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.

An answer is correct if and only if its value matches the chance that an answer with that value will be selected. — Michael

I think that formulation is incorrect, because if this truth condition yields "true" for more than one value, the chance to be correct <i>overall</i> is greater than for any of the individual values.

Take for example:

a) 25 %
b) 50 %
c) 50 %
d) 60 %

A has a value with a probability of 25 % to be chosen, so it's correct. B and C both have both have a value that has a chance of 50 % to be chosen, so they're correct, too. But that would render the chance to be correct overall at 75 % and according to the problem's formulation, none of them would be correct. But if none of them is correct, then the way we arrived at the correctness of the individual values isn't valid, as it doesn't address the problem.

I don't even know how to formulate this problem in mathematical terms. I don't understand the truth condition.

I'm still waiting for you to explain the problem mentioned in the first sentence above. It does not follow from the fact that we have all sorts of knowledge about bricks that that knowledge is problematic for treating a brick as a physical object.

I really have difficulty with the way you're employing the notion of perception. Perception is not equivalent to understanding. We perceive a brick. We understand it as "a brick". The dog perceives the same brick. He doesn't understand it as(something called) "a brick". — creativesoul

Sorry for making you wait. I'm too slow a writer, reader and thinker - and this thread outpaces me. Also sorry that my answer's likely going to be unsatisfactory since simply catching up with the thread takes up most of my forum time.

I think percpetion is a complex mental activaty that involves understanding what we see at various steps. Every individual, whether human or dog, faces the same stimulus: a brick. But we're not perceiving something and then interpeting it; our interpretations don't come after perception; they run simultaneously to the point that by the time the brick enters our consciousness it's already a brick - fully integrated into our full perceptory state (that includes everything we see, hear, feel...). It's not that we see a physical object that is a brick, it's that we end up seeing a brick and sometimes it's relevant that it's a physical object. Our interpretations of what we see guides what we pay attention to and sometimes supplements what's not there (I'd need to find evidence in experiments for that and don't have the time) - by the time we "see" an "object" a lot of interwoven mental activity has taken place, so that you simply can't say (other than analytically) that by the time you've isolated a brick as an object what you see is merely a representation of what's there in the physical world.

Seeing isn't just "burning the image into the retina", and if it is what you're seeing is not yet "a brick". And perceiving isn't just "seeing" - integrating various input, I think, is already a meaningful activity guided by interpetation.

I don't think that's all that different for dogs either, maybe a ted less complex (but maybe not).

The object of belief can't be a physical object anyway. I believe that brick. That makes no sense. I believe that the brick is red. That makes sense. — frank

What's your criterion for what makes sense? Grammar? And what is it to be the object of belief? Must it be limited to what would render the sentence grammatical? — Sapientia

I'll start from here, because it's easiest for me.

Whether or not a physical object can be the object of belief cannot be determined by saying that "I believe that brick," makes no sense. "I believe that brick," is ungrammatical and has no immediate meaning (though you might guess at any itended meaning depending on the context of the utterance). It's ungrammatical because the pattern is "I believe that [clause]", but here you have "I believe that [noun]". A noun doesn't always describe a physical object. ("I believe that justice," is equally meaningless.)

The usual phrasing when you make a single entity the object of believe is with "in": "I believe in bricks," or "I believe in a/the/this/some brick." These result in grammatical sentences. What remains is a question of meaning. What would I be saying, if I said "I believe in bricks?"

If you say something like "I believe in bricks," do you have to be able to analytically detail what it is that you believe in? If we take the definition of this thread of believe as a propositional attitude, "I believe in bricks," would be a blanket formulation that references but does not spell out a bundle of propositions. But do you have to be able to provide an exhaustive list, before you can be said to believe in "bricks"?

In my first post, I used the example "I believe that God exists," rather than "I believe in God," precisely to avoid this problem. But it's sort of important.

If you can believe in single entities without being able to detail an exhaustive list of implied propositions, what does this mean for the act of believing. Is "believing" this way the commitmental equivelant of blank checque?

Once again, the question is whether a proposition is a sentence, or a special type of meaning expressable in varying degrees of success by varying sentences. If it's the latter, you might well "believe that brick" (a non-native speaker, for example, or a very small child might not know better), but you'd be advised to actually come up with a better formulation. If a proposition <i>is</i> a sentence, rather than simply being expressed by one, "I believe that brick," is ungrammatical nonsense, and not a proposition at all.

This is also the tie-in with belief in non-human entities (from dogs to thermostats). If a proposition is not a sentence, but expressed by one, then maybe propositions can be expressed also by actions, or maybe even by mere behaviour.

And finally, there's a problem with treating a brick as merely a physical object. When you see a brick and recognise it as a brick, you activate knowledge about bricks you have. The knowledge about bricks that you have also prevents from seeing the brick as it is: brick-naively, so to say. What you see is always already an object-subject relation. This is especially the case with human artefacts, like bricks, which are made to purpose. Seeing a brick as a brick is not so different from understanding the meaning of a word, or not understanding the meaning of a word but recognising it as a word whose meaning you don't understand. So in that sense believing "that brick" could be affirming your learned world view, while centering your attention on a brick. Whether or not it's useful to stretch the term "belief" this far, again, is a question of what you're intending to do with the word. I could designate that sort of meaning to "I believe that brick," using an ungrammatical and thus unintutive phrasing to highlight an unintuitive concept.

If that's too long and confusing, my central point here is this: You can't just assume that a proposition is identical with its phrasing. Saying that a proposition has stable meaning, no matter how you formulate it, and saying that proposition is identical with its phrasing has different implications.

Physical objects are out there in the world and can be perceived by anyone (capable of perceiving physical objects), but you can only perceive them as a specific type of object (say, as a brick), if you have that type already in your mind. If you come to an object naively, you'll still have a world view, and your attempt to deal with an object will eventually create a type. As soon as we have a type, there's potential for calling that belief. I wouldn't, but it's not absurd.

Thank you for the welcome. I'm mostly hanging back and reading: I'm a slow writer, and by the time I have something to say threads usually have moved on and someone else has said what I would have.

It's nice to have a forum where people talk to each other rather than at each other.

"Semantic field" is a term used in structural linguistics and anthropology, and it's simply the range of meaning associated with a word or a set of closely related words. It's not the most precise concept out there, and it's theoretical in the sense that you cannot meet a pure semantic field "in the wild", because it's always already organised (say into a word, a set of words, a taxonomy...). It's a useful concept, I think, when comparing things like languages. I found it personally useful when figuring out the technical terminology of linguistics and sociology, since the same "sign body" (say "adverb", or "social role") doesn't always cover the same things (i.e. it depends on who uses the term).

You say a definition can be wrong, but before you can determine whether or not a defintion is wrong, you'd need to know what it is you're talking about, and that's sort of the problem in a thread titled "What is belief?" What I also meant to say, but what I probably buried a bit too much in excess verbiage, is that I think "A belief is an attitude towards a proposition," is an operational definition - not a theoretic one. It drives at methodology rather than meaning. Normally, such a line is connected to a theory that sheds light on all the short cuts in the operational defition. For example, the question of whether a belief needs to be linguistic or if it can be pre-linguistic would have been addressed in the theory. When I first replied to the thread, I probably took it to be a shortcut something like "A belief is an attitude towards something that's expressable as a proposition," but I didn't properly think this through until you brought it up (even though other people have been talking about pre-linguistic beliefs and I nodded in appreciation when I read 's post, here).

It's a bit premature to say a definition is "wrong", when we can't even be sure yet, whether we're talking about the same thing. Some people might indeed only use "belief" for propositional attitudes in its most literal sense, and whether that's sound or not depends on what other words they use and when and how. It's not like we can encounter unmediated beliefs and ask what they are: we encounter things that imply belief - behaviour, linguistic and otherwise. Or artefacts that represent language (like a forum post).

It only follows that there are no pre-linguistic and/or non-linguistic belief unless propositions existed prior to language. That alone is more than enough ground to warrant our dismissing the above belief statement, because there most certainly are such things. — creativesoul

That depends on how we organise the semantic field, though. In an experimental set-up, for example, I could see "A belief is a relation between an individual and a proposition," as an operational definition derived from a theoretical definition - you'd need a well-founded theory of how the linguistic faculties connect to the pre-linguistic faculties of the mind. That is: we believe a lot of things we never formulate, but it is possible to formulate them and test them this way.

That there are different ways to organise the semantic field is a key problem in this thread. If we're interested in a semantic field that we might describe as "taking things for true", we may come up with different words: knowledge, belief, assumption... But even if we have the same words, they don't necessarily relate the same way in different people's usage.

JTB for example sees "knowledge" as a subtype of "belief", but it's equally possible to see them as distinct cognitive behaviour - two flags planted on a continuum so that one either knows or believes, even if there are cases where it's hard to tell which applies.

The more I read this thread and think about it, I lean towards a definition that keeps knowledge and belief separate and that has us generate "belief" to the extent that knowledge becomes problematic. What got me thinking more along these lines is ' specific example:

When I enter the room and see the pens and papers I know there are pens and papers. Once I start thinking in terms of belief, then doubt enters. — Janus

I tried to think about this in terms of 's diagram of JTB, and failed, precisely because of a basic difference in the way the terms are used. If we see "belief" and "knowledge" as distinct cognitive behaviour, with belief arising out of problematised knowledge, I think we need to broaden the context.

One of the things I think is important is the relationship between meaning, truth, reality, and motivation:

I walk into a room, and there's an apple on the table. It's not a fruit, but a wax-simulacrum. If I never found out that fact, did I "know" that there is an apple on the table. Rather, if I notice the apple in passing, but it's not in anyway relevant to me in the situation, then the proposition "There's an apple on the table," might be true on the abstraction level relevant to me: that is the differentiation between a fruit and the wax simulacrum of one is irrelevant to what the proposition means to me.

But that means that all knowledge, belief, and truth - as it occurs in the world - is context bound. And since contexts can change, truth is not a stable thing, and it gets complicated to figure out whether "There is an apple on the table," is true or not. Complicated, but not impossible. What we have is an intricate truth system attached to a proposition.

And this is where the linguistic nature of propositions come in: the sign body of the proposition "There is an apple on the table," remains a constant, even if context changes. In real life, we re-contextualise all the time. Socially, we negotiate meanings, and as our own motivational structure changes, so might the elements of the truth system "There's an apple on the table," that we pick out as relevant. That is a photographer might be fine with a wax simulacrum in a way a hungry person decidedly will not.

Now, as soon as we topicalise the proposition "There is an apple on the table," we enter the meta realm. We might be arguing just for the sake of being right, or we might have motivations that make it important that the proposition be true (e.g. I might win a game, if it is, and the rules haven't foreseen the ambiguity). That is: "belief" can, in situations like this, rescue a proposition from being false, by ordering the semantic field in a way that makes it true. (Side note: This is only hypocritical if the semantic field was ordered in a different way, not if you differentiate from an unspecified level of abstraction.)

So, basically, "belief" has two general meanings:

a) Belief that facilitates action in the face of uncertainty: Belief in P to interact with the reality that P represents, or

b) Belief that takes P as symbolic for some related goal: deciding the outcome of a game, group membership...

I think (a) can reasonably be pre-linguistic; (b) can't.

I find this thread extremely interesting, but since I'm no experienced philosopher, I also find it hard to follow, since I don't always understand the terms an expert would. I apologise if I don't always follow up on posts, but I sometimes need to take the time and read up on related concepts, and by the time I'm done there's almost always something else to read up on.

For me, having a belief about believing is motived directly from social interaction, where different people are comfortable with different levels of certainty, and if you can only take one course of action some people might prefer to minimise risk while others might prefer to maximise (potential) reward, and this in turn is dependant who feels what outcome the most. So "belief" might be a factor that gives people advantages through various avenues: less anxiety, less time spent thinking...

Now, the degree to which belief needs to be justified in the first place is a matter of social negotiation, too. I'm not quick to make up my mind. The result is that not only do I not often get my way, by the time I get any way I'm usually not sure what my way would have been, and in a sense this means I always have to deal with other people's decisions. This can lead to frustration and motivate a world view that suggests that "all belief is unjustified". But I'm not sure I actually belief that, see?

But I do see a continuity here: belief about belief is not that different from the belief that the sky is blue or that sandwiches are nutritious. It's just that the more abstract terms become, the harder it is to describe and circumscribe the referential objects as well as the concepts in our minds. And this is why we have this thread to begin with. What is belief?

So, if we talk about animals in terms of expectation and frustration of expectation, as Janus suggests, then I have to ask why we don't do the same for humans? Do we reach limits? Is there something we can't express? And if so, is the same true for animals, but in different ways? It's very hard to imagine what human language use would like from a different system, perhaps one we can't understand. When we hear a word, we hear a word. When we hear a language we don't understand and whose prosody we're not used to, we may not know where one word ends and another begins, but we still recognise language. The less "like us" things become, the more meaning disappears, but how do we deal with it?

When we talk in terms of expectations for animals but belief for humans, what becomes difficult is comparison. In a sense, making that distinction is a comparison in itself - but what it means isn't clear other than that humans are different from all other animals, which is trivial (and true for all other animals as well).

So when we move away from humans towards thermostats on belief-similarity slide, how do we map the journey semantically? What about belief do we share with apes? With mammals? Vertebrates? Life? Inorganic Matter? At what point does the comparison stop yielding results.

One thing about the thermostat discussion that's drawn my interest is the formulation "The thermostat believes it is cold." What struck me here is the word "cold". The thermostat activates at any temperature we set; the distinction between warm/cold doesn't come into it. This is a judgement that goes away from the very specific temperature. It's an abstraction, and one that has different implications. There's a hidden should-proposition in that word: the thermostat should activate because it is cold. And it's not a should-proposition we can lay at the thermostat, because it's us who set the temperature. All the thermostat can "belief" is that it is time to activate (according to its setting).

But if we set activity pairs (activate/don't activate in this case) as an indicator for belief (and the thermostat has two belief settings: it's time to activate/it's not time to activate) - then what does that mean for the distinction between value judgements and facts. Theoretically, the thermostat can be wrong about the specific temperature, but to what extent can it be wrong about "when to activate"? Does the origin of the setting matter?

When a dog who misses its previous owner refuses to eat, have the should-settings changed? When *I* refuse to eat, because I miss someone I can directly detect whether my should settings have changed: I should eat, but I can't bring myself to. When it's you, I can ask. With a dog? There is no shared language, but does that mean there is no dog-internal language whatsoever? How would we know?

What I wonder is whether we need an inside-view to talk about belief, and if so, when we stop granting an inside-view. I'd say the gradiant is one of similarity with the only inside-view we know directly (our own) as the initial point of comparison.

Wouldn't we distinguish instinct by the fact that it doesn't link up to any proposition? Or would you say that it actually does? — frank

No, I agree. Instinct is just an impulse to execute a specific behaviour. I think belief is more complex than that.

It's just when I go back to the edited original post and read:

So, that John is hungry, and that John believes eating a sandwich will remove his hunger, we have a sufficient causal explanation for why John ate the sandwich. — Banno

I personally run into a problem, because I think both eating and believing are component actions that branch off the same development. We recognise a sandwich as edible the moment we see it; it's not an instinct, because a sandwich is an artefact we create. That is, if I follow the section about action I end up with belief as an internal modelling of the world (a concept already brought up in this thread) rather than with belief as a propositional attitude. But at that point it's not much more complex than an instinct, sort of the flip-side of one: if the instinct is to eat food, the associated belief would be simply the ability to recognise food. That precedes any proposition, though.