Monday, September 28, 2015

Living gay (and ace)

Recently, there was a very short documentary entitled “I’m Graysexual” (NSFW), featuring a man about my age, and using the same identity as I do: gay and greysexual.  He does nothing more than briefly explain his personal experience, which is somewhat different from my own, and as I said, it’s very short.

What was particularly significant to me was not what was said, but what was unsaid.  Specifically, the documentarian chose a stream of clips that imply close interaction with urban gay culture.  He walks around what appears to be West Hollywood (the gay neighborhood in Los Angeles).  He hangs out at gay nightclubs, watching go-go boys.  He looks quizzically at packaged dildos, racks of porn videos, Grindr.  This is all incredibly familiar to me.

I often feel like I’m the only ace who interacts with that kind of gay male culture.  This is not surprising: this is only one of many gay cultures, the ace community is dominated by women, and not all ace men are homoromantic, gay, or bi.  But even among those in the right demographics, I often hear that ace men simply aren’t willing to put up with it.

That, too, is not surprising, and can be explained in one word:  S-E-X.  I don’t need to explain the stereotype, you already know it.

Gay culture… is not really what I would have created if I were dictator.  But because of my disposition, I find it tolerable.  I even find benefits to it, since a space where people openly talk about sex gives an opening to talk about asexuality.

And to be honest, I’d take it over straight culture any day.  Straight people are space aliens.  They think that the only way to proceed in life is to get married and have children.  They think men should have initiative, and women should just be receptive.  I don’t understand it, and I feel sorry for all the people who have to live in it, particularly the non-straight people.  Other people have lamented a lack of older single role models, so I should mention I’ve known plenty of older gay bachelors.  I’m in a stable relationship so I’m not going in that direction personally, but it wouldn’t feel odd to me if I did.

So here I am, choosing to deal with a very sexual culture, rather than dealing with that other heteronormative one.  I’ve been to gay nightclubs packed full of sweaty men.  I’ve had awkward encounters with rice queens, and then befriended them because what else are you going to do?  I’ve wandered the Castro many times, where inexplicably the best place to get beer is the wine bar.  And I’ve sat through a million conversations about Grindr (a popular hookup app), and seen a million more online articles about it, from the many online gay websites that are basically like teen girl magazines, except for older gay men.  People argue back and forth about Grindr the same way that they argue back and forth about looking at smartphones during social outings.  It’s the same argument, really, because what else do you use a smartphone for, amirite?

I spend a lot of space talking about Grindr, because that represents the amount of attention it gets in reality.  Eh, it’s more amusing than talking about sportsball, another aspect of space alien culture I don’t miss.

In gay culture, I blend in fairly well.  Acquaintances assume I’m gay until otherwise noted.  It eventually becomes otherwise noted, as I haphazardly come out to people as ace.  At that point I become an oddity, that one asexual guy that people know.  They’re puzzled how that works, why I’m bothering to be here, and what I do with my boyfriend, but they rarely ask such questions directly.  I wonder if this is how bisexual men feel.

If there’s one advantage of heteronormative straight culture vs hypersexual gay culture, it’s that heternormativity can be opposed.  Sexual culture cannot be opposed, because at least superficially, it has some decent justifications.  There is an ongoing discussion about the level of sexuality in gay culture, but it’s not a discussion that aces play any role in.  The discussion is about Grindr, about hookup culture, and about assimilationism vs liberationism.

I don’t give a shit about assimilating, but I would like it if there were more public concern about sexual assault, or even the social capital placed on sexual desirability and ability.  Sadly, such concerns are more typical among feminists, who are typically women.  I will be waiting for a long time for the gay male feminist revolution.

So that’s the social life I have, and it’s okay.  There are some problems, but nobody is pressuring me to follow a fixed life trajectory.  Dropping heteronormativity is great, I recommend it.

Friday, September 25, 2015

How actions are like literature

The author is magic

"Death of the Author" is a famous 1967 essay by Roland Barthes regarding the interpretation of literature.  He argues that the intentions and context of the author are irrelevant when interpreting the author's work.  At most, the author provides a single interpretation, which must compete with all other interpretations.

"Intent! It's fucking magic!" is an influential 2010 essay by Kinsey Hope regarding the moral judgment actions.  There's a common circumstance wherein a person tries to justify their mistakes by emphasizing their good intentions.  The essay snarkily observes that good intentions have the strange and magical power to erase all harms.  "Intention isn't magic" has become a common saying among activists.

Though the two essays live in completely different contexts (literary criticism vs moral discourse), I would argue that the sentiments behind each are substantially similar.  Indeed, in the modern age, when we increasingly look at popular works of fiction through moral lenses, and when "actions" often consist of tweets or other comments, it is questionable whether they even live in different contexts.

Each essay is questioning the importance of intention. The intention of the author, the intention of the actor, what is the relevance of either to our judgment of the result?  If an poet fails to articulate a compelling interpretation of their own work, does that make it a bad poem?  If a celebrity says they didn't mean to offend anyone with their comments on black people, does that protect them from charges of racism?

Intent isn't completely irrelevant; rather, people frequently overrate its relevance.  Once we abolish the common misconception of the authority of intent, we can then quibble over the relatively small ways in which intent might matter after all.

Intention as predictor

Some small insight can be gained by considering a form of fiction which maybe wasn't so popular in 1967: webcomics.  Alternatively, we can consider fanfiction, ongoing TV shows, or any medium where we consume the work at the same time that it is actively updated.  As the work is being updated, our interpretations of it must also be updated.  Insofar as we are offering a coherent interpretation of a single body of work (as opposed to string of interpretations of a series of disconnected works), our interpretations must care about what will happen in future updates.

Intention doesn't change the past, but it is a predictor of the future.  Thus it is necessary to speculate on the intention of the author(s), at least until the time of completion of the work.

When we apply moral judgment to past actions, it might seem that intention doesn't matter because past actions are already past.  But moral judgment is the most future-looking way of looking at the past.  The practical purpose of morally criticizing an action is not to lament what has already happened and can never be changed, but to discourage similar actions in the future.  Thus, moral judgments care not just about results, but about the processes by which the results are produced.  In short, moral judgments must care about intention.

Still, intent is not the end-all-be-all.  A person can have the best of intentions but still produce evil actions.  Actions are the product of intent and execution.  Declaring one's own positive intent is a poor defense against moral criticism, because a positive intent may still be executed poorly.  The purpose of moral criticism may be to suggest better methods of execution, not necessarily to impugn people's motives.

Similarly, in literature, we want to look at what's there, not just what's intended.  An author can intend to write the greatest literature in the world, but so what?

Monday, September 21, 2015

This blog's history in numbers

I intend to close down Skeptic's Play very soon, and move to another blog called A Trivial Knot.  Now that I'm wrapping things up, I thought it might be interesting to summarize my statistics.
We can also correlate the statistics with a few major events in my life:
Late 2009: I came out as gray-A
Mid 2010: I graduated with a BS in Physics, and started physics grad school
Mid 2012: I launched The Asexual Agenda
Mid 2014: I moved in with my boyfriend

In terms of page views, Skeptic's Play saw initial growth in the first couple years, and then it leveled off.  Initially, it might appear that coming out as asexual greatly increased my page views, and then after The Asexual Agenda was launched, those eyeballs shifted to the other blog.

But in fact, the drop in 2013 can be traced to a different event entirely.  On exactly January 1st, 2013, I saw a precipitous drop in search engine hits, particularly on this particular page.  This coincides with a big change in Google's search algorithm.  I'm not sorry for it, since people just wanted to use an image I posted.  It just goes to show how meaningless page views can be.

When I initially started blogging, I was much more prolific, basically because I was enthusiastic about this new hobby.  This fell over time, but soon leveled off.  Recently, in 2015, there's been an uptick in the number of posts.

Finally, when we look at the word count per post, there's been a very slow and steady increase in time, except in the last year.  I was surprised by this, since I recall many times over the years when I've set out to write shorter and sweeter posts.

In total, there were about 605,000 page views, 1,188 posts, and 642,000 words (as of last month).  For comparison, The Lord of the Rings is about 450,000 words, and the entire Harry Potter series is just over a million words.

Friday, September 18, 2015

Improving on Gödel

This is the final post in my series on debugging the ontological argument.

In this series, I've already rebutted every form of the ontological argument that can be expressed logically, but of course that was never really the point of the series.  The point is to dive into technical details and learn a bit about logic and philosophy.  Keeping with that spirit, this, the final post of the series, will go off on a complete tangent.

The central question I want to discuss is, what is necessary existence?

Sameness across modalities

In modal logic, necessary existence can be tricky to define, because we don't really have a sense of "sameness" across possible worlds.  Suppose there's an alternate timeline where I become a mathematician instead of a physicist.  Is that alternate version of me the "same" as me?  Could you say that I exist across both of these possible worlds?

By Gödel's definition of necessary existence, I do not exist across both worlds.  An alternate version of me is only considered the "same" if it has all the same properties as me.  Symbollically, the definition is: $\forall x ~NE(x) \Leftrightarrow \forall Z~[Z~ess~x \Rightarrow \square\exists y~ Z(y)]\tag{1}\label{1}$ In English this says "x has necessary existence if given any essential property of x, there necessarily exists an object with that same property."  Next we have to define what an essential property is.  $\forall Z \forall x ~ \{Z~ess~x \Leftrightarrow Z(x) \wedge \forall Y ~ [ Y(x) \Rightarrow (Z \rightarrow Y) ] \}\tag{2}\label{2}$ In English, this is "Z is an essential property of x if Z is a property of x, and also entails all properties of x."

A few things immediately follow from the definition of essential properties.  First, we can prove that each object has exactly one unique essential property.  The essential property, or "essence" is simply the conjunction of all properties that the object has.  Thus if two objects have the same essence, then they have all of their properties in common.  In order for something to have necessary existence, then there must exist in every possible world an object which has all the same properties.

Pathological sameness

In my opinion, this is not a very good definition of necessary existence.  The idea of two objects sharing all properties is far too strong.

You can come up with a lot of pathological properties.  For example, in an earlier post in this series, I defined H(x) to mean "There exists a monk singing chants in tight leather pants."  H(x) does not say anything about whether x is a monk singing chants in tight leather pants, it merely says that x is in the same world as said monk.  If x has Gödel's necessary existence, then we would conclude that monks singing chants in tight leather pants exist in all possible worlds, or none of them.

Or consider another kind of pathological property, PS which is the property that object x belongs to set S.  The set S can be chosen arbitrarily.  In fact, why not just choose S to include exactly one object x in one possible world?  No other objects in any other possible world will share property PS, so we can conclude that x does not necessarily exist.1

Now suppose we have an object which is a candidate for God.  As above, we prove that this object does not necessarily exist, and is therefore not God.  How's that for a reverse ontological argument?

I am convinced, however, that this is a purely technical problem in Gödel's argument, and that it could be fixed, although not in any elegant way.  Rather than considering two objects to be equal if they share all properties, we can consider them equal if they share all "relevant" properties.  "Relevance" can be a second-order predicate, just like "positivity", only it obeys different axioms: $\forall Z \forall Y~ (R(Z) \wedge (Z \rightarrow Y) ) \Rightarrow R(Y)\tag{R1}\label{R1}$ $R(\lnot Z) \Leftrightarrow R(Z)\tag{R2}\label{R2}$ $\forall Z~R (Z) \Rightarrow \square R(Z)\tag{R3}\label{R3}$ $\lnot R(H)\tag{R4}\label{R4}$ $R(B)\tag{R5}\label{R5}$ H is the property of existing in a world that has a singing monk, and B is the property of being a singing monk.2

I'm sure you could use the axiom of choice to construct an acceptable second-order predicate somehow.  Etc. etc., therefore God exists.  Now you're convinced, right?

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1. I'm assuming that there is more than one possible world.  If there is only one possible world, then every object in it necessarily exists.

2. Fun exercise: prove that the axioms I chose are inconsistent.

Tuesday, September 15, 2015

GLBT backwards

On The Asexual Agenda, I wrote a satirical piece which imagines an alternate world where instead of gay men being the central example of queerness, asexuals are.  Rather than starting with the acronym GLBT and arguing that asexuals should be included too, I start with the acronym AABT (asexual, aromantic, bisexual, transgender) and feebly argue that gay people should be included too.

Silliness aside, I've long thought that the acronym GLBT is completely backwards, and reflective of backwards priorities in queer activism.  Let's not even talk about asexuals and aromantics because I am biased on that point. Compared to bisexuals and trans people, gays and lesbians are more privileged, and should not be the center of the movement.  We really should be talking about TBLG or BTLG.

A few quick citations.  Basically no one denies that trans people have it the worst off, attempting suicide ten times more frequently than the general population, and twice as frequently as the LGB population.  That's just the tip of the iceberg though, and you can read about many more problems in the National Transgender Discrimination Survey.  From my understanding, trans people are less common than gay or lesbian people, but if you care about raw numbers you'd have to prioritize bisexuals.  Bisexuals are more numerous than gays and lesbians, and fare worse on most measures of quality of life.

It seems to me that the reason so much money and attention is given to gay and lesbian issues is precisely because they are relatively privileged.  It's not that there aren't real concerns worth addressing for gay and lesbian people.  But rather, bisexual and trans people have problems that run so deep that they even infect the focus of activism.

And when I started thinking about it this way, I started seeing its effects everywhere.  For example, in my satirical essay, I mock the way that "queer" is seen in opposition to "straight".  If trans people ruled queerdom, then the opposite of "queer" would be "cis", and then we'd spend a lot of time arguing that gay people were still queer despite many of them technically being cisgender.

Or consider a recent drama where a well-known blogger said a bunch of transphobic things (and is continuing to say them from what I hear, but from a position of more obscurity).  Her defenders complained that critics are taking ideological purity too far.  But would we take this defense so seriously if she was instead expressing homophobia?  No, because we simply have higher expectations with respect to homophobia.

Put another way, we're more likely to let transphobia slide precisely because transphobia is more widespread than homophobia and has done more harm.  There's a logic to it, but it's also fucked up.

Saturday, September 12, 2015

Make an ass out of you and everyone

Pop quiz

Imagine that I give you a quiz where you're supposed to determine whether a bunch of statements are true or false.  Upon reading the statements, you find that they are too obscure, and you have no idea what to make of any of them.  However, I give you the hint that 80% of the statements are true, and the other 20% are false.  How should you proceed?

If you say that 80% of the statements are true and the other 20% are false, then your expected score will only be 68%.  Clearly, you should guess that every single statement is true.  You will only get an 80% on the quiz, but that's the best you can do.

Now imagine instead that we're talking about people.  You're at a high school reunion, and to be honest you haven't interacted with a single person here since graduation.  You know that around 5% of your former classmates are queer, but you don't know which ones.  How would you make your guesses?

This is a loaded question of course.  Why would you ever need to guess?  Why not just assume nothing of anyone?

The irony is that while queer people (or anyone who invisibly deviates from the norm) are the biggest losers in the assumption game, they are also in a unique position to recognize the value of the same assumptions.

Assumption spaces

There's a reason why queer safe spaces are needed.  They are spaces where you can assume that everyone else is queer, or at least very sympathetic.  When an intruder comes into a safe space and attacks people, it's considered worse than the same attack outside the safe space, because it's also an attack on our ability to make assumptions.

Queer dating, clubbing, and hookups are even more in need of assumptions.  Among my queer male friends, it's a perpetual problem to be meeting men in straight spaces (such as the gym), and to have to guess, based on subtle cues, whether they're straight or not.  In an ideal world, you could just ask, but in the real world, this is potentially dangerous, as a lot of straight guys don't take kindly to the mere thought that they could be like us.  Even when not dangerous, it can be uncomfortable, and just plain disheartening to know you'll be automatically rejected 95% of the time.  A lot of queer guys simply aren't up to the risks, and prefer to meet people through designated queer spaces.

[cn: sexual assault] Spaces with special assumptions can have problems.  For example, one of the things I complain about is the ubiquity of sexual assault in gay night clubs.  The problem is there are multiple ideas about what kinds of assumptions are acceptable.  Some think it's okay to grope people non-consensually because they think it's the social assumption in those spaces.  Other people in the same spaces think that's not an acceptable assumption anywhere and you should get consent first (nonverbal consent due to loud music).  The common response is that it's the victim's fault for not understanding the assumptions.  No, I understand the assumptions, I just reject them, and reject the supposition that everyone in the space has ever shared those assumptions.

Signals vs stereotypes

Moving beyond queer spaces, many queer people are still sick of the assumptions placed upon them on a daily basis.  So often they'll adopt signals to make their queerness more visible.  Often the most effective signals you can adopt closely resemble stereotypes.  With gay men in my area, there are a number of fashion markers and mannerisms that allow a gaydar to work.  People aren't necessarily signalling intentionally, but many gay men happen to like these markers, and aren't especially bothered by appearing gay, since they are gay, after all.

This is understandably uncomfortable, because aren't we basically contributing to the stereotypes?  And by merely reading those signals, aren't I imposing those stereotypes on possibly unwilling people?  Rather than combatting assumptions, we're trying to take advantage of them and guide them in the right direction.

And what about people who can't access those stereotypes?  Black queer people can't make themselves white, but unfortunately in our culture that's basically what they'd have to do to send a clear signal.  "I hate signals so much!" "I wish I could signal too!"

Guessing is a battleground

Many people have talked about a distinction between "ask" culture and "guess" culture.  In ask culture, if you want something then you ask for it, even knowing that you may not get it.  In guess culture, it's only polite to ask for things that you're reasonably sure you'll receive.

Ask and guess culture also apply to gender.  In many queer spaces, it's common to ask people for pronouns, because in general you can't tell what gender a person is by seeing how they look.  This is especially important for inexperienced people (unfortunately the same group of people who tend not to understand why it's important), since they may otherwise base guesses on harmful stereotypes.

But trans people, understandably, don't want to spend their entire lives confined to queer spaces, and they have to deal with these guesses and assumptions everywhere.  I've heard many queer people express a desire that we should ask people for pronouns everywhere, not just in queer spaces.  Unfortunately, this strikes most people as extreme.  Society at large clearly has a guess culture with respect to gender; many people would find it insulting if you asked their pronouns when they think they're being perfectly clear.

It's a common saying that "When you assume, you make an ASS out of U and ME".  But people clearly like assumptions and derive some value from them.  Assumptions in the public realm are defended fiercely.  Queer people also derive value from assumptions and create spaces and signalling structures around them.

It's about time that we recognize assumptions on their own terms, containing both good and bad.

Wednesday, September 9, 2015

Ignoring the dystopia

Instead of committing any words to my own novel, I spent the last month or so reading Pride and Prejudice.  It was research, I say.  Research!

Pride and Prejudice of course takes place in the dystopia that is Georgian England.  True to the dystopian genre, there are multiple fantastical constructs which are slowly introduced to a horrified audience.  For instance, there's the idea of an "entail".  I don't really get the purpose of it, but apparently it's a restriction on whether an estate can be passed on in your will.  And then there's "elopement" which just means that a woman runs away with her lover.  It doesn't sound like there's anything wrong with that, but within the dystopia it's a horrible thing to do, and a complete disgrace to the entire family.

There are also many neat world-building details.  I like how the servants are always there, but no one ever thinks about them much, because that's just how wealthy people in this universe think.  At the same time, rudeness towards servants signals an unsympathetic character, and kindness towards servants signals a noble character.  That's the only way the lower classes are ever important: in relation to wealthy people.

I also like how we know exactly how many pounds each character is worth.  In Capital in the 21st Century, the great literary critic Thomas Piketty explains that this is because there are relatively low inflation and constant returns on capital.  Thus, an author can list exact money amounts and expect readers decades in the future to have the same understanding of how much it is.*  Jane Austen really put a lot of thought into that one.

*Upon research, I discovered that Piketty's claims are disputed by quantitative literary theorists.

Changing the subject, the other day, my boyfriend and I saw Never Let Me Go, a film based on the book of the same name.  I had read the book and thought the movie was a terrible adaptation.  My boyfriend, however, detested the movie, because of the way it ignored its own dystopia.  Without any spoilers, the movie involves some extremely questionable bioethics, and nobody ever questions it, much less gets angry at the system.  Bioethics simply isn't a theme in the movie.  Instead, bioethics is just a plot device, a metaphor for the brevity of life.

My boyfriend thought the story wasn't very American.  Which figures, since the writer and screenwriter are British.

But actually I think there's something interesting about that idea.  A dystopia where nobody fights the evil of the system, or even notices that it's evil.  Evil is simply there, and the story addresses completely different themes of love and life.

Although come to think of it, maybe that's too trite.  Maybe that describes every story ever.

Pride and Prejudice ignores the evil of its own dystopia, and instead criticizes smaller evils.  Like how some people are so proud, other people are so prejudiced, and some people are so depraved as to join the priesthood, or to elope.  But sometimes those people learn that they were in the wrong, and eventually come to admit it.

I love that there's a classic romance where the central plot is about two people changing their minds about each other.  Changing minds!  What a rational value!  This also implies that the woman in the romance has a mind to be changed.  A romance where the woman has agency?  It feels like the most progressive romance I've known in ages!

Probably the worst part of the book is that the main reason the woman changes her mind is in response to the man's display of financial generosity.  He's so wealthy, and sometimes he sometimes assists other wealthy people who are on the verge of losing their wealthy status!  The main problem with this part is that it reminds us, the readers, of the dystopia which we were so carefully pretending to ignore.

Generally, I'm not a fan of so-called "classic literature", particularly when people praise it as "timeless".  There is no way that I am reading classic works of literature the same way that contemporaries did.  I don't think I should read it that way.  But Jane Austen was a pretty decent writer, and this novel was worth reading.

Sunday, September 6, 2015

Gödel's positive predicates

This is part of my series on debugging the ontological argument.

As explained in the previous post, the basic structure of Gödel's Ontological Argument (GOA) is to first prove the "consistency" of God, and then it follows that God must exist.  In this post, I will how we prove God's consistency.

The GOA introduces a second order predicate, that is, a predicate that is applied to other predicates.  This second order predicate is called "positivity", but the name is more suggestive than meaningful.  For example, we could say that the property of being red is a "positive" property, or we could say that being red is not a positive property.  Symbolically, we would write this as $P(R)\tag{1}\label{1}$ where R means "is red" and P means "is positive".

GOA at first appears to stipulate a definition of "positivity", and of course it is fine to stipulate a new definition for a new concept.  But my objection is that the definition is poorly formed.

Too many premises

The GOA takes the following premises about "positivity":

$\ref{P1}$: If positive predicate Z entails1 predicate Y, then Y is also positive.
$\ref{P2}$: Given any predicate and its negation, exactly one of them is positive.
$\ref{P3}$: The conjunction of all positive predicates (called "God-like") is itself a positive predicate.
$\ref{P4}$: If a predicate is positive, then it is necessarily positive.
$\ref{P5}$: Necessary existence is positive.  Necessary existence basically means that in every possible world there is a copy of the given object.

And in symbolic logic:2 $\forall Z \forall Y~ (P(Z) \wedge (Z \rightarrow Y) ) \Rightarrow P(Y)\tag{P1}\label{P1}$ $\forall Z~ P(\lnot Z) \Leftrightarrow \lnot P(Z)\tag{P2}\label{P2}$ $P(G);\qquad \text{Definition of G:}~ \forall Z~ P(Z) \Rightarrow (G \rightarrow Z)\tag{P3}\label{P3}$ $\forall Z~ P(Z) \Rightarrow \square P(Z)\tag{P4}\label{P4}$ $P(NE)\tag{P5}\label{P5}$ I leave out the logical definition of necessary existence because it's very technical and not relevant yet.

The GOA is not an especially popular form of the ontological argument, and perhaps now you can see why.  It gets rid of some of the questionable premises in other ontological arguments, but it replaces them with five whole new ones.  Five!  It's easy enough to just say, one of those premises must be wrong.

Indeed, I can't think of any reason we should think that any of the premises are true.  As far as I can tell, the proof is not referring to any natural concept of "positivity".3  In particular, I don't see why every property either needs to be positive or its negation does.  What if being red is positive in some contexts, but in other contexts it's better to be not red?  Or what if it's positive in this world, but there's a possible world where it's not positive?

Indeed, we can stop here, as far as rebutting the GOA is concerned.  It sure is a fancy argument, too bad its premises aren't remotely persuasive.

But the purpose of this series is to dig deeper.  So we turn to the question: exactly which of the premises is wrong?

Stipulative definitions

Since "positivity" obviously doesn't correspond to any real concept of positivity as far as I know, the only way I can interpret the word is simply as a placeholder.  We're creating a whole new concept, and "positivity" is just the name we gave it.  And since it's a whole new concept, we can stipulate whatever definition we like for it.

Indeed, I believe that none of the premises are individually "wrong".  "Positivity" is a meaningless word, and we're allowed to stipulate certain things about it.  Any of the premises, taken individually, I find acceptable to stipulate as a partial definition.  Taken together, however, there might be an issue.

It is not true that you can stipulate just any definition for a word.  The Stanford Encyclopedia of Philosophy lists two criteria that a stipulative definition must follow, the first of which is relevant here:
A stipulative definition should not enable us to establish essentially new claims—call this the Conservativeness criterion. We should not be able to establish, by means of a mere stipulation, new things about, for example, the moon.
The whole project of establishing the existence of God by stipulative definitions, therefore seems rather quixotic.  The very success of the proof only demonstrates that the stipulative definition that we began with was wrong.

What's happening here, mechanically, is that the definition of positivity is overly constraining.  As a second-order predicate, "positivity" has only so many degrees of freedom.  As we give it partial definitions, we are constraining its degrees of freedom, but at some point we begin also to make constraints on the world (or on the set of possible worlds).4

It's quite similar to giving a single word two definitions.  I can define a "foo" as an eight-legged snake, and I can define a "foo" as Socrates, and either of those definitions are fine on their own.  Taken together, they can be used to prove that Socrates is an eight-legged snake, which is a sign the definitions too constraining (even if by a quirk of history it turned out to be true that Socrates was an eight-legged snake).

If I were to pinpoint any of the five premises as particularly problematic, I would say that the $\ref{P1}$ is.  The concept of entailment is based on the material conditional, which as I argued previously is a very counterintuitive concept.  Using this premise, if any impossible predicate is positive then all predicates are positive.  I'm not sure what "positivity" is really intended to signify, but this premise would seem to go against the spirit of it.

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1. As explained in the previous post, entailment means necessary implication.  In the case of predicates, if Z entails Y, then it is necessary that for every object which has predicate Z, it also has predicate Y.

2. Here are some details on how the proof follows from these premises.  Using premises $\ref{P1}$ and $\ref{P2}$, we can prove that all positive predicates are strictly consistent.  If a positive predicate were not strictly consistent, then it would entail a both Z and not Z, which would mean that both Z and not Z are positive predicates, which contradicts $\ref{P2}$.  Using the rest of the premises, we show that being God-like is positive, and therefore strictly consistent.

3. According to Gödel, "Positive means positive in the moral aesthetic sense (independently of the accidental structure of the world)".  Thus it is clear that he intended to capture some sort of natural concept of positivity, although I think the proof fails to live up to these intentions.  I will disregard Gödel's intentions with the hope of exploring the best possible version of the proof.

4. Premises P1, P2, and P5 suffice to make a constraint on the actual world: they prove that something exists.  Just P1 and P2 suffice to constrain the possible worlds: they prove that it is possible that something exists.  Though what they prove is trivial, it is a sign that the definition is already too constrained and cannot be stipulated.

Thursday, September 3, 2015

Dimpled model with curves

Here's one of the very earliest origami models I made, in fact the first 30 unit model.  At the time, I was more interested in documenting the process of creation, so I have a bunch of photos

Shown are 30 units of various colors.  These days I usually assemble the units together as I make them, instead of making them all first.

I assemble the units together in a dodecahedral pattern.

The last few pieces were the hardest.  I recall taking pieces out and putting them back in a few times.

Dimpled model with curves, from Exquisite Modular Origami by Meenakshi Mukerji

Looking back, the coloring of this model is interesting.  Many unique patterns are used, but they're arranged such that the dominant colors form somewhat of a symmetric pattern.  They don't form a "symmetric coloring" in the mathematical sense, but rather, colors shift from red to green to blue.  I feel this is actually more evocative than the mathematical symmetric coloring.

At the same time, I'm critical of the choice to use patterned paper.  There are some pretty curls in the paper, and between the curls and patterned paper it's too busy.