The mechanism is the stipulation. — Banno

If by stipulation you simply mean convention, then I think we are kind of saying the same thing. The convention is itself part of the causal-historical events. The dubbing is how it started, the convention is how it is used and ongoing part of the the name being carried on.

OK.

Sorry for any misunderstanding. — Count Timothy von Icarus

No worries. I wish I too was a model of clarity!

"If it is not possible, then it is in some sense necessary."
— Count Timothy von Icarus

This proposal is a neat and simple way to bring out different alleged senses of "necessity." We look at event X; it is no longer merely "possible," since it has occurred, been actualized; therefore we're tempted to say that it must be necessary, since it has been removed from the realm of possibility.

But what exactly is the "necessary" part here? Compare two statements:

(1) "It is necessary that X occurred."

(2) "It is necessary that, since X occurred, it cannot un-occur, or not be the case."

Statement (1) is pretty clearly not what the proposal means. My cat is named Bunny, but it could have been otherwise.

Statement (2), though, does seem to express what we mean by the original proposal. Now that my cat is named Bunny, we can't rewrite the past so that she is named Methuselah. Her being named Bunny is "necessary" in that sense.

In fact, before I develop this any further, let me ask whether you think (2) is a fair elaboration of what you meant by "If it is not possible, then it is in some sense necessary."

The bulk of part three places Quine's position in a few historical arguments involving Church, Carnap, Lewis and particularly, Barcan.

(37) is curious. "An object, of itself and by whatever name or none, must be seen as having some of its traits necessarily and others contingently, despite the fact that the latter traits follow just as analytically from some ways of specifying the object as the former traits do from other ways of specifying it." But after Barcan, and then Kripke, we might permit an object to have necessary yet contingent traits. That gold has a certain atomic number is contingent, yet necessary. Some properties (like being H₂O for water or having 79 protons for gold) are essential to the object, despite having been discovered empirically rather than analytically derived.

There's that words, "essential".

If anyone is following this, they might well be interested in the section from the SEP article on Quine's misunderstanding of Barcan, and related topics. In particular, Barcan argues that Quine is mistaken to think that modal logic is committed to Aristotelian essentialism.

And so we arrive at the Barcan Formula, ◊(∃α)A⇒(∃α)◊A.

There's a lot here to work through.

In fact, before I develop this any further, let me ask whether you think (2) is a fair elaboration of what you meant by "If it is not possible, then it is in some sense necessary."

Obviously, you can rename a pet, but it seems accurate in the sense that something that has happened cannot possibly have not happened. It has already been actualized.

However, I don't think we'd want to limit this sort of consideration only to the past.

Consider: "In order for the green conscripts to be effective in battle it was necessary for Napoleon to train them into a disciplined army first."

This is the sort of sentence historians commonly write. Are they deficient in their understanding or does this make sense?

I think it makes sense, but it can be taken in ways that don't. For instance, it can hardly mean "in all possible worlds this set of individuals needed to be trained by Napoleon to become a combat-effective fighting force." It seems possible that this set of men might have received training at some other point, by some other means, or that they might have some sort of preternatural aptitude as soldiers and not require formal training.

Rather, I think we can correctly interpret it as: "Given the conscripts lacked combat skills it was necessary for this potentiality (to be good soldiers) to be brought into act because potentialities necessarily do not go from potency to act without some sufficient cause." Basically, people who lack skills necessarily don't spontaneously gain them for no reason at all, but will only gain them through certain actualities (a sort of physical necessity). This is falls under the more general principle that actuality must lie prior to any move from potency to act, else things could happen for "no reason at all."

And this sort of relationship between actualities and potentialities can be layered on in many ways, which is what we often see in complex counterfactual reasoning.

Consider: "In order for the green conscripts to be effective in battle it was necessary for Napoleon to train them into a disciplined army first." — Count Timothy von Icarus

In all the possible worlds in which green conscripts were effective in battle, Napoleon had first trained them into a disciplined army. It's just access, again. The only worlds in which green conscripts were effective in battle were those accessible from the worlds in which Napoleon had first trained them into a disciplined army.

Whether it's true or not is a different issue.

But it can be set out clearly with possible world semantics using accessibility.

It might be expressible in terms of accessibility, (although I would say you are losing things); that's not really the point. Framing modality in terms of possible worlds requires a radical, counterintuitive retranslation of counterfactual reasoning into terms speakers themselves are unlikely to recognize as true to their intentions, while at the same time requiring either a bloated ontology of "existing" possible worlds, or some other sort of explanation of what they are.

Why must we be under a commitment to understanding modality in these terms? Certainly not because this is how modality has been historically or widely conceived, or because it's what most people mean by the common usage of the term.

I will throw out a very similar example. You can also explain probability in terms of frequency alone. This will work quite well in some situations, when you are picking colored jelly beans blindly out of a jar for instance. "A randomly chosen jelly bean has a 25% chance of being red" just means "25% of the jelly beans are red."

Frequentism is not the only way to understand probability however. It only really becomes popular in the 20th century due to some quite contingent events (I don't think its eventual dominance is unrelated to the switch to viewing modality in terms of possible worlds either). One can claim "probability is just frequency" just as one could try to claim that "modality is just possible worlds."

But there are several other views of probability: propensity, subjectivism, logical, etc. and it's far from obvious that these aren't better ways to look at things. Frequency can, for instance, be explained as the result of propensity. Frequentism often leads to grave mistakes because it is very counterintuitive for certain sorts of issues.

For instance when we say "Trump had only a 20% chance of winning the 2016 election," do we (must we?) mean something somehow parsable into frequentist terms? E.g., "in only 20% of possible worlds including the election did Trump win," or "if we ran the election 100 times these polls suggest Trump would win 20 of the 100."

These are, IMO, bizarre rewriting exercises that dogmatic frequentists have to engage in as a means to hold up the assertion that probability and potentiality just are frequency. A propensity view suits one-time events far better, or the Bayesian view. Possible worlds sometimes looks a lot like frequentism, only of a sort particularly concerned with what occurs with 0% or 100% frequency. It also has to rely on bizarre rewriting exercises.

It also often seems to get things completely backwards. There are no possible worlds without x because x is necessary, not "x is necessary because no possible worlds exclude it" (this is essentially just a special case of the frequentist dogma that probability just is frequency, which has been appropriately lampooned in recent years). This, in turn, leads to having to explain complex cases (although perhaps fairly simple in naive counterfactual reasoning) with ever finer webs of relations. This is the opposite of the goal of explaining complex things in terms of more general principles, e.g. principles like "conscripts who aren't soldiers don't spontaneously know how to be good soldiers without being taught because potential isn't spontaneously actualized without a cause sufficient to its actualization; a cause is necessary."

Or more simply, if something is impossible, this is in some sense necessary, since the impossible, being "not possible" necessarily cannot occur. It will occur in 0% of potential futures.

If you try to sprout pinto beans by putting them in an incinerator, this will not work. Anyone is free to rebut this by successfully starting a garden by first incinerating their beans. Otherwise, the claim seems pretty secure.

So why commit ourselves to a conceptual apparatus where we must say: "Actually, the impossible is actually possible because we can string together the words 'I incinerated my beans to sprout them'" and thus be committed to the "existence" of some "possible worlds" where the impossible is possible?

Why collapse all necessity into one sort? It seems clear that there are different sorts. A triangle cannot have four sides. This is impossible in a way that seems to vary from how incinerating beans cannot possibly result in their sprouting however.

Kolmogorov's axioms effectively define probability in terms of a collection of sets of possible worlds, together with a probability function that maps those sets of possible worlds to values in the unit interval, where the accessibility relation between worlds is implicitly represented by one's design choices. As for whether the probability function denotes logical or frequential probability, this depends on how the probability function is defined.

If the probability function is defined so as to quantify the mathematical proportion of possible worlds having a particular property, then we are dealing with logical probability, but not necessarily frequential probability. For example, if there are three possible worlds of different colours, then why should the existence of these three distinct possibilities automatically imply that each colour is equally likely or frequent? In my opinion, the fallacy that logical probability implies frequential or even epistemic probability is what gave rise to the controversial and frankly embarrassing Principle of Indifference.

On the other hand if the probability function is chosen to represent non-mathematical facts concerning observational frequencies, then we have frequentialist probability but not logical probability.

In my opinion, there is no such thing as epistemic probability or propensity probability, because I think that the belief-interpretation of probability consist of a poorly articulated muddle of logical probability, frequential probability, and unarticulated subjective bias that at best expresses the mental state of the analyst rather then the phenomena he is predicting; of course mental states and reality are sometimes correlated but not always.

The best way of expressing ignorance with regards to the likelihood of a possible outcome is simply to refrain from assigning a probability, and the best way of using Bayesian methods is to interpret them as inferring frequency information from logical information expressed in the design of the sigma algebra over the sample space, plus observational frequency information expressed in the probability measure.

The best way of expressing ignorance with regards to the likelihood of a possible outcome is simply to refrain from assigning a probability — sime

Then how are you supposed to update your ignorance when you encounter new evidence?

Bad judgement can apply to any interpretation of probability. Infamous examples include people being sent to prison for years, having their lives ruined, because of poor interpretations of probability. Perhaps these examples only tend to involve frequentism because it is already dominant, or perhaps it speaks to its being truly counterintuitive?

A famous case from the UK involved a woman being convicted of murdering her own children after two of them died of SIDS. The lead witness in the case, an expert in statistics, argued for conviction on the grounds that the frequency with which a woman of her demographic background could be expected to lose two kids to SIDS was incredibly low, meaning the odds of foul play should be considered far higher. But this is simply bad reasoning, since the question should be "given a woman has already lost one child to SIDS, what is the chance that they will lose another?"

Actually, families that experience SIDS are much more likely to experience it again, and there are causal explanations for this that don't involve foul play (although, it seems obvious that people who murder their kids are also more likely to do so in the future as well). The explanation that the prosecution offered in terms of population frequencies was clearly deficient (leading to exoneration).

A proponent of frequentism might argue, however, that the problem is simply that the wrong population was chosen by the expert. The population in question should have been "mothers who have already lost their first child to SIDS." So, the frequentist can say the mistake is looking at frequency in the wrong population. The obvious rebuttal here is that the population of "mothers who lost their first child to SIDS" is relevant because this population has a much higher propensity to experience SIDS. That is, population selection often has an implicit notion of propensity that is built in.

You see the same thing with the Monte Hall Problem, Mr. Brown's kids, etc. Originally you had PhDs focusing on probability writing in to give the wrong answer to this question. The answer only seems obvious now because everyone gets taught it in intro stats. But of course, if you use Bayes' Theorem, something you can teach to a middle schooler, the correct answer is easy to come by.

For example, if there are three possible worlds of different colours, then why should the existence of these three distinct possibilities automatically imply that each colour is equally likely or frequent? In my opinion, the fallacy that logical probability implies frequential or even epistemic probability is what gave rise to the controversial and frankly embarrassing Principle of Indifference.

It doesn't, at least not in the Principle of Indifference as described by Leplace, Keynes, etc. It's the simplest non-informative prior. Obviously, it cannot be applied to all cases, rather a special set of them. But the general reasoning used here tends to be at work in more complex non-informative priors.

Anyhow, part of the reason why subjectivist probability has made such a comeback is through information theory. On a frequentist account, the question of "what is the relevant distribution" vis-á-vis information becomes extremely fraught. For the (now I believe minority) group that wants to deny information any "physical reality" the argument is that, for every observation/message, the values of each variable just are whatever they happen to be, occuring with p = 1. Hence, mechanism is all that is needed to explain the world. I think Jaynes' work is particularly instructive here.



Exactly. There are indeed plenty of ways to misapply the Principle of Indifference, or cases where it will not be appropriate. There are other non-informative priors, PI is just easiest to teach for simple examples. However, critiques of it often simply include information in the example that would necessarily preclude using PI in the first place, which doesn't really say anything more than "if you misapply a rule is doesn't work right."

Then how are you supposed to update your ignorance when you encounter new evidence? — Apustimelogist

Knowledge is represented in terms of

1) A deductive system, that apart from the logical connectives is comprised only of constants, sets, types and functions, e.g such as a model of a road network.

2) Statistics that report how the deductive system is used, e.g traffic statistics.

It makes no sense to represent ignorance. To me that's a contradiction in terms.

Structural Equation Models are another reasonable example, provided one steers clear of non-informative priors and sticks to making deductions rather than making inductive inferences; Personally, I think Bayes rule should only be used when inferring a conditional distribution of a known multivariate distribution, for what does it mean to say that " Hypothesis A is inductively twice as probable as Hypothesis B when conditioning on an observation"?

It doesn't, at least not in the Principle of Indifference as described by Leplace, Keynes, etc. It's the simplest non-informative prior. Obviously, it cannot be applied to all cases, rather a special set of them. But the general reasoning used here tends to be at work in more complex non-informative priors. — Count Timothy von Icarus

The Principle of Indifference is supposed to be a normative principle for assigning probabilities on the basis of ignorance. As soon as a non-informative prior is used, posterior probabilities are epistemically meaningless in general, even if their distributions are useful for convergent machine learning.

The way i interpret non-informative priors is in terms of the following analogy:

Imagine using a net to catch a fish in a lake. Using a big net that covers the entire surface of the lake is analogous to using a non-informative prior. Reeling in the net to obtain the fish is then analogous to Bayesian updating. But would you really want to say that the net represents your indifference as to where the fish is? rather, isn't the net simply part of a mechanical procedure for ensuring the fish is caught, irrespective of your state of mind?

- Perhaps a Bayesian will remark that the net represents the fisherman's credence as to where the fish is. I think my reply would be to say that the meaning of "the fisherman's credence" should be given in terms of where the net is, rather than the meaning of the net being in terms of "the fisherman's credence" which I have no prior understanding of.

Also, why choose the simplest prior? Occams Razor? what justifies the use of that?
In fact, if one isn't interested in asymptotic Bayesian convergence and has no frequency information, then why use a prior at all? Why not just stick to saying what one knows or assumes, and gamble without saying anything else?

Framing modality in terms of possible worlds requires a radical, counterintuitive retranslation of counterfactual reasoning into terms speakers themselves are unlikely to recognize as true to their intentions, while at the same time requiring either a bloated ontology of "existing" possible worlds, or some other sort of explanation of what they are. — Count Timothy von Icarus

You place a lot of weight in intuition. What, then, if my intuition differs from yours? Which is to be preferred?

What would one make of someone who suggested that predicate logic "framing predicate logic in terms of p's and q' requires a radical, counterintuitive retranslation of sentential reasoning into terms speakers themselves are unlikely to recognise as true to their intentions, while at the same time requiring either a bloated ontology of "propositions" , or some other sort of explanation of what they are?" One would hope that they had misunderstood what was being done, and try to explain tot hem that if someone's intuition is that a modus tollens argument was incorrect, then the intuition might well be questionable.

Of course it might also be that the intuition has been misinterpreted in applying the modus tollens, and here the predicate logic might be of use to set out where that misinterpretation sits.

But it will not do to say that one will not accept predicate logic simply becasue it does not suit you.

"Why must we be under a commitment to understanding sentences in these terms? Certainly not because this is how sentences have been historically or widely conceived, or because it's what most people mean by the common usage of the term."

Teach an introductory logic course and you will quickly find that applying patterns such as modus tollens to sentences is not intuitive to many, nor how people string sentences together. A large part of your teaching sentential logic is correcting those intuitions.


Predicate modal logic and possible world semantics give us strong and coherent ways to use the language of modality. We know it is coherent, we know it works, from the structure of the formal language. If soldiering needs to be taught, then so does reasoning.

, , in probability theory the possible worlds are the outcome of a stochastic process, a coin flip or whatever. But in Modal Logic possible worlds are stipulated, hypothetical stats of affairs. They are not the same sort of thing. Care is needed in order to not be misled by the analogy.

in probability theory the possible worlds are the outcome of a stochastic process, a coin flip or whatever. But in Modal Logic possible worlds are stipulated, hypothetical stats of affairs. They are not the same sort of thing. Care is needed in order to not be misled by the analogy. — Banno

No, it is the same in probability theory. There, the "set of possible worlds" refers to the sample space, where a "possible world" is normally referred to as an event or element of the sample space. A coin flip or stochastic process refers to a random variable, namely a function whose domain is the sample space and whose codomain is another set, usually the reals or the naturals.

So the input to a stochastic process is a particular possible world, of which the output is a set of observations of that possible world.

Any accessibility relation defined on a set of possible worlds can be interpreted as placing restrictions on the probability measure defined on (a sigma algebra of) sets of the possible worlds.

(post recently edited due to a mistake when describing the codomain of random variables)

OK. In probability theory possible worlds are elements in a sample space, which consists in all possible outcomes of some experiment. These possible worlds are fixed by the definition of the probability space, they are mutually exclusive in that only one world can be the outcome of any one experiment. They are not hypothetical, but points in a mathematical space.

Wearers possible worlds in modal logic are stipulated, are not mutually exclusive and sit within a structure R which determines what worlds are accessible, one from the other.

Even counterpart theory would have these modal characteristics. Neither approach to modality involves a structured space of possibilities.

This looks to be the mistake in 's "Trump had only a 20% chance of winning the 2016 election". (Let's move away from using Trump in our examples. please... He gets much more attention than he deserves.) That is, it misses the part where modality is stipulated, not found.

K. In probability theory possible worlds are elements in a sample space, which consists in all possible outcomes of some experiment. These possible worlds are fixed by the definition of the probability space, they are mutually exclusive in that only one world can be the outcome of any one experiment. They are not hypothetical, but points in a mathematical space.

Wearers possible worlds in modal logic are stipulated, are not mutually exclusive and sit within a structure R which determines what worlds are accessible, one form the other. — Banno

Yes, you're right to challenge my previous post, as I realize that I wasn't quite correct in my interpretation of possible worlds in probability theory. But I still see no fundamental incompatibility.

Ultimately, i think the question we're addressing is "Can a set of possible worlds be adequately modelled in terms of a sigma algebra defined over a sample space?"

I think the key is to think of an element of the sample space as a trip through possible worlds that obeys the accessibility relation. This is essentially how finance uses probability theory when modelling movements of a stock price, where an element of the sample space is a sequence of binary values representing a sequence of price directions. Following this approach,

- An event is a possible trip through possible worlds.
- The sigma algebra defined on the sample space represents the possible history of the trip at each stage.
-A stochastic process represents possible histories of observations as the trip proceeds.
- An additional element can be added to the sample space to represent termination of the trip.

Yes — sime

Thank you. I very much appreciate this simple gesture towards agreement.

Ultimately, I think the question we're addressing is "Can a set of possible worlds be adequately modelled in terms of a sigma algebra defined over a sample space?" — sime

This is what needs tracing out, to be sure.

In considering this I have been struck by how accessibility in modal logic resembles a Markov process, with states resembling possible worlds and transition probabilities resembling Accessibility relations. A directed graph resembles a Kripke frame... but Markov processes are not binary, unlike modal logic. Would that I had a stronger background in the maths involved.

Again, there is a lot going on here.

"In fact, before I develop this any further, let me ask whether you think (2) is a fair elaboration of what you meant by "If it is not possible, then it is in some sense necessary."

- J

it seems accurate in the sense that something that has happened cannot possibly have not happened. It has already been actualized. — Count Timothy von Icarus

Good, glad I understood you.

So we're working here with a sense of "necessary" that means "impossible to change." As you point out, past events may not be the only things about which this can be said, but let's stick to that for now.

The first point which arises about this usage is that it seems to rely for its truth on certain beliefs about the physical world. I'm thinking of something like: "The causal 'flow of time' is unidirectional, toward what we call the future. Nothing can reverse this causality, and nothing can return to a previous moment in the flow and 're-cause' something in a different manner."

Do we know this to be true? I would say we do not -- we know so little about how time functions, physically -- but let's grant it. Is it, then, a necessary truth? This, notice, would be a necessary truth that guarantees a whole host of other necessary truths, but on quite different grounds. Do we need it to be a necessary truth? Could the (in 2025 allegedly necessary) truth that "Washington was born in 1732" depend for its necessity on a contingent truth that "Nothing can be uncaused or re-caused"? Well, why not?, we might reply. Why shouldn't a contingent truth ground a necessary truth? Isn't it the same case as the (contingent) truth that GW was born in 1732 causing the (now necessary) truth that "GW was born in 1732"?

But there's a flaw here. We're equivocating. We don't want to say that GW's birth in 1732 caused anything here other than the truth of a subsequent statement to that effect. Whereas, with a law about "causality and the flow of time," we do want to say that this law, whether necessary or contingent, literally causes events to become necessary subsequent to time T1 -- that is, when they in fact occur.

So, pausing again before I go on -- do you think this is a reasonable analysis of some of the issues involved in "necessity" statements involving the past? I know that some of this is modeled more precisely in Logicalese but I have my reasons for wanting to stay with English, as you'll see . . .

It makes no sense to represent ignorance. To me that's a contradiction in terms. — sime

But surely, ignorance is directly related to probabilities. If an event has a probability of 1, you can predict it perfectly; if all the probabilities are equal, then its like maximal unpredictability.

for what does it mean to say that " Hypothesis A is inductively twice as probable as Hypothesis B when conditioning on an observation"? — sime

The probability that some hypothesis was the cause of your observation; and even if your prior is wrong, probability theory is the only logical way of changing probabilities when you see the evidence if you know the likelihood afaik.

So to the end of part three:

The upshot of these reflections is meant to be that the way to do quantified modal logic, if at all, is to accept Aristotelian essentialism. To defend Aristotelian essentialism, however, is not part of my plan. Such a philosophy is as unreasonable my lights as it is by Carnap’s or Lewis’s. And in conclusion I say, as Carnap and Lewis have not : so much the worse for quantified modal logic. By implication, so much the worse for unquantified modal logic as well; for, if we do not propose to quantify across the necessity operator, the use of that operator ceases to have any clear advantage over merely quoting a sentence and saying that it is analytic.

I find myself agreeing with Barcan, that Quine is mistaken to think the choice is between an Aristotelian essentialism and rejecting quantified modal logic altogether. And so the issue becomes the various and diverse notions of essence and how they might cohere and confute one another.

Again, there is a lot going on here. — Banno

I love this thread. When I first started doing philosophy, I despised the historical uses of "necessary", because they discolored the readers' lenses, through which my writing was being read. I remember thinking I needed to invent my own term(s) in order to avoid having my writing filtered through such sense(s).

Quite the interesting discussion involving the different senses of "necessity" and "necessary".

The misunderstanding between J and Von Icarus was quite helpful for me. I suspect that such misattributions of meaning/sense often go unrecognized and result in an ongoing unarticulated misunderstanding.

Anway, just complimenting the thread and its participants. I'm very interested and will continue to read along in the background. I've nothing to add. Better listen and learn a bit more about the historical context(s) involving the senses of "necessary" that later plagued the interpretation of my early writing.

Hope you and the wife are happy and healthy.

Cheers.

Hope you and the wife are happy and healthy. — creativesoul

Avoiding Cyclones by cancelling our travel plans, as it turns out. As a result I find i have time on my hands.

Thanks - I didn't really expect many to pay much attention to this thread, to the extent that I would not have started it but for @J's interest.

In considering this I have been struck by how accessibility in modal logic resembles a Markov process, with states resembling possible worlds and transition probabilities resembling Accessibility relations. A directed graph resembles a Kripke frame... but Markov processes are not binary, unlike modal logic. Would that I had a stronger background in the maths involved. — Banno

Your suggestion is essentially equivalent to what I suggested in my last post, and indeed the likely tool for constructing the sample space i was referring to.

A Markov Kernel on a measurable space (S,B) onto itself, i.e. (S,B) --> (S,B), is a direct way of defining a state-transition probability matrix on a generally infinite set S. But as you indicate, what is needed is a binary valued state-transition matrix rather than a probability matrix. This just means swapping the state-transition probability measure B x S --> [0,1] for an unnormalized binary valued measure B x S ---> {0,1}. By iterating this 'markov process', one obtains a trip on S. The construction I suggested earlier that directly identified trips with events, has one sample space that consists of the product of n copies of S:

S1 x S2 x .... Sn.

in which the sigma algebra of possible trips obeys the accessibility relation.

But surely, ignorance is directly related to probabilities. If an event has a probability of 1, you can predict it perfectly; if all the probabilities are equal, then its like maximal unpredictability. — Apustimelogist

The distribution of an unknown random number generator could equal anything. If an analyst knows that he doesn't know the rng, then why should he represent his credence with a uniform distribution? And why should the ignorance of the analyst be of interest when the important thing is determining the function of the unknown distribution?

The probability that some hypothesis was the cause of your observation; and even if your prior is wrong, probability theory is the only logical way of changing probabilities when you see the evidence if you know the likelihood afaik. — Apustimelogist

Ever heard of imprecise probability?

The distribution of an unknown random number generator could equal anything. If an analyst knows that he doesn't know the rng, then why should he represent his credence with a uniform distribution? And why should the ignorance of the analyst be of interest when the important thing is determining the function of the unknown distribution? — sime

I feel like this kind of issue can still be talked about in the same kind of framework; for instance, Bayesian model selection where you are using Bayesian inference to select priors and models you want to use; and things like hyperpriors and hyperparameters.

Ever heard of imprecise probability? — sime

I don't think it rings a bell

Your suggestion is essentially equivalent to what I suggested in my last post, and indeed the likely tool for constructing the sample space i was referring to. — sime

That's what I thought. "One simple space" - so the step-wise structure disappears? That would presumably be the case if we implemented S5 in this way. Our trips through the space would correspond to moving within one big equivalence class. To model the sort of thing @Count Timothy von Icarus has been suggesting* we might use S4; we would have Reflexivity and Transitivity, but no more, and therefore some structure. This might allow something closer to our intuitions for physical necessity.

So if S={a,b,c,d} and the accessibility was {a,b}, {b,c},{c,d},{d,d} by transitivity and reflexivity, then not all states are accessible form each other - not {d,a}, for example, and accessibility is nested - {b,c},{c,d} implies {b,d}.

The result could model a causal hierarchy.

Oddly, the lack of symmetry means this is not reversible - a time-like direction?

I'm finding this quite unexpected, and intriguing. If we move to S4.3, and □p→□□p, we bar looping back, reinforcing the time-like directionality. In effect it implies a sort of entropy...

Too speculative, I think; And on reflection I am not sure it achieves more than S4.3 might by itself...except that paths might be traced probabilistically.

*(added) so we might have "If Socrates is sitting, then Socrates is necessarily sitting" in S4.3, but not in S5. Necessity that persist forward.

I'm getting a lot out of the thread too, and I'm especially glad to see you pointing at the exchange between me and @Count Timothy von Icarus. I think this kind of "accidental disagreement" is extremely common, and not just on TPF. Sometimes, of course, people really do use terms differently and/or differ as to whether they refer to real things. But charitable interpretation stands a very good chance of straightening it out. I hate to see exchanges in which each person seems to want the other to be defending a dumb or inconsistent position. Count T is certainly not such a person, and I hope I'm not either.

This really gets to the heart of Quine's problem with modal logic. Going back a bit from the passage you quoted, Quine explains:

We can see pretty directly that any quantified modal logic is bound to show . . . favoritism among the traits of an object . . . — Quine, 155

The favoritism he has in mind, if we could quantify in modal logic, would be:

An object, of itself and by whatever name or none, must be seen as having some of its traits necessarily and others contingently, despite the fact the latter traits follow just as analytically from some ways of specifying the object as the former traits do from other ways of specifying it. — Quine, 155

I have a number of questions about this analysis, but let me start with this: What does Quine mean by "must be seen"? Is this referring back to the act of quantification? Is this a doctrine (like "To be is to be the value of a bound variable") that would state, "To be a bound variable in modal logic is to entail a choice of some necessary predicate(s)"?

A lot of weight must rest on intuition. A rational argument in support of rational argument must presuppose the authority of rational argument. You cannot rationally justify reason in a non-circular manner. One cannot justify all the laws of thought, or one's inference rules, without at least starting from accepting some of them. Like Gadamer says, one needs prejudices to even begin.

The classical inference rules are not counterintuitive. They are so intuitive that man studied them for millennia and largely came to the conclusion that they could not be otherwise. What is counterintuitive is having to translate things into logical form and properly apply the rules.

But more to your point, the reason I bring up probability is simply because it is a good analogy in terms of the sort of disagreement here. Were I a subjectivist, a frequentist, etc., I could give exactly the sort of response you've given. "Ah, but that can be framed in frequentist terms." Indeed, both subjectivists and frequentists have some sort of explanation to cover every case. If they didn't, it would be a decisive deficiency. Nonetheless, some explanations require much more "stretching" than others. And there is also a similarity here in that both sides make use of the same methodology and formalisms, and then sometimes point to the formal apparatus to say "see, this works, so the interpretation must be correct." But of course, the fact that Bayes' Theorem is useful doesn't really say much to undercut frequentism.

This is similar to Spade's point re Quine's sort of austere Platonism. Perhaps he is wrong about why Quine chooses this sort of theory of predication, but supposing he is right, it would be an example of the cart pulling the horse. In this case, metaphysics would be dictated by the particular formalism one is familiar with. This is "I have a hammer, so the world must be composed of nails.



And, to the contrary, Klima and other Aristotelians claim that this framing of modality, and of essence in terms of modality, is in fact hostile to Aristotle. But this shows the problem of pointing to formalisms to attempt to adjudicate metaphysics. Here we see an influential philosopher claiming that a formalism must be abandoned precisely because it seems to him to lead to metaphysical conclusions he disagrees with.

Klima's point is that contemporary modal framings of essence seem to be leading to a sort of conceptual blindness vis-á-vis classical notions of essence, and that one difficulty is the demand that realist theories be translated into systems made by nominalists with a nominalist bias. And right here we can see just one example of a nominalist saying "let's ditch this system because it isn't consistent with the proper metaphysics."

Yet then philosophers will turn around and point to their preferred formalisms, designed with these biases and aims in mind, and try to call on them to adjudicate metaphysical questions. "Look, truth is not relational, it cannot ultimately apply to the adequacy of intellect to being, because in this formalism it applies to propositions and has an arity of one."

Obviously, this sort of appeal to formalism will be particularly inadequate if the camp using it has themselves claimed that such formalisms are just a few among an infinite number of possible creations that must be selected for on the basis of some vague criteria of usefulness

The first point which arises about this usage is that it seems to rely for its truth on certain beliefs about the physical world. I'm thinking of something like: "The causal 'flow of time' is unidirectional, toward what we call the future. Nothing can reverse this causality, and nothing can return to a previous moment in the flow and 're-cause' something in a different manner."

I think the Principal of Non-Contradiction is enough. Something cannot happen and have not happened. George Washington cannot have been the first US President and not have been the first US President (p and ~p).

The idea of the "past changing" would seem to imply some sort of second time dimension by which there is a past that exists at some "second time" ST1 and then changes at some later time ST2. But if the past changes and George Washington was not the first president then he was never president.

Philosophers of time have discussed if such a notion is even coherent, but at any rate I see no reason why we should trouble ourselves too much about it. It seems on par with questions like: "but what if the world was created 5 seconds ago and then all our memories shall change in another 5 seconds?," "what if an evil demon has messed with all my concepts and I don't really even know what a triangle is?," or the misologist's "what is reason has no authority and does not lead to truth?" or "what if nothing is really true or false?"

My personal thoughts are that, if one walks down the cul-de-sac of radical skepticism, there is no "certain" way out. The various coping mechanisms created by modern thought's love affair with radical skepticism are all subject to the challenge: "but what if it is radically wrong?" Reason has the capacity to question anything. Yet I also think that philosophy is under absolutely no obligation to start from radical skepticism. And I think having to maintain that:

"It is possible that giving my child milk tonight shall transform them into a lobster.";

"It is possible that if I recite this incantation, Adolf Hitler will become the first President of the USA, retroactively changing history."; or

"It is possible that I did not eat this dinner that I just ate"

Are all out in the realm of "radical skepticism." Certainly, on a common sense usage of "possible," I should not worry about the possibility that giving my child milk will transform them into a lobster, nor do I think the actual necessity in play here is inaccessible to the human mind (else the project of the sciences and philosophy would be doomed). Likewise, my having both ate and not ate my dinner seems straightforwardly contradictory.

Do we know this to be true? I would say we do not -- we know so little about how time functions, physically -- but let's grant it. Is it, then, a necessary truth? This, notice, would be a necessary truth that guarantees a whole host of other necessary truths, but on quite different grounds. Do we need it to be a necessary truth? Could the (in 2025 allegedly necessary) truth that "Washington was born in 1732" depend for its necessity on a contingent truth that "Nothing can be uncaused or re-caused"? Well, why not?, we might reply. Why shouldn't a contingent truth ground a necessary truth? Isn't it the same case as the (contingent) truth that GW was born in 1732 causing the (now necessary) truth that "GW was born in 1732"?

But there's a flaw here. We're equivocating. We don't want to say that GW's birth in 1732 caused anything here other than the truth of a subsequent statement to that effect. Whereas, with a law about "causality and the flow of time," we do want to say that this law, whether necessary or contingent, literally causes events to become necessary subsequent to time T1 -- that is, when they in fact occur.

So, pausing again before I go on -- do you think this is a reasonable analysis of some of the issues involved in "necessity" statements involving the past?

I am not sure if this is a good way to go about it. You're splitting everything up into individual propositions. So, you have it that the specific individual proposition involving Washington's birth is necessarily true in virtue of the particular event of Washington's birth. This is not how it is normally put at least. The necessary relationship between the truth of a proposition and the fact that what it describes obtains is generally framed as a general principle. It's true for all true propositions, in virtue of the fact that they are adequate to being. Causes are many and are instantiations of principles, but necessity "flows" from principles.

Existential, metaphysical, and physical necessity are normally described as ordered, which I think is the right way to look at it. One is able to describe physical necessity through appeals to more general principles, rather than as some sort of heap of propositions that can either be true or false and necessary or contingent. That George Washington can't have been both born in 1732 and not born in 1732 is explicable by the more general principle that a thing cannot both be and not be in the same way, at the same time, without qualification.