I think there are genuine changes between the deep past and the present, and those changes include new forms of political economy that don't just amount to gang warfare. Economics may be the science of decision-making under scarcity, but that scarcity is relative, defined by opportunity, and not necessarily some definite depletable amount, but a pool we can grow and shrink by our actions.

Isn't Possibly P also ~▢P? — Luke

No, it isn't. ▢P ↔ ~◇~P and ◇P ↔ ~▢~P. That's the standard, and it maps onto quantifiers in an obvious way.

I wouldn't think it follows from "the marbles in the urn are not necessarily red" that there must be at least one marble that's not red. I would think it follows from "the marbles in the urn are not necessarily red" that all the marbles in the urn are (possibly) red. — Luke

Dang. I'll try again.

We have a set of marbles you're going to pick from. We're going to look at claims about what necessarily results when you pick and what possibly results when you pick.

If when you pick a marble, you get a red one, without exception, that's necessity. Necessity is like a universal quantifier with a restricted domain. Necessity means all the marbles are red. There's only the one result possible when you pick.

If when you pick a marble, you at least once get a red one, that's possibility. Possibility is like an existential quantifier with a restricted domain. Possibility means at least one of the marbles is red.

That might be hard to see at first, even with the analogy to ∃, but suppose you pick all the marbles and not one of them is red. Then we would say it was not possible to pick a red marble from that set. I think that fits our intuitions perfectly. To say it is possible to pick a red marble from that set must mean that there is at least one red marble to be picked.

Not Necessarily is Possibly Not, so that's our existential quantifier. It says you can pick a non-red marble from the set because there is at least one non-red marble to be picked. If you can't pick a non-red marble, that's because all the marbles are red; that's the situation we say we are not in.

And it should be clear that there being at least one non-red marble in the set is consistent with there being only non-red marbles in the set. That is, Possibly Not Red is consistent with Necessarily Not Red.

From this we conclude that Possibly Not Red is not the same as Possibly Red, because if it were, we would have to say that Possibly Red is consistent with Necessarily Not Red; we would have to have a set of marbles at least one of which was red and all of which were not red. No go.

Better?

I asked about non-necessity - why it's not equivalent to possible/possibly - and you've responded that we need to beware of necessity...? But I'm assuming non-necessity. — Luke

Ah, okay, I see what went wrong now.

My point was that we don't derive Possibly ~P from Possibly P, because for all we know Necessarily P.

Here you have Not Necessarily P

~▢P

and you want to know why it's not equivalent to Possibly P

~▢~P

We could try proving that, but we don't have any axioms, so let's try an example.

I've got my usual urn of marbles, and I tell you that the marbles in the urn are not necessarily red. You can conclude, given that the urn is not empty, that there is at least one marble in the urn that is not red. Good so far? By restricting our domain to an urn of marbles, we get to cash out the modal claims as quantifiers. Can you conclude that at least one of the marbles is red, that the urn contains a mix of red and not red? No, you cannot. "There is at least one non-red marble in the urn" is the entirety of what you know; it is a complete translation of "The marbles in the urn are not necessarily red."

Of each marble in the urn, it is false that it must be red. Clearly, that condition can be satisfied by it being false of every marble in the urn that it is red. (That is, it being true of no marble in the urn that it is red.) If this turns out to be the case, we would have that it is necessarily false of each marble that it is red. That's consistent with it not being necessarily true of any marble that it is red.

Since Not Necessarily P is consistent with Necessarily Not P, it's not equivalent to Not Necessarily Not P, else we'd have a contradiction. Or we can say: Possibly Not P is consistent with Not Possibly P, so it's not equivalent to Possibly P.

Sorry this is so repetitive. I'm never sure which may of putting things will be clearest.

But if there's a limited pot of wealth, then what material form could that thanks take other than a bigger than before share of that pot. — Isaac

But is there a limited pot of wealth? I buy my IBM mainframe on credit backed not even by how much fiat currency is attached to my name within the banking system, but on how much the bank expects me to have available to me over the coming five or ten years. There's a lot of something going on here, but it doesn't look much like one doubloon being passed around and bits getting snipped off it.

Truth is, I assume you're right. If we could cash out all the social systems in play, we would eventually get down to rocks and plants and water and animals, and it's inconceivable that anything else actually sustains us — you can't eat notional value. (Now we've wandered into schop's thread!) So I'm arguing against myself here along with you, but in part because an idea like theft — well that's social right? How far would you want to take the claim that British colonists stole North America from its inhabitants at the time? Did they own it? These were societies too. Some of them famously said no one owns the land, but there were a lot of wars over territory, so a lot obviously believed they could at least defend claims to exclusive use. Were their claims to ownership "natural" somehow? Or stronger than our later claims because earlier? Is that how we divvy up the earth — whoever gets there first?

I believe in the material basis of culture and society; I'm just wary of analyses of that basis in cultural or social terms, as if the basis of society was a certain amount of wealth, wealth that could be stolen.

Not Necessary (◇~) is equivalent to Possibly Not (◇~). — Luke

Yes, and I should add I think that matches our intuitions: if something isn't necessarily the case, then it's possibly not the case.

It is unclear to me why Not Necessary (◇~) is not also equivalent to Possible (◇). — Luke

The problem is necessity.

Saying something is true might seem to entail that it could be false, but it doesn't, because what you're saying might be necessarily true. 3 + 4 is 7 doesn't entail that 3 + 4 might not be 7.

So it is with possibility: to say that P is possible might seem to entail that ~P is also possible, but we can't do that because it may be that P is necessary, and that's why it's possible. Same as above: it is possible that 3 + 4 is 7, because it is, and it is necessarily.

Does that make sense?

It is absolutely true that we tend to reach for "possible" in epistemic situations that have a kind of constructivist flavor to them, that we say possible when it's all we know, and we don't have actuality or necessity in hand. (That's what I mean by "constructivist" there, that we use possible when we have not demonstrated actual or necessary.) So in a lot of cases where we want to say "possible" we really want to say "possibly not" too as a way of covering our bets; but that's a mistake: we need to demonstrate possibly not, because for all we know it will turn out possibly not isn't actually an option.

Of course that only matters if you're working in a domain where necessary makes sense, and for a lot of the everyday matters of fact we deal with, we often assume we can rule out necessity. "He might be on time," in everyday reasoning, does seem to entail that he might not. Whether we should make those assumptions, I dunno.

Possible is opposed to Not Possible. Isn't Possible also opposed to Not Possibly Not? — Luke

Meaning what? What does "opposed to" mean? Does it mean distinguished from, or actually is the negative of? I take opposite to indicate the negative, and anything else is ambiguity we can do without.

So, no, Possible (◇) is the opposite of Not Possible (~◇), and nothing else.

The opposite of Necessary (~◇~) is Not Necessary (◇~).

While we're here, we can do "necessarily not," which MU mentions now and again: that's ~◇~~, which reduces to Not Possible (~◇), or impossible, which, duh. So we can also say that the opposite of Possible is Necessarily Not — and it isn't anything else.

We could, if we liked, take impossibility as our primitive. Then we would have

Impossible
Possible = Not Impossible
Necessary = Impossibly Not

since the necessity of P is just the impossibility of P's opposite.

Metaphysically speaking, I take these terms to mean:

1. Impossible = cannot occur
2. Possible = can occur
3. Necessary = must occur

This does not make "necessary" and "possible" the same. It opposes the concepts of 1 and 2 to each other, and the concepts of 2 and 3 to each other. This does not require "possible" to be in a distinct category. — Luke

This is not a happy use of "opposes"; see below.

Yes, that's exactly the problem. If (1) is defined as opposed to (2), and (3) is defined as opposed to (2), then (1) and (3) must have the very same meaning, by definition. — Metaphysician Undercover

Unless by "opposed to" you mean something different from "is the opposite of," or by "is the opposite of" you mean something besides "is the negative of," then this is another scope error. We have

$\ \ \ \ \$Possible (◇)

Then there's "impossible," which is just

$\ \ \ \ \$Not Possible (~◇)

The opposite of impossible is

$\ \ \ \ \$Not Not Possible (~~◇)

which is of course just Possible (◇), unless we're contemplating an intuitionistic logic, and we're not. That just leaves necessity, which we get by putting a negative inside:

$\ \ \ \ \$Not Possibly Not (~◇~)

To complete the set of possibilities, we could mention

$\ \ \ \ \$Possibly Not (◇~)

which obviously tends to run alongside Possible (◇), without being it's opposite. (It's the opposite of Necessary.)

Evidently, you agree with the use of negation to produce opposites, or you wouldn't have said that two opposites of one thing must be the same thing. But you're not paying attention to what you negate to produce the opposites; you're not paying attention to scope.

While interesting, that's all about the max. Not what I was talking about, and really it's probably clearer too use a word like "value" instead of wealth. And it's important not to think just in terms of stuff, but to keep in mind services and intellectual property. My point was that IBM created a lot of value, meaning stuff, services, and intellectual property, that did not exist before, and their customers handed over wealth to get it. I'm not sure there's an argument about whether the earth could sustain high-level programming languages, which Jim Backus and his team invented at IBM, but if there is, it is a very long way around. In there meantime, there is an increase in the *amount* of value in the world, whatever the max. That's why the concept of theft is of somewhat limited use here.

Incidentally, if I recall correctly, Pierro Sraffa (Wittgenstein's friend at Cambridge) builds an economic theory from the ground up along vaguely the lines you describe. Interesting little book I read many decades ago, and the focus was on stability, or so my memory tells me.

the opposite of necessary, necessarily not (impossible) — Metaphysician Undercover

I'll address this, since it's clear enough.

You are making what I would consider a scope error.

The opposite of "The car is blue" is "It is not the case that the car is blue," which we can also express as "The car is not blue" because there is only a single level here. (And note this doesn't imply that there is a color we call in English "not blue".)

But suppose our sentence is embedded in another:

(a) "Sheila knows that the car is blue."

What's the opposite of that? Is it

(b) "Sheila knows that the car is not blue"

or is it

(c) "Sheila does not know that the car is blue"

It's (c). To find the opposite we must negate the outermost, enclosing scope "Sheila knows that ...", not the inner scope "The car is blue". The opposite of knowing something is not knowing it, not knowing the opposite. Everyone knows that.

So it is with modal operators. If I say

(1) It is possible the car is blue

the opposite of that is

(2) It is not possible that the car is blue

negating the outermost scope. We do not push the "not" into the scope of "It is possible that ..." producing

(*3) It is possible that the car is not blue

anymore than we do with "Sheila knows that ..." That's a scope error.

The opposite of

(4) Troy believes that Sheila said that it's possible that Dave knows today is my birthday

is simply

(5) Troy doesn't believe that Sheila said that it's possible that Dave knows today is my birthday

We're spoiled for choice as to where else to stick in our "not", but all the others are wrong. You negate the outermost scope and there's your opposite. Here are all the others, they all mean something different, and none is the opposite of (4):

(*6) Troy believes that Sheila didn't say that it's possible that Dave knows today is my birthday
(*7) Troy believes that Sheila said that it's not possible that Dave knows today is my birthday
(*8) Troy believes that Sheila said that it's possible that Dave doesn't know today is my birthday
(*9) Troy believes that Sheila said that it's possible that Dave knows today is not my birthday

Donald Hoffman has a lot to answer for. — Tom Storm

Well, it's early days, and if these beetles survive it stands to reason that the individuals that did not try to impregnate beer bottles will be represented in coming generations at substantially higher rates than those that did. That might be luck. Or it might be that some beetles have a slightly more elaborate criterion for mate identification that excludes beer bottles. So the beetle population should gradually steer away from this particular dead end.

I can't take Hoffman seriously, so I haven't looked to see whether his model allows this sort of refinement. I don't think evolutionary biologists were committed to a view that species jump to knowing everything all at once.

it's just that we get to decide what counts as a simple. — Banno

"Decide" seems an unusually cognitive word for you to lean on.

They don't get to decide what is or is not food. It's food or it isn't, it's a mate or it isn't. So no.

We get to say that this counts as Tuesday, that counts as money, and so on. — Banno

I see. That's rather a different claim than I was addressing.

And judging by the quote next, your idea is that other organisms lack institutional facts.

A dog might be able to ask for food, but it can't ask to be fed next Tuesday. — Banno

Right, but dogs do ask to go outside, which is interesting because it means they are not purely responsive to their environment. It's not like the sight of the door to the backyard triggers the desire; they go to the door. The natural thing to say here is there is some kind of idea of backyard even when they're not immediately experiencing backyard, so that's at least some kind of displacement.

Animals don't do the "...counts as..." thing that we do as a matter of course. — Banno

Don't they? Doesn't just about every living organism? Counts as food. Counts as protection. Counts as scary predator. Counts as my territory. Counts as invader.

Then again, there are those beetles that mistakenly "mate" with brown beer bottles. Maybe a lot of organisms skip the class step and only have the criterion of class membership. But then you're right back to counts-as-the-criterion.

Of course, evolution is a cheapskate, so it gave the beetles a really crappy mate selector that was just good enough until it was foiled by the arrival of brown beer bottles

us tankies* — Isaac

Hmmmm.

Are the old IBM inclusive nationally but extractive internationally? Did their subsidising of middle management jobs come out of profits, or out of exploitation elsewhere — Isaac

We're neither of us economists or historians, so I'll not be answering that, but I'm going to ask you to question what someone else might be able to explain to us. That true-believer asshole who took both econ 101 and econ 102, so now he knows everything there is to know (for example, Ben Shapiro) is going to say this, and he's right: the amount of wealth in the world is not fixed.

IBM was not a middleman between consumers and third-world rare metals miners, buying predatorially cheap and selling predatorially high. Much of the value of an IBM product or service was generated by IBM employees at IBM. Some large portion of the wealth that they captured in the course of doing business was wealth that they created out of thin air.

It is a further step, and a good one, to ask under what conditions IBM could do such a thing, freedom from want, political stability, research universities, on and on. And then you may ask how those things were possible, and so on, and we all know that colonialism is out there in the explanation somewhere, at some level.

But what's not going on is IBM taking, for itself, some fixed amount of wealth from some third-world society. Colonialism is an important part of the story, but it's not a simple matter of theft (as you put it earlier). What about exploitation? Yes, of course, but we have to start with an analysis that doesn't treat exploitation as simple theft.

Simple example of how we do this, instead of all this concept juggling:

(1) It is necessary that the book falls if and only if it is not possible that the book does not fall.

(2) It is possible that the book falls if and only if it is not necessary that the book does not fall.

"Not" seems to be used in two ways, but it really isn't; under this scheme it is always a proposition-level operator, just like "possibly" and "necessarily". You build necessary this way:

(1) The book is falling.
(2) It is not the case that (1), the book is falling.
(3) It is possible that (2), that it is not the case that (1), the book is falling.
(4) It is not the case that (3), that it is possible that (2), that it is not the case that (1), the book is falling.
(5) It is necessary that (1), the book is falling.

(5) is here just shorthand for (4). There is a single complete proposition (1), and three operators applied to that proposition, which we can abbreviate as a single operator.

This simplified usage of "not" avoids many confusions: you never predicate "not falling" of an object, you deny that it is falling; you never predicate "not possible" of a proposition, you deny that it is possible. By maintaining discipline in the treatment of "not", you avoid any possibility of confusing, say, "I know it's not Tuesday" and "I don't know it's Tuesday". We can be clear about the scope of the operators we apply to sentences, and we can be clear about the order in which we apply them, and we need not abide ambiguity. This is how we win.

laws guaranteeing a decent wage and working conditions. — Isaac

I think there's actually research showing that states with higher minimum wages do not have higher unemployment, but there may be confounding factors, so that may not simply refute the inevitable conservative argument that raising the minimum wage will cost jobs. But what's the conservative answer to this: what kind of business model did you have, if you have to pay people so little even to keep the business afloat? Maybe that's a business that doesn't really work.

The pain — which will be real in particular sectors, no question — is corrective, and we should both raise the minimum wage and provide support for employers and employees to get through the transition to a better way of doing things. To say, it will hurt to change, is not an argument that where you're at is good.

It's possible, is it not, that the reason capitalist countries are rich is nothing more than that they stole resources from other counties and didn't pay their ecological 'bills'? — Isaac

Yes, that's what I was saying; I mean to leave open that explanation, at least because I don't know any better. Acemoglu and Robinson use their own scheme for classifying societies as having inclusive or extractive institutions. It's obvious that capitalist arrangements can land on either side.

Here, I'll give an example I think is okay: during the great boom in the American economy, large American corporations had endless layers of middle management. One result was that there were always promotions to be had, so there was considerable upward mobility, people bought houses in the suburbs, all that. Then management consultants convinced big corporations this was all terribly inefficient, that they could cut the number of layers between the C-suite and the workers on the line from 17 down to 4 or 5, and incidentally they could just pocket the savings. (IBM, for instance, reduced their workforce for the first time ever in like 1981 or something. Until then, so long as you did your job, a job at IBM was a job for life.) I submit there's a transition there from a business arrangement that is in some sense inclusive to one that is extractive, but not a shift from socialist to capitalist. It used to be normal for the fortunes of employees to rise with the fortunes of their employer, but then this way of doing business came to be seen as leaving money on the table. No one noticed that building in this sort of indirect profit sharing was precisely what built the American middle class and ensured the growth and prosperity of these great corporations.

But then we need to give "possible" a position, because "possible" provides a truthful description. It appears like "possible" ought to be opposed to "impossible". But it also appears like "possible" ought to be opposed to "necessary". And those two are already opposed to each other, so the real problem begins. — Metaphysician Undercover

Modal logics define necessary and possible as a pair of operators that apply to propositions; either can be taken as primitive and the other defined in terms of that one, or you can just allow that you're defining the pair together; the interaction of the operators maps naturally to a number of ways of talking about modality (alethic, epistemic, physical, temporal, etc.), but can be defined purely syntactically without specifying a particular interpretation of the operators; a particular modal logic will usually be defined by axioms intended to capture the particular sort of modality desired, and those axioms will vary.

In particular, if we take the necessary operator ▢ ("box") as primitive, then the possible operator ◇ ("diamond") is defined as ~▢~, that is, not necessarily not. Similarly, the necessary operator is defined as ~◇~, that is, not possibly not. This pairing has been very fruitful in clarifying modal issues, and is at this point in the history of logic no more controversial than the standard quantifiers ∀ and ∃. (And in fact, it turns out that one very useful way to think of ▢ and ◇ is as a kind of restricted quantifier over possible worlds, which ought to be obvious because ∀ is ~∃~ and ∃ is ~∀~.)

+++

If it isn't clear, the interdefinability of such operators means you only need one of them, but using the pair is way more convenient, and foregrounds how common and important two particular ways of using such an operator are. In other words, we could get by with just ▢ for a modal operator, and we would find ourselves writing formulas with ▢~, and ~▢, as well as unadorned ▢, but we would also find that we were writing one particular little phrase all the time: ~▢~. Same is true for ∀ and ∃: if we just used ∀, we'd have to write ~∀~ all the time.

(There are no doubt deep reasons for this neg sandwich pattern, but I don't know what they are. Interested, though.)

Because it's a non-suspect, honest, down-to-earth arrangement which can be used to justify the gross immorality of corporate profiteering. — Isaac

Exactly my point, and I am more or less granting that such arrangements really are good and bad, respectively.

I think that possibly the rot at the heart of the whole thing is this risk/reward model of business in the first place. If communities really do need the corner store is it a sensible strategy to encourage someone to gamble on one at 20:1 odds with the incentive being a high payout. Maybe we ought to just build the corner store ourselves as a community? — Isaac

No matter what we might wish to be the case, this does not appear to be a live option most of the time. I don't know why. (And my speculations are not so well-informed as to be interesting.)

What does appear to be the case, is that societies describable as "capitalist," in whatever sense, appear to have higher standards of living across the board compared to societies that aren't. I mean that to sound like a minimal reading of the record, not a simplistic one. I'm an adult, so I've heard of colonialism. I also understand how the last few hundred years have been a sort of experiment in turning fossil fuels into civilization — not a great plan, as it turns out. So I'm open to arguments that there is something else underwriting the disparity, but the starting point has to be admitting that there is such a disparity and putting the obvious label on it.

Reading the first half or so of Why Nations Fail (before I got bored) convinced me that the data is not really ambiguous here. My son's conclusion was that we ought to treat capitalism like nuclear power — yeah it works, and maybe nothing else works nearly as well so it's our best option, but it's super dangerous and we should carefully contain it.

Belief about the future goes from prediction to knowledge when it becomes true, and from prediction to falsehood when it becomes false. — creativesoul

No. Very, very no.

My answer would probably be the same as MU's on this point. — Luke

Whoa! Do I get some sort of prize for bringing this about?

Even if I freely chose to have toast instead of cereal for breakfast and nothing about having toast was inevitable, you would call this event "necessary" only because it is no longer possible to replay the event and to choose again. This fails to answer whether the original event was necessary or merely possible in the first place. — Luke

I agree with all of this, at least in spirit, but you have to be careful about the position from which such a claim is made. We have to be able to say that what is cannot not be without falling into a modal fallacy of treating all truths as necessary. (Sometimes it's trickier than it looks, and I said things to @Janus way back in this thread (or maybe the omniscience thread) that were dangerously close to fallacious.)

MU's point is, I think, a little different: from our position in time, we can only "really" think of the past as fixed, so claims about what was or was not possible in the past, at a time before some event occurred or didn't, are inherently somewhat suspicious. And that's not crazy: counterfactual reasoning is famously dicey; but it is just as famously indispensable.

Helpful video. I now "understand" the experiment @Andrew M was trying to explain to me over in the truth thread, and it — sadly or happily — connects to the discussion I'm having with @Metaphysician Undercover about past, future, alethic modalities and determinateness. Was so hoping I could stay out of quantum stuff, but I guess I'll have to give up that dream.

I haven't watched all of this, because I try not to think about quantum mechanics, but Alastair Wilson has interesting things to say about the relation between physics and metaphysics as someone near the frontlines.

QM is not a matter of "different rules for small things." — frank

Yes, this is the view I find incomprehensible because the whole point is that our big stable things supervene upon the small unstable things. It's not like we can keep them in separate rooms with separate rules, like the rooms of a preschool.

Yes, I'm far more concerned about the disparity between the Exxon CEO and his workers then the local restaurant owner and his staff. That my bag. It doesn't on it's own make the narrative any less viable. — Isaac

Absolutely.

Only in a minority of cases are the owners taking a comparable risk to the workers. The majority of cases they're not, so the justification based on the increased burden of risk is not sound. — Isaac

It's a large-ish minority, but even that 45% is actually too big, because about 20 million Americans are sole proprietors, self-employed and self-financed.

Anyway, yes, I take your point, and it's absolutely fair. There is, ahem, a narrative about risk that is used to justify the allocation of profit to owners rather than employees, but that risk is, in most cases, highly indirect and mediated; it's nothing like what one side is putting up versus the other side. Most days of the year, risk is a technical matter, numbers on paper, and doesn't *personally* touch the stockholder. (But of course every once in a while it does.)

But this sort of thing goes both ways: just as risk taken on is not quite a universal description of the difference between owners and workers, so profits taken isn't either. It's the rule, but not universal, and while the great bulk of profits — taken en masse — go to dividends and stock buybacks, that's not essential to the relation of owner and employee.

Maybe look at it this way: there's a reason "conservative" politicians justify corporate giveaways in the name of the corner store, because that business structure is not suspect. A small number of employees, razor-thin profits, this is not what's ruining the world. If we focus on that fundamental structure, we're sort of playing on the conservative's turf. I'm suggesting this is not where the trouble is, but in the financialization of business and in other rent-seeking (rather than just profit-taking) behavior. Insofar as those enable scales of employment (for a single firm) unimaginable in the past, there's distortion of that relation. (The corner store is more dependent on each employee than, you know, Exxon Mobil.)

Does that make any sense? I think we absolutely can and should demonize rent-seeking as not only not productive but actively harmful, and dangerous to long-term prosperity. But I also think there's an empirical case that business formation, with institutions to support it, raises the standard of living of a community. Look at the success of micro-lending programs, for example. So I need room to consider the corner store blameless, rather than exploitative just because it includes an owner and a few employees. (Of course if the corner store mainly sells booze and lottery tickets, we have a different problem.)

The world works differently at different scales. Why would we think that wouldn't be true. — T Clark

Because we believe in the uniformity of nature and the unity of science.

Are there really different "laws of nature" at different scales? Really? That sounds crazy to me. What doesn't sound crazy is that different methods of approximation work at different scales, and it's not even hard to think of examples of that, just based on selecting granularity. But that's a change in how we approximate what's happening, not a change in what's happening. We all know that regular Newtonian mechanics works pretty darn well for a lot of purposes, and is in some sense always false.

And yes of course there are differences between how a crowd of 50,000 behaves and how a group of 5 behaves. Yes, scale matters. But it should be explicable how you crossover from one scale to the next — even if there is no simple, non-fuzzy boundary. We should still have a single theory of group behavior and changes in behavior should track changes in the size of the group for good reason. The crowd of 50,000 is made of the same bits as the group of 5. As the quantity of people increases, new properties of the group become salient, in a predictable way, I should think. And so it is with our world of medium-sized dry goods and the critters of the subatomic zoo they're made of.

We observe a lot of stability; we know there's nothing like that in what our stable stuff is made of, so I assume those instabilities somehow combine to produce larger scale stabilities. (I assume it's vaguely similar to how fundamentally stochastic processes predictably result in Gaussian distributions and power-law distributions, and so on, all the randomness yielding order.) That's not a change in the rules, but a predictable result of the rules, and the rules that apply only to stable stuff (if there are any of those, even as approximations) are also a predictable result of the rules down below.

Anyhow, that's why at least one person (me) would think that wouldn't be true, based entirely on my assumptions and with hardly any knowledge of quantum theory at all. I've just never understood the "it's just a matter of scale" view — as if Mother Nature checks the size of what she's dealing with and then picks the appropriate rule-book to follow for that size object. That leaves the events at different scales isolated from each other in a way I find incomprehensible.

The immutability of the past is just a brute fact, which is upheld by empirical evidence, like gravity, the freezing point of water, etc.. — Metaphysician Undercover

Well, there's an answer.

(This thought experiment isn't important to me in itself, but if it were, I wondered how knowledge would work if the world were like this: would we, after the past had changed, have our knowledge become false beliefs — oh! this is the Mandela effect — or would all knowledge just vanish along with the other effects of an event that now has not occurred? If the latter, then of course we'd simply not know that the past had ever changed, and never could know...)

So the immutability of past events is a property we come to know a posteriori, good. But even if our knowledge is a posteriori, it could still be an essential property of a past event — and therefore necessary — that it be immutable. But you say it is not logically necessary that the past be immutable, so if it is, it is only in virtue of natural law, that sort of thing, physical rather than logical necessity.

Now you also agree that it's only events of the past that are immutable in this way, right? Events in the future are not only not immutable, they're not even fully determined; and the present, well, the present is presumably the moment of an event being fully determined and thereby becoming immutable.

It's easy to see how we could come to believe the future is not fixed, because we can experience making decisions, exercising our will, in ways that seem to determine how the future becomes concrete in the present. Even if we're completely wrong about that, it's clear how we would come to believe it. How would we come to know that this is not the case with the past? We cannot act upon the past, but maybe if we could, it could be changed. We have no experience of attempting to change the past and failing. So is the past immutable only in the sense that we cannot act upon it?

Or, consider this: we don't actually act upon the future directly either; that too, we are incapable of doing. We can only act in the present to select which possible future is realized. But every time we do that, we are also, immediately, filling the past with events of our choosing. The past is what we have some say-so in, never the future.

My goal was to see if we rely upon some independent conception of ideas like possibility and necessity in characterizing some portion of time as past and some other portion as future, rather than our ideas of possibility and necessity being derivative of our ideas of past and future. I think that in a great many cases when we say, things might have been different, the clearest meaning to attach to that is that at some earlier time, when certain events we know to have happened were still in the future, a different future might have come to pass, so that our past would now be different from what it is. If that sort of analysis is always available, then temporal modality would be logically prior to alethic. And that's not implausible.

But it also seems to me that to characterize the future as undetermined, the realm of possibility, and the past as fixed and incapable of change, is to rely on those ideas as given, so they are logically prior to our substantive understanding of the past and the future. That's my conundrum.

Only it turns out to be harder than I expected even to characterize the immutability of the past clearly, and we've barely talked about what challenges the future might pose.

And all of this is still circling around the problem of truth, because the past is the paradigmatic realm of truth, eternal and unchanging, while there is no truth about the future and for that reason no knowledge but only belief.

I personally consider them to be somewhat independent — Luke

Well, see that's the thing. We might define the past relative to some time as all the times before that, just the times. But what about the events that have happened in the past? Is it inherent to the past that an event which occurs at a past time cannot change? Or is that something *else* we know about the past only a posteriori?

once they have occurred they are in the past. Your example does not appear to indicate otherwise; the cup falls and then “unfalls”. — Luke

I mean, it's not possible. You're substituting another impossibility for the one I was entertaining: your question (if you were inclined to ask) would be, why don't cups unfall? My question was, why doesn't the past change? I pitched it as if some sort of backwards causation were possible, but trying desperately to avoid the word "cause".

Of course the past doesn't change. My question was whether this immutability is logical or merely, as one might say, thermodynamics, or even just the brute fact of time's arrow.

All in hopes, if it wasn't clear, of understanding how temporality relates to alethic modality. Is one logically prior to the other? Which one?

+++

Here's a dead obvious example of what I mean, with no cups unfailing: It's a Wonderful Life. In the film, the erasure of George from history is frankly miraculous: does that mean it violates the canons of logic or only the laws of nature?

So, is my notation correct? — Michael

Unless I'm missing something no, because it's the first term plus the sum of a bunch of products, so you need a sigma not a pi.

I know the Collatz conjecture, but not much about attempts to prove it or disprove it. (Was it Halmos who said our mathematics is not ready for the Collatz conjecture?) We can assume it can't be proven directly by mathematical induction, or it would have been done long ago. (And it's probably obvious why it can't be, but I would have to think about it for it to be obvious.)

So what do you do when you can't use mathematical induction? It was a long way around to proving Fermat's last theorem, through more general results in algebraic geometry that included Fermat as a special case, IIRC. Yikes.

I think it's valuable to explore the logic of risk and reward, owner and employer, and you've raised some interesting questions, but your analysis is throughout colored by an image of the likes of the board of directors of Exxon Mobil, on the one hand, and the guys and gals working on the oil rig, on the other. Google small business employment statistics and you'll find there are many other stories to tell. Something like half of employed Americans work for a company with more than 500 employees, and something like 45% work for a company with fewer than 20, and the bulk of the latter are self-financed businesses. So I gleaned from a very quick scan, but there are loads of statistics out there. It's really not just fat cats vs. working stiffs.

@Metaphysician Undercover @Luke

At time A, my coffee is precariously perched on my car.
At time B, after A, the coffee falls off the car.

At time A, it is true of the coffee that it may or may not fall at some future time. At time B, it is no longer true of the coffee that it may fall, because it has already fallen.

No one is confused by an event having happened or not. What keep us up at night, is wondering whether things might have been different. No one can do anything, at times B and after, about my coffee having fallen; the question is specifically whether it was inevitable that it would fall. We believe we can make a distinction between events that were bound to happen, and events that were not; in which case, there must be a difference between (1) saying, at a time B or later, that nothing can happen that will make it so that the coffee has not fallen, and (2) saying at a time A or earlier, nothing can happen that will make it so that the coffee does not fall. To say that an event in the past was not inevitable, is to say that (1) is true of it but (2) false.

We assume, in fact, that (1) is true of all events — since we're not doing quantum mechanics or something here. Suppose (1) is false. Then there is a time C, after B, at which an event occurs such that my coffee did not fall off the car. The aftermath of my coffee falling lasts from B to C, at which it is undone; before B, and after C, the coffee has not fallen. Of course, that's not "possible," given thermodynamics and whatnot, but is it logically impossible? My coffee falling is not in the past for any time before B, of course, because B is still in the future; it is in the past for all times between B and C; and it is no longer in the past of any time after C. The time B is in the past for times after C; it's just that what happened at time B, for times C and after, is not the same as what happened at time B, for times between B and C.

Is there any non-question-begging way to deny this is possible? We cannot, ex hypothesi, object that an event in the past at time X is in the past for any time after X; the hypothesis is exactly that this is not so. In what, then, does the immutability of the past consist? Is it brute fact? Could it conceivably not be?

Then you will have much to discuss.

Seems straight forward to me. — creativesoul

Maybe you should discuss it with @Metaphysician Undercover.

If gambling had an equal payoff:risk ratio for each group then the sum gain for each group as a proportion of their investment, would be the same. So each group would, in sum, get x% richer. But that's not what we see, because the gap between the two groups even in relative terms, is getting bigger. — Isaac

Say I'm worth x and you're worth 1000x. I wager x/10 and win earning say 5/4 my wager, so my wealth becomes 9x/8. You wager 10x and win, earning 50x/4, so your wealth is now 1012.5x. The ratio of your wealth is to mine is now 900:1, instead of 1000:1. So my hunch about how this would work is *wrong*. By wagering 10 times as much in absolute terms, but one tenth in relative terms, you allowed me to close the ratio gap. On the other hand, you used to have only 999 more dollars than I; now you have 1011.375 more. I've closed the ratio gap, but am further behind absolutely. Interesting. What happens when we go again? ****

I suspect, as you note, part of it is that there are just better rates of return for high rollers. I also suspect that high rollers needn't limit how much they risk, as I surmised here. My initial post in this thread suggested that the principal use of profits (once they reach individuals, I wasn't thinking about the firm) was to create new debt. When you have great wealth and an impressive stream of income, you don't need to spend much of any of it; people lend you money. So as a wealthy gambler, I'll have the opportunity to bet with Monopoly money, perhaps placing bets that altogether are many times my at-the-moment wealth. Then I can easily outrun the poor gambler, who has no future value to mortgage.

****
Oops, that was weird.

I also neglected to consider that your ratio to my initial wealth is now 1012.5:1, but mine is 1.125:1. Mine has grown faster but much less, and I had to risk a percentage of my wealth ten times greater than you did.

But we're the blind leading the blind here. — Isaac

I've never even met an economist.

gambling — Isaac

As I said before, part of the point here is that the absolute amount risked can be greater, while still being a far smaller portion of the total wealth, when you compare the wagers of the wealthy and the poor. I haven't had time to run through the math, but if you assume that a wealthy and a poor gambler have the same rate of success (win as often) but the wealthy gambler is betting more, then their payoffs are also going to be bigger. When the poor gambler wins, they win less, right? My thought was simply that everything can be scaled up, the risks and rewards, but needn't be scaled up by the ratio of total wealth to total wealth. See how that works? I can bet more and win more, without risking my entire advantage relative to you, and the ratio of my wealth to yours will just keep growing.

bankruptcy — Isaac

Dunno. But it cannot be the case that starting a business is guaranteed by law to be risk-free, can it? But I really don't know. Maybe in some no-blood-from-stones sense it is, but there's opportunity cost (yay! I get to walk away with nothing after 15 years, might as well have just had a job) and for an individual maybe a risk to their notional creditworthiness.

If the risk were genuinely matched to the reward they'd be, on average no better off as a group yhsn they started. — Isaac

Yeah, you said that before, although I think before it was that we should expect them to be no better off than workers.

Are you sure about this argument?

You're basically claiming that the wealthy class aren't really risking much of anything, and there's clearly some truth to that, but there are counterexamples too, aren't there?

Try walking through the example with gambling, one rich gambler and one poor, and see how it works out.

owners have broad portfolios — Isaac

This is just equating owners with shareholders. It's obviously not the case for small businesses, partnerships and such.

However, in general owners lose more when a company goes belly up
— Count Timothy von Icarus

...but I see no evidence of this. I mean, generally owners are the rich and workers are the poor. — Isaac

I think you can grant the claim that owners may lose more in absolute terms, but less as a portion of their total wealth. Why not just say that? It's a solid point.

If the owner is normally taking such a big risk, then there'd be as much incentive to cautiously share that risk as there would be to recklessly bet the house on it. — Isaac

Also an interesting point. Presumably part of the issue here is access to capital to start the firm. You have to take on risk before hiring anyone. So what risk gets shared? Under the usual scheme, I don't ask you to take on some of the risk I accepted before you came along. If the firm fails, or even if you just quit, you walk away without that burden. While you're employed, I do indeed use your labor to pay off the debt I accrued without your input. If, instead, part of the package of my hiring you is that you accept some small part of the firm's pre-existing obligations, that's quite different, more like a (weighted?) partnership occurring over time. Sounds like a reasonable idea for the owner, as you suggest, but you'll compete for workers with firms just offering burden-free salary. If the rewards are potentially great enough, people may be willing to enter into this more risky sort of employment arrangement.

Gettier is hard. It seems clear there is no general way to block Gettier cases, because whatever you come up with will generate a revenge case purpose built to block your solution. What we should conclude from that pattern is hard to say, but most take it as bad news for the analysis of knowledge.

The other issue raised by this particular case (and @Michael this might be relevant to the difference between first- and third-person accounts) is whether the actual reasoning relied on de se modality, since there's reason to think this is often the case with epistemic questions. That is, the question of whether I would or could know something is sometimes irreducibly about me, so the first level of analysis isn't really about whether there are possible worlds in which I know or don't, but whether my epistemic alternatives know or don't, whatever world they reside in.

Also, I don't think anyone, including me, has given an adequate response to what I take to be @Metaphysician Undercover's position, that alethic modality reduces — or, rather, should reduce — entirely to temporal modality. I don't think that position is prima facie wrong.

I've been at pains to say that we're only talking about implication not literal meaning.
— Srap Tasmaner

Then I'm not sure what relevance it has to the discussion. — Michael

Consider:

But we’re not just interested in what people mean by what they say.
— Srap Tasmaner

Why not? If "I'm not certain" means "I don't know" then "I know but I'm not certain" means "I know but I don't know" which is, of course, a contradiction. So it doesn't make sense to say "I know but I'm not certain".

And if it doesn't make sense to say "I know but I'm not certain" then it shouldn't make sense to say "I can know without being certain". — Michael

Here you are, trying to decide whether an agent S can simultaneously be in a state of knowledge and in a state of uncertainty, but you choose to test this possibility by figuring out whether it would "make sense" for an individual to say, of themselves, that they are in both these states.

Not a great plan.

The case is perfectly clear when it's a third party saying it: you and a friend are watching your daughter at a spelling bee, she's floundering, looking overwhelmed; you can straightforwardly say, "She knows this one — we reviewed it last night and she had it cold — she's just flustered and second-guessing herself." There is no general problem attributing both knowledge and uncertainty to someone; there seems to be some weirdness when that someone is yourself. If I talk about implicatures and such, it is only to block mistaken reliance on "what it makes sense to say."

it is also the case that "It might be in the car" implicates (but does not entail) "I don't know for sure where it is"
— Srap Tasmaner

No, the speaker might know that the book is in the car but choose to be coy, though literally honest and correct, in saying "The book might be in the car". If I was looking for the book, then I would not appreciate my friend being coy that way, but he would not be logically incorrect. — TonesInDeepFreeze

Indeed. That would be why I said "does not entail." This being coy, it's a violation of Grice's maxims — quantity I think, because you are sharing less information than you have.

Look, I'm only talking about this because I want to wall off these sorts of considerations: it is a fact that if you know that something is the case, then there are circumstances in which saying only that it is possible is misleading. I'm pointing at that phenomenon so that I can block it from undermining our claim that actuality entails possibility. If it's only a conversational implicature, it has no bearing on the relevant entailments.

If I candidly assert an indicative sentence, I imply that the content of my belief is represented by that sentence
— Srap Tasmaner

Yes, you imply it. But that asserting a sentence implies something isn't that that sentence (or assertion) means that thing. [ ... ]

This is where I think you're conflating different senses of "meaning" or "expression". — Michael

Except for the part where I'm clearly not, because I've been at pains to say that we're only talking about implication not literal meaning. It's right there. What what you say means is one thing, sentence meaning, and what you mean by it is something else, speaker's meaning. I'm not conflating them at all; I am acknowledging that there is more to our utterances than the literal meaning of what we say so that it doesn't interfere with the logical analysis.

You can't assert that the book is in your room, or that you believe the book is in your room, and that it is not true that the book is in your room.
— Srap Tasmaner

Sure I can: I believe that the book is in my room but the book isn't in my room. I can assert anything I like. — Michael

Sorry, yes, I should have said "without falling into Moore's paradox," and so on.

Both @Isaac and @Metaphysician Undercover are going to consistently deny that there is anything at all to your asserting P than that you believe (using various accounts and locutions for this) that P, in every instance. Notably, that includes any hypothetical. If you say "Suppose the book is in my room, but I believe it is not ..." they will ask who holds the belief that it is in your room, whose judgment that is, and so on. translates claims of fact into predictions about the agreeability of our discourse. (Is that Lewis's scorekeeping, or Goodman's worldmaking?)

We proceed on the assumption that we can analyze "naked" propositions with no speaker; they do not. Every proposition is an utterance of someone, for a purpose, even if that someone is only virtual or something. Think of it as a sort of Nietzschean perspectivism. The kicker, of course, is that the "naked" view is linguistically indefensible. You have to invoke a generalized competent speaker of English. The right question is whether you can "factor out" linguistic competence through your analysis of semantic content...

We don't have to take this position into account; we can just go about our business. But if you want to engage with the loyal opposition here, you have to find some way of making the point that is not simply question-begging. I'm working on it. ;)