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The use of maths
Warning: this is an extremely long discussion (25 printed pages), starting with the use of maths, and digressing into discussion of post-modernism and philosophy.

The Editor
By Chi Kin Ho (P1942) on Tuesday, February 01, 2000 - 08:41 pm:

Well, I think a lot of people consider maths as a subject that is to do only with numbers. In fact, I think maths means a lot more than this.

If you think about it, the whole world is written in a mathematical language, in a sense. For example, physics, which is one of the subjects that helps explain natural phenomena, is all about equations. E=mc2, F=ma, these are all famous equations that help to explain the world and the universe we live in. Guess what is an equation? Merely a form of maths!

Moreover, if it wasn't maths, how on earth do we build bridges, create computers, and put people on the moon? Now you tell me how maths is not useful!

By Sean Ferguson (P2104) on Thursday, March 02, 2000 - 12:55 pm:

You're right, but I'd say Maths is also useful because it makes us think and it's useful as well because some people, probably including most people who use this site, find it fun. If people enjoy something, do they really need a reason?

By kwatkins on Saturday, March 11, 2000 - 09:23 pm:

Maths is also a universal language for communicating across international barriers - if there wasn't a mathematical language then it would be really hard to talk about some of the discoveries made to build bridges, create computers, and put people on the moon etc. Now you tell me how maths is not useful!

By Matt Daws (Mdpd2) on Wednesday, March 22, 2000 - 04:12 pm:

If you're interested, get hold of and read "The Number Sense" by Stanislas Dehaene. He's a biologist who has done work on numeracy in humans: he presents evidence that babies can count and reason in a mathematical sense long before they can talk. In fact, one of the first things that we can tell about objects in the world is the *number* of them; this is before we have an idea of shape, colour etc. It's quite fascinating, and shows that number sense, if not mathematics, is an intristic part of our species.

By Han on Thursday, March 23, 2000 - 12:55 pm:

I think Maths is an interesting subject but not all the time do we need to know all the things that we are learning.....does anyone agree?

By Clare Nicholson (P1732) on Thursday, March 30, 2000 - 09:42 pm:

Maths is important, but not that many people in life are going to use half the things that people learn in school. Numbers as such are almost as important as words:
e.g date of birth, time, change, measurements.
But there are several things we don't have to know.

By Julian Steed on Friday, March 31, 2000 - 06:29 pm:

Maths (in a similar way to philosophy) is one of the few academic pursuits in which it is possible either to work on problems or to expand the frontiers of knowledge whilst sitting in an armchair or in the bath. As a frustrated philosophy graduate, who also enjoyed maths at school, but is now "condemned" to a legal career to earn money to pay the bills, I find fiddling with maths problems is an excellent way to keep the mental cogs greased. But you can't have the "consolation of mathematics" any more than the "consolation of philosophy" without doing the groundwork early on. And believe me, it's a whole lot easier to do the learning before age 21!

By Mac2 on Monday, April 10, 2000 - 10:59 am:

Perhaps the use of maths is like the use of any other language. It depends on the users. The communicator and the communicant. It's bound to be useful in different ways for different people.
Ther are maths jokes, maths fiction (lots of it) and maths poetry etc.
Joke:- Tortoise and the Hare
Poem:- eip
Anyone know some others?
However for a classroom of year 9s how can they be convinced it's worth their time?

By Matt Daws (Mdpd2) on Monday, April 24, 2000 - 01:50 am:

Having been a year 9 at some previous point in my life, I have to say that I imagine most year 9's would question why school in general is worth their time.

A slightly less flippant (though no less true) remark would be to ask why learning anything is important? Most of us will never use most of the English we were taught at GCSE, never mind A-Level. I read novels, though a lot of people don't even do this, but I don't have to know how to write a critical essay on them to enjoy them (though it probably adds to my enjoyment that I do know something about critic). Similarly geography, history, science etc.

However, I for one believe that it's important we do have as wide a possible knowledge of, well, the world around us I guess. This especially applies to history, geography, science etc. Though mathematics underpins so much of science etc., it would seem silly to teach one without the other.

On the other hand, Julian is quite correct in saying that you need the basics to get going. Quantum Mechanics, say, might be deeply mathematical, but you'll need probably 4 years of maths to get close to the cutting edge; whereas to explain in words (say in a New Scientist magazine), people with A-Levels should find no problem understanding it. So there is a large gap between what is feasable to teach in schools, and the cutting edge applications of maths.

That is not to say we should give up trying at all times to motivate maths. You can do a great deal of practical maths in pure and applied with GCSE or A-Level standard. Simple mechanics, prime numbers, graph theory etc. etc. are all very interesting, but easy to state, and start to understand.

Hmm, I seem to have wondered off topic. Oh well, a final remark. Last week's Guardian education supplement carried the results of a survey, carried out at train stations, on what departments at universities should be closed, if funding suddenly became short. To my surprise, Maths came 2nd only to English as the *last* department to be closed! People obviously think mathematics is very important. Pity it's not funded better...

By phil on Wednesday, July 12, 2000 - 10:27 pm:

It's worth adding that the study of maths represents, in some sense, the history of civilisation. Geometry and trigonometry were born out of necessity; number theory through pure intellectual curiosity at a time and place (Greece) when some learned souls had the space to freely develop these (now valuable) tools.
When faced with the question "but what's the use ...." I often include this culture aspect in my response. I tell the pupils that they are ENTITLED to sample the greatest certain body of knowledge ever assmebled by humankind - it is their right and they should welcome the experience.
Falls on some deaf ears but it does make an impact with others, especially if you routinely include cultural/historical allusions in your lessons

By Marcus Hill (T3280) on Monday, September 25, 2000 - 08:28 pm:

One of the problems with explaining the "use" of maths, especially the kind that gets researched at universities, is that it tends to be difficult to explain in any depth what the research is about to anyone who has not had a lengthy mathematical education. In many other fields, one can at least put the topic of ones research (say, using lasers to clear clots from arteries safely) into words which anyone can understand.

By Diana Stirling on Saturday, October 21, 2000 - 04:57 pm:

I think the biggest problem here is with the question itself. In my mind, math is no more a separate topic than art, or English, or science are separate topics. I teach dance, art, English and math! To me, everything is patterns. Once a person learns how to discern and create patterns, vast regions of understanding appear in what was once an entirely uncharted landscape. Are tesselations art? Ask Escher. Are they geometry? Ask the geometry teacher. Are polyrhythms art? Ask the dancer or the musician. Are they math? Ask the creative mathematician. What is composition in visual art? What is proportion? Is math language? Ask the computer programmer, the animator. And what is chaos?

It has been said that the next generation will change careers 3 to 5 times in their lifetimes. It becomes apparent that the most important skill an individual can acquire is the ability to learn. Our students need to know this. They need to practice learning in all areas of academic pursuit. They need to understand that in math, as in all endeavors, the pursuit of an answer is more important that the answer itself. They need to understand that problem solving is one of the most crucial of life skills, both within & without one's career.

When it comes to the practical aspects of learning math - the multiplication tables, formulas, etc., which students may find tedious, remind them that, long before they learned to read, they had to learn the alphabet. Learning the alphabet doesn't seem to have anything to do with reading. The letter "a" has no meaning, in & of itself, and is certainly a far cry from a novel or a philosophical work. Conversely, the novel remains incomprehensible to those who do not know the alphabet. The child doesn't demand to know how learning the alphabet is going to help him or her later in life, and we feel no need to justify the teaching of it.

By A.C. Smith on Friday, November 03, 2000 - 01:05 am:

The use and purpose of math is beyond important. Its many concepts may be difficult for many to grasp, but the mere attempt to grasp these concepts is what sparks the thought process and opens doors for creativity. This thought process leads to frustration for some, but by the time frustration is reached, the mind has already been opened, and to at least some extent, enlighted; which is the purpose of education.

By kate on Wednesday, November 22, 2000 - 08:56 pm:

I am a 15 year old girl in my last year of school. I know you may not think that I'm mature enough to be saying this but I personally don't find maths important, of course I know that it is but I really do struggle with the subject and find it impossible to learn. And considering that I want to study preforming arts when I go to college do I really need to understand maths? And I honestly don't see the point in doing revision for exams when the whole point in doing exams is to test what you know, not what you can remember for a day or two, even though I revise anyway as I know I need the knowledge to gain the grades I just don't see the point.

By Anonymous on Monday, December 11, 2000 - 09:55 am:

we (two 15 year old girls)think that maths is important but schools do not make learning maths fun. It seems all algebra,but we think that it would be of more use to us if we learnt more general knowledge instead of things we are probably going to have forgotten by the time we are 20! Maths is important for people going into businesses but do we REALLY need to know how to find the hypotenuse of a triangle? Maths is seen as the most boring subject, but it could be made to be one of the most interesting if we didn't have to do pages and pages of algebra!

By Dan Goodman (Dfmg2) on Wednesday, December 13, 2000 - 12:47 am:

Anon, I completely agree. I'm doing maths at university now, but when I was doing my GCSEs I was in the "slow stream" (i.e. the class for people who aren't good at maths) because I had no interest in the subject (at the time I wanted to go to art school after school). I'm pretty sure that the reason I wasn't interested was that it was taught in such a boring way (I remember one class where the teacher told us to work out the area under the curve y=x2 by dividing it into 10 trapeziums or something like that). Unfortunately for everyone, algebra is really important if you want to be able to do anything with maths. Some of the most important and most boring courses I've done at university have been advanced algebra. It's somewhat similar to having to read the Canterbury Tales and Beowulf if you do English at university (written in middle and old english I think). Some people like it, but for most people it's just something you have to do.

By Anonymous on Tuesday, December 19, 2000 - 01:52 pm:

I love my maths lessons at school. My teacher always seems to be able to show us how we can use most topics outside of school even down to the obvious one - being able to check your salary. I appreciate for some maths might seem boring but perhaps part of the problem could be down to the teacher and how they teach - i.e with or without enthusiasm. Also people are different in lots of ways. We each have our own likes and dislikes and so some will either love it or hate it. I hope to study maths at university and had it not been for the interesting lessons and the obvious enjoyment my teachers have over their maths things might have been different.

By katherine on Friday, December 29, 2000 - 04:45 pm:

I work as a general practitioner (doctor)and use maths daily. I think maths is more important nowadays for everybody. Essential skills we need apart from basic ones are an understanding of risks and probabilities and fianancial matters. If you are not sharp at maths, people particularly banks and financial advisors will rip you off repeatedly. I don't think this was such a problem in the past. Nowadays people have to calculate risks and have a knowledge of probability as they will need to make their own decisions about medical treatment. For example a 15 year old girl may wish to work out for herself the risks of contraceptive choices based on several sets of statistics. Venturing into the modern world as an adult without good maths armoury is like walking out blind. Studying maths probably also makes your brain grow. The more years one studies the less likely one is to get dementia, statistics say.

By Sarah Hutchinson on Thursday, January 18, 2001 - 04:26 pm:

As a trainee teacher I have realised that Mathematics is an essential part of the education of young children. Without it, they are cut off from a large part of the society in which they live. From the basics of money to measurements, children need to be confident users in all areas of maths if they are to have equal access to the opportunities available to them as they grow up.

By Janet Moorhouse on Tuesday, August 14, 2001 - 11:47 am:

The study of Maths nurtures a valuable life skill - the ability to solve problems using only the available resources.

By bhart on Wednesday, September 26, 2001 - 11:31 am:

In a world that is constantly changing, it is reassuring to know that there are still some things that don't....some absolutes.

What is more permanent and stable than:
2 + 3 = 5?

It might be written:
II + III = V

or

10 + 11 = 101

or

2 + 10 = 12,

but the fundamental concept of number is an unchanging absolute. Pretty neat, huh?

By Henry Sealey on Thursday, October 18, 2001 - 10:02 am:

I think that maths is a great subject because instead of testing what you can remember it tests how you use your mind to get to an answer. It also trains the mind and builds a useful skill which is needed in all parts of society.

By Brad Rodgers on Friday, October 19, 2001 - 05:08 am:

I think math is great because it is at once accessible yet totally sublime. Need more be said?

By Tim Martin on Monday, October 22, 2001 - 10:06 pm:

Brad, I think more does need to be said, if you are intending to convince anyone else. In what way is maths "sublime"? What does "accessible" mean when applied to something as nebulous as the whole of mathematics?

Henry, what skills are you gaining from mathematics exactly? Are they useful skills? Why should testing how you can use your mind be "better" than testing what you know?

bhart, I agree that 2+3 = 5 is as near as we can get to an absolute, but what does it actually mean? Does it correspond to anything in the real world? If not, what use is it?

By Brad Rodgers on Tuesday, October 23, 2001 - 02:52 am:

I suppose you're right that my comments are not really convincing for someone already possessing an aversion towards math; I just didn't think that too many people falling in that category would be perusing through a website devoted entirely to math. In case they are though, I suppose I'll explain my quote:

Generally, when something is very elegant, it is available to only a few. But math is available to anyone. Not many other things are like this.

I don't think explaining the reasons why something is useful will convert anyone to its side. Most people realize that math is useful. But they also realize that computers can perform math far more accurately and far far more eficiently than them. This, I think, is the large failure of how math is taught. The way to actually dispel some of the antipathy towards math would be to show people some of its more interesting problems (which is apparently harder than teaching a group of kids disliking everything about the subject at hand...)

Sorry that was so garbled,

Brad

By Tim Martin on Tuesday, October 23, 2001 - 11:38 pm:

If everyone here agreed with you, there would be no point in having this section of the message board. In any case, I believe that arguing, even with people you agree with, often helps to clarify and develop your own ideas and can be very beneficial.

I'm interested that you say maths is available to anyone - in the broadest sense of mathematics you are of course right, but surely one of the satisfying things about mathematics is doing something which hasn't been done millions of times before by other people, i.e. doing original research. This is certainly not available to anyone.

What are you particularly thinking of which is elegant, but not accessible? Music and art are often compared with maths (somewhat falsely, IMO) but both of these are at least as accessible as mathematics, and probably more so.

I think a lot of the apparent apathy towards mathematics among school children is caused by apathy towards the education system in general. I have my own views on why this is, which wouldn't be appropriate here, but the bottom line is that it's difficult to motivate children in any subject. Again, poor teaching in mathematics seems to me to be a result of problems in the education system as a whole.

By Dan Goodman on Wednesday, October 24, 2001 - 12:03 am:

I have to disagree with Tim's "it's difficult to motivate children in any subject" - I think it's enormously difficult to stop children being inquisitive and motivated to learn. Rote learning, learning facts disconnected from meaning, on the other hand, is not a natural desire of children. Emphasis on this, to some extent in all subjects, but particularly in mathematics, is the problem. OK, maybe not "the problem", but a big one.

I agree with Brad. Having to learn formulae and algorithms is mind numbingly boring, and it probably makes the teachers feel as helpless and depressed as the kids. Children should be shown the more interesting parts of maths, to the extent that this is possible.

For example, the finite Ramsey theorem proof R(3)=6 would be a good example. It can be stated and proved in entirely intuitive terms, parties and so forth, with pictures and colours in a way that even relatively young children could get a handle on. To anyone who hasn't seen this proof, there should be a conversation about it in the Asked NRICH archive.

By Tim Martin on Wednesday, October 24, 2001 - 12:27 am:

What I meant to say and didn't was "In the current system teachers don't manage to motivate children in any subject" - I didn't intend to imply that children are not naturally motivated to learn, merely that the education system knocks that all out of them. I don't, however, agree that it is difficult to stop children being inquisitive and motivated to learn - all the children I was at school with had been totally put off learning by the age of 10, if not before.

Perhaps part of the problem is the emphasis on getting the "right answer" and getting high marks in exams, brought in by the national curriculum, SATs and now the national numeracy strategy (don't start me on that).

An interesting point I heard recently is that until relatively recently (1600ish IIRC) school work wasn't marked numerically - not just that they didn't do it, but the concept of assigning a number to the quality of a piece of work did not exist. Since then we have moved to the other extreme, where almost nothing else but a numerical mark is considered valuable. Of course, it's difficult for a numerical mark to correctly express concepts such as how creative or neat a piece of mathematics is, so that ceases to be valuable.

[Current practice is now moving away from giving scores in favour of constructive comments. - The Editor]

I don't think that introducing concepts of formal proof to children is going to be easy. Of course, the Ramsey proof you mention is easily expressed in a manner which has meaning to children, but it's difficult to know whether they are actually understanding the deeper concepts or not. Is it even a desirable thing for school children to understand proper mathematical proof? Is it going to be helpful to them in later life?

By Brad Rodgers on Wednesday, October 24, 2001 - 04:16 am:

I think the knowledge of a proof is going to be far more useful than simply memorizing a formula or an algorithm. Mind you, this needn't be a rigorous proof from set theory, just something that flows logically and is convincing. Perhaps if people actually saw logical thought in school they would then actually try to think independently. At current, I'm not even sure most people know they can think independently.

Furthermore, showing people that there is indeed such a thing as logic would end all this postmodern-relativism rubbish present throughout schools today. Let people draw there own conclusions about reality instead of telling them that nothing is ever wrong. Perhaps then, some actual social progress could occur. (this paragraph is intended to spark controversy; its been a while since I've had a good debate)

Concerning the desire to learn, however, I totally agree with Tim. I would say that while everyone has an inate desire to learn at birth, usually before someone even enters school their outlook on questions is already predetermined. Children are continously taught to not question authority. This makes the parents duty monumentally easier, and thus it almost always is taught. But what is this really teaching children except to not act independently, or perhaps even not to think independently (and logically) at all?

I think Tim is also right in placing the blame largely on getting correct answers. This entirely eliminates any creativity or independent thought (and real logic as well) from schools. It just makes the poor souls memorize and repeat. Perhaps this creates some poor sort of Machiavellian stability in schools and thus in life, but it eliminates all sort of progress anywhere.

"I'm awfully glad I'm a Beta, because I don't work so hard. And then we are much better than the Gammas and Deltas. Gammas are stupid...I'm so glad I'm a Beta"

Not too far off...

Brad

By Tim Martin on Wednesday, October 24, 2001 - 06:20 pm:

How exactly is knowledge of a proof going to be useful to the average person? When do you use mathematics in your daily life?

Could you explain in a bit more detail what you mean by "postmodern-relativism"? I think I know what you mean but I don't want to waste everyone's time by getting the wrong end of the stick.

Actually, I think the amount which children are taught to respect authority has decreased a lot in recent years. Whether the lack of respect for maths is a recent phenomenon or not I couldn't really say. What I do believe strongly is that the general attitude of society is shifting away from independent thought, and I agree with your comments about "Brave New World". I strongly recommend you or anyone else interested in this sort of thing read Neil Postman's "Amusing Ourselves to death", in which he puts just that argument in a much better way than I ever could.

By Dan Goodman on Wednesday, October 24, 2001 - 06:42 pm:

"I don't, however, agree that it is difficult to stop children being inquisitive and motivated to learn - all the children I was at school with had been totally put off learning by the age of 10, if not before." - Just because it happens to everyone doesn't mean it wasn't difficult to do so. A great deal of effort has gone into making the education system like it is now, years of development. I would agree that emphasis on quantitative achievement is part of the problem.

Proofs are not useful in themselves, but understanding proofs does develop the ability to think logically. Perhaps more important than understanding proofs is understanding the logic behind the mathematics; understanding the process that leads to an answer and why it does rather than just knowing a process which leads to an answer. As part of an overall education strategy I would also include things like philosophy which develop the art of reasoning with things which are not rigorously defined. The two complement each other rather well I find.

As to "all this postmodernism-relativism rubbish", I'm quite sympathetic to it myself. But I'd also like to know exactly what you mean by it before I comment. :-)

By William Astle on Wednesday, October 24, 2001 - 06:52 pm:

I'm sure children are taught to respect authority more than ever it's just the nature of the authority is changing slightly and is slightly subtler. I doubt that the degree of 'respect' for maths is much changed either (though I could be wrong). Its very difficult to make a independent comparison when your whole expererience is contempory.

By Brad Rodgers on Wednesday, October 24, 2001 - 07:53 pm:

By postmodern-relativism, I'm of course talking about the doctrine that no one is really right or wrong, everything is just a "worldview". And even if these views are unsupported, illogical or even contradictory, they still are not wrong, and all too often, at least in school, you can't even tell people why the ideas are contradictory. I'm all for people being able to form their own views about the world, however, I cannot accept that all these views are correct, and I certainly cannot accept that any debate of these views is entirely repressed in schools. Once again, I'd like to itterate that I do think people should be able to develop their own conclusions, to write about them, and I think there is often no real proof for an ideology, but certainly, warrant and explanation for these views should be encouraged. I'll try to post some examples what I'm talking of when I get home, which should give you both a pretty precise basis for understanding what I'm talking of, and also of my bias (which I'll admit is readily apparent).

Brad

By Jenny Peters on Wednesday, October 24, 2001 - 08:48 pm:

As a Y11 pupil at a secondary school I feel I should enter a student perspective on the limitations set by exam syllabuses and student respect for authority.

Unfortunately I feel I should argue that I believe most students at my school have either no or very little respect for their teachers and their teacher's authority. I would not say it is that the nature of authority is subtler but that the authority of teachers is at serious risk of collapsing as their power to combat appalling behaviour is gradually removed.

In regards to previous comments about the limitations put on mathematical creativity by strict syllabus details I would sadly agree and say it is true that in all subjects we are taught what we need to know to pass exams - not what we need to know to develop a clear, rounded understanding of the subject.

This is not the teachers fault. There are some things on the syllabus that would be very hard to make inspiring. However, most maths teachers I have encountered are trying their best to make it relevant and are trying to make it interesting. I have been priviledged enough to encounter teachers who have encouraged me to be creative and suggested new subject areas to pursue. I have been lucky enough to meet teachers who have willingly given up their own free time to explain principals of proof and number theory not encountered under the syllabus. I feel very lucky to have been given the chance to explore fascinating subjects I may never have otherwise met.

Sadly though, many of my fellow students would have strong objections to giving up some of their time to find out how inspiring and exciting maths can be and they thus remain stuck in the cycle of 'this is pointless and boring', while the under appreciated teachers struggle to make finding areas beneath graphs with trapeziums exciting enough to keep a class of 15/16 year olds (with their notoriously short attention spans) interested.

I think this is wrong but there is very little that can be done about it - the freedom of the teacher is a thing of the past!

By Dan Goodman on Wednesday, October 24, 2001 - 09:08 pm:

Jenny, thanks for that post, it's good to get a contemporary school perspective, my view is somewhat outdated, although judging by what you say, not that outdated. Curiously enough, when I was writing my previous post I almost mentioned finding areas beneath graphs with trapeziums as an example of a mind numbingly depressing and boring thing that school students are forced to do. I have a vivid personal memory of doing this for y=x2 between 0 and 1. The teacher mentioned that the exact answer was 1/3 but refused to go into any more detail about why. I was really annoyed. Although in that particular case the teacher really wasn't very good, in general I agree that it's not the teachers fault, many of them (most?) are trying to do the best they can given the constraints on them.

By William Astle on Wednesday, October 24, 2001 - 09:18 pm:

I didn't express myself very well. What I meant was, those with the power no longer choose to use schools to teach children to 'respect' their authority. Perhaps I was a little naive; perhaps it has become a little less necessary to teach respect for authority since authority has become stronger. Possibly 'respect' in some schools is not 'what it was' fifty years ago. I'm also sure that there is a lot of propaganda designed to hide the real problems.

By Tim Martin on Wednesday, October 24, 2001 - 09:23 pm:

Dan, I don't think it makes sense to say that the effort put into the education system is evidence that it is difficult to prevent children from wanting to learn. The effect on children is just a side effect of the changes made for other reasons - if a deliberate attempt were made to prevent children from wanting to learn I don't think it would be very difficult at all.

I think you're right that logic has to be combined with other things in order to be useful. An over-reliance on pure deductive logic can do more harm than good IMO, because deductive logic is relatively useless in areas other than maths. I certainly wouldn't advocate not teaching maths properly, but I think mathematicians tend to see it as being more important than it is - the fact is that it doesn't really make that much difference to most people's lives.

OK Brad, I think I see where you're going with postmodern relativism. I challenge you to tell me one thing, just one, which you know for absolutely certain (and I mean something outside of deductive logic and mathematics, since my understanding of Godel's theorem isn't good enough to avoid embarassing myself in an argument).

Jenny, I think my experience at school up to year 11 (which wasn't all that long ago) was rather similar to your own. Unfortunately, I think the problem lies deeper than just the teaching of mathematics, and I can't offer any solutions.

By Tim Martin on Wednesday, October 24, 2001 - 09:30 pm:

In response to the post that Dan made while I was writing the last one, I remember my A-level teacher telling us what the integral of e^(-x^2) over the real line was without proof, which annoyed me somewhat. Two years later I got to see a proof in 1A vector calculus, and I remember thinking "What a boring, dull and rather pointless proof" as I copied it into my notes without caring.

Not knowing things can be frustrating, but that doesn't necessarily mean learning is always fun.

By Brad Rodgers on Wednesday, October 24, 2001 - 10:42 pm:

I'm a year 10 student in a public High School (in America, if it matters), and generally, while I would say that students are generally disrespectful to teachers (when the teachers aren't around of course), they would never think of questioning a teacher or an adult's authority: a law is a law because it's a law. Some of my teachers have students do ridiculously stupid things, but narry a student ever asks them why.

I agree that teachers should have more freedom in what they teach though. With standardized tests so omnipotent, they have to simply make sure the bottom of the barrel students end up passing, and thus (at least it has been my experience) neglect entirely students with real ability and/or drive.

Tim, I don't think I know too much to be a priori. However, I do know that I exist, that others exist and that we can all think. I take this for granted. And I also take for granted that a viewpoint is nothing without some sort of justification using that aforementioned thought available to all.

Since I promised examples, here is one example that happened about a month ago: A teacher in my English class was talking about mythology. I offered that as most themes and even most images are archetypal when there is no reason for them to be, the motivation for the characters is at least partly the Jungian collective unconscious, that these wise old men and sun gods in myths are probably inate imagary in our species. She said 'perhaps that's true, but that's not my worldview' or something to that effect. When I asked her after class whether she wanted to hear some of the support for Jung, she simply reitterated that we had different worldviews, and that I'd just have to accept that. She wouldn't give an indication as to why she felt differently, just that she did.

I think that is terrible, that a person would go so far as to denounce an idea, but not give any reasons why, and then say that the idea "is still right".

One more thing that I'm sure is true: there is only one reality, and that we as humans experience this reality, therefore can know this reality. While what I took for granted above may be academically open to doubt, this latter is not. This does not mean that we do know everything about reality. I'm still open to discussion concerning what actually composes reality or what laws reality obeys simply because there is no known proof for these things, and perhaps there never will be. But the only way we as a human race are ever going to get closer to knowing this reality is to start accepting that some "worldviews" must have at least some backing. "Everyone has a right to their opinion, but no one has the right to be wrong in their fact"

By the way, an excellent article that every sentient being should read is "Student as Nigger" by Jerry Farber. It was written in the 60's, and uses language to challenge traditional authority (hence the title), but it contains some great thought and excellent analysis of a situation probably more present in today's high schools than colleges.

And finally, as for my challenge (though I alrady included several examples), one thing I know to be definitely true is "I think therefore I am". How could it be false?

Brad

By Tim Martin on Wednesday, October 24, 2001 - 11:53 pm:

I'm afraid I don't have time for a full reply right now, but I'd just like to point out that you've rather shot yourself in the foot by admitting that you take the matter of your own existence for granted. You don't have any proof.

"I think therefore I am" is fine as an implication, but it merely reduces the problem of proving that you exist into one of proving that you think. Which I don't think you have done.

I'll reply to the rest of your post (which is very interesting) later, since I've got lots of work to do for tomorrow.

By Dan Goodman on Thursday, October 25, 2001 - 12:19 am:

Tim, I quite liked that proof (you did the ò e-x2dxò e-y2dy one, right?), I thought it was pretty neat.

Brad, the problem is that none of the statements which you have no doubt about are of any use in most of the cases to which relativism is important. Less significantly, they're only true to the extent that most people would agree with them (and even then, not all people).

Actually I think I probably agree with you to a certain extent. Using relativism as a means to dodge debate is no good at all. However, using it as a means to analyse social and political structures can be quite fruitful.

The example you gave of your teacher refusing to debate a point with you is disappointing, but maybe she hadn't heard of Jung and didn't want to be shown up in front of one of her students. If that were the case, I wouldn't be too hard on her, Jung isn't exactly mainstream (although anyone who had done an English Literature degree probably would have heard of him).

By the way, the article that Brad mentioned is available online at http://ry4an.org/readings/short/student/.

By Tim Martin on Thursday, October 25, 2001 - 12:50 am:

To be honest, I can't remember what the proof was. I didn't say it wasn't neat, just that I didn't find it interesting. I have no reason to believe the average GCSE student would find proofs interesting if they were shown them. I think part of this is to do with the fact that maths is more enjoyable when it is not too difficult (a level which is dependent on the person concerned). People have no right to think that because they find something enjoyable it should be forced on others.

I agree that relativism shouldn't be used to dodge debate (at least in part - if someone doesn't want to debate they don't have to, but they can't duck the debate and claim to have won, as some do). However, I do think that it is impossible to completely prove anything, and that it is possible to have different self-consistent world-views.

In terms of your teacher's behaviour, it's obviously annoying but don't forget that teachers are human. There are times when I don't feel like debating things (mostly when I've got too much blood in my caffeine system).

By Jenny Peters on Thursday, October 25, 2001 - 06:05 pm:

I would just like to comment on what Brad said about pupils not daring to be disrespectful to teachers' faces in his American school.

I have friends of my age in America who I regularly talk to and they all say that the teachers they encounter are generally treated with far more respect than I would say some British teachers are. I think what may also add to this is that teaching is treated as a more valued career in America than it is in England.

Here, if a pupil doesn't like what they are told to do they will debate it, they will refuse, they will hurl abuse until ultimately they are thrown out of the lesson. Next lesson they will be back and we will go through the whole charade again. This isn't just when they don't want to do something that seems stupid - this is when they don't want to participate in the lesson becauese they don't see the point.

- OK negative impression I'm giving there, but I've just returned from school after a day of the above and have seen it all in a rather negative light.

On a more positive note my maths class was very good and despite it not being on the syllabus our teacher gave us the derivation of the quadratic formula - what is even more interesting is that following his explanation people began to think and ask further questions about the algebra encountered. It was very good to see and gave me at least a little hope that all is not lost! It seemed today that students are most inspired when they are pushed a little and given room to think!

By Brad Rodgers on Friday, October 26, 2001 - 03:59 am:

While I can appreciate different "self-consistant" philosphical systems in the sense that they should be even encouraged, I think that most of the differences in these philosphies is generally tautology, and that, if they are contradictory they shouldn't be "left alone". Furthermore, I do still think that there is only one true reality (ei. Axiom of Choice may yields truths as either true or false, but it is certainly true or false, not both). Similarly, I hold faith that this reality can eventually be proven. I also hold axiomatic that even self-consistant realities have evidence or a lack theorof, and thus, if there is no evidence for a "worldview", it shouldn't be thought true either. And lastly, I certainly hold it true that only one system of ethics exists. In this respect, I do not think relativism is beneficial in social structures. I think that one reality must be deduced (the one with the most evidence), and that reality should be used as a standard for ethics.

It's fine with me if people want to ignore facts, and diregard inconsistencies, so long as it makes them happy and harms no one else. But the moment they destroy someone else's felicity because of unfounded beliefs, I'm afraid there beliefs should not be tolerated at all.

I do once again though, think there is only one reality, and I'm sure that nature is not so incorrigible as to make this reality ultimately indeterminable.

By Dan Goodman on Friday, October 26, 2001 - 09:45 pm:

Brad, you may like to believe that there is a consistent well defined notion of truth, but it is just that, a belief.

With regards to the axiom of choice, it has been proven that ZF+C (Zermelo-Fraenkel axioms for set theory with the axiom of choice) and ZF+~C (ZF with the axiom of choice negated) are both consistent (assuming ZF consistent). One of the consequences of this is that we cannot construct a set (within ZF) with cardinality strictly between Aleph 0 and c (the cardinality of the reals).

Now, set theory, specifically ZF, is an entirely man made construction and has no direct relation with reality. It serves as a useful model at a macroscopic level (and this itself is an ill defined concept and depends a great deal on the nature of perception for example, which is sufficiently subjective to make it a useless tool for a discussion of objective truth) but there is no reason to suppose that it corresponds with any aspect of reality at all, in any way. So, even if you hold the belief that "there is only one true reality", you cannot deduce from this the truth or otherwise of the axiom of choice; neither in theory nor in practice.

Considerations like these (there are similar such considerations for ethics or any other area of thought) are what suggest the idea that there is no consistent and universal way to define truth.

What we can do, in terms of ethics, is to try and persuade people that they should behave in certain ways if they believe in certain principles. In terms of morality, we can try and persuade people that they should hold certain principles. The former task is better defined in some sense because it is a bit like deductive reasoning. The latter task is ill defined in this sense in that it involves appealing to example, indirect persuasion, experience of life, some innate psychological properties of people, etc. In other words, the philosophical study of ethics and morality is really just an exercise in persuasion.

To pretend ethics and morality are the study of truth as applied to human relations is just sophistry - a subtle method of persuasion based on a widespread, unfounded, misunderstood cultural notion of truth. It also probably serves a psychological purpose for those who study ethics and morality. Because they too have this ill defined notion of truth it would be painful for them to admit to themselves that their lives' work is an exercise in persuasion rather than discovering universal truths.

Well, that's my opinion. I hope I've managed to persuade you - after all, that's the purpose of discussion. Feel free to persuade me otherwise. :-).

By Brad Rodgers on Saturday, October 27, 2001 - 12:13 am:

I wasn't really proving anything with AC, just using it as an example.

I would agree with you that the best method to convince others of ethics is by persuasion based upon previous life experience they've had, but that is not the way I try, at least, to convince myself of an ethical proposition, nor does your method in fact validate an idea, it simply confuses people into support. Ethics should be based solely upon something everyone can agree upon, not emotions felt by one person, nor by the way it has been engrained in one's mind by culture.

In ethics, the first assumption to be made is that other people actually exist, and that they can experience happiness and sorrow. We next define that happiness is good and sorrow is bad. (this is an assumption that happiness exists, which is not already unstated). From this, I think most ethics will follow.

As an end note, if we as a human body don't agree on a few simply principles, in what sense

"Those are my principles, and if you don't like 'em, I have others."- Groucho Marx

By Brad Rodgers on Saturday, October 27, 2001 - 12:17 am:

By the way, without my first assumption, such a thing as ethics does not exist. With it, ethics must exist.

By William Astle on Saturday, October 27, 2001 - 12:23 am:

According to your ethics it must be moral to murder familyless friendless depressives. :-)

By Dan Goodman on Saturday, October 27, 2001 - 12:45 am:

That's OK, I was just using the Axiom of Choice as an example too, to illustrate the idea that there are statements which do not have a truth value.

For the moment, I'll stick with the notion that the study of ethics is the art of persuasion by another name. Suppose I don't agree that happiness is good and sorrow bad. Suppose, for example, and it is not a far fetched example, that in some cases I prefer to be sad than happy. Would it be ethical to force me to be happy against my will? Perhaps you could refine the idea to be that satisfaction is good, so that if I achieve what I desire I am satisfied and this is good. But this begs the question, what motivates my desire and should the formation of my desires not be considered as part of ethics? We could go on all night about this. We could talk about whether or not happiness is a meaningful, well defined notion, how it could be defined in a culturally independent way, whether or not this definition corresponded with something we think is good, whether or not satisfying desire is good, whether desire can be defined in a culturally independent way, and so on and on and on. If you stuck to your guns and wanted me to believe that happiness is better than sadness, then you'd have to try and persuade me of that fact. This cannot be done by rational argument alone, although rational argument almost certainly would form part of your persuasive toolkit.

Also, I'd take issue with the idea that any ethical theory follows from a definition of happiness as good and sorrow as bad. For example, would you quantify happiness? Would you then try and maximise total happiness, average happiness, minimum happiness or what? Assuming happiness can be quantified (a highly dubious proposition at best), is there a sensible way of deciding between different distributions of happiness (even if you only have an ordered scale of happiness rather than a numerically quantified one)? To the last part, the answer is probably not and I've written a good, mathematical, article explaining why which I'll provide a link for if you're interested?

By the way, there are moral theories which do not utilise the notion of happy or sad, good or bad. For example, Robert Nozick's "Anarchy, State and Utopia" (which I'm in the process of reviewing, unfavourably) in some sense proposes an ethical system whereby what is sought is not "happiness" or "good" but freedom to act, within a sphere of liberty whose boundary is defined by others coordinate sphere of liberty, without forceful coercion. So it is possible for ethics to exist without your first assumption.

We seem to have strayed from "What is the use of mathematics?" - oh well. :-)

By Brad Rodgers on Saturday, October 27, 2001 - 01:36 am:

Your points are good. To avoid linguistic problems with happiness, perhaps it would be beneficial to call one fullfillment of one want to be an "A". Therein, we realize that the more A's we have, the better off we are. This is both quantifiable and well defined. (1 want is tricky to define, I'll write about that in a later post)

Obviously, we cannot only use rational argument to form a philosophy, but I do think that a philosophy may be developed from a number of axioms that no one can disagree with. I think Spinoza has done a reasonably good job of this (though, he sometimes seems to get mixed up with semantics, a problem not really recognized on a conscious level until logical positivism).

I'll try to write out a compelling argument for the system of ethics I outlined above with A's in a later post

William, if the person is as you described, really wants to die, and stands no chance for recovery from the depression, is it really wrong to kill him? Thankfully I think this is pretty trivial as people can indeed recover from depression, but food for thought...

Brad

By Sean Hartnoll on Saturday, October 27, 2001 - 01:36 am:

To jump in at this point, seing as the conversation seems to have digressed somewhat, just a few words about postmodernism and truth and all that. I think Brad you will find it really quite hard to get around the postmodernist arguments. All your arguments, for a start, will be written in words, but what do these words mean? If you look them up in a dictionary they will be defined in terms of other words and therefore ultimately self-referential. So how do we know what the words mean? Where is the meaning? Ultimately the body of language and even maths must therefore go outside of itself and you need some kind of feeling for what things mean that will based on your experience of the world. But your experience is conditioned by the culture you are in and the particular experiences you have had. Not to mention the fact that most sensory data is hardly objective. So in some sense your words will never mean quite the same thing as some-one else's. This is the idea of hermaneutics, the idea that the validity of your arguments is restricted to situations in which you are speaking to other people who have a similar enough set of concepts for the conversation to make sense. For instance, an extreme example due to Wittgenstein "if a lion could speak, we still wouldn't be able to understand it", because the experience of being lion is to different from the experience of being human. So it really is quite difficult to find somewhere to start building from, axioms if you like, because we won't necessarily agree as to what they actually mean.

Sean

By Brad Rodgers on Saturday, October 27, 2001 - 06:05 am:

Can't words be defined perfectly well by pictures? Obviously somethings are not defined culturally, as mathematics is nonetheless very specific, and developed by a number of cultures at the same time.

As far as the lion comment, philosophy is I suppose not entirely objective. In fact, I would go so far as to say it is entirely subjecttive. I merely desribe and reason about what I have seen. I have no way of knowing if that's what another person has seen, or even if that person has seen at all. I'm inclined to say it's a reasonable assumption to assume that other people do in fact exist (quite an epiphany, eh.) and that they observe in largely the same way as I do, and thus I think any real philosophy can get around postmodernist traps by choosing sufficiently small axioms and going from there.

Whatever happened to Occam? The simplest explanation is most likely the true one. On top of this, I know that a) I live in one reality, b) that other people around me seem to act as though they live in this reality too, e.i. they say red when I see red, they agree upon my notions of logic, and so on. These three combined surely suggest that other human's experience the same reality as I do, or else they do not exist at all.

To move to the lion example, what basis do you have for suggesting that there experiences would be entirely different from mine. Sure, they walk on all fours and have a tail, but I don't see any reason to suggest that they fundamentally view reality differently from me. It of course is obvious that if they do indeed have a different transcendental view of the world, they do see a different reality emerge, but I don't see a reason to think that they have an entirely different conception of the world.

I was going to type more, but it's getting very late, and I'm likewise getting very tired. I'll try to type some more tomorrow.

Brad

By Brad Rodgers on Saturday, October 27, 2001 - 06:23 am:

I've just realized that simplicity is a culturally defined thing, so perhaps I should change my statement to whatever happened to Occam's amended razor, if there is no basis for an idea, it generally is not true.

By Sean Hartnoll on Saturday, October 27, 2001 - 12:22 pm:

Pictures are not objective either, for a start they various symbols carry different connotations to people, or else they are a direct reference to a sensory reality that is not objective. Also, have you seen the picture of the duck-rabbit? (it's a picture that can be seen both as a duck or a rabbit depending how you look at it). What Wittgenstein does for instance, is talk a lot about how we actually learn things, a lot of it is through pictures and so on, and the whole point is that none of this learning is objective. A picture will always carry implicit value judgments.

It is of course a reasonable assumtion that other people exist and are similar to ourselves. The point is that you can't put that assumption on a rigurous basis. In fact, you can't even formulate in a way that you can be sure that everyone will agree on what it actually means.

So various cultures did develope maths and indeed aspects of language in parallel. And this is a good indication of some kind of external reality. But only some of the postmodernists actually entirely reject external reality. It's more about saying that you can't have big interpretational schemes (so for instance Lyotard defines postmodernism as the "rejection of metanarratives", where a metanarrative is some overarching theory, social or scientific, that claims to hold the truth about the way the world functions.). And one way of rejecting these big explanatory systems is to point out that there is dependence on particular use of language. And these langagues and mathematics are also slightly different, espite similarities. Anyone who knows two languages well will see that there are phrases that you just can't translate properly, because the spirit of them is intimitly tied up with the language and culture as a whole. And the only way you can understand it is by living there, but this is then language going outside of itself.

ps. I don't actually agree with postmodernism. But I think one should acknowledge that their critique of other philosohies is not one that you can get round easily, if at all.

Sean

By Brad Rodgers on Saturday, October 27, 2001 - 07:49 pm:

It perhaps is difficult to disprove postmodernism, however, it is also difficult to disprove the notion that there is no such thing as logic. The latter is of course contradictory in its basis, but it is impossible to point that out.

However, I think I may have a pretty good critique of postmodernism. I start with postmodern assumptions:

I see some subjective reality when I view the universe. Other people exist in this reality. They are functioning in this universe. Now, for others to function in this universe, they would have to see what I see to some large extent. Furthermore, these people act as though they see what I see. In fact, I have no way of knowing for sure what they see, but all that I can gather supports that they see what I see. Now, in what sense do their reality differ from mine. In no way can I determine that it does not. Certainly then, if their fundamental conception of the world does differ from mine, they are entirely superfluous to me, as they are not someone I am observing, nor can I observe them as they are not a part of my reality. In what sense do they exist (to me)then?

I can't believe that we have a dependence upon language either. Words are not thought or ideas, they merely reflect these ideas. If words were ideas, then how would it be possible for me to learn a new language in which those phrases you mention have no meaning in my previous language. If anything, language has a dependence upon ideas.

Mind you, the postmodernism you mention is a far cry from what I originally complained about, the type used in my school. You see, in my history class, the validity of an idea is judged not by the thought that went into it, or anything like that, but by the size of the empire it came out of. Furthermore, in other classes, postmodern ideas are applied to places they don't even make sense in. For example, a person might say of evolution, 'it's only an idea, and who am I to say that it's right or wrong?'.

Brad

By Brad Rodgers on Saturday, October 27, 2001 - 07:54 pm:

Also, Dan, I'd like to see that link.

Thanks,

Brad

By Sean Hartnoll on Saturday, October 27, 2001 - 09:05 pm:

Brad, I agree with most of what you said, especially that is completely ridiculous in many cases to treat things that are manifestly true as "only ideas", such as evolution. So it is certainly true then that postmodernism can be used as weapon to defend all sorts of inconsistent and downright wrong ideas, and it can also lead to silly conclusions such as the nonexistence of other people if you take it too far.

However, the flipside (and this is certainly what the founding fathers in Paris would have had in mind) is a critique of authority that is quite powerful. It looks at hidden assumptions in the way we speak. Or not so hidden, for instance various postmodernist feminists have looked through classic philosophical texts - supposedly "objective" - and claimed that there is a masculin bias in the use of language. So if you like a basic claim of postmodernism is that language is not something neutral, and that therefore any "explanation" of the world will implicitly be biased, because it will be phrased in language.

And I'm not sure I agree with you that language and ideas are so distinct, what is accessible to your thoughts is clearly limited by the concepts you have to work with, which are linguistical. This works in maths too, the sort of things you can think about are often limited by the mathematical vocabulary you have.

Sean

By Dan Goodman on Saturday, October 27, 2001 - 09:19 pm:

Brad, the link to the article is http://www.bbc.co.uk/h2g2/guide/A568613. Hopefully the application to our current discussion will be clear, let me know if not.

Will write some comments on the discussion a bit later, must do some work at the moment though.

By Brad Rodgers on Saturday, October 27, 2001 - 11:16 pm:

I think I agree that language is not neutral, and that different statements can be said to bias a person one way or another (the whole premise behind politics, right?). But this is merely statements, how a paper is written, and not a perception to reality. Perhaps postmodernism can dictate that there are different confusions of reality; I agree with this. But, these are merely confusions, not realities nor validities. And, we are not concerned with confusions when talking of reality. If a person is seeing the same thing I am, then they can talk of reality with me. Reality is not written in semantics after all. It is entirely spatial.

The critique left open to this is that all people have these confusions. But this does not mean they must. Rather, by thinking with actual ideas, and by using spatial logic (something empirical), we can refer to reality as it is.

By Dan Goodman on Sunday, October 28, 2001 - 01:53 am:

A few comments:

Brad, the problem with your "A"s is that "1 want" is not easily definable. If I want a banana and an apple, it's easy to define "1 want". Suppose, though, that I want a fruit salad. I'd prefer a fruit salad with kiwis, bananas, apples and oranges, but what if there are no kiwis available. My want for a kiwi, banana, apple and orange salad is going to go unfulfilled, but my slightly lesser want for a banana, apple, orange and melon salad could be fulfilled. You have to have some sliding scale of wants, I can't imagine that you could quantify this.

"but I do think that a philosophy may be developed from a number of axioms that no one can disagree with." - I'll believe it when I see it, I've not found any well defined axioms that everyone agrees on yet. I look forward to seeing your "A"s system of ethics.


Quote:

Brad: Mind you, the postmodernism you mention is a far cry from what I originally complained about, the type used in my school. You see, in my history class, the validity of an idea is judged not by the thought that went into it, or anything like that, but by the size of the empire it came out of.



This is annoying, of course, but try and set aside your, understandable and justifiable, irritation that you're being taught such a load of crap, and look at what you are taught at school from outside for a moment. Isn't it interesting that this happens? Why does it happen? These are the sorts of questions that make cultural relativism and things worthwhile and interesting. For example, apparently something like 80% (I can't remember the statistic, all I can remember is that it is a large percentage) of Americans think that the phrase "From each according to their ability, to each according to their need" comes from the Constitution (or was it the Declaration of Independence, I can't remember). As you probably know, it actually comes from the Communist Manifesto written by Karl Marx and Freidrich Engels. I leave it as an easy exercise for the reader to consider why so many Americans aren't taught this.

Quote:

Furthermore, in other classes, postmodern ideas are applied to places they don't even make sense in. For example, a person might say of evolution, 'it's only an idea, and who am I to say that it's right or wrong?'.



Well, strictly speaking they are right. It is only a theory, and one that it would be difficult to falsify (which Popper would have us believe means it isn't science at all). Although most rational people don't believe in the literal truth of the whole adam and eve thing, you can go too far in the opposite direction and assert the unquestionable truth of evolution. This is dangerous because our understanding of evolution is quite political. For example, Richard Dawkins proposes a gradual model of evolution whereas Stephen Jay Gould proposes a punctuated model. The debate rages on and on, but it is interesting to note that the proponents of the Dawkins model are mostly politically right wing, whereas the proponents of the Gould model are mostly left wing. So, evolution is less straightforward and more political than it seems at first.

Finally, "Reality is not written in semantics after all. It is entirely spatial." But what does "spatial" mean? Most people's intuitive notion of space is that of Euclidean space, but general relativity suggests that space is actually curved. So if we had a language that expressed meaning entirely spatially then we would have had a language based on an erroneous model of the universe (at least until 1910 or whenever GR was formulated). Who is to say that our current notions of space and time are any less wrong than the Euclidean one?}
By Brad Rodgers on Sunday, October 28, 2001 - 03:08 am:

While I agree with you that it can be interesting to look at why people believe what they believe, but all too often this is taken too far. Many times people, especially those people worth reading about believe something because of a genuine thought they've had, not some underlying cultural movement or stagnancy. I think this is the way that most people think, but people like Russell, or Newton, we can't analyze their actions like this. I think that you agree with me here though, so I'll move on.

When I talk of evolution, I of course talk about it in the general sense, that change occurs in a species. I don't see how someone can argue with this, once they accept that mutations occur in a species and that those better adapted will better survive. This is able to be disproved (though I'll squeeze in that Popper's a moron). Also, I'm sure that your correct in your left->Gould, right->Dawkins statistic, but any idea why this would be?

When I talk of spatial reasoning, I'm largely talking about things like Venn diagrams, and positions. This will adapt to whatever geometry you choose (though will not be intuitional).

Alright, the want's: I think most of the time, there is no need for a distinct quantification. THe system of A's I speak of really isn't very much an advance, but merely a way to get around the measurability problem. We define a negative number of A's to be wrong. This isn't very self explanatory, so here is a paper I wrote on abortion about a year ago. It was written for a speech where I had to state contentions, and I've edited it to have less gabble in between the lines as it's rather long to start with.

Principle A- we should always do what is good for society, good being rather undefined at this moment.

Principle B- It is good to have a some happiness- happiness being defined as an emotion brought upon by a fulfillment of wants.

First, we must define evil as "the lack of good" and may be replaced by it in any sentence.

It follows from Principle B that when peoples whose wants could’ve been met are not met, and someone else’s wants are not met either, it is not a good thing-it is evil. Call this proposition A.

Similarly, it follows from Principle B, that when there isn’t happiness, which simply means there are no wants, there is not an action good or evil, so long as the action concerns solely that with no wants. This is analogous to the use of a rock. Solely as the rock doesn’t cause unhappiness for another, anything may be done with it.

Denote contention I as "If there is no happiness or unhappiness, then actions concerning solely that medium are not good or evil"

Now, let us define the condition of consciousness by “recognition of self”. Now, in order to have a want, one must want something for oneself. Thus, one must recognize oneself. Thus, to have wants, one must have consciousness. Therefore, to have happiness or unhappiness, one must have consciousness.

Denote contention II as “To have happiness or unhappiness, one must be conscious”

It is a scientific fact that consciousness originates in the cerebellum, which is part of the brain. Therefore, and denote this as contention III:
“if something has a consciousness, then it has a brain”

But, from the statement of our resolution, we are specifically aborting something without a brain. From III, it therefore has no consciousness. From II, it therefore experiences no happiness or unhappiness. And finally, from I, actions concerning solely the thing we are aborting do not concern good or evil. Therefore, if we solely consider aborting the fetus before it has a brain, we are not doing evil nor good. But, the mother must be put in the picture. She, before having an abortion, wishes to have an abortion. Therefore from proposition X, by forbidding her to have an abortion, we are doing evil. So we have arrived at this heavily disputed antithesis: It is not morally wrong to abort a fetus before the brain develops.

In some cases, this system doesn't work, though, not because it would yield a falsehood, simply because it doesn't work. But I think ethics may be developed from this though.

Now, you mentioned using the ideal of freedom for a basis for ethics. Isn't this just a byproduct of happiness though?

I haven't yet had a chance to look through your link, but intend to do so soon.

Brad

By Dan Goodman on Sunday, October 28, 2001 - 04:52 pm:

Brad. One suggestion that someone made to explain the left=Gould right=Dawkins thing was that socialists naturally prefer the idea of revolutionary change and right wingers prefer the idea of a gradual progress. Personally, I think that arguments a load of rubbish, but amusing nonetheless. I've no idea why there is this political divide, it might be entirely chance, people sticking by what other people on "their side" say.

I enjoyed your argument for why abortion is not wrong, it's roughly the same argument that I come up with when having a debate on abortion. How did it go down? I can see several places where your argument could be attacked, perhaps most importantly "It is a scientific fact that consciousness originates in the cerebellum, which is part of the brain." Comparisons with the belief (Descartes?) that the seat of consciousness is the pituitary gland would be inevitable.

I don't think freedom and happiness are necessarily causally related. For example, you could have happiness without freedom (consider the Betas and Gammas and their Soma habit in Brave New World). Similarly, you could have freedom without happiness (loads of literary examples of this I think). Nozick's point is that a system of ethics based on an "end state principle" (i.e. one in which you prescribe certain states as desirable and try to achieve one) runs the risk of being paternalistic and imposed. Brave New World is the obvious example here.

Finally, I don't think it's worthless to construct ethical systems based on fixed principles and so on. Far from it. I just think it is misleading and confusing to talk about them as if you were discovering a universal truth.

By Sean Hartnoll on Sunday, October 28, 2001 - 05:09 pm:

Actually, Dan I don't think that's the point about Dawkins and Gould. It's more to do with reduction to genes. Dawkins talks about people as computers "programmed" by genes and talks about DNA as discs of information whilst Gould has a less bottom-up approach (i.e. there is interaction between proteins and DNA right at start of embrionic development, and throught life there is a continual interaction between genes and the cell environment which can determine which genes are expressed etc.). So the point is that socialists tend not to believe in "human nature", and so they have problems with Dawkins. Personaly I have found interesting things from both of them.

Brad as for your system there are problems right from the start. For instance a certain ex. British Prime minister that I'm not too keen on famously said "there is no society, only individuals", so as far as she was concerned, your starting with concepts that don't actually mean anything. Similarly many neurologists would deny that "consciousness" exists as a concept. And then as you point out there is a certain fuzziness in the word "good". The idea of happiness as fulfilments of wants is also surely something some people would disagree with. Etc.

Sean

By Sean Hartnoll on Sunday, October 28, 2001 - 05:11 pm:

ps. I do basically agree with your argument though, but it couldn't be called watertight.

By Dan Goodman on Sunday, October 28, 2001 - 09:44 pm:

Sean, you're probably right about the Dawkins/Gould thing. Although the left/right split also applies in the continuous/punctuated evolution debate (which is, I think, a separate debate), your explanation of the political divide coming about from the debate about reductionism seems more likely.

Also Brad, why is Popper a moron?

By Brad Rodgers on Sunday, October 28, 2001 - 10:04 pm:

Oops, I typed that? Anyways, he just replaced induction with "Falsificationism", and the two were really the same thing. I certainly didn't mean that his works were without merit, just that most of his ideas had really already existed, he just renamed them. He was a bright man though, and I didn't really mean that he was a moron.

By Brad Rodgers on Sunday, October 28, 2001 - 10:15 pm:

By the way, I think I agree very much with your latest post, Dan. Certainly, in the lack of any proof for God, or really any watertight proof of anything being a priori, I don't think that anything should be heralded as the be-all-end-all truth. I do, though, believe that there is a be all end all truth in the sense that there is one reality, and that reality is determinable by things perhaps not a priori, but nonetheless sufficiently small axioms (like the axioms used in math).

By Sean Hartnoll on Sunday, October 28, 2001 - 11:23 pm:

Brad, I think inductionism and falsification are quite different, or at least the emphasis is on very different things. And that this is fairly widely recognised.

Sean

By Brad Rodgers on Monday, October 29, 2001 - 08:05 pm:

They do indeed emphasize different things, but they still in basic form are really one and the same idea. In order to falsify something, one must induct that it does not occur, or from induction gain a casual relation to disprove something. This is still induction, or so I was to think...

Nonetheless, I'd never before given little more that a casual glance at Popper, but I looked through the internet today, and some of his ideas, specifically that we learn through falsifying, not induction (while only an academic distinction) do differ from the induction school of thought.

By Sean Hartnoll on Monday, October 29, 2001 - 08:10 pm:

No, for something to be falsified it only needs to not happen once, so you don't need to use induction. Induction is the process of going from a finite number of examples to the general case. So what Popper is saying is that although you can never know something is true generally because it has only happenned a finite number of times, you can know that it is wrong on the basis of just one counterexample. And then he defines science as those statements which can in principle be falsified, which has no anologue form the induction perspective.

(there are still problems with all this, but that is beside the point here).

Sean

By Brad Rodgers on Monday, October 29, 2001 - 09:34 pm:

Popper believed one and only counterexample to be sufficient to disprove a theory? I suppose if that's what he believed axiomatic then that's what he believed axiomatic, but I don't think I can agree with that. I mean to assume that the theory would always test false, wouldn't you still be inducting in the sense that you are saying

one counterexample -> infinite counterexamples

Just as with induction of the true you say

many true examples -> infinite true examples

It's not exactly induction in it's ordinary form, but there is a tacit assumption of induction included.

If your making Popper's premise as axiomatic, then I suppose you can state it relies in no way upon induction, but certainly the principle of falsification can be a precipitate of induction, and thus is not really anything new.

Furthermore, Popper's claims as to what science can deal with simply confused matters. He offered a new definition of science, which people now mix up with the (support) = (roughly true) definition. This is entirely a semantic distinction, and is not an epiphany.

That's just my two cents though,

Brad

By Sean Hartnoll on Monday, October 29, 2001 - 09:51 pm:

It's simpler than that. Suppose I have the statement "all swans are white". Now, the inductivist approach is to say, well this is true because I have many white swans. Popper says that this is a scientific statment because it could be falsified the next time I see a swan. But I only need to see one black swan for it to be falsified. I don't need to induce that there are infintely many black swans. Of course this gets complicated because how do you falsify the statment "70% of swans are white"? But this is why his book hi several hundred pages long (Not that I've read more than the first 50 or so, it got kind of boring...).

Sean

By Brad Rodgers on Monday, October 29, 2001 - 10:43 pm:

Interesting. It's off topic, but in what way do we actually end up with a useful statement at the end of Popper's theory. We'll end up with something like 'at least one swan is black', which is not a statement that is scientific in the general useful sense. Perhaps science needs falsification to be tested, but in no way is science developed by falsifying ideas, if it were, we'd have very little certainty.

I'm sure a refutation exists for this, but still, isn't induction used in a sense in falsification? Particularly, I think it's used in that we induct that what we see, hear, detect with a microscope, etc. is actually consistent with other senses?

By Brad Rodgers on Wednesday, October 31, 2001 - 10:21 pm:

Dan, I've been rather busy lately, but I managed to read through the article you made. It's very interesting, however, the only application to measuring happiness that I could think of is that there is no way to measure what one thing makes one person happy. I'm not sure it limits the idea of a hedonistic calculus though.

Brad

By Dan Goodman on Wednesday, October 31, 2001 - 11:01 pm:

Brad, the point about Arrow's theorem is that there is no way to aggregate individual preferences. So if I would be happier in state A than I would be in state B, and you would be happier in state B than in state A, which state should we choose? Arrow's theorem says that, in general for an arbitrary set of states, a finite set of individuals, and a set of preferences for each individual, this question does not have a mathematically satisfactory answer. In some cases there is an obvious solution though. If every individual prefers state A to B, then society as a whole prefers A to B, so we choose A. It gets more difficult when people disagree unfortunately.