Yes, but that much is obvious from the fact that words mean things, and what they mean might be opaque to their users. Invoking a dubious notion like Fregean senses is probably not a good idea, unless this obvious fact is all one means by it. — Snakes Alive

I am unsure why you think that the notion of Fregean sense is dubious. For one thing, it appears to solve the problem that you raised for Kripke regarding the possibility that one may fully understand the meaning of "Water is H2O" and not know a priori that it is true.

What I've never seen, and it's not for want of looking, is what that field of inquiry achieves. It doesn't explain ordinary language, because people don't think in terms of possible worlds. — andrewk

It's just a modeling tool. It has a potential to mislead or confuse, especially when the processes of model construction are misconceived, or the models are abusively reified (David Lewis, I'm looking at you!) But when used properly, talk of possible worlds can help make arguments regarding modal claims explicit. As such, it can be revealing of confusions that were already in play in philosophical discourses about necessity and possibility.

One area of philosophy that I am especially interested in is the debate on free will, responsibility and determinism. Issues of necessity and possibility abound, and confusions about them are endemic. Possible worlds are being used a lot in this literature, and although the arguments that they convey can be made without reference to possible worlds, their use by the proponents of various theories about the scope of the powers of rational agents often allows one to pinpoint what the specific flaws are in their conceptions of free (or unfree) agency.

I suppose it is possible, but he would have to take the senses not to be the sort of descriptive entities that interact with the compositional semantics that they're often taken to be. — Snakes Alive

For sure. Singular senses aren't shorthands for definite descriptions. But they are quite useful in accounting for the fact that co-referential names (or co-referential natural kind terms) can be used competently by a rational thinker who can wrongly believe them not to be co-referential (or be agnostic regarding that) without being deservedly charged with irrationality.

I understand what you are saying, but it is not how I'd define "metaphysically necessary." There is no metaphysical reason a chess bishop can't move like a knight, rook or in any other way. It is merely a convention. — Dfpolis

The rules of chess indeed are arbitrary conventions but it is only thanks to those arbitrary conventions being what they are that the chess phenomena, and the chess pieces, likewise, are what they are. Chess games, and the objects that are involved in chess games, are socially constituted. There indeed are no metaphysical reasons why the rules of chess ought to be what they are, but given that they are what they are, (as they are agreed to be within some determinate community of chess players,) then, necessarily, the pieces that are being called bishops must be subjected to the normative rule that they ought to be moved along diagonals on the chess board. If they weren't thus governed, then, they might still be called "bishops", but in that case, "bishops" would designate the pieces of a different game. The sort of necessity involved can be called metaphysical since it refers to a necessary condition for the bishops of the conventional game of chess being what they are.

I don't think myself that this is the right way to put it, since if Kripke is right, 'water is H20' just means 'water is water,' and we already knew this trivial proposition a priori. What we learned, if you like, and which is genuinely contingent and a posteriori, is that all along we referred to the same thing with both these words. This is just a fact about linguistic usage (which of course may be a substantive discovery with huge implications, since we resolve what we thought were two things into the true one just by learning this). — Snakes Alive

It seems to me that Kripke can avoid this problem since although "water" and "H2O", construed as co-referential natural kind terms, have the same reference, they can still be taken to have distinct Fregean senses. Hence someone may grasp (as Frege would say) the senses of both terms and not know that "water is H2O" is true, and a fortiori not know either that it's necessarily true. It's true that Kripke thought that he was improving on Frege with his conception of proper names and of natural kind terms; but that's because he though (wrongly in my view), as many other philosophers have thought, that Frege was committed to a descriptive theory of senses. Gareth Evans and John McDowell, among others, have argued that the Fregean senses of proper names and of natural kind terms are better construed as object dependent senses or, as they're also called, singular senses.

Well that's what I'm calling into question. I might counter by saying that the term "water" refers to whatever liquid makes up the Earth's oceans and falls from the clouds as rain and that in some possible world the chemical composition of that liquid is H2O2. That water is H2O is just a contingent fact about the actual world, much like Earth being the third rock from the Sun. — Michael

In that case you are using the term "water" to refer to a general definition and hence what you are saying about water, and possibles worlds in which water had alternative chemical constitutions, doesn't really have any bearing on what Kripke (and Putnam) have said about the the semantic properties of natural kind terms, or the metaphysics of natural kinds. It is natural kind terms, and not general descriptive concepts, that are deemed by Kripke to function as rigid designators. (Putnam has further shown how this thesis dovetails with semantic externalism).

It depends on how you define "metaphysically necessary." Can you define it without invoking possible worlds semantics? If not, how can this claim be relevant to reality? — Dfpolis

Saying that something is metaphysically possible just is to say that it isn't inconsistent with the way things can be in accordance with the constitutive rules that govern how those things fall under concepts. (For instance, it is a constitutive rule of bishops, in chess, that such pieces only moves legally along diagonals; and it is a constitutive rule of the concept of a human being that it is an animal). A state of affairs is metaphysically necessary if its non-obtaining (or the negation of the statement that it obtains) isn't metaphysically possible. Under that definition, I think it can be shown that if "A" and "B" are meant to function in the way ordinary proper names are used, and they both actually name the same individual, then it is metaphysically necessary that A and B are numerically identical.

Then perhaps if we use a simpler example of an inanimate object. In another possible world the Taj Mahal was built using different materials, or at a different location, or with a different architecture. Does that make sense? Is it just a matter of stipulation that we consider them the same thing (or different things) in each possible world? — Michael

There is an interesting issue that arises here. When we talk about ways the world might have been (or possibly could have been), some features of the world as it might have been are foregrounded, while others are backgrounded, in accordance with the pragmatic point of the counterfactual albeit possible scenario being considered. It may be that possible world models for the semantics of modal statements obscure this pragmatic feature of talk of possibilities when possible worlds are reified with excessive determinacy. (This may be a reason why Lewis runs into problems that he seeks to eliminate through getting rid of backtracking conterfactuals when he analyses statements of causal dependence between events).

Consider the statement that an aircraft that has actually (and accidentally) collided with the Taj Mahal might possibly have avoided destruction if the Taj Mahal had been built 50 meter further to the West, or had been made out of a gaseous material rather than being made out of stone. We have no trouble evaluating those statements as true. While the historical location and/or material constitution of the Taj Mahal are being foregrounded, the issue of its identity are being backgrounded. This backgrounding of irrelevant features (i.e. irrelevant with respect to the pragmatic context of the consideration of the counterfactual scenarios) also allows for so called counterlegal counterfactual statements. (Counterlegal counterfactual statements are being discussed by Marc Lange in Natural Laws in Scientific Practice.)

In another context, we may inquire whether or not the Taj Mahal could, in the first place, have been built in the different location and still count (in accordance with our actual linguistic practices for naming functional artifacts of this sort) as the Taj Mahal. In that case, we may be picturing an alternate history where the builders of the actual Taj Mahal have settled for a different location, 50 meters to the West of the actual location, and inquire whether it's still numerically the same artifact that would have been built. In that case, it's the issued of the identity of the artifact that is being foregrounded. So, it may be senseless to ask the bare question whether a specification of a "world" in which the Taj Mahal has been built 50 meter further to the West than its actual location is or isn't a specification of a metaphysically possible world. Whether or not it is might be felicitously(*) taken to be a metaphysically possible world might depend on the pragmatic point of the question and hence on whether or not the issue of the identity of the Taj Mahal is meant to be foregrounded or backgrounded.

(*) I am using "felicitously" rather in the way @StreetlightX recommended in his recent thread.

What makes it the case that one thing in one possible world and one thing in another possible world are the same thing? — Michael

It's the exact same sort of thing that makes it the case that "A" and "B" are numerically the same in the actual world: criteria of identity and individuation. Those criteria vary as a function of the sorts of things that are at issue. Planets, persons, sports teams, cell lineages, ocean waves, etc., have different principles of individuation. Sometimes those principles mainly are matters of social convention but they can also be, in part, objects of scientific inquiry.

So, what makes it the case that, in the possible world where you catch the flu tomorrow, say, you are the very same individual human being than you are in the actual world (in which you don't catch the flu), is the very same principle of individuation in accordance with which we judge that, in the actual world, people don't cease to exist and their persisting bodies come to materially constitute numerically distinct human being at a later time just because they catch a bug. (Maybe there is some alien race, somewhere in the universe, where personhood conventions are different and individual organisms who catch a bug are deemed to be turned into a numerically different person or animal).

Let’s say that I’m the eldest of two brothers in the actual world and that there’s a possible world where my parents have two daughters and a possible world where my parents have two sons. Which child, if either, am I in each world? Is it simply a matter of stipulation?

There are possible worlds where your parents have two sons neither of which is you. This is equivalent to saying that it is possible that you would not have been born but that your parents would nevertheless have had two sons.

Do we simply say that I’m one or the other (or neither)?

Perhaps in the first possible world it’s me and my brother if we were female? Perhaps in the fourth possible world it’s two different children who happen to look and behave like my brother and I do in the actual world?

Your puzzle stems from the question: what it is that distinguish a possible world where a son is born to your parents that looks and behaves just like you, but isn't you, from a world in which this son is you? Those two scenarios are indeed metaphysically distinct and, what distinguished them precisely, are our ordinary criteria of identity of persons as they are meant to apply in the actual world. It's possible, though, that our criteria of identity of persons aren't fine grained enough to determine whether or not your would have been the same person if the sperm and ovum that your are issued from had combined at a different time, or if the sperm itself, say, has been a different one that accidentally shared the very same sequence of nucleotides with the actual one, etc. That just means that our ordinary concept of a person, and its associated criteria of identity and individuation, isn't meant to deal with such unlikely possibilities since there is little pragmatic point in dealing with them.

This is awesome. Please, keep going ;-)

That part of my objection is that words express concepts, so if you want to know what they mean, you have to examine the concepts in terms of the experiences that elicit them. The reason that an empirical discovery is required for the identification is that the concepts are anything but identical. — Dfpolis

As Frege pointed out, names have a sense and a reference. For a time, it has been contentious whether the Fregean senses of proper names are equivalent to definite descriptions or if they rather are object dependent (i.e. "singular senses"). Kripke has argued for the latter thesis (as have Hilary Putnam, Gareth Evans, David Wiggins, John McDowell and several others). If we accept that the senses of proper names are object dependent, that doesn't preclude them having conceptual contents as well. The objects that we name typically fall under sortal concepts that express their conditions of persistence, identity and individuation. This is all consistent with Kripke's claim that proper names function as rigid designators, and also with his claim that statements of identity of the form "A is B", where "A" and "B" are proper names, are metaphysically necessary.

If you read the full objection, you'd see that this is a rhetorical step, not the full objection. — Dfpolis

I don't understand what your full objection purports to be either. Your objection seems to rely on analyzing "Hesperus" and "Phosphorus" as definite descriptions rather than proper names. If they are thus analysed, then Kripke's remark about the metaphysical necessity of numerical identity don't apply. Kripke would readily agree that the statement "Hesperus is Phosphorus" expresses a contingent identity in the case where "Hesperus" and "Phosphorus" are shorthand expressions for definite descriptions that merely happen to have the same reference in the actual world.

Read up on it. — Snakes Alive

Yes. The SEP has a good entry on rigid designators. Another good place where to start is Gregory McCulloch's book The Game of the Name: Introducing Logic, Language, and Mind, Clarendon Press, 1994.

I am pretty confident that, given the choice between my interpretation and one involving all the metaphysical baggage of the possible worlds paradigm, that average person would say that mine is the closest to what they meant. — andrewk

That may be so but if you ask ordinary people what they mean when they say that something is possible or impossible (and not provide determinate contexts of use of those words) they aren't likely to disambiguate between different senses of 'possibility', which a somewhat more careful conceptual analysis would. The specific paradigm of use that will first come to their mind likely will orient their initial responses in a way that wouldn't match the way in which they actually use and understand those modal operators in accordance with several other paradigms of use. If you look at the arguments that Kripke adduces in Naming and Necessity -- for instance, arguments in favor of the thesis that proper names are rigid designators or that numerical identity is a metaphysically necessary relation -- most of them aren't grounded into contentious metaphysical theses but rather into ordinary intuitions and ordinary linguistic practices.

I don't agree with the notion that news reporting should not strive for objectivity. You ditch that, and then you get propaganda like Fox News in it's place. — Marchesk

I'm not sure you are disagreeing with the OP. I don't see what @hypericin is proposing as undercutting norms of trying to avoid political bias or of refraining from lying for the benefit of a hidden agenda. I rather hear him/her as arguing that the process of public news reporting can't, even in principle, be culled from the narratives that motivates the selection of the news items that are being reported as well as the gloss that is put on them.

If news media are going to report on a typhoon hitting Japan (as they often should) isn't this precisely because typhoons hitting densely populated areas fit within significant sorts of narratives on account of their destructive potential? Should news media report all, and only, "events" that result in x+ deaths (for some x)? How are they to individuate discrete events objectively and assess whether or not some events are significant enough to merit reporting merely on the basis of objective factors that don't speak to their relevance for widespread human concerns, and hence relate back to significant narratives?

A :: A is true IFF A<->A is a tautology. So if ~(A :: A) then ~(A<->A) which is a contradiction. But I wonder how one would express the contradiction so obtained? A &~A? You seem to disagree. — TheMadFool

I appreciate your separating the case of particulars from the case of propositions.

What I am unsure of is what it might mean to be denying that a proposition A is (numerically?) identical with itself. It is unclear to me that it is equivalent to denying that "A<->A" is a tautology. Maybe you are glossing "A=A" as equivalent to "A :: A", but I also am also unclear about the rationale for that. The relation of numerical identity just makes more sense to me as applied to particulars, or Fregean objects, and maybe also to Fregean functions (or properties). The issue of the individuation of propositions (either Fregean or Russellian propositions) is trickier.

My response is that it is impossible to interpret the 'est' to mean 'equals', because the equals relation is transitive and the est relation in the diagram is non-transitive. — andrewk

Either that or, as I suggested earlier, following Peter Geach, one endorses a relative conception of the relation of numerical identity between substances. I don't endorse that, myself, but I am not committed either to defend the Christian doctrine of the Trinity.

Trinities are everywhere.
The following one looks perfectly logical to me. — andrewk

Your comment may be tongue in cheek but you remark relies on interpreting "non est" as the negation of numerical identity and "est" as the copula rather than the affirmation of numerical identity.

The law of identity (A=A) is a logical necessity.

Imagine A is not A. We would then have the logical contradiction A & ~A, violating the law of non-contradiction. — TheMadFool

You seem to be using "A" as the name of a proposition rather than the name of a particular. The "=" usually names the numerical identity relation, which obtains between a particular and itself. If you use "A" as the name of a proposition, and thereby "A=A" to express the claim that the proposition A is identical with itself, then, the negation of this claim isn't expressed as "A & ~A" but rather as "~(A=A)".

What about the second part of the question. Has there been an equivalent of noneuclidean geometry in Aristotelian logic? Is the law of identity kin to euclidean axioms? Thanks for the help though, this is a complex field and its easy to think you've got a handle on things when you dont. — jlrinc

As I mentioned in another thread recently, Peter Geach has been an advocate of the thesis of relative identity. According to this thesis, two objects A and B can both be, and fail to be, identical depending on what sortal concept they are made to fall under. For instance, as applied to the Christian doctrine of Trinity; the Father, the Son and the Holy Spirit can be deemed to be the same unique God but three different persons. To take a less contentious example (albeit still contentious) the original ship of Theseus might be the same functional artifact as the later ship that has been maintained thought replacing the old planks, although both of those ships aren't the same historical artifact. Under that interpretation, the ships A and B are the same functional artifacts but not the same historical artifact.

The thesis of relative identity still is very contentious. I much prefer Wiggins' thesis of the sortal dependence of identity, which, unlike Geach's thesis, remains consistent with Leibnitz' Law (of indiscernibility of identicals). Under that new thesis, while it's still true that what it is that determines whether the referents of A and B are identical is the individuation criteria associated with the sortal concept that they both fall under, objects that fall under different sortal concepts always are distinct objects. Hence, for instance, the original functional artifact and the original historical artifacts that we may both call ambiguously "the Ship of Theseus" are two different objects even though they may, at an early time in history, have occupied the same spatial location and have had the exact same material constitution. They have, though, separate later histories and aren't individuated according to the same criteria.

This I think would be an example of an effort to explain a text which seems inconsistent or unreasonable but assumed to be relating a truth. It's a kind of salvage operation. — Ciceronianus the White

That might be a fair characterization of Geach's motivation for coming up with the thesis of the relativity of identity. But that would be a bad mischaracterization of Wiggins' thesis of the sortal dependency of identity since the purpose of the latter was to disentangle the philosophical insight embodied in Geach's flawed thesis from Geach's own motivation to salvage a particular Christian doctrine.

Peter Geach, who was Elizabeth Anscombe's husband and a very fine logician-philosopher, developed his thesis of relative identity in order to account for the seeming contradiction pictured in the OP. I don't think the thesis is correct, or that the inherent contradiction pictured in the OP can be rationally resolved, but there nevertheless is an insight embodied into Geach's thesis of relative identity. This insight is salvaged by Wiggins' thesis of the sortal dependency of identity, as expounded in his brilliant Sameness and Substance (and its most recent edition: Sameness and Substance: Renewed)

Solo Voice (male) - Russell Oberlin, Bach's Canatata "Wiederstehe Doch der Sunde"
https://www.youtube.com/watch?v=SFgxED6eIWE — gloaming

Great! I discovered this aria a couple years ago, through watching the very same YouTube video, and was blown away by the richness and boldness of the harmonies. Bach is quite the master, but this aria is remarkable even by his own standards. Few composers would dare opening a piece with such a chord for a century to come. And Gould is my favorite pianist...

Russell Oberlin's performance is quite good but I like Andreas Scholl's rendition even better.

Everything is what it is. — Michael

Wittgenstein was reportedly fond of Bishop Butler's aphorism: "Everything is what it is and not another thing".

Arguably, this isn't so much an anti-metaphysical attitude as it is a repudiation of reductive analysis. Arguably, also, Wittgenstein's own philosophical quietism can be construed as being consistent with the practices of connective analysis, and of descriptive metaphysics, in the sense Peter Strawson used those phrases.

Connected with taking methodological naturalism as a metaphysical principle, which it isn't. — Wayfarer

I concur with @StreetlightX and yourself. In line with this modern alteration of the meaning of "objective", and together with the rise of metaphysical realism (Putnam's phrase for the thesis that what exists objectively must exist entirely separately from human concerns and/or concepts), another main culprit, it seems to me, is representationalism in the philosophy of mind and in contemporary cognitive science. This is an inheritance from Descartes methodological skepticism; stemming from its underlying assumption that what it is that we really are in cognitive contact with in the world can only be the highest common factor between the way it affects us in the case where we really perceive it and the case were we are subjected to some illusion. Such common factors or cognition or perception, allegedly produced "in" the mind, taint all cognition of the world with subjectivity and problematize both the concepts of objectivity and of subjectivity. It makes it hard to conceive how the very same cognitive act could be unproblematically objective and, at the same time, necessarily imbued with human subjectivity.

Why not do it in audio? — The Great Whatever

Maybe it could be done in video with no audio. The participants would need to mime their philosophical arguments as best as they can.

The general problem would be something like this: can you improve your performance even in situations where you are unable to evaluate your past performance? — Srap Tasmaner

I don't quite understand what you mean. What are you referring to as one's "past performance"? Is that the amount of money in one's envelope before one has been offered the opportunity to switch?

What I'm saying is that there is no real-world component present in the OP. You can use real-world examples to illustrate some properties, but that is all you can do. Illustrate. The OP itself is purely theoretical. — JeffJo

That's what I'm saying too.

If it would be your own money at stake here, you shouldn't be playing at all. — Srap Tasmaner

One way to adjust the game so that your own money is at stake would be to merely write down the two amounts in the envelopes. The cost for playing is the value v that's written in your envelope. If you chose to play, and switch, then you must pay this amount v upfront and the game master must give you back the amount that's written down in the second envelope. On the assumption that you gain no knowledge at all (not even probabilistic knowledge) about the the probability that your cost is smaller than the potential reward, then the paradox ensues since if we make no assumption at all regarding the prior distribution being either bounded, or unbounded and uniform, then the arguments that the expected value of switching is v or 1.25v seem to be equally valid.

I don't believe that for a moment. I think that why science is currently embroiled in what Jim Baggott calls 'fairytale physics' is precisely the complete and total absence of an 'immanent unity'. — Wayfarer

There is an abundant contemporary literature on what's called scientific practice. The focus on scientific practice is a focus on what productive scientists actually do. More emphasis seems to be placed on the work of physicists and biologists rather than cognitive and social scientists. Thomas Kuhn and Joseph Rouse are two philosophers of science who are focusing on scientific practice.

There appears to be a significant disconnect between the metaphysical assumptions that scientists make, as manifested in their practice, and the sorts of metaphysical pronouncements that they make while trying to articulate what it is that they view as "the scientific method", or their views of the nature of the "physical" word. I often refer to the later as the modern scientific (and scientistic, foundationalist or reductionistic) view of the world. Maybe what @apokrisis is saying applies to current (and old) scientific practice as manifested in most of the productive natural scientific fields of inquiry whereas what you say applies to the crudely materialistic world view that permeates much contemporary scientific thinking: that is, to what scientists say rather than what they do.

So to make this a better analogy, let's say that some third party asks us both to play the game. He will roll two dice, and if I win then you give me £10 and if I lose then I give you £5. He doesn't tell us what result counts as a win for me and what counts as a win for you. It could be that 1-11 is a win for you, or it could be that 1-11 is a win for me, or it could be that 1-6 is a win for me.

I would be willing to play, as I have more to gain than I have to lose. You, presumably, wouldn't be willing to play, as you have more to lose than you have to gain. — Michael

Indeed, if you assume it to be equally likely that the odds of winning (irrespective of the amount) are stacked in your favor as that they are stacked in my favor, then, with this specific and asymmetrical payoff ratio, your overall expected value is positive while mine is negative. But this problem is importantly disanalogous to the two envelope problem.

To make this example more relevantly analogous, the game master would need to hand out to each of us an envelope while only informing us that one envelope contains twice the amount of the other envelope. She would then roll two dice, both players would reveal their envelope contents, and whoever wins will be entitled to switch envelopes just in case she doesn't already have the larger amount. The odds of winning, as before, are unknown. In this version of the game, each player, who initially knows only the content of her own envelope, still stands to win twice as much as she stands to lose. So, you would still seem to be committed to conclude that it is rationally mandated that they should chose to throw the dice (after having been dealt their envelopes and seen its content). And this is true for both of them. Does that make sense?

Imagine you're given £100 and are offered the choice to pay £100 to play a game with a 5/6 chance of winning (say a dice roll). If you win then you win £1,000,000 and if you lose then you lose all the money you've won up to that point.

The average return for repeated games is 0, as you're almost certain to lose at some point. But playing it just once? That's worth it.

This is why I think talking about average returns over repeated games is a red herring. — Michael

This is a nice example but you seem to be offering it as a purported counterexample to the principle that what makes it rational to play a game (and apply a given strategy) only once is for that game (and specific strategy) not to yield a negative expected value and hence not to tend to average negative expected gains when played repeatedly.

But your example is defective since if you are offered the options to "play just once" or play until you lose everything, then what you are comparing are two strategies applied to a single game and it is quite clear that the first strategy has a very large expected value (namely, £5,000,500/6) while the second strategy has a null expected value. Those are the amounts that you can expect to gain, on average, while playing the game repeatedly while applying those strategies. The best strategy, in order to maximize your expected value, would be to play until (and if) your total earnings exceed £5,000,000 and then stop. Past that point, your expected gain from rolling the die once more becomes negative. What dictates your choice of strategy still is its average return, or expected value, even if the game only is being played once.

It cannot be equally likely without postulating a benefactor with (A) an infinite supply of money, (B) the capability to give you an arbitrarily-small amount of money, and (C) a way to select a random number uniformly from the set of all integers from -inf to inf.

All three of which are impossible.

But the reason you should reject the solution you use is because it is not a correctly-formed expectation. You are using the probability of picking the smaller value, where you should use the probability that the pair of values is (v,2v) *AND* you picked the smaller, given that you picked v. — JeffJo

I just want to note that we seem to be in agreement on everything. The only reason why we seemingly disagreed in our recent exchange is because you objected to my stated requirement that the game be conceived as a "real world" problem, and hence that the possibility of a uniform and unbounded prior distribution ought to be precluded, in order that the switching strategy could be shown to yield a zero conditional expected gain rather than a 0.25*v conditional expected gain. I was thus merely expressing the caveat that you are now making explicit in your first paragraph. There is an abundance of discussion of the ideal and impractical case where this "real world" constraint doesn't apply in the literature about the two envelope paradox, and this is the case which, unlike the "real world" case where the prior distribution is well behaved, still is controversial. (See the Chalmers' paper, mentioned earlier in the thread).

How is this any different to saying that I'm equally likely to win as lose? — Michael

It is obviously different since on the assumption that you are equally likely to win as lose it follows that the expected value of switching is 0.25*v whereas saying that the odds neither are nor aren't in your favor is equivalent to saying that the average expected value of switching is v.

(I'll come back to this conversation tomorrow)

No, because I know the probabilities aren't in my favour. If I know that they're not in my favour then I won't play. If I know that they're in my favour then I will play. If I don't know the odds then I will play. — Michael

In the two envelope case, you don't know the odds of winning. But you do know (or ought to be able to deduce) that the odds aren't either in your favor, neither in your disfavor. The expected gains from either switching or sticking both are zero. That is the case, anyway, on the assumption that the game master doesn't have access to infinite funds.

But you're also not saying that sticking is a winning strategy. If sticking isn't preferred then I am going to switch, because I am willing to risk losing £5 for the chance to win £10. I have more to gain than I have to lose. That neither strategy gains over the other after repeated games doesn't change this. — Michael

That only makes sense if you favor taking the chance of gaining a larger amount A than the amount B that you can possibly lose irrespective of their relative probabilities and, hence, irrespective of the expected value of the outcome.

Suppose I offer you to play a game with two dice. You throw them once and sum them up. If you roll any value from 1 to 11, you must give me £5. If you roll 12 then I must give you £10. Let us assume that we only are going to play this game once. Would you also say, in this case, that you are willing to risk losing £5 for the chance to win £10?

If there's no reason to believe that we're more likely to lose than win on switching, i.e. if there's no reason to prefer sticking, and if we can afford to lose, then switching is a good gamble for a single game, even if not a winning strategy over many games. I either lose £5 or I gain £10. That's a bet worth making for me, and so if I were to play this game and find £10 in my envelope then I would switch. — Michael

I would say that, if it's not a winning strategy over many games of the same kind, then it's not a rational strategy over just one game of that kind; unless you aren't averse to playing money games with negative or null expected value. Playing the game only once merely increases the variance. It changes nothing to the expected value. (Although, as andrewk earlier noted, what choice you ought to make also depends on what your personal utility valuations are; here I am simply assuming that the player's only goal is to act such as to maximize expected value).

What would make the switching choice worth making would be if the chance of your losing £5 isn't at least twice as large as your chance of winning £10 is. But you don't know that to be the case either. If you naively rely on the principle of indifference, this will lead you to make a mistake in every case where you are playing this game, are being dealt an envelope with value v, and, conditional on the amount in the envelope dealt to you being v, the chance of your losing £5 is more than twice as large as your chance of winning £10. In the other cases, your choice to switch yields a null or positive expected value. The only thing that you know for sure is that, over the long run, such mistakes would exactly cancel out your gains. So, the expected gain from switching, when you have no clue at all where the value v that you are holding is located within the probability distribution of the possible envelope values, is exactly zero. It is not 1.25v.

Lastly, if you have no clue at all what the distribution is, and you expect any possible distribution to be equally likely with no constraint at all on the maximum or minimum amounts possibly (and plausibly) being contained in the envelopes, then, yes, the expected value of switching, conditionally on v being the value of your envelope, is 1.25v. But that can only happen in a world where the game master has an infinite fund of money.

The Transactional Interpretation of Quantum Mechanics, 2012, p.33 — Wayfarer

Thanks. Since I am not familiar with the transactional interpretation of quantum mechanics, I downloaded the new paper by Kastner, Kauffman and Epperson. At first gloss, it seems to me like the best features of this approach are shared by the relational/pragmatist approaches favored by Heelan, Rovelli and Bitbol. The relational/pragmatist interpretations, though, appear to me to better comport with Aristotelian metaphysics, and to more radically jettison the foundationalist and reductionist prejudices of modern scientific thinking than the transactional interpretation appears to do. But I'll have to read the paper more carefully to see if my worries are warranted and before expressing more precise objections.

What interests me about that article, however, is the idea of 'potentia' as 'real but not actually existing'. 'The unmanifest' was tacked on by me at the end, it might be misleading - that's not the main point of the article. — Wayfarer

It is to be applauded that some physicists will grant existence to pure potentialities, but it seems to rub against the spirit of Aristotelian metaphysics to suggest that what is actual takes place in spacetime (or in the phenomenal world of ordinary experience) whereas what exists as pure potential is outside of spacetime (or in some Platonic intelligible world). This idea doesn't mesh with Aristotle's idea of there being first and second actualities, since first actualities, themselves being kinds of potentialities, would have to exist both within spacetime and outside of it. Some person's property of being sighted, or of being able to speak French, for instance, are first actualities, while the exercise of sight, or the act of speaking French, are second actualities. When a doctor restores the ability of sight in a formerly blind person, it would be weird to say that this restored ability is something that exists both outside of spacetime (qua potentiality to see) and inside of it (qua first actuality).

Maybe those physicists would hold that only very special and fundamental sorts of potentials, namely, quantum potentials, exist outside of spacetime. But now the objectionable dualism is being replaced by a crude reductionism. What are we to make of the ontological status of the unactualized potentialities of ordinary things, and of the unactualized powers of objects of sciences other than those of fundamental particle physics?

So we’re assuming that the other envelope is equally likely to contain either £20 or £5, and that’s a reason to switch. We either lose £5 or gain £10. That, to me, is a reasonable gamble. — Michael

It's not necessarily equally likely. It may be equally likely, conditionally on £10 being the value of the first envelope, but it may also be morel likely that the other envelope contains £20, or more likely that it contains £5. In the first two cases, you may fare better if you switch. In the third case, you fare worse. (It ought to be twice as likely that the other envelope contains £5 rather than £20 for the switching strategy to break even). On (weighted) average, over all the possible values that you can be dealt initially, you don't fare any better by switching. Only in the case where the prior distribution of possible envelope values is uniform and unbounded do you have a positive expected gain from switching conditionally on any value v being seen in your envelope.