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yelsgib

296 karma · joined December 17, 2007

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yelsgib··on Death
"I am convinced that there is no possible external measurement for value"

I agree with this. However, this does not mean that we can't form systems for interpreting our our observations in terms of values or structuring our lives to create them. This might be seen as the goal of philosophy.

There's no possible external "measurement" or standard for anything, period. It's not as if we can actually -prove- math - it's just an agreement which we all come to. We don't come to it consciously; you might even say that it's in some sense the least common denominator of human computation; but "math" as an academic phenomenon is no more external than philosophy or anything else.

"the best we can hope for is get a better idea of the implications of our actions"

See, this is where I think you're wrong. Social systems have utility (buddhism, christianity) for some people because they give a method for aligning our values - they give external focus. In Japan, it's customary to say "it's cold, isn't it?" all the time in winter; this assures that a Japanese person's idea of cold is shared.

Philosophical systems are useful in large part because they enable us to communicate, and create external standards. Talking about love in the abstract is useful because it both gives me insight into my own deep feelings and into those of others. Religion is in some sense primitive philosophy.

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You seem to be missing my big point which is that the aim of philosophy is to distill our difficult-to-verbalize notions into words. You claim that we shouldn't discuss consciousness because it is not defined. But if we don't discuss anything that is not defined, how can we ever come to a definition?

If you look at the history of mathematics of physics, for instance, you'll see that people use strange and undefined terminology relatively frequently. It's hard to communicate in this forum, because I don't know your background, but formalization in mathematics didn't really take place until the end of the 19th century, early 20th century. Before that, math and philosophy were very similar.

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My point is not that you are not entitled to have an opinion - I am merely encouraging you to keep an open mind about things you don't understand. Try to put yourself in the position of someone who knew little or no math, for instance. You might say things like "all those symbols don't make sense" or "it's just gibberish, it's not useful" or whatever.

I think there are a large number of problems here, really. One is that "philosophy" is hard to define. There are big branches (so-called "Western" vs. "Eastern," etc.) and smaller branches ("Analytic," "Structuralist," "Existentialist," etc.). But these are just branches of what has been traditionally referred to as philosophy. Some of these don't even really share traits (e.g. Structuralism doesn't really bear any resemblance to Analytic or Objectivist philosophies - they kind of talk in orthogonal directions).

Another problem is that you are asking for a "use" of philosophy, which is kind of missing the point. Philosophy is not an object to be used (neither is Math, in its total form, incidentally), it is more of a large structure. Philosophy as an academic institution has had profound effects in the past - it shaped the creation of the United States and the constitution, it arguably stoked the nationalist fervor of nazi germany, it affects art, literature, relationship, gender. Feminism is a philosophical institution, in large part.

My point is that as society "progresses" - as we have to deal with larger and more difficult to interpret social structures - as democracy arguably breaks down - philosophy becomes vital because it is in some sense our actual lingua franca. Philosophy -can- define the boundaries of what we can talk about. Philosophy -can- help us structure our worldviews and communicate them so that we can meaningfully cooperate.

I'm not being rigorous or anything, I'm just trying to give you a taste of how I feel/think about the subject to help you see why I find your standpoint somewhat offensive. I'm not even really trying to argue, I'm just trying to communicate -my- values/feelings/thoughts.

I also have a math degree, and I think that math is very important. Incidentally, I do NOT think that most current philosophical thought is important (I think that Foucault was important, and that he had effects, but after him I don't really know of any philosophers who I particularly "like") and I can completely understand why you think the way you do.

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As for your last point, I think you should be more careful in interpreting the statements of others. I was not saying (admitting! what harsh rhetoric) that philosophy is for those unintelligent (whatever that means) to do math. I was saying that one of the roles of philosophy is to give us a lingua franca so that we can communicate about how we structure our lives. People want to communicate, but it's hard to talk about things like love, value, etc. unless you have a structure to do it in. My claim is that philosophy (in some of its forms) achieves this task.

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As a capping point, I guess I want to say that the biggest flaw that I see in your thinking is that you essentialize "philosophy" and "math" and "economics." These things are not objects, they are sprawling and diverse academic structures whose effects are profoundly complex. To say "philosophy is snake oil" or "math is useful" is to make a major error in making objects out of things that cannot effectively be thought of as such. To say that philosophy "pretends to be important" is to draw together thousands of years of intellectual thought into one tiny heading and characterize it all (despite ignorance of most of it). For instance, why is Mahayana Buddhist Philosophy snake oil? Why is Post-Structuralist thought snake oil? What about Existentialism? What about Hegelian Metaphysics? You don't know about any of these things (most of which really do NOT "pretend to be important") but you characterize them nonetheless.

So in the end, all the rigor with which you purport to think is thrown down the tubes because you obstinately refuse to be skeptical about a vast field which you ultimately do not understand.

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EDIT:

Sorry, I know this is long, but this is something that I feel passionately about and it is very useful to write about it. I won't be terribly offended if you ignore my post.

I wanted to add something which I think you might jump on:

I am _NOT_ equating math and philosophy when I say that they are equally internal. I think that there are VAST and important differences between them. My claim is that their relative "objectivity" is not one of them.

Do you know all the axioms of ZFC? Can you justify them? Do you know category theory? Do you know multiple axiom systems? How do you justify axioms?

Most mathematicians I know (and I know a decent number) do not actually engage in foundational mathematics. In some sense they work in the "academic cloud" of math. They can't prove their ideas all the way down to ZFC. But because of the way that math as a field is structured, and because it is the abstraction of a simple concept or a small number of concepts (unit and/or set and/or "process/object" - corresponding to Peano Arithmetic, Set Theory (ZFC), and Category Theoretic bases, respectively), it is easy to work in the cloud and not run into bullshit.

Philosophy has the problem that (as I said) it is attempting to find common language for things which we do not yet have language for. This means that a lot of the meaningful computation of philosophy is pre-linguistic. This makes it difficult to interact with, externally.

One reason for this is that some philosophers (e.g. let's take the Deconstructionists) kind of live in their own world with their own specialized vocabulary. They all "understand" it, but to give a full exposition of it from basics would take forever.

Philosophy's justifications are external, but they often take place in a difficult and idiosyncratic language which is inaccessible to outsiders. This does not mean that there are not the same standards of rigor (after all, many notable past philosophers were mathematicians and one might find it very hard to believe they would drop their logical standards for mere philosophy).

yelsgib··on Death
What does "subjective" mean? This question is not so straightforward as you (may) think. This is a microcosm of my point.

What is value? How do we determine the relative values of our life decisions descriptively? How do we do so prescriptively?

My claim is not that my understanding of the subjects is great - it's that your understanding of them (from what you've said in the comments) is shallow. Subjects do not exist independent of semantics - math and economics are only "useful" if we can transform our observations into their abstractions and vice versa (1 apple and 1 apple -> 1 + 1 = 2 -> 2 apples).

Philosophy can give us tools for performing those transformations. It's very difficult to say what is of value in life (is a family of value? food? shelter? what are their relative worths?) and so is correspondingly difficult to use our abstract tools (math, economics, game theory) on the components of our observation (money, time, etc.)

I'm not saying that chapter 23 is great, but I can motivate its use in -normal people's- lives. Normal people can't understand game theory, but that doesn't mean that they -should- or that they -need to- in order to survive or think about how they want to structure their lives.

My real point is just that it seems very arrogant to me to assert that some hack Yale professors ideas validate your "prejudices" re: philosophy. It's better to say honestly that you don't understand philosophy. Maybe you don't want to. That's fine. I don't care. My point is that you shouldn't rail against it if you don't understand it. No one cares about your personal preferences, so you conflate them with moral high-ground and assert them in a public sphere.

Good luck with everything :)

yelsgib··on Death
The salient question is "what is value?"

One aim of Philosophy is to align our abstractions with our intuitions. Game theory/math can't do this, sorry.

Your prejudice is undoubtedly based on your lack of understanding of math, economics, and philosophy. Please do not be so arrogant. (note that I'm not claiming a perfect understanding of any of these - and yes, I realize this is ad hominem - but I'm fairly bored/frustrated by reading these same tired criticisms of philosophy)

yelsgib··on Death
"well"

Dying is not easy to understand.

yelsgib··on A Coder in Courierland
It always frustrates me when people pay more attention to word than meaning.
yelsgib··on Labels used to suppress ideas
God, even worse is -Capitalist-. Socialists say the US is Capitalist, Libertarians say the US is Socialist. Who knows? What a waste of words.
yelsgib··on Labels used to suppress ideas
"Is it wrong to call something unscientific?"

I'm surprised PG didn't follow this with: "Is it wrong to call something wrong?"

I think that:

wrong, bad, good, evil, should, right, etc.

Form the oldest and most commonly used category of meaningless, superficial, idea/difference suppressing labels.

yelsgib··on Paul Graham - from social shyness to patronizing
It takes many years to learn to play a violin. Violining is reserved for "violinists." You are confusing -description- with -prescription-.
yelsgib··on Paul Graham - from social shyness to patronizing
Most of the comments I've seen in response to this post are either that "the author was wrong" or "the author didn't give enough evidence." I think that you are completely missing the point of what this guy Cecil wrote.

His point was that pg's essays on philosophy/art made him cringe. Ok? That's his whole deal. He goes on and tries to explain why, but I think that what is really valuable here is that Cecil (who I'm assuming is an artist) is expressing a point of view which has largely gone unstated.

To be honest, reading Cecil's post made me feel better in some way. I don't know anything about art, but I have been thinking about philosophy for freaking forever and I have to say that PG's essays often make me cringe when he traipses into topics which he really -does- seem naive about. Note I said "seem." I don't have examples offhand because I haven't read one of his articles for weeks. Also, the point of -this- post is not at -all- to talk about PG, it is to talk about my understanding of Cecil's post[1].

I think that in general my aversion to internet discussion comes from the fact that people seem to spend approximately 1 second understanding each other and 20 minutes formulating counter-arguments to what they are assuming/hallucinating their "opponents" -meant- (not said). They often miss the -point- of what others are trying to say (and yes, I recognize the massive potential hypocrisy in meta-meta-criticism). Have some heart.

"Be kind, for everyone you meet is fighting a hard battle."

[1] I think that I could, in fact, explain why they make me cringe. (I assume that Cecil could, too, actually - I assume he could sit down next to you, read through them with you, and whenever you saw him cringing you could ask him why - I don't think he's making up the fact that he cringed.) I could go back and re-read his essays and write up long responses explaining what classic philosophical and logical errors he is making (most of which have to do with assuming context/over-generalization/etc.), but the problem is that his errors are very deep. His errors (like so many people's errors) have to do with his big complicated worldview - to reveal them would take a book. And frankly, I don't care - it's much more interesting and fulfilling to respond to someone who's really spent their whole life "thinking" about deep philosophical problems (Chomsky, Foucault, Nagle, Graeber, etc.)

yelsgib··on [dead]
Of course, there is something to be said for the ability to exist within a free (non-systemic) community, no?

I mean, we can have a "system" where the members of the community come to a consensus about appropriate content, downmod people who violate that consensus, etc.

I dislike very much the knee-jerk reaction to create rules, order, etc.

yelsgib··on Senate Approves Telco Immunity for Illegal Wiretaps
No, let's blame our parents for raising us to be this way!

No, let's blame THEIR parents.

I blame you.

yelsgib··on Startup School 2008
Great list, yo. I especially like #1. Hadn't thought about it, but I bet it would work.
yelsgib··on Ask cperciva: Are great mathematicians born or made?
What does it mean that the brain "obeys the same physiological rules" that the body obeys? This point is incoherent.

My point is that yes, there is a genetic aspect to intelligence (duh), but that doesn't mean that there is a genetic component to how "fast" your brain is or how much "memory" you have. These could be emergent phenomena - not directly determinable.

Please tell me more specifically how my prejudices are clouding what I'm reading/saying. You didn't follow this point up.

yelsgib··on Ask cperciva: Are great mathematicians born or made?
"There's no reason to think that intelligence -- regardless of definition -- doesn't work the same way."

I agree if what you mean is that there's no reason to believe that there is no fixed, genetically-determined components to intelligence. I disagree if you are making any sorts of claims about what these components are (as I said, I don't even think we can make gross claims like people are born with "good memories").

I also agree with the point that cultures look for certain intellectual traits in young children. I cannot say whether these particular traits are determined genetically because it is highly possible that we learn a great deal (and abstractly) even from the first day of our lives.

The thing is that (as another poster pointed out) there IS a salient statistic (g - for general intelligence) which we can be "better" or "worse" at - but its value in a field like math which requires highly specialized mental strategies is questionable.

---

I think that you should look at the example of the polgar sisters - they were raised to be grandmasters in chess and 2/3 of them did (the other one become an international master). I think this puts a bullet in at least one interpretation of your theory.

yelsgib··on Ask cperciva: Are great mathematicians born or made?
I agree with this point, but I think that what you run into is that there are certain important cross-cultural trends which might cause g to be pertinent. What I mean is that perhaps the set of tasks which we "regularly perform" are governed by g - these tasks usually involving "problem solving" of the you-give-me-a-well-defined-problem-and-I'll-solve-it variety. It's a kind of reciprocal process - society will produce lots of jobs/roles which fit mass statistics it can determine, and it will also screen for that mass statistic.

What interests me, and what I'm worried that focus on this sort of gross statistic deprives us from thinking about, is the non-regular. I'm interested in the philosophical, the revolutionary, the artistic. I'm interested in what made Einstein Einstein. I don't think it's "g."

Slightly more abstractly/hypothetically: The way I kind of see intelligence is that we can function within contexts (e.g. functioning within the "Math context" would be doing math problems) and "g" corresponds to our ability to manipulate symbols generally, so that we are generally good at working within contexts. This is a really abstract way of saying g corresponds to our ability to solve problems. However, I don't think g says anything about long-term problem solving (involving abstraction, self-reflection), novel content creation (involving cross-context thinking), etc.

Does this make sense?

yelsgib··on Ask cperciva: Are great mathematicians born or made?
This is a good point. I agree that my feeling smarter does not actually mean that I am smarter. I -do- produce a lot more, but this could be due to other factors.

I think you're hitting very close to the important issue here which is that all of this is very difficult to define/think about without a really good idea of what sorts of computations our brains perform.

My point isn't really so much that I think it can change, even, it's that we should be way more skeptical when it comes to making claims about subtle concepts like these. Usually I find that those who say "we are only really growing intellectually until we're 5" have a very limited and kind of rigid conception of intelligence.

yelsgib··on Ask cperciva: Are great mathematicians born or made?
I don't think that we can really investigate "genetic intelligence" until we have a definition of intelligence which makes -any sense at all-, which we don't.

I find a lot of the opinions of neuroscientists I've talked to/read articles from to be really dogmatic in their interpretation of intelligence (probably because they aren't regularly faced with Very Hard Problems in the sense that mathematicians/computer scientists are - their conception of intelligence is often a little more superficial - but anyway, I'm massively generalizing).

My entire point is that I don't think it's useful to think about intelligence as a "thing." I think of the brain as a computational structure. At birth, it has certain properties. It changes in certain ways. It can get better or worse at certain tasks. Because Official People have to say Official Things they always treat their own statements about Intelligence as if they're objective and well-informed which, let me tell you, they are not.

yelsgib··on Ask cperciva: Are great mathematicians born or made?
You're justifying a hypothesis circularly.

I was somewhat gifted at an early age, but I consider my intellectual growth over the past 5 years (17-22) to vastly outstrip my growth before that.

yelsgib··on Ask cperciva: Are great mathematicians born or made?
I think you're being presumptuous. I'm not saying that I'm "turned off" by the -fact- that I can't get tall(1). I'm saying that this is not a -fact- at all. Even if it -is- a fact, it certainly is much more uncertain/open for debate than the question of whether you can get tall at a late age. I'm saying that the fact that you -claim it is a fact- is what turns me off. Perhaps I was slightly imprecise. I should have said "I am highly turned off by assertions to the effect that we can't become smart after an early age." This turns me off because belief/assertion creates cultural structure, and cultural structure changes the world. This point is too complex to go into here, sorry.

My claim is even slightly deeper/more provocative than that - I don't think that efforts by a lot of academics (including a lot of my friends) to propagate an idea of "general intelligence" which solidifies at a young age are entirely benign. I think that they are largely founded in worry and attempts to create an elite academic class. Once you're in, you're in (since getting in means that you have a "good" brain which is not really subject to change). It's self-reinforcing and (in my experience) always based in self-doubt.

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As an aside, the idea that "people get so much more upset" about the intellectual than the physical is completely absurd. I know a ton of people (girls and guys) who freak out constantly about their appearance. I know like 3 guys (including myself) who are the least bit worried about our intellects. Admittedly, most of my friends are academics, but my interactions with people outside this sphere indicate that the trend is not peculiar to my social group (and is probably even more physical-attribute oriented, in general). Seriously, I can't believe that you wrote this. This isn't meant to be mean or like ad hominem - but seriously? Do you actually believe what you wrote? Do you know anyone who isn't an academic?

To answer what I think you might have meant (namely: why do _I_ get much more freaked out about my intelligence than my physical attributes - which is also presumptuous because you have -no- idea how much I care about my physical attributes) I would like to observe that in modern western society "we are our minds." Your mind is essentially the limit of your capabilities in the sort of world I'm sure both you and I live in (the quote unquote information world). The mind is connected with the ability to create beauty (art), the ability to connect with other human beings (sex), the ability to experience spirituality (love), etc. In the academic world, at least, our physical bodies are a burden. They wear out. They get cancer. They die.

Did you seriously ask this? Were you being rhetorical? I can't tell. I don't mean to be mean, but sheesh.

(1) and I accuse you of attempting to employ an underhanding rhetorical trick in making this implicit comparison, I might add.

yelsgib··on Ask cperciva: Are great mathematicians born or made?
I definitely, definitely agree. A lot of mathematicians I know are kind of self-appointed "kings of the mind" and so pontificate tremendously on subjects they're not really qualified to talk about. Not saying that cpervia is, but it's definitely a trend.

That being said, mathematicians definitely have (as a class) some good mental attributes - they usually think very consistently and can see very subtle flaws in arguments (especially common ones (it gets frustrating)). They also solve really tough problems which means that their ideas about problem solving (probably pretty central to the question of "what is intelligence?") are probably good, assuming they're self-reflective.

yelsgib··on Ask cperciva: Are great mathematicians born or made?
What is "intelligence?" Can we separate it from society's conception of it? Can we state a computational definition rather than a definition in terms of satisfaction of cultural standards? We undervalue a lot of mental attributes - consistency of thought, sensitivity to subtle differences in concepts, patience, self-reflection, the ability to "go meta" etc. which cannot be detected by the rough and rigid abstract problem solving required by low-level Math (e.g. the Math problems which would qualify prodigies).

I am highly turned off by the idea that we can't "become smart" after an early age. I feel like I "got smart" after I started playing go, I feel like I "got smart" after I learned category theory. I feel like every year I get smarter - and not smarter in the sense of "having more knowledge" but smarter in the sense of being able to solve larger classes of problems, and more complicated problems.

and c.

yelsgib··on Ask cperciva: Are great mathematicians born or made?
People vary in mental attributes. Let's get this out of the way right now. It -has to be the case-. We should obviously remain agnostic about what these attributes are (for instance, I would be hard pressed to say that "good memory" is even genetic because it is hard to disambiguate "memory software" from "memory hardware" in the brain).

Cultures screen for genetic attributes at a young age. This is not necessarily a good thing, but it just happens to be the case. Attractive children are treated differently. "Bright" children are treated differently. "Slow/inattentive" children are treated differently.

The sum of genetic attribute and cultural reaction to that attribute produces higher-order attributes which are consumed by new cultures, etc.

There is an academic culture of Mathematics. To participate, you need to have had the right experiences (enabled by the right genetics, pre-conditions, and cultural/socio-economic starting-point). People like MIT's Daniel Kane or Reid Barton were made-and-born.

So no, you can't become part of the culture of mathematics if you're not. Sorry, they're very picky. They also have a lot of resources (people to talk to, seminars to attend, journals which are expensive) which you can't have if you're not in the club.

Another unfortunate thing is that new math research really has to be presented in terms that "old math" can understand. E.g. constructivist mathematics struggles to get widespread approval. Adoption of ZFC axioms seems arbitrary in some senses (the C part).

So what does it mean to do "good" research? You need to create a result and argue it. Creation requires resources, argument requires facility with standards and ears to listen. Without acceptance into the community, you have neither.

That's one definition, anyway.

Do you just want to develop truth for yourself? Do you want to understand math deeply?

The fact is that there are many people who are extremely gifted in terms of genetic skills, who can do good math, but who don't quite "fit the mold" (trivial example: people with tremendous visuo-spatial reasoning abilities vs. people with tremendous pure-abstraction symbolic-manipulation abilities). These people can still do good math. They just have to do it largely on their own and they may have trouble communicating it with others.

In short, it's insanely complicated and has to do with the marriage of genetics and -culture-, not nurture, per se. If you want deeper insights into this question, I recommend you look at the history of mathematics and mathematicians.

---

Anyway, if you want a good example of a non-stereotypical mathematician, I recommend you look at the autobiography of Grothendiek. Good read.

yelsgib··on Mobaganda - Propaganda For Your Friends
What stage of release is this in? Are there any significant changes coming up?

In particular, I don't see any attempt to prevent spam. I'm not even talking about purely bot-generated spam - I mean, I just submitted that "Ghandi Christ" (email abcd@efg.hij) will not be coming to the following event:

http://mobaganda.com/rev2party

Which I found on google.

I don't really know/see how you can fix this problem. As I noted, captchas won't work.

On a completely unrelated note, I also really long for search and the ability to make an event "searchable/unsearchable".

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THAT BEING SAID, I think this is a really wonderful idea. If you can get it to "work" without sacrificing any simplicity I will definitely be using this.

Anyway, these are some random guy's first impressions. Good luck, yo!

yelsgib··on Ask YC: Help Me With A Math Problem
http://en.wikipedia.org/wiki/Lambert's_W_function

This seems related.

yelsgib··on Wall Street fears for next Great Depression
I think this could be the source of a lot of interesting discussion w/r/t startups. In particular, I'm interested in people's opinions regarding the influence that this will have on the ability to create startups in the US in the future.

I am (was?) planning on starting a company with a few friends when I come back to the US this September - will this still be feasible? What sort of impact can I expect this sort of event to have in terms of getting funding/etc. Do you suggest that I just scrap the whole intention to create a startup and try to buckle down and get a job (in case the economy gets really bad)? Should I consider leaving the country?

I expect that most of the answers will be "things will be bad" or "it will be hard" - but I guess I'm looking for something more concrete/specific (if possible?). I'm pretty naive about matters concerning such large scale systems as the US economy/etc.

yelsgib··on Ask YC: What is your favourite paradox?
http://en.wikipedia.org/wiki/Prisoners_and_hats_puzzle#Count...

"In fact, even if we allow an uncountable number of different colors for the hats, the axiom of choice provides a solution that guarantees that only finitely many prisoners must die."

This is by far the craziest result coming out of AOC.

yelsgib··on PG on trolls
Perhaps the reason that people troll (or take part in any sort of asshole behavior, really) is that they don't have anything better to do. Hear me out.

Hacker News is a "forum" whose main purpose is getting people to talk about/think about/post links to information related to startups. It has a very explicit purpose and to this end I would not expect it to be "infested" to the extent of a lot of other forums.

For instance, would we expect to see a lot of trolls on a forum devoted to advanced topics in theoretical math? "Orbifold cohomology is so much better than Hopfschild cohomology!" No. No, we wouldn't. A serious, well-defined, topic begets serious discussion.

This is the real problem with reddit, digg, etc. - there's no clear GOAL. Like, there's no -reason- that people shouldn't be assholes. What are they getting in the way of?

It's like if you opened the doors to your house and just held a "general forum." At first, discussion would be great (it's just your friends). Later, discussion would get worse (it's your friends' friends). Eventually it would degrade into the biggest losers who have nowhere to go sitting around and making fun of all the fun they're not having out in the real world (outside the house).

I agree with pg's sentiments that the architecture/rules of hacker news make it a much more intelligent, even (gasp) friendly forum, but I also think it's the community. They keep coming back because they have active interest. They have active interest because hacker news has established as its goal the provision of things of interest.

As always, I might just be woefully naive about human nature; but things seem so simple!

yelsgib··on Ask Hackers: Are you planning to do your startup in Arc?
Not only do I plan to do my startup in Arc, I've already decided to use holographic storage to do my backups (it's big, you know).
yelsgib··on How to Do Philosophy
Consider any "vocalizable concept" X. There are 4 directions you can move from X.

"Meta" - you can ask the set of questions "what can we say about claims about X?"

"Anti-meta" - you can ask the questions "what can X say about other things?" (make X a meta-concept of some other concept)

"General" - you can ask the question "do there exist generalizations of X?" (commonly known as abstraction, although the term is ambiguous - generalization is more precise)

"Specific" - you can ask the question "do there exist instances of X?"

Answering questions in these 4 directions gives you information about what you really want to know - what is X? What is "true" of X?

Philosophy is exploration and characterization of this "idea space." Nothing more. Nothing less. Very useful, if people would only do it once in a while.

---

Quick example:

"What is free-will?" = X

Meta:

Does free-will correspond to a thing? What classes of things is it in? What are our intuitions? What can we meaningfully say about free-will?

Anti-meta:

Suppose we define free-will well. What concepts does it enable? Are those concepts meaningful?

General:

Are there generalizations of free-will? How about just plain old "will"? What can we say about "will"? How about "freedom?" What's that?

Specific:

Are there any hard-and fast examples of free will? Are there any "thought-experiments" we can perform to try to shake out our intuitions? For instance, if everything were systematic/deterministic, what would this imply?

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My claim is that this method is useful for getting terms to be well-defined in the way that PG requires of math. You just keep doing this sort of analysis over and over until you get down to essential definitions.

Best to start from the bottom, though.

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