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Topics - Brother Daniel

Philosophy / Help me understand doxastic logic
Doxastic logic is concerned with beliefs.  The idea "it is believed that" is taken as a modal operator.

So for a proposition p, we could write Bp to mean "it is believed that p".

Presumably, if we have more than one person in view (say, X and Y), we could mark the belief operator to say which believer we're talking about.  So BXp would mean "X believes that p".

I've taken a look at the Wikipedia article on doxastic logic, and parts of it strike me as awfully weird.

A big chunk of the article is concerned with categorizations of different "reasoners" ("believers", I suppose), as defined by Raymond Smullyan.

For example, a reasoner is described as "accurate" if he/she never believes anything that is false:
and a reasoner is described as "consistent" if he/she never believes both a proposition and its negation:
OK, those makes sense.  Similarly, there are (rather peculiar) definitions for "conceited", "consistent", "normal", "peculiar", and "regular" reasoners that also make sense and are (I think) adequately non-weird.

But I'm reduced to "what the actual fuck" when I read about his definition of a "reflexive" reasoner:
I mean, I think I can make some sense of this, but why is this case interesting?  When would it ever arise?
If we take p = "Hillary Clinton is POTUS", for example, and imagine that I'm a "reflexive" reasoner for the sake of argument, what the hell might the corresponding q look like?

I'm nearly as befuddled by his definition of a "modest" reasoner:
What is "modest" about this?  And how is it anything but weird?  Take any proposition having the property that I believe that I don't believe it:
Then, assuming I can handle basic logic, we'd have
So (under the same assumption) we'd have
So "modesty" (by Smullyan's definition) would entail Bp.
IOW, if you're "modest", and you can handle basic logic, then for any p, if you believe that you don't believe p, then you actually believe p.  Utterly bizarre.
So C-16 (2016) became law in June of 2017.  It seems pretty straightforward at first glance:  adding gender expression and identity to the protected categories under the Canadian Human Rights Act.  So you can't pick on people for (e.g.) being trans.  My gut reaction here is some combination of "of course" and "bloody well about time".

But to hear conservatives complain about it, they claim that it's an attack on freedom of speech -- that it's all about dictating which pronouns people are allowed to use in referring to someone.

I looked over the bill and didn't see anything about language at all, let alone anything in particular about pronouns.

So is this complaint just a typical conservative lie?  Or is there a grain of truth in it somewhere?
100 years ago.  That day was rather unfortunate for this city.
Why did no one tell me before about the dance your PhD contest?

(See also here for last year's results.)
General Discussion / collective nouns: a ______ of lurkers
An imaginary audience of lurkers?
Let's take suggestions for what the collective noun for a group of lurkers ought to be.

"Imaginary audience" isn't bad, but I think we could do better.
Science / weird deep space radio bursts
I dunno what to make of this.
Yeah yeah so the whole campaign is going to take only a couple of months before the vote*, so I'm over 2 years early with this thread.  Who cares.

[* October 2019 is the most likely timeframe.  Theoretically it could happen earlier, but IMO that's unlikely. ]

- -


Liberals.  Currently 183 seats.  Leader is Justin Trudeau (or "J-Troods" as at least one teenager calls him).  Last time around, his opponents tried to paint him as a moron.  Turns out he isn't.

Conservatives.  Currently 99 seats.  Leader is Andrew Scheer.  He recently won the Conservative leadership VERY narrowly.  (Thank dog our mini-Trump dropped out of that race.)  Surprisingly for a Conservative, Scheer appears not to be completely shitty on every possible issue.

NDP.  Currently 44 seats.  Leader is Tom Mulcair.  But the party has voted to turf him out, and they'll be choosing a new leader soon (this October, I think).  Current candidates are Charlie Angus, Niki Ashton, Guy Caron, and Jagmeet Singh.  I don't know anything about any of them.

Bloc Québécois.  Currently 10 seats.  Leader is Martine Ouellet.

Greens.  Currently 1 seat.  Leader is Elizabeth May.

+ 11 other parties, all with zero seats.

Did you know that one of our two Communist parties picked up 3 seats in 1945?  (But IIRC they had temporarily dropped the word "Communist" from their name at the time.)

- -


Or not.  Whatever.  Your call.
It seems that 51% of Canadians now agree with "religion does more harm than good".

I'm not sure I agree with the statement, myself -- I'm not sure where to draw the boundaries of this category "religion", and I'm not sure how to construct an adequately realistic mental model of the religion-free alternate universe that's implicit here.

But I'm encouraged by the trend.
Just kidding.

But it would be nice if this forum had some non-GIA threads.
Don't we traditionally have a hurricane tracking thread every year?

Rednose usually starts them.  Where is he?

This thread is a couple of months late in starting.  But we can talk about Matthew anyway.  Nassau is getting pretty much demolished as I type.  Fun in Florida next.
Philosophy / Fun with pi
So does anyone want to see a proof of the irrationality of pi?

(The one proof that I've read requires some basic differential calculus in order to follow it.)

hit us up brah.
OK!  I'll try to go step by step through a proof that pi is irrational.

I'm taking this proof from An Introduction to Classical Real Analysis by Karl Stromberg (1981).  He attributes the proof to Ivan Niven, and his bibliography includes a 1956 monograph by Niven called Irrational Numbers, so I assume he got it from there.

The method of proof is "proof by contradiction".  That is, we'll start by assuming that pi is rational, then without making any other questionable assumptions, we'll derive something impossible from that premise.

So.  First step:  Assume that π is rational.  Then π 2 is rational.  And we can find natural numbers (i.e., positive integers) a and b such that π 2 = a/b.

Next, let N be a natural number that is big enough so that a N/N! < 1/π.

Why can we do this?  Because as N grows, N! ultimately grows faster than a N.  So we can make a N/N! arbitrarily small by picking a big enough value of N.

(In fact, you can make an infinite series, summing the terms a n/n! as n goes from 0 to infinity.  This series converges to e a, which is a real number for any real a.  In order for that convergence to come about, the individual terms have to get arbitrarily small.  If anyone is unhappy with this part, we can have a little(?) digression about infinite series.)
Fake human sacrifice prank at CERN

h/t to gib for this.

(Was tempted to put this in either Science or ASS.  But nah.)
Philosophy / on Lying
On lying.

Suppose I make a declarative sentence that is universally interpreted as communicating some proposition X.

One possibility is that I actually believe X to be true, and I'm trying to enlighten someone regarding X.  Another possibility is that I don't believe X to be true, and I'm trying to deceive someone regarding X.  There are many other possibilities too.

I would suggest (though I don't think I can argue for it) that declarative communication can be divided fairly neatly into the "straightforward" and "non-straightforward" categories.  Both of the possibilities that I spelled out above would be straightforward:  I say X simply because I mean X.

Non-straightforward declarative communication would include joking, sarcasm, and probably a whole bunch of complicated rhetorical tricks that I can't think of at the moment.

Is such a division acceptable?  (Or am I in trouble already, even though I have not yet got anywhere near my point?)

If it is, then let's turn our attention strictly to straightforward declarative communication.  In which cases am I being "honest" (or "truthful"), and in which cases am I "lying"?  And is there a middle ground?

If I believe X, and I (straightforwardly) declare X, I think we can agree that I'm being honest, regardless of whether X is actually true or not.  If it isn't, but I believe that it is, then I'm mistaken.  If it is, and I believe that it is, then I'm right.  Yay.

If I don't believe X, and I (straightforwardly) declare X, then that's not so honest.  Again, it doesn't matter (for purposes of judging my honesty) whether X is actually true or not.  It's about what I believe to be true.  We can probably agree on that.

At what point am I lying, when I (straightforwardly) declare X?  If I believe ~X but say X, then I'm lying; that much is clear.  What if I neither believe X nor believe ~X, but say X?  If I think X is improbable but say X, then I suppose that counts as a lie too.  If I think X is fairly probable but not quite to the extent that I can be said to believe it, but I say X, then is that a lie?  Maybe it is.  I dunno.

But there's a further complication:  I'm not convinced that pure, idealized propositions are ever directly communicated.  Our declarative communication consists of rough approximations to propositions.

Suppose I make a statement by which I intend to convey the proposition X.  Someone misunderstands me as saying Y, something different from X.  Perhaps Y is even contrary to X.

Whose fault is the misunderstanding?  It could be mine.  Perhaps I misspoke or mistyped.  I may have forgotten a "not", and thus conveyed the opposite of what I intended to convey.

But in some cases, the fault could lie with the listener or reader.  I expect that nearly everyone here has had this experience, where you say something that (even on close review) seems to have a plain meaning, but someone else reads you as saying something entirely different.  And you're not responsible for someone else's shoddy inferences - are you?

In yet other cases, perhaps, there's no real "fault" anywhere.  After all, there is no objective standard by which a set of sounds (or a set of pixels) maps to a proposition.  Language is messy.

And don't people deliberately exploit ambiguity at times?

What if you make a statement that could in some contexts be interpreted as X, but you know full well that your audience is likely to interpret it as Y?  You may tell yourself that you're being honest (because you believe X to be true).  But if you don't believe Y to be true, and you know that Y is the message that your audience will take from your statement, what then?  I suggest that you're not being honest in this case.  I might even go so far as to say you're lying.

- - -

An old woman (let's call her Dorothy) decides that it is time to move into a nursing home.  Some of her children and grandchildren descend upon her apartment, to claim the items she is leaving behind.  Negotiations ensue.

One of Dorothy's daughters (let's call her Alice) declares:  "Dan wants an ironing board."  (Dan, who is not present for this discussion, is Alice's son.)  The other relatives agree to let Alice take the ironing board and give it to Dan.

Now Dan has no desire to add an ironing board to the clutter of his own small apartment, as Alice probably knows (and certainly would know if she consulted him about it).  Alice simply thinks he ought to have one, as it is one of those things that any civilized person should have (in her opinion).

Let's examine the honesty of the statement "Dan wants an ironing board".

Alice, as a former English major, is familiar with the archaic sense of the verb "want", and is using the verb in that way:  simply to mean that Dan lacks an ironing board.  Based on that intended meaning, her statement is honest (and indeed true).

But given that her siblings and nephews and nieces are relatively unlettered (some of them not even having finished high school), and probably familiar only with the more recent meaning of "want" (related to desire), one could argue that Alice is not really being honest.

(end of example)
- - -

Of course, you don't always "know" how your audience will take a statement.  But often you can make a pretty good guess.

To what extent are you responsible for deducing how your audience will take your statements?

Again, suppose you believe X but not Y, and you make a statement that could be interpreted either way.

For purposes of judging the honesty of your statement, we might imagine that the key variable is "intent" - i.e. that the key question is which meaning you intend to convey.  And sometimes this does matter.  It can make the difference between lying and merely "misspeaking".  There's a difference between accidentally leaving out a "not" and deliberately leaving out a "not".

But intent (as someone once said) is not magic.  If you know, or can reasonably infer, that your audience will universally hear Y when you make your statement, it doesn't matter if you tell yourself that your intent was to convey X.  It's up to you to convey the message that you actually mean.

Another variable:  If you have prescriptivist leanings in your view of language, you might imagine that a grammatically "correct" parsing of your statement will lead to the X interpretation, while those who interpret your statement as meaning Y are simply wrong.  And you can't go through life worrying about what the idiots will think you're saying.  You're not responsible for them.  It's not your fault if your audience is unskilled in the language that you're using.

But that view doesn't really work.  If you know, or can reasonably infer, that your audience will universally hear Y when you make your statement, it doesn't matter if you consider the X interpretation to be the "correct" one.  It would mean that you and your audience are using similar but not identical languages, and that you are deliberately exploiting the difference in order to make a statement that means X in your private language while sounding identical to a statement that means Y in the language of your audience.  The misunderstanding, in that case, is your fault.


(I'll cheerfully take ownership of any internal contradictions in this post.  They are simply an indication of my confusion.)
Philosophy / less-than-uncool preschool
I'm hoping that uncool will show up and reboot the uncool school.

Until then, I'm going to hold the board hostage and torture it with horrible shitposting.  Mwahahaha.

Introducing:  The less-than-uncool preschool thread!

In particular, this thread is (mainly) for the very basic stuff that you pretty much have to be comfortable with before getting anywhere with any sort of pure maths.

I intend my contributions to this thread to be very easy.  However, I imagine that there is some relatively deep stuff that some really smart people* could add, which I wouldn't treat as off-topic.

And why Philosophy?  Because there's no Maths forum, and IMO Philosophy is a better fit than Science.  So there.

[* I notice that Linus is around, for example. ]
Philosophy / Monty Hall
On another forum there was the 3 doors question.
There was a guy that could not accept the switching doors strategy.
And he was able to reword the question in such a way that anyone new to the thread would agree with him.
But of course he wasn't asking the original question.
The Monty Hall problem?

There was a substantial thread about that in the early days of TR.

The now-canonical answer (that switching doors is the best strategy) is based on an assumption that wasn't in the problem as originally worded.  It's a reasonable assumption, but it's still an assumption.

If someone questions the switching-doors strategy, one of the standard responses is to challenge the questioner to write a simple simulation to test the problem out.  In order to make it possible to write that simulation, most people end up making the canonical assumption without even thinking about it.  So of course they end up with the canonical answer.

It isn't hard to come up with other scenarios, also consistent with the problem as originally worded, where switching doors is not the best strategy.
Hey ST.

In the Philosophy section of the previous TR lifeboat forum, you linked to an interesting article.  I didn't get far into it, but I intended to read it at some point.  Do you have the link handy?