Anyway, if we were avoiding semantics and ONLY talking about grammar per se, then obviously the subject of "It is raining" is "It." — Terrapin Station

Yes.

As soon as you ask "What does 'it' refer to" you're doing semantics. — Terrapin Station

Yes.

Semantically, "It" is "the meteorological conditions outside." — Terrapin Station

That's the tricky part. It is not a given that "it" is referential in the first place. One possible answer to "What does "it" refer to," is nothing, and for most (but not all) linguists that's the answer.

One question we can ask about subjects (as arguments of verbs) is what the participant role of the subject is in relation to the verb. Is it an agent as in "I go to school," where going is an action the speaker undertakes? Is it an experiencer, as in "I'm dying," where the speaker is experiencing death?

What is the relation between the verb and it's primary argument?

My take on this topic is that any attempt at answering these questions is post hoc; the meaning is emergent rather than referential. "It" is referentially empty and has no semantic function until you enter the meta level and ask what sort of function it might have.

I also don't see any reason to ask these questions. Syntactic relations are enough. I do realise that it's not a clear cut issue. Take a potential exchange:

A: "It's raining."
B: "No, it's not; it's snowing."

There are three "its" in this exchange, and if I speak carelessly, I'd say that all three its refer to the same thing. Except it's a dummy it and refers to nothing, so how can it have the same reference? This is a problem, so at the very least your position is valid, if not even right.

Consider this sentence:

"It's true that it's raining."

Two its, both dummy its, but clearly not "referring" to the same thing in the way the three its in the previous examples do.

This is a situation where I see problems on either side, but my personal priorities find the problems with a generalised referent to be more severe.

To summarise, I think the meaning of "it" arises out of the interection of grammar with the semantics of the verb and is thus vague and general. It's not referential; but it has some sort of substance, such that you can differentiate between different sorts of dummy-its. What that semantic substance is like is a problem I'm not sure how to address, but it's not a problem severe enough for me to abandon the dummy-it interpretation.

Does this make sense?

(To make matters worse, we shouldn't be confusing subject-predicate of philosophical propositions with subject-predicate of a sentence structure. It's harder than it should be.)

"Fuck you." makes perfect sense, but it lacks a subject. — Bitter Crank

Actually, that's an interesting case. "Fuck" in "Fuck you," looks like a lot a verb in the imperative, where people usually posit an understood subject, "you". However, if that were the case, we'd be expecting "Fuck yourslef," as in "Buy yourself a drink."

I still think it's a normal sentence whose verb is in the imperative mood. I'm not sure what to do about the "you", though. It looks like an object, but if it were I'd expect a reflexive pronoun.

When it comes to "It's raining," I prefer the "dummy subject" interpretation: "It" is all syntax and no reference. The verb carries all the referential meaning in the text.

? Not that I agree with the idea of "empty names" in the first place (as I stated earlier, I think the whole notion of there being a problem stems from misconceived theories of reference), but names for fictional characters are often given as an example. Why would that be a category error then? — Terrapin Station

I think it would be more accurate to ask whether referring to names that reference fictional entities as "empty" constitutes a category error. And, as I said, it may be wrong to say that, but it's not a category error. Even if what you mean by "empty name" is a name that designate nothing and further assume that, by definition, all names designate unique objects (leaving aside paradoxes about referring to non-being), it's still not a category error. It would be like asking "are all primes are divisible by 2?" The statement is wrong analytically, but it's not a category error because "being divisible by 2" is still a property that belongs to numbers and so is within the same category as primes. Similarly, talking about empty names is wrong - and wrong analytically - on certain reasonable assumptions about how names work, but it is still in the category of a linguistic claim so not a category error. — Mentalusion

You're both skipping ahead of what I'm actually saying. The piece about "category error" was part of bigger and more complex point I was trying to make, and it was about type/token not "empty names". I wish I remembered why the type/token distinction has come up. I wasn't part of that conversation until it was nearly done, and none of the original participants ever engaged me on that. What I'm saying is about names in general, not "empty names" in particular.

The sample sentence I gave was:

"The Harry Potter from Rowling's book is an empty name." (I should have said "books".)

The category error is this: "Harry Potter's" name is an empty name; Harry Potter himself is a character.

This is so obvious that it's normally not worth saying. I think I may not have made my point very well, if you think I mean to say that "Harry Potter's name is an empty name." You probably haven't picked up why I think it's worth it's saying in this context.

A name that's not assigned yet is still a name. It follows that names must have meanings as themselves, too. If I type sample sentences, like "Joe likes to sing in the shower," then you recognise "Joe" as a name. But the person behind the name is even less real than Rowling's Potter, since I just typed a random sample sentence, without any reference in mind. The sentences gains its meaning from the fact that we all know how naming works, and how we use them. Just using the name in not even a fictional context conjures up the expectation that there's a person (how ever hypothetical its existance). What's more, we recognise the name as a name other real or fictional people held.

"Joe", as a name, is one name in a list of names we might choose for our children, and this is the meaning we inwoke when we attach articles to the name.

On the other hand, this very meaning implies that there are person who are referents for those names: when used for individuals (without an article) the name actually starts functioning as a name: in a way it becomes active.

"A Joe" in "A Joe has eaten your cake," and "Joe" in "Joe has eaten your cake," work differently with respect to the type/token distinction: it exists in the former case, but not in the latter.

A thought experiment: A group prepares pseudonyms for participants at a meeting who wish to remain anonymous. Those names are assigned at random. Fewer people than expected show up. Some names have not been assigned. In what ways did the meaning of the unassigned names differ from the assigned ones during the meeting?

For me, there's a disjunct. If I talk about the names themselves, they don't really differ. They're all different from each other and they were potentially to be assigned to people (some were, others were not). But they're all names.

When we look at the transcript of a meeting, only the assigned names show up, and when they do they refer to the person in question. This is what they're supposed to do. But the connection is unique. If they re-use the names for the next meeting with different people involved, again assigned at random. The name, considered as a name, has now the property "Provided twice, assigned once" or "Provided twice, assigned twice", but that's something we know about the name. The relation between person and name, though, resets. The facts about the name itself are irrelevant, except when we look at the person as a token of the type "has been assigned the name".

Or do situationally assigned (or chosen) names differ from names who have all your life? (That's been an issue is in this thread.) The question of "real names".

Basically, if you insist on physical objects as the referents of names (as I understood the concept, and as the wikipedia link seems to suggest), how do you conceptualise the difference between a name that's been assigned to a fictional person, a name that is neither assigned nor used (see my thought experiment), or a name that is never assigned but used anyway (e.g. in a sample sentence)?

Out of those three situations, the name of a fictional character seems the least empty. However, a name that isn't used doesn't actually work like name. And invoking the name in a sample sentence can invoke the idea of a person, even though the name has never been assigned.

I'm not sure how to deal with this, but my hunch is that a name is something a person "has" not something a person "is". Referring to an individual entity is the function of a name, but unlike regular words, they confer no meaning unto the entity who's assigned it.

That's different from regular words, where a word confers meaning: a [word] is something that you are, not something that you have.

The problem with this is that a lot of this is dependent on the how any society organises the institution of naming. Telling names aren't impossible, but in general names need to be meaningless in themselves so that they can refer to individual entities continously (impervious to change). Basically, to be an idiot you have to behave like an idiot, and if you stop behaving like an idiot, you stop being an idiot. Similarly, to use a name you need to have that right (however that's organised), and if you lose that right, you no longer have that name.

In the case of words, the assignation of the sign to the thing is extrinsic to the meaning behind the sign. In the case of a name, the assignation of the sign to the thing is instrinsic to the meaning behind the sign. Beyond that, any real life behaviour of the object creates connotations, not denotations.

I think my conclusion would be: all names are empty when considered as names; no names are empty when used as names. Or something like that. I'm not sure.

It was for that reason the scenario didn't seem to me to get at the issue of "empty" names as well as other examples. — Mentalusion

I used the scenario in response to a question why the holder of a name isn't the token of a type (or so I understood the question). It wasn't meant to get at the issue of empty names.

That said - and this is a parenthetical issue - I still don't think calling references to fictional entities "empty names" constitutes a category error. It's not the correct use of the concept of a name to be sure, but it's not a category error. It's just wrong. Not everything that's wrong is a category error. — Mentalusion

Of course referring to fictional entites as "empty names" is a category error. A fictional entity is not of the category "name", therefore your What am I missing here?

I'm also not quite sure how you see the relation between what a person intends to say, and what that person actually says. Grammar is something you learn as you go; it's something you can get wrong. At the same time, if enough people get the same thing wrong for a long time it changes. The category error is on the language level, not on the concept level.

Generally I don't have an issue with your claims about how syntax can operate with proper names, and even think the type/token distinction could be useful for explaining the non-definite use of the proper name vs. the definite. I took my claim about the "lexical entity 'john smith'" to be basically consistent with that. However, my concern is exactly with what the actual context of the situation is here and the intentional state of the postal carrier. The package carrier not standing at the door wanting to give the package to anyone who happens to be named John Smith so he can happily walk off feeling like he did his job competently. Rather, he wants to give the package to the John Smith to whom the person who sent it addressed it to, he just doesn't know who that is. In other words, s/he isn't just looking for "a" John Smith, he's looking for "the" John Smith the package is addressed to. So, I just don't see that the syntactic distinctions you bring up - while legitimate in and of themselves - apply to this particular situation here since, in fact, given the context, it does not seem to me that either of the names are empty in the example given. — Mentalusion

But a lexical entity "John Smith" being different from a proper name "John Smith" or not is highly relevant for the type/token distinction. (I've had some minor linguistic education, but I know most about syntax and less about semantics, so there's that to bear in mind when reading my posts.)

Yes, there's an ambiguity with the names. But to talk about the ambiguity you need a word that encompasses both names.

With respect to empty names, ambiguity matters, too. "Harry Potter" is not itself an empty name. You need to know who it refers to (i.e. a fictional character) to know whether it is empty.

We have three cases, here:

1. "John Smith is a common name." -- Referent of "John Smith": a name

2. "This parcel is for John Smith." -- Referent of "John Smith": a specific person.

3. "This parcel is for a John Smith." -- Referent of "John Smith": a group of persons defined by holding the name "John Smith"; Referent of "a John Smith": a specific (but not specified) person.

"Harry Potter is an empty name," uses "Harry Potter" in the first meaning, but there's an implicit assumption as to the identy:

The sentence "The Harry Potter from Rowling's book is an empty name," is a category error. The Harry Potter from Rowling's books is a person, not a name. You'd have to say "Harry Potter is an empty name when it refers to Rowling's character." When I'd be arguing that "Harry Potter" is not an empty name because my neighbour is called that, I'd have misunderstood the concept.

Now, it is actually possible to create a concept of "empty names" such that an "empty name" is only an "empty name" if there are no real entities with that name. "Harry Potter (= 1) is an empty name because there is no Harry Potter (= 3)" is a different concept from "Harry Potter (= 1) is an empty name because Harry Potter (= 2) does not exist", and it's useful, if at all, in different contexts.

I think it's an important distinction, because it's easy to slip, and there may be contexts in which it's not clear what's being talked about, or in which the distinction is meaningless.

In my scenario, there is no empty name. But if someone played a prank and there is no "John Smith" at that address, then one of the names would be empty. (Or formulated for people who don't like the homonym theory: The name would only be empty if it referred to the non-existent recipient of the prank parcel.)

[For what it's worth, this thread is the first I ever heard of "empty names". My intuition was that it's about names that really don't refer to anyone. Maybe an author has made up a name, but is undecided if he'll ever use it and certainly has no character in mind. Such a name would exist, but it'd be "unused" and have no reference - i.e. the name can't be traced to any person fictional or real.]

I'm not sure the example gets to the difference between type/token and proper names. It seems to me that both speakers there are using proper names. the only possible type/token implication is that one could see the lexical entity 'john smith' as a type for the two token names "John Smith [1]" and "John Smith [2]" given the name is a homonym. I think the more nature description though would just be say there's any ambiguity in the name: they just sound alike but in fact reference two different things, like a river 'bank' vs. a financial 'bank'. — Mentalusion

When two or more people have the same name, there's ambiguity. You're right about that. But the hint, here, is in how language treats words syntacticly:

A proper name doesn't take articles; semantically, it doesn't need to, because a proper name is definite by itself. Normally, ambiguities are resolved pragmatically rather than through syntax: "Joe" is far from a unique name, but if you say "I'm talking to Joe," people usually know who you mean through context. (It's, of course, possible to miss parts of the context and create an ambiguity that your conversation partner doesn't automatically resolve.)

If you resolve the ambiguity syntactically, by adding articles (either indefinite, or definite), you make a shift from a proper name to regalur noun: "a John Smith" does not have the same meaning as "John Smith", even though the same person can be the referent for both (more precisesly "a referent" in the former case and "the referent" in the latter case). In the case of "a John Smith", he's part of a class (all people named "John Smith" are "a John Smith" - being named like that becomes the meaning of a type, and having that name makes you a token); in the case of "John Smith" he's uniquely named (and it doesn't matter that other people have the same name).

What's philosophyically difficult here, I think, is the precise relation between semantics, pragmatics and syntax (and theoretically morphology - but not in this case).

I'm basically asking you why aren't proper names also referred to as tokens for things? Is this an issue? — Posty McPostface

Consider the following exchange:

A: Am I speaking with John Smith?
B: Yes. How can I help you?
A: Please sign this receipt for...
B: Oh no, you want my uncle.
A: No, I want John Smith. That's you right.
B: I'm also a John Smith, but the John Smith who sold....

In this exchange, A uses "John Smith" exclusively as a proper name, but B, in the last line of the exchange, uses "John Smith" as type/token word with the meaning "people named John Smith".

Words generally have meanings, and then you check whether an object qualifies for those meanings.

Proper names don't work like that. There's a 1:1 relationship of reference between the name and a single object. The object can change completely; what matters is that it retains the name, and that's a matter of social convention and not meaning. You don't have to fulfill any sort of semantic criterea to qualify for any proper name attached to you; the continuity of the relationship between the name and the ting itself is what matters, and it's also what's invoked when you say the name.

It seems clear to me that types are the descriptive content of tokens. So why not include token under the monkier of proper names which would designate that descriptive content?

Because there's no descriptive content in a proper name. "Harry Potter" describes nothing - it's just the name assigned to a fictional character. I assume there are Harry Potters in real life, and they don't have to be anything like the fictional character. I could call my favourite coffe cup "Harry Potter", if I wanted to. The act of assigning a name is all that matters for proper names. That you henceforth associate the proper name with the person/thing in question and expect certain features of the person/thing to remain constant has little to do with the name itself.

Yes, but haven't I already proven that we are posting anonymously with my silly nickname? — Posty McPostface

No, you haven't. Your posting under an alias, which is different.

All post written by the user "Posty McPostface" are attributed to that user. No other user is called "Posty McPostface". If ALL users would change their name to "Posty McPostface", then we'd all be posting practically anonymously (of course, we'd also have to choose the same avatars, or have the board disallow avatars.)

I don't know about that. You can always be wrong about me being a nice Posty McPostface and am evil instead. When is "enough information" accurate in forming a picture about someone? — Posty McPostface

You may never have enough information to form an accurate picture of a person. Luckily, that's not a requirement to connect a person to a name. But if I at least get the name right, I can tell who it is that I have an incomplete or even wrong picture of. Finding the referent of a proper name is a lot easier than making a list of all referents of a less exclusive category. (There are different people with the same name, I know, which can cause confusion.)

Imagine what a fun forum this would be if we were all posting anonymously.

But you just created meaning right now by referring to the place where I post under the guise of "Posty McPostface". — Posty McPostface

Rather than "it has no other meaning," I should have probably said, "it has no other type of meaning," or something like that? It's not that easy to talk about - names identify, they don't describe. That would be pretty straightforward, if you didn't need some sort of description to identify things.

The point is this: as long as I have enough information to identify you, it doesn't matter how accurate my picture of you is.

Also, I just squished a tomato a little, and now it's got a rather ugly brownish spot. I need to get better at judging pressure.

I agree, and think that Posty McPostface is just a persona on these forums. Nothing more to it given the limitations of this form of communication between us. If I were to meet you in real life, I could tell you my real name. — Posty McPostface

Okay, let's say I lie so convincingly that you end up thinking my hobby is polishing tomatoes. Since that's a rather unusual hobby you remember it. So we meet, and you say "Ah, you're that guy who's hobby it is to polish tomatoes." You'd be wrong, but you'd be referring to the right person.

Proper names work like that. They identify unique things; they don't describe them. Sure, I can ask the question with the meaning you have in mind, too: "Are you Posty McPostface?" But that's a derived usuage that means something "Is that really how you are?" It's a philosophical question about identity and little to do with naming. "Are you Posty McPostface?" is equivent to the question "Are you the person who posts on thephilosophyforum.com under the name Posty McPostface?" It has no other meaning. That you can add a nomen-est-omen layer to the question and transform it into something else isn't relevant for determining reference.

What are "thinglys" as you describe them? — Posty McPostface

"Thingly" is merely an adjective that means "of or related to things". I'm not sure philosophers use the term; I don't read a lot.

But, ontologically I exist as a concept in your mind made possible through our context of my interactions with you on this forum. — Posty McPostface

Yes. And that's the only mode of your existance that's accessible to me. I do think that's not the full extent of your existance, though.

The thingly is a concept as you have noted, no?

Well, the divisions between concept/thing and between phenomenon/thing are themselves concepts, but within that concept, things are things, not concepts, and only accessible as phenomena.

Phenomena are things as they appear, and the as-they-appear part is what connects things to concepts, though concepts exist even if no things appear. It's a little messy.

Can you expand on this? It's quite interesting... — Posty McPostface

Well, I come from linguistics, not philosophy, here. In linguistics, there are (at least) two major ideas of meaning:

The first is the semantic triangle: We talk about the real world. We see a thing, we associate a conept with it, and then we encode that in a word - then the word is decoded into a concept and the concept related back to a thing. (That's Ogden/Richards.)

The second is the structuralist approach, where a word consists of signifier (a sign) and a signified (a concept). The structuralist approach keeps reference within the word, and words derive meaning from the difference between words rather than the real world. The common way to illustrate is that if you point to a tree and say "tree", you can't possibly know that what the other person actually means is "tree". He could be saying "big," or "plant", or "look!"...

Both approaches have their limitiations, but I find them both useful. Neither of them go deeply into what constitutes real life, though. And that's what's sort of difficult here:

When we use words to define other words, we're firmly in the structuralist territory. You say "Posty McPostface" is your alter ego, but by saying that as Posty McPostface you imply some level of overlap. That overlap is an overlap of signfireds, though, of concepts. We can play a game: "Posty McPostface is a person." Ture or false? A series of such questions can make the meaning more clear, but all the while I have no access whatsoever to any referent - there's only my imagination. And while you <i>do</i> have access to the referent, it doesn't seem like you care much about it: in fact, you seem to be taking it for granted and try to make some difference that you can't count on others going along with. But that's only possible because there's a body out there that carries both tags (according to social levels of appropriateness).

Now when it comes to the thingly layer, I find Husserlian phenomenology attractive: it's unaccessible in pure form; all we know are phenomena. That complicates things for the current issue:

Back to the structuralist pointing at a tree: he's seeing a phenomenon, something that presents itself as a tree. It's not that the tree isn't a tree, and while others might not know whether he says "tree", he himself does. My "tree" may not be your "tree", but there's a referent out there, a thing, that arbitrates between us. We can run into trees, for example, they're solid. We should have similar experiences.

So the question is: Is this putative referent, the thing behind the phenomenon that serves as referent, relevant to "naming"?

A name is also a type of phenomenon: it's a tag. When I read a post by "Posty McPostface", I contrue a continuity there - a person behind the post. I have no other access whatsoever to you, nor do I seek one. But because of the meaning I attach to "person" I assume that there is a phenomenon out there that correlates to Posty McPostface in the same way that Dawnstrom correlates to "me" (which is the only fist person experience I have access to). As such, "Posty McPostface" is primary to me, and if we were ever to meet by accident and uncover our mutual identies (alter-egos, if you will), then that's the only shared history we have, and it should dominate our real-world interactions, too. It's all about day-to-day relevance structure: which name applies does not change according to who we are; it changes according to who we are with or in what context we move. Meanwhile, there is no other body who can bear the label of "Posty McPostface" and no other body than mine who can bear the lable of "Dawnstorm". The names say nothing about us; they just identify us phenomena. Because we know the meaning of a name, and because we apply the name, a persony thing becomes a bit more of a person.

Your "Posty McPostface" persona may differ from your other personae in many ways; but it's no less what you're doing with your body. And that's what makes negotiating when to use what name possible in the first place. It's a perspective game: if I meet you in real life, Posty McPostface is the only label I have for you, and you have to decide whether you're fine with that, or whether you don't want that name in that context. But none of that is a question of whether or not I have the right referent. Similarly, if I meet you in real life, and I refer to you as Posty McPostface, I'm clearly not reducing you to your online posts. I can't meet your online-posts in any other way than on a computer screen. The only thing that the name would imply is that this person before me at one point in the past made those posts. You're Posty McPostface if that's true, and you're not Posty McPostface if that's not.

Your online name and your offline name(s) have only one thingly referent - there can be no other.

What do you mean by that? — Posty McPostface

Well, when you use a word you have a meaning in mind, and when I hear the word I have a meaning in mind, too. Those meanings don't have to be the same; they just have to be compatible in a way that they don't cause problems in our interactions (or that they cause problems that don't lead to the termination of the interaction, or whatever). What connects us in communication is a real world, and the assumption that we're to one degree or another talking about it.

So when I'm taking a bath, I'm not Dawnstorm, but when I'm typing a forum post I am. In the real world, there's really only one me, and if I'm typing a forum post and someone interrupts, I'm both Dawnstorm and not Dawnstorm at the same time. All that is analytic nonsense, though. There's only one of me. I can want to save that distinction, because it matters in one way or another, but I - as the referent - don't change no matter what name I go by.

So here's the problem: if what name applies to me depends on activities, the name refers to a bundle of activities or maybe a related and perceived identity: that's a concept, though, and not a thing. That's the reference and not the referent. I'm really only talking about the difference between signifier and signified. But if a name names a person than that referent would have to be me, no matter what I'm doing. I can't exclude Dawnstorm from the more comprehensive person and say only the more comprehensive person is real. That's nonsense.

Insofar as names are bound by context, names have no direct referent. The reference, the meaning of the word, is always a layer we push over real things.

Insofar as names refer to things, I'm the referent of both the name "Dawnstorm" and "XXXX", because there's nothing else that applies. Clearly, the concepts, the reference, the signified, differ in its properties to one degree or another, but there's only one real world object that is me, no matter with how many concepts I might frame it.

It's possible that I, Dawnstorm, am lying, and that the person currently typing this post is part of a collective who alternately handle this account. In that case, the me typing this post is not the whole Dawnstorm, but only part of Dawnstorm. In that case, the difference between "Dawnstorm" and "XXX" would be a difference in referent: I'm not Dawnstorm, I'm part of it.

It's also possible (no it's not, but humour me), that I'm one of the infinite number of monkeys on an infinite number of keyboards supposed to be produced Shakespear, but failing and coming up with this instead. In that case, no only am I not who I claim to be, this isn't really a conversation, and none of this is meaningful on my end, though it might be on yours. In that case, Dawnstorm would be fictional, and so would be the "XXX" I keep referring to, but they'd still putatively be the same real-life referent, if that referent had a physical reality.

So when you say that "Posty McPostface" doesn't refer to your true self, you're talking on the level of concept, not on the level of thing. The concept of "referent" is genrally the thing-level (I'm not 100 % confident about that, but that's how I've always seen it). The person typing your posts is no less real than the person eating dinner. Whether either of them has a true self is a completely different question whether they have a name. And the same person can have two names at once - which one to use is a matter of convention, not reference. Or differently: if I were to address you as Posty McPostface during dinner, and you say that you're not Posty McPostface right now, I'd read that as an appellative rather than as a descriptive speech act, because I assume you know that I know that you're not engaged right now with a forum post. (You don't have to worry about me suddenly showing up in real life; I'm speaking hypothetically. I don't even really know if your proper ego usually eats dinner. That's just a non-absurd assumption of mine.)

I think that's what I'm getting at here. I think the point here that I'm making is that contextualism is the only way to go about discerning meaning present in empty names. There really doesn't seem to be any other alternative. — Posty McPostface

I don't really have anything against that, except framing it like this I agree with StreetlightX: all names are empty. It's sort of like the move from Ogden/Richards to Saussure and eliminating the referent. The problem is that no-matter what meanings you attach to them real world referents aren't really divisible in any other way than analytically.

Yes, no disagreements apart from the fact that I am known on these parts by the nick I go by. My usage of "my" is indicative of showing that I identify with my nick. But, again it doesn't denote my true self. — Posty McPostface

But your usage of personal pronouns doesn't differentiate. Neither does mine. I've been Dawnstorm online forever, with only two exceptions, once preceding the name, and another having to do with forum etiquette on that particular forum. I also have a name given to me by my parents, and I share a family name with them. All those names have the same referent (i.e. real world object), and that referent is simply me, not anything as specific as a "true self", which is a good thing, too, since I have no such thing and couldn't be referred to at all. I'm a horrid compartmentaliser: different personae for every social context, even one for when I'm alone in my head. It would be impossible to name my true self. But it's rather easy to name myself - with different names for different context. If someone were to approach me in real life and ask me whether I'm Dawnstorm, I'd be rather surprised. I'd have to ask which Dawnstorm, before answering, too, since it could be a rather strange coincidence, and the other person could have arranged to meet with someone under a code name. In the age of doxing it might be a good idea to walk away instead, though, to be safe. In any case, under the alternat-ego interpretation, "Not right now," might be a possible answer to "Are you Dawnstorm," in that context. Right now, as far as I'm typing, I'm definitely Dawnstorm, though. I'm also still going by my given name, and I'm not using that here. "I" as the origin of first-person experience is the only constant, here. And in the end it doesn't much matter what name I go by. Pleased to meet you. Hope you guessed my name.

My alter-ego, Posty McPostface. — Posty McPostface

This is a post from Posty McPostface, right? So are you, Posty McPostface, claiming that Posty McPostface is the alter ego of Posty McPostface? If the theory of the person behind Posty McPostface is correct than that person can't use "my" for anyone else than Posty McPostface. And when I say "you", I'm talking to Posty McPostface, and not that person. Therefore Posty McPostface can't be your alter ego, it's that person's alter ego. However, I have this - perhaps far-fetched - theory that the person whose alter ego is named Posty McPostface slipped and attempted to refer to himself with a first person pronoun, not properly realising that the pronoun must refer to Posty McPostface in a post by Posty McPostface.

This post might be flippant, but I'm actually sincerely curious how you explain usage of first person pronouns in a post where the referent is necessarily ambiguous between proper and alter ego, if the two do not refer to the same real world referent. First person pronouns are not names; they're indexical expressions, and their referent is whoever is uttering them. According to your theory that is... who or what? Who or what do first person pronouns in Posty McPostface's posts refer to, so that the quoted reply above makes sense in the way that we both presumably understand it?

Like my age? That changes on my birthday? I am always "my age," but my age changes. "people my age remember the assassination of President Kennedy." A stable truth using a changing predicate. — unenlightened

Hm, this is actually surprisingly difficult to answer for me.

On the surface of it, I have an easy "no, not like that". "My age" has a stable meaning, no matter when you say it. "Grue", in my reading, does not. "Grue" does not mean "first green, then blue". It means "either green or blue, depending on which side of time T we check".

There is something they have in common though: they both invoke context. To endow "my age" with meaning, you need to know who speaks and - approximately - how old s/he is. To endow "grue" with meaning, you need to know when the utterance is spoken in relation to time T.

At the same time, though, there's still a difference. You can point at a picture of a man and say "that's a man my age", and if it was true when the picture was taken, it's still true when you look at the picture. However, if you take a picture of grue object and look at it after time T, you're not looking a grue object, even though the object was grue when you took the picture and the colour hasn't changed.

Similarly, when you say "I want to see a grue thing," you know that you want to see either a green or a blue object, and that seeing a green thing too late or a blue thing to early won't count.

Words like "my" are indexical. Words like "mortal" describe a typical form of change. Words like "grue"... have something much like natural language change worked into the definition? The closest real-life equivalent I can think of is applying legal terms when laws change the interpretation of the terms at a certain date (except it's defined into a word from the get go and isn't actually change; you could define "grue" as undergoing a the meaning change every other day (even/odd dates), except defining it like this creates a regularity you can observe and isn't very useful for challenging induction).

I thought Goodman proposed a predicate that involves a scheduled meaning-change of a word, rather than word that describes a change in an object. Am I wrong?

not sure your point here, but I wasn't making any argument, just giving you the correct Catholic teaching. — Rank Amateur

I'm an Atheist who grew up and still lives amidst Catholics, and what you say is certainly what they preach. But it's also, generally, what they do. Nobody's ever told me I'll go to hell for not believing in God. I generally come away with the impression that all "good" people go to heaven, and when I ask what "good" might mean, I'm a lot more likely to get counter questions than a sermon (which is consistent with the idea that your relationship with God is personal). There are probably regional differences when it comes to practise, though. I live in Austria. How about Ireland? Brazil? Indonesia?

I'm a relativist, so I'm fairly sure what millieu you start out in is rather important. Nobody's an atheist because the cornerstone of their worldview is the non-existance of God. Generally, an atheist has a world view of his own, like any other person, and that world view does fine without God, but they only ever notice that when they consider theists, and so your atheism will likely have certain focus, depending on what theist intrusion in your life looks like.

I grew out of God (the Roman Catholic variety) together with the Easter Bunny, so the image of God I have inside is rather childish. Other people grew up and their concept of God grew up with them, but they have problems making themselves understood by me, because it all looks equally childish to me. But, see, the childishness is mine. I'm aware of that. None of the people around me believe in that childish God who is the only one I can imagine. Curiosity? At that point, people very rarely tell me things I haven't heard before. The likelihood that I spend a lot of time listening to things I've heard multiple times before is high, and the likelihood that I finally get it now is low. That puts a dampener on my curioristy, to be honest.

I'm lucky in that people who talk to me, generally don't try to convert me, so I don't have much in the way of an aversion to God talk. My childhood God memories are full boredom and repetitiveness and unenlightening religious education, so the concept of God is vaguely associated with boredom. I'm not really curious about God at all, but I do want to understand theists, and that's a minor interior conflict that can at times escalate.

Generally, there are points of friction in daily life. My mum, for example, thinks I'd be happier if I could talk to God. Well, that may be true, but I can't, since I don't believe He's there. Now, when I'm visibly depressed is when she most wants to bring it up, and when I least want to hear about it.

It's also a little grating, when you're trying to figure out the details of what you believe in (emotional reactions and self-observations are the cue), and all the present theists have to contribute is "What about God." Being an atheist is, as strange as it may sound, already a concession to theists. On my own, I'm fine just being primarily a relativist, a not-quite naturalist, a hardly-at-all-but-maybe-a-little humanist, and so on. It's not easy to figure out what I believe, so, dear theists, please don't distract me with God. We'll talk later, yes?

Those aren't grave problems, but they do provide little hiccup in the daily praxis of theist/atheist interaction. Now imagine, if an atheist were to face grave problems (say, legal persecution), wouldn't they have more of a baggage with the concept of God than I have?

Atheism isn't a philosophical position; it's a way to classify various philosophical positions (from naturalism over secular humanism to nihilism). And often for an atheist to talk about God at all is to abandon their home-territory: God just isn't a very important concept in their native believe structure. (Ex-theists may have it easier, at least, if their memory is good. And I imagine for some I-don't-believe-in-God-but-I-used-to is a rather important mental gestalt.)

Would I believe in God, if I had evidence? To me that line is a red herring. No theist I know personally is waiting for evidence for God. One once told me that everything is evidence for God. Nobody's trying to set up God experiments with the hope of creating a miracle machine. Prayers suffice (and are more respectful to God, too). If there were such a thing as "scientific evidence for God", I'd expect theists to tell me what it is. "God" is their concept not mine. Nobody I know personally has ever put forward such thing. Nobody's ever seemed in interested in such a thing. I can't accept evidence for a blank concept in my mind, and even theists would laugh at me if I were to look for evidence for that childish God-concept I have inside. If I ever have a change of heart, it's going to have to come from some personal experience, rather than empiricist reasoning.

I've typed up and deleted replies to some of the other threads that float around. It's fiendishly hard for me to come up with posts that I wouldn't immediately regret after clicking "post comment". It's probably easier here, since this thread is more about what being an atheist is like than it is about proving or disproving things that aren't very relevant to my day-to-day business.

Maybe "Jo ate the cake, but that one didn't like it" would be better.

When I took Latin, we routinely said "that one" in translations. I just like it because it doesn't contradict other grammar. — Michael Ossipoff

Well, there's a reason I said "I much prefer..." rather than a more convinced "...is better." But "this" vs. "that" doesn't make much difference for the problem at hand. The only difference is perceived distance. I'm not sure I'd use "this one" for Latin translations either, unless you have something in the original that merits it like (like some instances of, say, "ipse/ipsa/ipsum", my Latin's a little rusty).

The problem I have is that "this" is demonstrative. It's the language equivalent of pointing. It feels, to me, like an act of singling-out, if you use it in cases where you'd usually just use personal pronouns.

It's true that it doesn't contradict grammar, but if non-binary felt called out be the usage (which would undermine the intended courtsey) I wouldn't be surprised.The only way to really know is try and see where it goes. It's certainly not up to me to make that judgment.

It's interesting, really. Many langauges still have infelctional endings to nouns and adjectives that indicate gender, so it's a lot more difficult to dodge gender, than just replacing a pronoun. (And with the neuter endings usually being reserved to things, that's usually not something a person wants to claim...)

By the way, would you use a singular verb with "They"? That doesn't have the long-established usage we spoke of, and it's a further direct contradiction in a sentence. — Michael Ossipoff

No. As far as I can tell, you treat singular they gramatically as plural with one exception: "themself" instead of "themselves". As it happens, that's exactly what happened around the 18th century with "thou" being replaced more and more by "you" (which was a plural form). Grammatically, "you" is actually a plural form for a singular referent, except nobody sees it like that, because there's no alternative and people have just internalised it as a singular form.

Using singular "they" for a specific referent is going to be a little odd at first, but I'm seeing evidence from people who use it a lot that there's actually a good chance to internalise it, if you give it a chance. Reading will at first also be a little slower since you're not yet automatically connecting "they" + plural verb with a singular referent, but I can tell from experience that it's a transitional problem.

Forms like "this one" are "stylistically raised" and not equivalent to pronouns. "Jo ate the cake, but this one didn't like it." vs. "Jo ate the cake, but they didn't like it." I much prefer "they".

I pointed out a few times that the sample space of event R and the sample space of event S are equal subsets of each other, which means mathematically we can treat them the same. I also pointed out that as soon as you introduce Y they are no longer equal subsets and therefore mathematically cannot be treated the same.

Here is an example. If Z=M and N=M then Z=N. — Jeremiah

I'm hopelessly confused.

I read your [[10,20],[5,10]] as: "Given that one envelope has the value 10, either [X = 10 and 2X=20] or [X=5 and 2X=10]". And that describes the sample space of both envelopes A and B.

A sample space of A[X, 2X], B[X,2X] gives you the following possibilities:

A=X, B=X
A=X, B=2X
A=2X, B=X
A=2X, B=2X

A=X, B= X (never selected, due to setup)

A=10, B=10
A=5, B=5

A=X, B=2X

A=10, B=20
A=5, B=10

A=2X, B=X

A=10, B=5
A=20, B=10

A=2X, B=2X (never selected due to setup)

A=10, B=10
A=20, B=20

So if look into A and discover 10 inside, all I have to do is to look through all possible constellations, which are both in the sample space you defined, and selected by the set-up:

A=10, B=20
A=10, B=5

This is the result of [[10,20],[5,10]] under the stipulation that A=/=B.

If this is not the case, I have read you wrong, and I can't for the life of me figure out where or how. Have I missed possible constellations? Have misread your sample space? What?

If you came at the problem from here, you'd realize at some point that the clever thing to do is introduce a single variable X that is orthogonal to your choice and orthogonal to which envelope has which value. |X - 2X| = X, no matter the rest. It gives you an invariant description of the sample space so that you can properly measure the consequences of your decisions. — Srap Tasmaner

But you have to remember if you go one envelope has X and the other 2X, then you're defining as the envelope that contains X as the one with the smaller value. So if you look into an envelope, you can't know which envelope you've opened, so the other must contain either twice that of the one you've opened, or half that of the one you've opened: it's the neutral value, split over an either/or situation.

X and Y are commensurable. It's the same thing. I don't see a difference.

If you can show me how to respect this difference within a subjective framework, I'd be all for it. — Srap Tasmaner

This is how I see the problem:

Objectively, you're in one game, where one envelope contains X and the other contains 2X.

As soon as you pick an envelope, though, you have a potential value Y, which is, again, either X or 2X, but that's a bifurcation point: you have now two games. That should be obvious, because saying that Y could either be X or it could be 2X would mean X=2X, and that would be nonsense in an objective framework. What this means is that you now have two subjectively possible games, only one of which you're actually in. This holds for both values, so you have three possible game in the meta-system, one of which - the objective one you're in - is selected twice: once for each envelope.

So, if you were to dimensionalise your variable for the three games, you get: X(1), X(2), and X(3) - where X(2) is the game you're actually in, and it's the only of the three games that's selected no matter what envelope you pick.

So when you're saying that Y could be either X or 2X, you're not talking about the same X. You're either talking about [X(2), 2X(1)] if you pick X(2), or [X(3), 2X(2)]. if you pick 2X(2).

You know that if you pick X(2) you win by switching, and if you pick 2X(2), you lose by switching. Objectively, the amount you're losing or winning can only be X(2). But all you know is the proportion: if you picked the lower amount you win Y, and if you picked the higher amount you lose Y/2. Even subjectively, the amount you win or lose is always X(2). But your frame of reference differs: If you picked the lower of the two values, the amount you could have lost appears to be X(1) [=X(2)/2], and if you lose, the amount you could have won appears to be X(3) [=2X(2)].

Both those values don't exist in the objective game, but you're problem is that - while playing - you don't know whether X(2) is Y or Y/2. You could be in any of two games, one of which game 2, the real one, and the other is either game 1 (the smaller-sum game), and the other is game 2 (the bigger-sum game), but from value Y alone you can't tell.

Because you can't tell, you have two options: take Y into account anyway, or ignore it. These are two perspectives on decision making, and neither really causes unpleasant surprises, because all that changes is the reference system. You either work with an indefinite certain value (in which case it doesn't matter whether you look into an envelope or not), or with two definite but uncertain values (if you look into one envelope and make that the basis of your decision), [or, for completeness sake, with three indefinite and uncertain values (if you don't look into any envelope and set the value Y as the envelope you currently have - this is the switch-back-and-forth constellation)]. In all three cases, the only value you can win is X(2), but depending on your reference system the value may look proportionally smaller or bigger.

I think the core difference between people here lies in the different ideas of what we should with context, or maybe even what should count as context, when it comes to real-life decisions. And that's something buried fairly deeply in our worldviews, so it's not that easy to untangle.

So how's this:

A, B = two envelopes; X = the smaller of two values, 2X = the greater of two values; Y = the known value of one envelope

P (A=X and B= 2X) + P (A=2X and B=X) = 1

Corollary: P (A=X and B=X) + P (A=2X and B=2X) = 0

This merely describes the set-up.

P (Y=X) + P (Y=2X) = 1

This describes the fact that if we know one value, we cannot know whether it's the samller or the bigger value (but it has to be one).

From this we get:

P (A=Y and B=2Y) + P (A=2Y and B=Y) + P (A=Y/2 and B=Y) + P (A=Y and B=Y/2) = 1

Corollary: P (A=Y and B=Y) + P (A=2Y and B=2Y) + P (A=Y/2 and B=2Y) + P(A=2Y and B=Y/2) = 0 [At least one value is by definition Y, and because of the set-up, both can't be Y.]

Now we look into envelope A and discover Y. This renders all the probabilities 0 where A=/=Y, so we get:

P (A=Y and B=2Y) + P (A=Y and B=Y/2) = 1

Corollary: P (A=Y and B=Y) + P (A=Y/2 and B=2Y) + P(A=2Y and B=Y/2) + P (A=2Y and B=Y) + P (A=Y/2 and B=Y) = 0

Did I make a mistake anywhere here? To me, this proves that saying both envelopes have to include either X or 2X and that if one envelope contains Y the other has to contain either Y/2 or 2Y are the same thing from a different perspective.

Okay, we have envelopes that contain a certain value. This thread has used X for the values in the envelope and [X, 2X] for the sample space of an envelope. This thread has also used Y for the value of an envelope. Here's the thing:

We can define the value in the envelope in relation to each other, and we get A [X, 2X], B [X, 2X], where X is the smaller of the two values. (Should we decide to make X the bigger of the two values we get A[X/2, X], B[X/2,X].)

But we can also define the envelopes in relation to each other. We get:

A [Y], B[Y/2, 2Y]

Note that this defines the relationship of the envelopes, in a way the other notation doesn't:

A[X, 2X], B[X, 2X] allows:

A = X, B = X
A = 2X, B = 2X.

We need additional restriction (such as A=/= B) to rule these out. We need no additional restrictions if we're looking at the contents of the envelope directly, rather than looking at the values first and then wondering what is in which envelope.

A [Y], B[Y/2, 2Y]

is a shorter and more complete way to look at "One envelope contains twice as much money as the other", than A[X, 2X], B[X,2X].

We're not making additional assumptions, we're just using different variables as our basis.

A[X, 2X], B[X, 2X] -- The values in the envelope defined in relation to each other.

A[Y], B[Y/2, 2Y] -- The envelopes defined in relation to each other, according to their relative value.

If we know that one of the values is 10, but not in which envelope it is, we get:

A[X[5,10],2X[10,20]], B[X[5, 10],2X[10,20]]

or

A[10], B[5, 20]

It's exactly the same thing, looked at from two different perspectives. There are no new assumptions. In both cases, we don't know whether 10=X or 10=2X. In the former notation we have to enter 10 in both envelopes and wonder which one picked. In the latter we just enter 10 in the letter we picked (obviously, since it's the one we've seen), and wonder what's in the other. And both notations have three values: 5, 10, 20. They're just organised into different either/or structures, because the notations define the letters differently (interchangable; defining in one in term of the other).

The distribution in the other letter cannot be [Y/2, 2Y] as one of those values simply does not exist. You have still created a sample space with impossible outcomes. The truth is that Y is not usable information. The error is making new assumptions based on Y. — Jeremiah

No, I have created a sample space with one impossible and one necessary outcome. It's an either/or situation, and that's appropriate because expectations are based on information rather than on what's actually the case. The statement that for every Y the other envelpe has to contain either Y/2 or 2Y is correct, and remains correct even after you check the other envelope and discover one or the other value inisde.

The distribution will be one of the two scenarios:

Y/2 = 100 %, Y = 0 %
Y/2 = 0 %, Y = 100 %

Y is not a random variable and doesn't have a sample space. That's why I said the random variable is a binary. Y = X? Yes/No. The other envelope has to take one of those values, based on two values:

- The value of this envelope (a fixed value)
- Whether you picked the envelope with X, or the one with 2 X (a random variable)

You need to know the latter to calculate the value of the other envelope, but you won't have the information until you check the other envelope, at which point the calculation becomes pointless.

Sorry about the correction. My head is swimming.

...which of 5 and 20 is even a possible value of X — Srap Tasmaner

I'm not quite done yet thinking, but 20 is definitely not possible value of X. It's like this:

For Y = 10:

5 is a possible expected value for X (alternative to 10=X).
10 is a definite value, either for X or for 2X
20 is a possible expected value for 2X (alternative to 10=2X).

This symmetry is systematic:

Y/2 = possible expected value for X
Y = definite value, either for X or for 2X
2Y = possible expected value for 2X

Y is definitely in the sample (because you're looking at it). If it's X the other card is 2X (and thus 2Y), and if it's 2X, the other card is X (and thus Y/2).

Or differently put: [5, 20] is [X, 2X] but not of each other - of the respective alternative of 10.

Let's call the two envelopes A and B. Now envelope A could have X or A could have 2X and likewise B could have X or B could have 2X. Those are all the possible outcomes so by the definition of a sample space our sample space is [A,B] where A is the set [X,2X] and B is the set [X,2X], which means our sample space could also be written as [[X,2X],[X,2X]]. — Jeremiah

I think I got it. We've got two variables, a numerical value X and a binary variable that tells us which letter we picked, the one containing X (smaller value) or the one containing 2X (the bigger value).

Let me explain step by step:

We have a value X. It's a numerical variable, and it describes the value of two letters in such a way that one letter has X, and another letter has 2X.

The second, the binary variable is E, for envelope, and it's values are yes/no. The question it answers is: Did we pick the envelope that contains the value X?

The sample space for X = N (natural numbers); the sample space for E is [yes, no].

Now we pick a letter and open it. We find it has the value 10. We now have new information about X. The sample space for X has shrunken from N to [5, 10], because 10 has to be either X or 2X.

We have no information on the "yes, no" question, but we do know that the letter we picked has the value 10. That leaves us with the following:

X [5, 10], E [yes, no]

We can use a if/then relation to connect the variables:

If E = yes then X = 10 (because if E is yes, then the letter we didn't pick is the larger one, 2X)
If E = no then X = 5 (because if E is no, then the letter we didn't pick is the smaller one, X)

Just for completeness sake:

If E = yes then 2X = 20
If E = no then 2X = 10

And in words:

If we picked the smaller letter X = 10, that means this letter has 10 (X), and the other is 20 (2X).
If we didn't pick the smaller letter X = 5. That means this letter has 10 (2X), and the other letter has 5 (X).

That means that if this letter is 10 (X | E = yes, or 2X | E = no) then the other letter has [5 (X | E = no), 20 (2X | E = yes)].

That's exactly the same situation as your [[10,20],[5,10]], viewed from a different perspective. Let me write it out: [[10 (X | E = yes), 20 (2X | E = yes)], [5 (X | E = no), 10 (2X | E = no)].

It's indisputable that if we pick up a letter and look inside and find a 10 we have:

X [5, 10], E [yes, no]

Everything else is just different groupings:

If we uncover a letter and it has the value Y, then the other letter has a value of [Y/2, 2Y].

Y ... [X | E = yes, 2X | E = no]
Y/2 ... [X | E = no]
2Y ... [2X | E = yes]

I believe this covers all our bases.

What this means for the switchers and the conundrum is currently beyond me. There's certainly something strange going on.

no matter what you imagine it might be or how much you know about the envelopes. — Jeremiah

Well, with full knowledge of the situation there's a 100 % chance that one envelope contains $ 10,-- and the other $ 20,-- and there's no need to invoke probablility. The reason we invoke probability at all is simply because we have incomplete knoweldge of the situation. And that's why a bet makes sense at all. I don't understand how can say that knowledge doesn't matter. It's the entire point of it.

Sorry no, that was not my intent. In the event of R you have A=10 and B=20. In the event of S you have A=10 and B=5. These are mutually exclusive events, which means in the case of R the amount 5 does not exist at all, and in the event of S the amount 20 does not exist at all. So one of those sample spaces is feeding you false information. The only way to avoid this is to treat X as the unknown variable it is. — Jeremiah

Hm, thinking about it a bit more, I think we're making a basic mistake, here. X/X2 is the relationship of the variables, not the sample space. I'll go at it step by step so we can see if I've made a mistake somewhere:

1. We have two envelopes with two different amounts of money:

Envelope1 = X $
Envelope2 = Y $

At that point E1 and E2 do not refer to specific envelopes, nor do X or Y refer to specific amounts. It's simply two variables with two values, and we have no more information. If we have 10 $ in one envelope and 20 $ in another, it doesn't matter whether we set 10 X and 20 Y, or the other way round. It's completely arbitrary. Both constellations describe the same event.

Both X and Y have the same sample space: any number that makes sense of $. Both sample spaces might be, for example, the natural numbers (weight, space, etc. are complications we don't need).

2. If we learn that one envelope contains exactly double the amount of the other, that tells us more. We now can get rid of one variable. But the sample space isn't X and 2X. It's the natural numbers for one (let's call it X), and depending on one of two assumptions we make about X, the sample space of the second is a transformation of X.

Two assumptions?

2. a) We assume X is greater of the two numbers.

Envelope1 = X $ (natural numbers)
Envelope2 = Y $ (X/2)

2. b) We assume X is the lesser of the two numbers

Envelope1 = X $ (natural numbers)
Envelope2 = Y $ (2*X)

These two assumptions both validly describe situation. We still don't define a real envelope; we merely define wether X is the greater number and Y is the lesser number, or the other way round.

In both these assumptions we don't know the actual value of X. So if someone tells us that one of the envelopes contains 10 $, then we don't know whether X is the greater or lesser number. With regards to the above, we don't know where to put it. But we do know it has to be one of the two: 10 $ is either the greater or the lesser number. This gives us two possibilities:

2. a)

Envelope1 = 10 $
Envelope2 = (10/2) = 5 $

or 2. b)

Envelope1 = 10 $
Envelope2 = (10*2) = 20 $

But what we've done here is twofold: we've set X = 10, and we've set envelope1 as the envelope that contains X. We do not know whether X is the greater or the lesser number. The question we care for is what's in envelope2, and the answer to that is:

If X is greater number, envelope2 contains 5 $.
If X is the lesser number, envelope2 contains 20 $.

The sample space for envelope1 was all the natural numbers, and the event is now 10. Since the sample space of envelope 2 is dependent on the sample space of envelope 1, there are only two possibilities: X/2 or 2X. We simply don't know whether X is the greater number or the lesser number.

It doesn't matter which envelope we open first, we never know which is the greater or the lesser. Because of this, we can set any of the envelopes as 1 or 2, and we always have the same situation:

E1 = 10 and E2 = 5 (X > Y, Y = X/2)
E1 = 10 and E2 = 20 (X < Y, Y = 2 X)

If we only open one envelope, we might open the other envelope first. We wouldn't know about 10, in that case, but either about 5 or 20, depending which is true.

For 20 we'd get:

E1 = 20 and E2 = 10 (X > Y, Y = X/2)
E1 = 20 and E2 = 40 (X < Y, Y = 2X)

The ratio remains a constant, no matter which number you draw, and that's why you alway stand to win twice as much as you would lose. This is a function of what you know about the ratio. However the natural numbers that make up the individual sample spaces differ.

If the envelopes contain 10 and 20 dollars, and you set E1 as the envelope you pick first you get:

For E1 = 10:

the sample space for E2 is [5, 20].

For E1 = 20

the sample space for E2 is [10, 40]

That's because the sample space for E1 is not X. The sample space for E1 is the natural numbers. X is the event.. However, once we know the event for E1, we know that the sample space for E2 is [X/2, 2x], and that's because of the ratio. We can't reduce the sample space to 1 item because we cannot know whether X is the greater or the lesser number until we look at E2. But E1 is chosen at random.

So we get the following:

Envelope1 = [X | € N]
Envelope2 = [Y | € [X/2, 2X]]

I'm not an experienced mathematician, so I might have gotten the notation wrong. But does the reasoning make sense?

The sample space is [[10,20],[5,10]]. Notice how there are two 10s. Now show me the math which allows you to eliminate both of them. — Jeremiah

I haven't read past this page and only skimmed the the next two, so if I'm repeating what someone else said, or if that's irrelevant by now, please ignore. But this is complicated and I don't have much time, and I'm sure I'll forget if I don't reply now.

The square brackets represent envelopes - I'm sure of that. In a sample space of [[10,20],[5,10]] you're not defining the envelope we picked; you're defining the envelopes according to "contains 2X [10,20]", "contains X [5,10]". If you defined the envelope as "the one we picked" you'd get "the envelope we picked [10 (=2x), 10 (=x)]", and "the envelope we didn't pick [5 (= X), 20 (= 2X)]". That's because the two envelopes are interdependent, and that's why the events are order-sensitive, i.e. [[10 (=2X), (10 =x)] and [5 (= 2 X), 20 (= X)]] wouldn't work.

Tha sample space in your post is: [[10 (=2 X), 20 (= 2 X)], [5 = X, 10 = X]]. That is the sample space is only correct, if we're not picking an envelope at all, but defining the envelopes according to whether or not they contain X or 2 X. But then the values are arbitrary.

In any case, there is only one "10", and that's the one in the envelope we opened, whether that's X or 2X. The interdependence between the two envelopes determines that the other envelope has either a 5 or 20, and which of those is in there in turn determines whether 10 = X or 2 X (such is the nature of interdependence).

***

Also, the bet is inherently not avaragable, since repetition either immediately makes each subsequent repetition a win (by revealing X, if we check the result), or (if we stack the results without checking the wins) reveals X as soon as we get a dollar bill other than the one we get first (50 % at the start of the first repetition, 75 % at the start of the second repetition, ... = the likelihood of figuring out X).

I'm not sure if, or how much I disagree with you here. A simplification: if we have (taking my rough definitions as a base) antonym pairs of:

simple-minded -- intelligent

and

foolish -- wise

We get four combinations:

A simple-minded fool
A simple-minded wise man
An intelligent fool
An intelligent wise man

Since I don't have problems coming up with stereotypical fictional characters for either of those types, the distinction is meaningful for me. How? That's a difficult question.

In your anecdote, I see the homesteader as a simple-minded wise man who sees Einstein as an intelligent fool (and who doesn't make the distinction I make).

None of that says what intelligence or wisdom actually is, much less that it is a single trait, or a latent ability. If I take the anecdote at face value, though, and I only have "intelligence" to work with, I find the anecdote much harder to read. "Intelligence" turns into a measure of success, and success is abstract enough that it encompasses both coming up with the theories of relativity and finding contentment in life. I'm not sure what to do with that reading.

Part of my motivation to reply in the first place, is a problem I had with many posts in this thread: a focus on success as a measure of intelligence. I'd like a definition of intelligence that allows me to ask questions like "Under what circumstances does higher intelligence make you more successful? When does higher intelligence become an obstacle?"

For example, if intelligence does have something to do with complexity, then an intelligent person is more likely to mistake a simple problem for a complex one than a simple-minded person, which makes the simple-minded person more likely to successfully solve a simple problem, or be more efficient at solving that problem (because no unneccesary thoughts get in the way).

Now, if we view intelligence as a measure for problem-solving success, we can't meaningfully address these questions. That's my prime problem with IQ tests: they predict success, but don't allow me to look at the relationship between intelligence and success because of that.

Of course, the problem might be that my conception of intelligent is... highly ideosyncratic to begin with. Take language: never mind being a "good" writer; even using language the way every five-year-old does is a highly complex activity. If I ever get serious about "intelligence having something to do with handling complexity" I have to address this distinction between using a complex system and holding its representation in your mind - praxis vs. analysis. It's definitely not a simple task. I'm not convinced yet it's a worthwhile task.

To the topic at hand, I'm highly skeptical of IQ tests, but I've never got the impression that the IQ was supposed to be a metric scale, more like an ordinal scale with huge overlapping categories. I mean, IQ tests come in modules, and everyone who's ever taken such a test has probably found some of those modules easier (I suck at the ones which require spatial perception). Two people with the same score do not have the same abilities in the same way that two people of the same height are equally tall. And I don't think anyone's ever pretended it did. So even if we're talking about IQ tests as they are, we're not talking about a single measure - at least not in the same sense as height or weight.

A little story which I'm sure you will have heard in different guises but I think is apt here. A homesteader being told about Einstein commented that whilst he (the homesteader) had lived a long and happy life, working outdoors and enjoying whatever life handed him, having a loving wife and three happy children, Einstein had worked at often menial jobs, could not sustain a marriage, had little or no relationship with his children and died racked with guilt about his part in the atomic bomb. Who's the most intelligent? — Pseudonym

Isn't that the difference between intelligence (~ the ability to "work with complexity") and wisdom (~ the ability to make things "work out fine for you")? You don't need to be intelligent to be wise, and intelligence certainly doesn't guarantee wisdom.

If people agree with the rough definition that intelligence has something to do with handling complexity, then we could also move away from testing intelligence via success at tasks. That always sort of bothers me, because there are types of mistakes you only make when you're smart enough for them ("overthinking"). Similarly, someone determined to believe a very simple thing can resist being convinced more easily, if their thought patterns can outmaneuver those of the people who are trying to convince them: Intelligence allows for successful rationalisation of appealing nonsense.

One might also predict that the more intelligent you are, the more easily bored you get by performing simple tasks. Things like that.

Basically, intelligence isn't always an advantage and can often work against you in terms of wisdom. I think any definition of intelligence should allow for self-defeating intelligent behaviour.

So, basically, the Einstein of that anecdote is definitely intelligent, but maybe not that wise, while we have no information whatsoever about the homesteader's intelligence, we could learn a thing or two from his wisdom.

I'm not sure that's entirely how I see it, but it definitely goes in that direction.

Heh. I don't know much about sports and very little about baseball, so I was staring at your post and didn't really understand it, until the edit. So basically, if you're already ahead you can make a go-further-ahead run, except that nobody says that. (My confusion stemmed from an instinctive association of "go ahead" with "give the go-ahead", so I was sort of expecting some sort of rule bound complication...)

The thing about language is that it's complex, but easy to use. Easy to use, hard to analyse - to the extent that sometimes analysing it can make you less effective at using it because you start seeing problems that should be there but aren't. Describing language as a formal system is still useful (especially in second language learning), but, IMO, it's important to realise that language isn't actually a formal system: it's a type of social behaviour that uses cues from outside to resolve formal ambiguities (famous example: "We saw her duck.") and in this way uses these ambiguities for versatility. On writing boards, they tell you that "you must know the rules to break them." But I think that's the wrong way round: "you must know the rules to follow them" - if you're literate you can write. When it comes to language, right/wrong is often open to negotiation, and the things that are not open to negotiation are usually not talked about (if you're ever bored look up the difference between nominative-accusative languages and ergative-absolutive languages and see how often that comes up).

Whether the use of a particular name (or nickname or description) is appropriate may not change the truth conditions of sentences it's used in, appropriately or not. I think if my son pointed at Venus of an evening and said, "Look, the Morning Star has risen," that would be true if a bit arch. — Srap Tasmaner

Well, true. But focussing on the sentence's truth condition may itself be missing the point. I don't know your son (or even if you have one), so I'm not trying to get personal here. But your son might say the sentence in full knowledge of this thread and intend it as a rib, because you care about things he does not, in which case the word choice "Morning Star" indicates irony, but you won't find the irony if you focus on the referential object and truth condition. That could cause a hiccup in the conversation, which could have been expected (or even intended) - a sort of private in-joke thematising differences in outlook.

It's not that easy to do something like this in a formal system like maths.

But something about that isn't quite right. The reason we feel there are different uses for "Hesperus is Hesperus" and "Hesperus is Phosphorus" is precisely because we feel they don't contain the same information. So it is with "4 = 4" and "2 + 2 = 4". It's that sense that these two equations carry different information -- they "say different things" -- that drives their different uses. So the semantics drives the pragmatics here. — Srap Tasmaner

I don't think it's quite that simple.

Take your sentence (3): "Hesperus" is another name for Phosphorus.

First, look at the word "another" and it's reference. If there's "another" name, there has to be a default name that the speaker would expect the hearer to know (pragmatics). But given a context such as "What's Hesperus?" the speaker won't know which name this is until s/he arrives at "Phosphorus". That is "Phosphorus" in that sentence does pragmatic double duty: it tells you which object it is, but it also raises the topic of that planet having the name "Phosphorus". That's exactly why ["Hesperus" is another name for "Hesperus".] is weird. It has everything to do with "another", and little with Hesperus/Phosphorus. The weirdness can go away if we take care of this in context:

A: What's "Hesperus"?
B: "Hesperus" is another name for Phosphorus.
A: Hm? So what's another name?
B: Huh?
A: Other than "Hesperus".
B: *flat tone of voice* "Phosphorus" is another name for Phosphorus.
A: *embarrassed* Oh.

Note that the word "another" no longer refers forward, now. The default name ("Hesperus") has been brought up in the exchange before and is the obvious referent for "another" here. The syntax is different from the earlier sentence. And the misunderstanding in this exchange is derived from A not noticing the double duty "Phosphorus" is doing in the early sentence.

**

A second (but to me less interesting) complication is that the planet Venus has the respective names in specific contexts only: even if you see the same object, you can't see the Evening Star in the morning - if you activate all its denotations and connotations (which you don't have to, but which you activate is a matter of pragmatics). Even though "Hesperus" and "Phosphoros" refer to the same planet, they're not complete synonyms, though they may be functional synonyms in many context (in most of which, we'd use "Venus" these days with overwhelming likelihood).

I always wondered what the point of the blue pill was. Isn't it just erasing memories? What about a person who took no pill at all? Wouldn't such a person have to learn to live in the matrix with knowledge he shouldn't have?

Personally, I'm interminably curious and would have liked to swallow both pills just to see what happens. But I'm a bit of a coward, too, so I'd probably have liked to say no thanks to both. With a choice forced upon me, I'd probably be sitting between both until they lose patience and I make a choice at random.

That sounds like a cop out, but this is a situation where people who care very much try to force a dichotomy on me that may not mean much to me. At that point, I certainly don't have enough information to make any sort of meaningful decision. Swallowing both pills is the wait-and-see-but-accelarate-the-process option.