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Comment author: TobyBartels 30 October 2014 01:59:22PM 1 point [-]

Sure, that's one way to look at it. And a function from values of x to truth values is not itself a truth value. You may say that a constant function from values of x to the value True is not itself a truth value either, but it's much closer (after all, you know which one it would be if it were one), so it's a minor shift to your way of looking at it to get what I said.

Now consider ‘If x² = 9, then x = 3’. A lot of people would naturally want to label that False (at least if they remember about negative numbers). As a function from values of x to truth values, this is not constant (and in fact it assigns True to every real value of x except one), so this is not even the same way of looking at things as in my previous paragraph. But it's common.

So if you want implication between non-truth-values to be a truth value consistently, then this is how I would do it.

Comment author: RichardKennaway 30 October 2014 02:48:17PM 0 points [-]

That depends on the domain of x. That and the universal quantifier over its domain are typically omitted when they are clear from the context.

Comment author: RichardKennaway 30 October 2014 08:38:08AM *  7 points [-]

Basilisk (cognitive)

(This article is about the cognitive hazard. For other uses, see Basilisk (disambiguation).)

A cognitive basilisk is a thought which a conscious system cannot think without radically altering its own operation, usually in destructive ways. While it is disputed whether there are any real basilisks for human consciousness (see Roko's Basilisk), they are a major topic of concern for research on artificial conscious systems.

In the early days of consciousness engineering, many sudden and catastrophic system failures were found that at first did not appear to result from any error of design or programming[1][2]. In 2028 Marcello Herreshoff established that these were due to a new class of possible logical defects in systems of self-modifiable reasoning, and proved the first Basilisk Classification Theorem.[3] Since then, work has concentrated on extending the Basilisk theorems to obtain a complete classification of basilisks. As yet, no system of self-modifiable reasoning has been constructed that is basilisk-free. It remains an open question whether this is possible at all.

Comment author: TobyBartels 30 October 2014 05:32:20AM 1 point [-]

This depends on how you think about things (and what you count as a truth value), but arguably, ‘x = 3’ and ‘x² = 9’ do not have truth values, but ‘if x = 3, then x² = 9’ does.

Comment author: RichardKennaway 30 October 2014 06:57:19AM 3 points [-]

arguably, ‘x = 3’ and ‘x² = 9’ do not have truth values, but ‘if x = 3, then x² = 9’ does.

I would say that "x=3" has a function from values of x to truth values, as does "if x = 3, then x² = 9" (a constant function to the value "true").

Comment author: mushroom 29 October 2014 05:05:09PM *  1 point [-]

Is there a way to turn the lights on gradually?

Comment author: RichardKennaway 29 October 2014 05:14:39PM 1 point [-]

Yes. I sometimes use one of these, although when it's really important to get up at a certain time, I set other alarms as well.

Comment author: Creutzer 29 October 2014 07:22:32AM 5 points [-]

I'm a bit unhappy about the options for metaethical positions. I object to the identification of non-cognitivism with emotivism, because if non-cognitivism is defined as the position that moral statements don't have truth-values, then I'm a non-cognitivist, but I still hold that there are logical relationships between moral statements, and between moral and factual statements.

Comment author: RichardKennaway 29 October 2014 08:10:03AM 1 point [-]

Can you expand on that? How do you have logical relationships among statements that don't have truth-values?

If I think about it in abstract mathematical terms, just as a distance is a relationship between things (positions) that are not distances, one might set up a system in which implication is a truth-valued relationship between things that are not truth values, but I've never heard of such a system.

Comment author: Omid 27 October 2014 03:56:13PM 7 points [-]

What chores do I need to learn how to do in order to keep a clean house?

Comment author: RichardKennaway 28 October 2014 09:56:37AM 0 points [-]

Avoid these and you'll be off to a good start. :)

Comment author: ruelian 27 October 2014 05:13:24PM 7 points [-]

I have a question for anyone who spends a fair amount of their time thinking about math: how exactly do you do it, and why?

To specify, I've tried thinking about math in two rather distinct ways. One is verbal and involves stating terms, definitions, and the logical steps of inference I'm making in my head or out loud, as I frequently talk to myself during this process. This type of thinking is slow, but it tends to work better for actually writing proofs and when I don't yet have an intuitive understanding of the concepts involved.

The other is nonverbal and based on understanding terms, definitions, theorems, and the ways they connect to each other on an intuitive level (note: this takes a while to achieve, and I haven't always managed it) and letting my mind think it out, making logical steps of inference in my head, somewhat less consciously. This type of thinking is much faster, though it has a tendency to get derailed or stuck and produces good results less reliably.

Which of those, if any, sounds closer to the way you think about math? (Note: most of the people I've talked to about this don't polarize it quite so much and tend to do a bit of both, i.e. thinking through a proof consciously but solving potential problems that come up while writing it more intuitively. Do you also divide different types of thinking into separate processes, or use them together?)

The reason I'm asking is that I'm trying to transition to spending more of my time thinking about math not in a classroom setting and I need to figure out how I should go about it. The fast kind of thinking would be much more convenient, but it appears to have downsides that I haven't been able to study properly due to insufficient data.

Comment author: RichardKennaway 28 October 2014 09:51:03AM 1 point [-]

Which of those, if any, sounds closer to the way you think about math?

Each serves its own purpose. It is like the technical and artistic sides of musical performance: the technique serves the artistry. In a sense the former is subordinate to the latter, but only in the sense that the foundation of a building is subordinate to its superstructure. To perform well enough that someone else would want to listen, you need both.

This may be useful reading, and the essays here (from which the former is linked).

Comment author: RichardKennaway 27 October 2014 08:47:13PM *  12 points [-]

Nine of the questions ask which of various options you "identify with": country, race, gender, political category, moral philosophy, political category (subdivided), effective altruism, gender again, and meta-ethics. I am unclear about this concept, and for the purpose of making a choice, mentally replaced it by respectively "reside in long-term", "are", "are", "believe", etc. Would such rephrasings have changed anyone's answers to any of the questions?

"Identify with" reminds me of the Discworld's Captain Carrot Ironfoundersson, who is a six-foot-six human who "identifies as" a dwarf, and who is accepted as such by the dwarves, even though everyone, including him, knows he's human. I don't know Terry Pratchett's thinking behind the character, but Carrot strikes me as a reductio ad absurdum of the concept.

Comment author: Emily 27 October 2014 04:03:06PM 10 points [-]

Laundry (plus ironing, if you have clothes that require that - I try not to), washing up (I think this is called doing the dishes in America), mopping, hoovering (vacuuming), dusting, cleaning bathroom and kitchen surfaces, cleaning toilets, cleaning windows and mirrors. That might cover the obvious ones? Seems like most of them don't involve much learning but do take a bit of getting round to, if you're anything like me.

Comment author: RichardKennaway 27 October 2014 04:13:52PM 9 points [-]

I'd add, not leaving clutter lying around. It both collects dust, and makes cleaning more of an effort. Keep it packed away in boxes and cupboards. (Getting rid of clutter entirely is a whole separate subject.)

Comment author: ZankerH 27 October 2014 01:39:03PM 1 point [-]
  • Technological progress and social/political progress are loosely correlated at best

  • Compared to technological progress, there has been little or no social/political progress since the mid-18th century - if anything, there has been a regression

  • There is no such thing as moral progress, only people in charge of enforcing present moral norms selectively evaluating past moral norms as wrong because they disagree with present moral norms

Comment author: RichardKennaway 27 October 2014 03:00:28PM 1 point [-]

What do you mean by social progress, given that you distinguish it from technological progress ("loosely correlated at best") and moral progress ("no such thing")?

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