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. ;)

It's simple that the poster is nuts to think that "Possibly P" implies "Not P". — TonesInDeepFreeze

Certainly it is not the case that ◇P ⊃ ~P.

But 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" — and, to connect the dots, if I don't know where it is I am not in a position to assert something like "It is in the car," some simple declarative statement P, but only a weaker ◇P — and it is a locution people resort to precisely to avoid admitting that they know exactly where it is and how it got there.

For all that, I will still say that P ⊃ ◇P is a solid axiom (or however you arrive at it) that captures some of what we have in mind when we reason about what's possible.

Side note: I recently had occasion to read this page about the Wason selection task, which I had forgotten all about. It seems often to have been counted as evidence against the everyday conception of logical consequence being captured by the material conditional, but there's further work that makes this less clear, and more interestingly there's this report:

A psychologist, not very well disposed toward logic, once confessed to me that despite all problems in short-term inferences like the Wason Card Task, there was also the undeniable fact that he had never met an experimental subject who did not understand the logical solution when it was explained to him, and then agreed that it was correct. — same wiki page

Now that's really curious, and leaves considerable room for the likes of logic, set theory, arithmetic, geometry, modal logic, and the rest to continue in the effort to axiomatize our intuitions, with the expectation that, even though ordinary folks don't think in precisely these terms, when explained to them, such systems will make sense and they will agree this is a good way to go about things.

This, @Banno, is how I would justify what we're up to. If this counts as "choosing a grammar that doesn't lead to confusion," okay. But I'm never going to put it that way because I think that way of putting it leads to confusion.

↪TonesInDeepFreeze The sad thing is that your clear explanation will not correct the confusion here. — Banno

It's not that simple.

For instance, I had a look at the SEP article about revision theory, and I was puzzled that we're treated to what amounts to a wholesale reconstruction of model theory to allow the proposed extension, complete with new versions of interpretation and everything else, and then I realized that you have to do this if you accept that Tarski's machinery is not up to the task.

I don't think we even have a complete syntax for any natural language; lacking that, there's no hope for a complete semantics.

So while I'm deeply sympathetic to the formal approach, and in particular with model-theoretic truth-conditional semantics, we can't claim to have managed more than some fragments of some natural languages. And formal semantics takes lexical semantics as just given, somehow, which means it is never going to address issues of reference; that's a non-issue for mathematics, where reference is essentially stipulative all the way down, but it's a big damn deal with natural languages.



I obviously don't have any problem with the specifics of what you posted, but I'm not clear on what you expect to achieve by posting it. The box and diamond operators are defined as they are because of our pre-existing intuitions about alethic modality. And similarly for the axioms of various modal logics. You're surely not arguing that someone's intuitions can be refuted by the definitions and axioms we've chosen... If those definitions and axioms don't match our intuitions, so much the worse for them.

I'm also not clear what kind of mileage you hope to get out of talking about models. What models? How do you construct them? Again, I'm all for this, but I don't think we get to assume this is all settled for natural languages.

If the point you wanted to make was "quit doing that, because you can do this instead," I'd endorse that!

I think you're conflating two different senses of "meaning" — Michael

I'm really not. If I candidly assert an indicative sentence, I imply that the content of my belief is represented by that sentence. It's simply false that I have to preface everything I say with "I believe."

I'm concerned with meaning in the sense of definition. — Michael

I get that. But I'm not sure invoking the word "definition" is going to get you very far.

"I believe that the book is in my room" and "the book is in my room" do not share a definition. — Michael

Neither one of them has a definition; they have semantic content. Which I think is the right thing to be talking about.

Otherwise how do you make sense of the "the book is in my room" part of "I believe that the book is in my room"? The latter isn't to be interpreted as "I believe that I believe that the book is in my room". — Michael

Well that's a question. The biconditionals I offered look circular, don't they? What are we to do about that?

I think you're just taking meaning-as-use to an irrational extreme. — Michael

You're confusing me with what I want to argue against, but we can't ignore that there is insight underlying the doctrine of meaning as use.

"It can be true that I believe something even if what I believe is false" is something I believe. — Michael

Now try it with a specific belief. 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. Someone else, let's say "George", can say it of you, and then there's nothing to stop a third party from saying that you believe the book is in your room and George doesn't, full-stop.

I think the right strategy is to block the supposed dependence of semantic content on beliefs.

The sentence that expresses that you believe it is "I believe that the book is in my room". — Michael

Or an assertoric utterance of "The book is in Michael's room."

At any rate, the content is where the action is.

it can be true that I believe something even if what I believe is false. — Michael

But you have no way of saying this as a report of your beliefs. And if someone else says it, of you, then it can be taken as report of their beliefs.

I think the trouble comes earlier and runs deeper.

Whether we're considering epistemic or alethic modality, if something is true then it is possible. — Michael

I mean, there's the Church-Fitch argument; if there's no way around that, then there must be truths that cannot be known.

Therefore, your claims that the meaning of "the book is in my room" has something to do with what I believe, or that truth is honesty, are false. — Michael

Here's the problem, as I see it:

(1) If you want to convey your honest belief that the book is in Michael's room, the words you choose to express that belief are "The book is in Michael's room."
(2) You choose those words because the literal (or conventional) meaning of that sentence represents your belief accurately.
(3) But that sentence represents your belief accurately precisely because it's what anyone who held the same belief as you would say if they wished honestly to express that belief.

The claim is that there is no more to a word's being appropriate for the purpose of expressing what you want to express than it being the word people use honestly to express that belief.

But your using that sentence honestly to express that belief is itself an element of the common practice that underwrites the use of that sentence to express that belief. That's not a paradox; it means that the words you are using are a solution (a stable equilibrium) to a problem in (cooperative) game theory, in which what you do is dependent on what others do, and what they do is dependent on what you do. This is the substance of the idea of the arbitrariness of the sign: any solution to such a problem is as good as any other.

But that's all about meaning.

You can take a further step and claim that there is nothing more to the book being in Michael's room than people who hold the belief that it is honestly expressing that belief by saying, or being disposed to say, "The book is in Michael's room."

Now what does this mean, that there is "nothing more to it"? That suggests there is a biconditional that looks like this:

P ↔ People who believe that P and wish honestly to express that belief assert, or are disposed to assert, that P.

Maybe here we give an account of belief, maybe we posit a language of thought and all of this is a way of saying that P is the canonical translation into our language from the LoT, maybe a lot of things, but some people are also going to be tempted to say (by a parallel argument) that there is nothing more to belief than what we assert or are disposed to assert, in which case the biconditional becomes

P ↔ People believe that P ↔ People assert, or are disposed to assert, that P.

That's the "nothing more" account, I believe. There are stops along the way where you might opt out, but this is its final destination.

The question of this thread has always been whether there is something more, whether there is, for instance, something more to the book being in Michael's room than the appropriateness of the sentence "The book is in Michael's room" for honestly conveying your belief that it is.

I think most people's pre-theoretical intuition is that of course there is, but the apparent difficulty of specifying what the something more is convinces some to give it up, or to give up in a slightly different way, something like this: if there is something more, it's not the sort of thing we can say, since all we can say is stuff like "The book is Michael's room," and that's already within the scope of the "nothing more" analysis.

So there's a summary of the what this thread is about. I'm not convinced the nothing more account is right, but the challenge is to offer an alternative as comprehensive, to say exactly where it goes wrong, or to show that it isn't actually what it seems to be.

"The book is possibly in my room" implies that I do not know where the book is. — Metaphysician Undercover

You just have to be careful about this. Given

(1) The book is possibly in my room.
(2) I do not know where the book is.

It is not the case that (1) entails (2). It just doesn't. But conversationally, we take an utterance of (1) to implicate a commitment to (2). And that commitment is purely conversational; you do not contradict yourself if you say, "Well, it might be in my room — as a matter of fact I know that it is."

There's no more a contradiction here than there is in Mitch Hedberg's joke, "I used to do drugs. I still do, but I used to too." Implicature is not entailment; that's the whole point. (To belabor the point: "used to" suggests that you've stopped, but it doesn't mean that or entail that; it's just an inference we tend to make when someone says it, and an inference we're expected to make. If any of this were different, Mitch would not have a joke here.)

And that's another reason that approaching all philosophical problems in terms of what people say or can't say is so misleading; there are other rules than logic at work in what people say to each other and what it will be taken to mean.

When you say that the book is possibly in your room, you imply that the book may be elsewhere.
— Metaphysician Undercover

But I'm not implying that the book isn't actually in my room. — Michael

It's a conversational implicature, that's all. To say "It might be in my room" suggests that you don't know where it is. A good paraphrase is "The book is, for all I know, in my room." This is an epistemic modality, and all it says is that the book being in your room is consistent with your total knowledge. Obviously if you know it's in your room, its being there is consistent with what you know! And that's the thing about the implicature: it suggests that you don't know, but your knowing doesn't make what you said false.

But we don't have to be talking about what people know, what they say, what's implied by what they say, and all that. None of that is implied or relevant if the modality is alethic. Considering only physics and geometry, for example, we might say truly that it is possible for any normal-sized book to be in your room, including this one, and impossible for any normal-sized (non-toy) semi-truck to be in your room. There's reliance here on what we know about physics and geometry, but no one's knowledge of the location any book or truck is in play.

It wouldn't hurt to distinguish the epistemic and alethic modalities now and then.

So possibility is likely some sort of feature of time. — Metaphysician Undercover

A lot of what we want to say using the alethic modalities clearly does have to do with time, and we do readily make these identifications, future = possible, present = actual, past = necessary. But to say that the future is as yet undetermined, for instance, or that we cannot change the past, if those are to be substantive claims, have to mean something besides the future is future and the past is past. What underwrites that understanding of the temporal modalities?

I think we can say more, and the way to say more is to turn to mathematics, from which time has been deliberately excluded. See what you still have without time. What we find is that there are ways to make issues we are familiar with most often in temporal terms tractable for reason in non-temporal terms.

Depending on what you mean by "not actual", "possible" does mean "not actual". This is because the two concepts are mutually exclusive, inconsistent with one another, such that if something is truthfully said to be possible, it cannot at the same time be truthfully said to be actual. — Metaphysician Undercover

This says {x: x is possible} is a subset of {x: x is not actual}. What's in the rest? What is neither possible nor actual? (Asking for a friend.)

Truss reminds me of a quote Christopher Hitchens once made about David Cameron:

Q: What do you think about David Cameron?

A: He doesn't make me think.
— Manuel

That's from Ayn Rand's The Fountainhead.

Toohey: Mr. Roark, we're alone here. Why don't you tell me what you think of me? In any words you wish. No one will hear us.
Roark: But I don't think of you. — Michael

Also Casablanca:

Ugarte: You despise me, don't you Rick?
Rick: Well if I gave you any thought I probably would.

there is no opposite to "possible". And to use "impossible" as the opposite to "possible" is to stray from the definition "what may or may not be". — Metaphysician Undercover

I use a different definition, but the ends are the same. — Mww

So if I have a stack of boxes, and I'm going to mark one of them with an X, then it is true of each of the boxes that it may or may not be the one I'm going to mark. Once I have marked a box, it is no longer true of any of the boxes that it may or not be the one that I'm going to mark: it is true of one that I have marked it and of the others that I have not, and that's it.

As a temporal sort of modality, that seems fine. Once I have marked a box, would either of you say that it is true of each of the other boxes that, though it is not the box I marked, it might have been the one that I marked? If actuality is the closing off possible futures, can we not imaginatively consider an early time at which the actual present was only a possible future, one among many?

Above I spoke hypothetically of having a stack of boxes one of which I intended to mark. How do you conceptualize what we are doing when we reason in this way? Am I talking about a possible future in which I do have a stack of boxes?

Is there any verb that isn’t fractive [ sic ]? How would One become apparent to me? — Mww

Sorry — couldn’t resist the opportunity to sic you. It’s “factive”. “Fractive” sounds cool though. I wonder what it will turn out to mean. Maybe something related to “fractious”.

Yes of course there are non-factive verbs, and verbs used in both ways. Earlier I gave a rewrite rule that I think captures the difference. For a proposition P and an attitude Φ, if

(A) S Φs P

can be rewritten, without changing its truth-value, as

(F) P, and S Φs that

then Φ is factive.

Obvious example is believes vs knows:

(1) Joe knows 7 x 6 is 42 ↔ 7 x 6 is 42, and Joe knows that

(2) Joe believes 7 x 6 is 44 ↔ 7 x 6 is 44, and Joe believes that

(1) is true and (2) is false.

+++ Correction +++

This is just wrong, for a couple reasons.

The right way to say this is the usual way:

Φ is factive if and only if S Φs P entails that P.

++++++

It’s related to the de dicto/de re distinction, and the two sorts of readings of “Joe is looking for a spy” (I think the example is Quine’s):

(3) There is a spy, and Joe is looking for it. ∃x(x is a spy & Joe seeks x)

(4) Joe is looking for something that is a spy. ∀x(x is a spy → Joe seeks x)

It matters that ∀ doesn’t have existential import: there may be no spy for Joe to find.

Chuck Norris doesn’t go hunting — that implies the possibility of failure. Chuck Norris goes killing.

I think the upshot here is that a propositional attitude report is factive if it has the same truth-value as its de re reading.

+++ Correction +++

This is also questionable. Not sure what got into me this morning. Maybe I'll take some time and figure out how this stuff does relate.

++++++

And.....what benefit in them is there for me? — Mww

If I know that P, then it follows that P. That’s helpful for you, because it means you can learn about the state of the world from my reports of what I know, without having to go see for yourself. If you don’t know, your only option is reasonable belief. But whose testimony is more valuable to you: someone you believe knows whether the dam has broken; or someone you believe thinks it has or hasn’t?

Possible that capitalism is not an economic system at all, but a type of (partial) government system.

If you designed a government to establish public safety to some manageable degree, to protect private property, to enable complex and mediated methods of trading by enforcing contracts, and then further stipulated that government was not to interfere in any other way with the activities of its citizens except when and to the degree that it can demonstrate it is necessary to maintain such a system of “ordered liberty,” then you’d have capitalism. Markets and trade and finance and division of labor, none of that is behavior exclusive to capitalist societies, but capitalist societies are those whose governments are constrained from interfering in these activities except as demonstrably necessary, and providing the underpinnings (again, public order, property, contracts, etc.) without which the scope of such activities might hit natural limits.

That you can take this as a partial definition of a type of government is clear from the various mixed models which incorporate all of this but empower government to serve other ends as well. Even in such mixed models, the point would be that government does certain things, but specifically refrains from doing things it conceivably could — putting a cap on income, say, something obvious like that, which is inconceivable in any sort of capitalist society, even if it spends lavishly on public goods like education or on anti-poverty programs, and so on.

TL;DR. Capitalism maybe not so much an economic system as a political one, a type of partial government.

I'm not saying the actual world is no longer a world. It's still a world just like the box with the X is still a box. — Metaphysician Undercover

Jolly, then it’s “just semantics.”

The X signifies that the box is not in the same category as the unmarked boxes, just like "actual" signifies that the world is not in the same category as the possible worlds. — Metaphysician Undercover

Fine. It’s not my usual usage, but if you want to reserve possible for non-actual, it makes no real difference. It makes world carry a little more of the burden, but that’s also fine.

I never used "impossible", you are putting words in my mouth — Metaphysician Undercover

Yes, I was. But I can adapt to your usage. All I need to say, using your terminology, is that the actual world is a world. Done. In my usage, if the actual world is not a member of the class of possible worlds, it’s a member of the complement, which would be the class of impossible worlds — if there are any such things, depending on the accessibility relation.

It is a common misunderstanding to think that impossible is the opposite of possible. — Metaphysician Undercover

I have no need for impossible worlds, so that’s that.

*

I can now rephrase my account of hypotheticals for you.

An assumption H, for the purposes of hypothetical reasoning, picks out a set of worlds at which H is true. The actual world may be such a world. (The set of all worlds at which the Allies won World War II includes this world and quite a few others where the course of history was slightly or largely different, but the good guys still won.)

The goal of hypothetical reasoning is to discharge the initiating assumption by means of a true counterfactual conditional, meaning that at all accessible H-worlds, the consequent of the counterfactual conditional is also true, with the usual fudging of the accessibility relation. Standard stuff. (It’s just no P without Q with a necessity operator that acts as a restricted universal quantifier over worlds, and the terms of the restriction depend very much on what you’re doing. For our purposes, it’s usually going to be more restrictive than logical or physical necessity but not so restrictive that we shrink our set to the actual world.)

All good?

Btw, I believe I read somewhere that Ryle once described himself as an old-fashioned “Cook-Wilsonian.”

in knowledge-first terms, Alice knew that it was raining because she looked out the window and saw that it was raining.
— Andrew M

In knowledge-first terms, I know it is raining because I already know what it is to be raining. — Mww

I should probably say something here. Williamson argues that there are several factive verbs (see, remember, regret, and so on) and that know is the most general factive verb, so every instance of one the others also “entails“ knowing. “Entails” is not quite right though; it’s that any factive instance of one of the others is necessarily also an instance of knowing.

The gist of which is that if I see that it is raining, I also thereby know that it is raining. If I remember that I have an appointment, then I thereby also know that I have an appointment.

You could nearly say that remembering, perceiving, regretting, and so on, are particular ways of knowing.

— Insofar as the point being made by @Mww is about our conceptual apparatus and its role in our mental acts, I’ve got nothing helpful to say about that. —

I know what is true because I already know what it is to be true. I know what is true because I already know what truth is. — Mww

On this sort of thing, I could say that the old argument, from Cook Wilson, against any analysis of knowledge, was that there is no non-circular way to carry out such an analysis. Insofar as think about things, we’re stuck with relying on what we know and that we know it. Williamson takes a rather different route.

What's strange here is that I accept that "I am certain" doesn't mean "I know" but it does seem to me that "I am not certain" does mean "I don't know". I suppose ordinary language just isn't always consistent. — Michael

Meant to reply to this.

The obvious explanation is that S knows that P entails that S is certain that P, in which case S is not certain that P entails that S does not know that P.

You know, there are other things we could say here. I think it's plausible that if and only if S knows that P, then S is entitled to be certain that P. It's like saying that certainty ought to be backed by knowledge. (It's also a way of acknowledging that there is a factive use of "I'm certain" right next door to "I know for certain." Other factive uses pull in knowledge with them, so some uses of "certain" ought to as well.)

I can even imagine there being particular circumstances or situations in which we would say you *ought* to be certain, to be without doubt or reservation. Not sure though. But if we're going to give certainty an epistemic, rather than merely psychological, role, we'll have to consider the sorts of norms that attach to knowledge at some point.

we'd take a bunch of boxes, and assign the same value to each of them, "possible". Then we take one, mark it with an X, and assign to it a special value, "actual". We cannot say that the one with the special value still has the same value as the others. — Metaphysician Undercover

Not *only* the same, because it's the one with the x on it, but it's still a box. You forgot to give an argument that putting an x on a box makes it not a box, or that you have to erase "possible" in order to write "actual".

What's odd here is that the complement of possible is impossible. Me, I assumed actuality implied possibility. I'm puzzled why you think actuality implies impossibility.