is mathematics crucial to understanding?

[Upchurch]

Originally posted by CWL

Originally posted by Upchurch

As an aside, I'd like to use this as a shameless plug for my ongoing (although, somewhat forgotten from time to time) crusade that an understanding of mathematics is crucial to understanding anything, including philosophy.

This is an interesting contention Upfunk, worthy of a thread of its own. As someone who is schooled solely within law and the humanities (thus having no credentials whatsoever within physics or mathematics), I for one am not certain that I can agree with that contention. If you want to explore the issue in a new thread I certainly would be eager to participate.
So start a new thread, I will.

Although not always obviously applicable, I assert that understanding mathematics is crucial to understanding the universe. Even if you are trying to understand it philosophically, that philosophy must take into account the mathematics.

For example, the discussion about "what is time" that was being had when CWL and I made the above comments, I gave what I felt were very precise definitions of time based on the mathematical/physical model. (There comes a point where you really can't seperate physics from math, ideas from one lead to new development in the other.) Some posters in that thread had difficulty understanding what was being said, I feel due to a lack of understanding of mathematics and, specifically, geometry.

Now sure we can describe things without the use of mathematics, but because language is impercise (sp?), the description becomes impercise. There is very little ambiguity in mathematics and it is because of that lack of ambiguity that I feel mathematics is crucial to understanding.

Does anyone agree or disagree?

[Franko]

Although not always obviously applicable, I assert that understanding mathematics is crucial to understanding the universe. Even if you are trying to understand it philosophically, that philosophy must take into account the mathematics.

Mathematics is based on Logic. Without Logic there is no math.

So obviously LOGIC is more fundamental to understanding reality than Mathamatics.

Furthermore, you haven't even defined what you mean by the term "Mathematics". What makes Math -- Math? Do computer languages (algorithms) count as 'Mathematics" according to you? What's the significant difference between a computer language, and the English language?

Mathematics is crucial to understanding- but I'm brainwashed because I have a degree in it, and one in statistics. :)

With that said, I don't mean you and cho' mama have to know how to solve partial differential equations... but rather that the ideas behind mathematics are so important- like someone said, it is the logic, the foundation, the mathematical reasoning that is truely important to learning.

[Akots]

Well actually, as a programmer, I can say that logic is actually programming... and programming, itself, is purely nothing but math. A very strange connection that... the realization that programming is ALL math, with a bit of text for interface.

I read a book once titled "Computers and the Imagination." A most unbelievably fascinating book, though I barely understood a lot of it. There is no denying that we live in a fractal world. We are, ourselves, fractal.

EDIT: On a special note, I'd just like to say that the single biggest influence to myprograming skills was the second time I learned trigonometry. So beautiful... :eek:

[Upchurch]

I worked on both philosophy and mathematics minors when I was in college, and I found I could apply methods from one to the other quite easily. Physics is really, in my opinion, the union of the two.

Like Whodini said, you don't have to have a degree in advanced mathematics to talk about things, but I do think you need the thought structure that mathematics provides. Also, if you're going to talk about "dimensions" or something like that, I think you really ought to know what you're talking about. (for example, you should know that a dimension, by itself, is not a place that you go visit.)

[Soubrette]

I totally agree Upchurch

Unfortunately my mind is very disorganised - I find with maths I have to be superorganised or I struggle.

And I have some weird intuitive ideas too :p

I need to work on my maths bigtime :)

Sou

Originally posted by Akots
Well actually, as a programmer, I can say that logic is actually programming... and programming, itself, is purely nothing but math. A very strange connection that... the realization that programming is ALL math, with a bit of text for interface.

I read a book once titled "Computers and the Imagination." A most unbelievably fascinating book, though I barely understood a lot of it. There is no denying that we live in a fractal world. We are, ourselves, fractal.

EDIT: On a special note, I'd just like to say that the single biggest influence to myprograming skills was the second time I learned trigonometry. So beautiful... :eek:

You've got it backwards. Programming is all logic.

One of the most enlightening experiences of my life was taking a computer class whereby we were forced to write programs in pure symbolic logic statements and then translate them into actual programs. It made me into a much better programmer to realize that the logic comes first and the trappings of the language come later.

[Upchurch]

Originally posted by Soubrette
I totally agree Upchurch
Maybe you shouldn't agree so fast. You may have brought up an interesting point without realizing it:
And I have some weird intuitive ideas too :p
What about intuition? That's something that I would say comes from out side the rigors of math or logic, but also aids in discovery.

Maybe it'd be more accurate to say that mathematics is crucial to understanding but not sufficient?

[Upchurch]

Originally posted by Akots
EDIT: On a special note, I'd just like to say that the single biggest influence to myprograming skills was the second time I learned trigonometry. So beautiful... :eek: Ah, mine was symbolic logic and the philosophy of math. both very fun subjects, espcially symbolic logic.

[Soubrette]

Originally posted by Upchurch

...What about intuition? That's something that I would say comes from out side the rigors of math or logic, but also aids in discovery.

Maybe it'd be more accurate to say that mathematics is crucial to understanding but not sufficient?

Only if the intuition is actually right - or at the very least on the right track - mine is way way of base :)

Plus I have this blindness when it comes to adapting formulae - if a formula has three parts and you can move them around to do different things - I have to memorise all three. I appear to be logically unable to deduce them:(

I think that's a practise thing too though :)

Sou

[Franko]

I read a book once titled "Computers and the Imagination." A most unbelievably fascinating book, though I barely understood a lot of it. There is no denying that we live in a fractal world. We are, ourselves, fractal.

Now you sound like an LD.

You're all over the place my little friend.

[Upchurch]

Originally posted by Soubrette


Only if the intuition is actually right - or at the very least on the right track - mine is way way of base :)

Plus I have this blindness when it comes to adapting formulae - if a formula has three parts and you can move them around to do different things - I have to memorise all three. I appear to be logically unable to deduce them:(

"mathematics without intuition is stagnet, intuition without mathematics is haphazard."

(appologies to A.E.) :D

[Franko]

You've got it backwards. Programming is all logic.

Isn’t Mathematics also All Logic?

One of the most enlightening experiences of my life was taking a computer class whereby we were forced to write programs in pure symbolic logic statements and then translate them into actual programs. It made me into a much better programmer to realize that the logic comes first and the trappings of the language come later.

So say 20 years from now somehow has a computer language that is almost indistinguishable from English. You could write a program in it, or you and I could have a conversation with it. How would that be any different than us having a purely mathematical exchange?

In other words, isn’t language already reducible to mathematics, we just don’t perceive it, because we don’t usually consider the underlying structure of language?

Think about it … who actually does differential equations on paper by hand in this day and age? When was the last time you did long division or multiplication without using a calculator? A calculator lets you avoid the steps in the process, but it doesn’t mean that the underlying process doesn’t still exist. So why is that any different for language?

Did someone say something? I could have sworn I heard something just now. Probably my imagination.

Originally posted by Upchurch
[B]



Although not always obviously applicable, I assert that understanding mathematics is crucial to understanding the universe. Even if you are trying to understand it philosophically, that philosophy must take into account the mathematics.


Understanding the what mathematics actually is is no less than pivotal in understanding the Universe.


(There comes a point where you really can't seperate physics from math, ideas from one lead to new development in the other.)


Ever more so as time goes by.

[Franko]

Did someone say something? I could have sworn I heard something just now. Probably my imagination.

very mature rebuttal. What is this "pledge week" for the cult of Atheism or something?

If I were going to take issue with the premise it would only be to say that the extent to which understanding relies on a knowledge of math appears to me to be the exact extent to which it relies on knowledge of logic. In other words since mathematics is an expression of logic, the underlying need is an understanding of logic rather than mathematics.

Of course this isn't true if the subject under discussion is mathematical in nature, such as the example of extra dimensions.

Originally posted by Franko


very mature. What is this "pledge week" for the cult of Atheism or something?

You know perfectly well why I have given up on you.

[Akots]

Originally posted by sundog
Did someone say something? I could have sworn I heard something just now. Probably my imagination.

In all seriousness, I'm sure it was just the wind.


Originally posted by sundog


You've got it backwards. Programming is all logic.

One of the most enlightening experiences of my life was taking a computer class whereby we were forced to write programs in pure symbolic logic statements and then translate them into actual programs. It made me into a much better programmer to realize that the logic comes first and the trappings of the language come later.

I do stand corected... I've spent too much time 'thinking' programming in my head. :) It's defeintely the application of logic and math, and it's too beautiful to see something given form and visible motion.

I remember once bringing up the topic of wether programmers were more or less inclined towards critical thinking... it's a little off topic, but I now wonder wether the "debugging" frame of mind is responsible for this; the analytical skills required to find errors in pure information.

What I wonder now is, is this "debuging" skill rooted more in logic, or mathematics? I always assumed logic... but mathematics is more solution oriented. I think.

As for Upchurch's comment... Philosophy of Mathematics? is that the history surrounding it's growth, or a philosophy about the concept of mathematics itself? I'm betting perhaps both, but you know what I mean.

EDIT: The above statement implies thati ever learned if programmers are more critical... i'm still not sure.

[Franko]

Sundog,

If I were going to take issue with the premise it would only be to say that the extent to which understanding relies on a knowledge of math appears to me to be the exact extent to which it relies on knowledge of logic. In other words since mathematics is an expression of logic, the underlying need is an understanding of logic rather than mathematics.

I agree with you completely Sundog.

Of course this isn't true if the subject under discussion is mathematical in nature, such as the example of extra dimensions.

Giving a triangle an extra side may be considered geometry and therefore mathematical, but it doesn’t make 4-sided triangles any more logical or any more real that imaginary extra dimensions.

[Upchurch]

Originally posted by Akots


As for Upchurch's comment... Philosophy of Mathematics? is that the history surrounding it's growth, or a philosophy about the concept of mathematics itself? I'm betting perhaps both, but you know what I mean.

Philosophy of Mathematics, the class, had to do with the philisophical underpinnings of mathematics. Set theory and that sort of thing. It was along the lines of "why does 1 + 1 = 2 and how can we prove this?" Despite it seeming obvious, the rigourous proof was rather involved as I remember. To be honest, while I loved the class, it was a bit over my head.

[fishbob]

...What about intuition? That's something that I would say comes from out side the rigors of math or logic, but also aids in discovery. Intuition is difficult to define.

Maybe intuition is just an internal quick look at evidence and formation of a reasonable hypothesis. Good intuition results in good success in predicting outcomes.

[gentlehorse]

Upchurch:
What about intuition? That's something that I would say comes from out side the rigors of math or logic, but also aids in discovery.

Maybe it'd be more accurate to say that mathematics is crucial to understanding but not sufficient?

I like it. Intuition is often underrated though it's absolutely necessary. The math helps us to see whether our intuitions have merit, at least as far as our maths will take us.

[MRC_Hans]

I would say that mathematics is a subset of logic. Everything in math is logical, but I dont think all logic can be expressed in math. Oddly, while being basically abstract, math is not well suited to handle abstract concepts, wheras logic is.

Math is strictly deterministic, logic can handle indeterminism too. None of them can handle intuition, hehe. Actually, Sou, I dont agree that intuition is only valuable when right, or at least, it is not always possible to know if it was right. What if you act upon intuition, and in the long run, the result is good? You cannot know if your action was the only one leading to a good result, or even the best one.

Mmm, I see I get a little philosophical, but then, this IS the R&P forum ;)


Hans

[Upchurch]

Originally posted by fishbob
Intuition is difficult to define.
Like pornography, "I know it when I see it." It is a bit of an abstract, isn't it?
Maybe intuition is just an internal quick look at evidence and formation of a reasonable hypothesis. Good intuition results in good success in predicting outcomes. I wouldn't even say it was that structured. You can formulate all the possibilities you can think of, but when you choose one to investigate on intuition, it's really a kind of gut reaction. It is for me anyway.

[Akots]

Hm... i get the feeling that Intuition is a calculated risk that ends up being correct.

if i suddenly feel like there's something wrong with the potato salad in my fridge, I open it up and look. If it's green and fuzzy, that's intuition. If it's fine, it's lunch.

Of course, sometimes something unrelated remidns me that the potato salad is very old... something reminds me of the day I met someone at the shopping mall, where I bought potato salad four weeks ago, and goodness... is it still good?

The more subtle and coincedental the chain of connections, the more intuitive it seems.

[Franko]

MRC:
I would say that mathematics is a subset of logic.

I agree with you up to here.

Everything in math is logical, but I dont think all logic can be expressed in math. Oddly, while being basically abstract, math is not well suited to handle abstract concepts, wheras logic is.

I’m not sure what you are saying? Can you give an example?

Math is strictly deterministic, logic can handle indeterminism too.

No. You’re Wrong.

In Logic things are either TRUE or FALSE, but not BOTH True and False, nor NEITHER True nor False. Indeterminism is the opposite of Logic. In Indeterminism things are NEVER TRUE or FALSE, but either BOTH, or NEITHER (something “other than” True or False (whatever that means)).

Computers are Deterministic systems, they are also entirely logical. An Indeterministic system would be like an anti-computer. (I guess that means a crystal ball, or a ring that makes you invisible???)

None of them can handle intuition, hehe. Actually, Sou, I dont agree that intuition is only valuable when right, or at least, it is not always possible to know if it was right. What if you act upon intuition, and in the long run, the result is good? You cannot know if your action was the only one leading to a good result, or even the best one.

Think so A-Theist? Intuition is far more Logical than you might imagine. Of course if you have “free will”, then I guess all of your consciousness would seem magical and utterly beyond comprehension …

[Franko]

Upchurch,

I just rescanned the thread, and i didn't see this, but ...

What is your precise definition of Mathematics?

[Upchurch]

Originally posted by MRC_Hans

Math is strictly deterministic, logic can handle indeterminism too.What about statistical mathematics used in thermodynamics and quantum mechanics? Those describe indeterminate systems.

Edited to add: Actually, anything with error bars is indeterminate because it can't be predicted exactly.

None of them can handle intuition, hehe. Yet ;)

[jj]

I will propose that philosophy is nothing but a branch of abstract algebra.

"nothing" meaning that it's a subset, rather than a judgement of value, please.

[Upchurch]

Originally posted by jj
I will propose that philosophy is nothing but a branch of abstract algebra.Ellaborate or support that a little maybe? I'm not quite following.

[Upchurch]

Originally posted by Akots
Hm... i get the feeling that Intuition is a calculated risk that ends up being correct. Maybe understanding is part objective and part subjective? My concern with this thread is that people embrace the subjective and forget about the objective.

[Akots]

Well... it's hard for me to elaborate on a comment like that. But here goes...

Just about any information you recieve or absorb is objective. it's what you do with it, or how you interpret it that is subjective; sometimes, a pattern is so clear and concrete, it's easily confirmed by others, no matter what subjective events brings those other people to the same fact.

Just because information is arrived at after a subjective train of thought does not make the information itself subjective. An intuitive train of thought can eventualy lead one to consider an objective event. The issue is wether or not one is willing to accept new objective data that disproves existing subjective data. I think a mathematics or programming base makes it easier to do that.

[Stimpson J. Cat]

A couple of comments:

Mathematics is a formal language for expressing logical statements. It is not the only possible one, either. In that sense, Mathematics can be considered a subset of logic.

As for intuition, I would say that intuition is simply a form of pattern matching. The brain is very good at matching complex patterns, and sometimes it can find relationships and correlations in cases where trying to work it out through formal logic would be extraordinarily difficult. On the other hand, it can also be easily tricked into picking out false relationships, or detecting correlations when none are really there. In short, intuition is a very useful tool for making educated guesses, but whatever your intuition tells you must be double checked through real logic, before it can be considered to be reliable.

Dr. Stupid

Originally posted by Stimpson J. Cat
A couple of comments:

Mathematics is a formal language for expressing logical statements. It is not the only possible one, either. In that sense, Mathematics can be considered a subset of logic.
Dr. Stupid

A very neat proof of this is that we use logical principles to construct mathematical proofs, not the other way around.

[Franko]

Stimpson:
A couple of comments:

Mathematics is a formal language for expressing logical statements. It is not the only possible one, either. In that sense, Mathematics can be considered a subset of logic.

Mathematics = a formal language for expressing logical statements.

Now that I can easily comprehend.

Stimpson: (continues …)
As for intuition, I would say that intuition is simply a form of pattern matching. The brain is very good at matching complex patterns, and sometimes it can find relationships and correlations in cases where trying to work it out through formal logic would be extraordinarily difficult. On the other hand, it can also be easily tricked into picking out false relationships, or detecting correlations when none are really there. In short, intuition is a very useful tool for making educated guesses, but whatever your intuition tells you must be double checked through real logic, before it can be considered to be reliable.

Well, giving credit where credit is due, you are a breath of fresh air in this thread Stimpy. I agree with your summary on this point as well.

So theoretically, a spoken language could potentially take on all the characteristics of what we normally would associate with “mathematics” (assuming it was a “formal language” (or “formal system”)) – would you agree?

[Upchurch]

Originally posted by Stimpson J. Cat
A couple of comments:

Mathematics is a formal language for expressing logical statements. It is not the only possible one, either. In that sense, Mathematics can be considered a subset of logic.True, but I would go one step further and say that it is the most commonly used formal language for expressing logical statements.
In short, intuition is a very useful tool for making educated guesses, but whatever your intuition tells you must be double checked through real logic, before it can be considered to be reliable.Well, of course. I don't think anyone was suggesting that intuition alone could be used to reach any sort of meaningful understanding. However, I think the point of what was being suggested is that without using intuition to make educated guesses, inquery would reach a stand still. Or, at the very least, be greatly stunted.

----
Math is strictly deterministic, logic can handle indeterminism too.
----


What about Probability and Statistics? That can definitely handle non-deterministic situations.

[SortingItAllOut]

Hi Upchurch,

An understanding of mathematics is key to so much in life, beyond the base ability to make change at Taco Bell.;)

I have had a love-hate relationship with it, mostly caused by a few poor teachers/professors that weren't inspiring or able to modify their teaching methods to present the material in a different way - I tend to learn best when I can ask LOTS of questions and attack problems from multiple angles.

My oldest is learning how to add these days. It is quite cool to see his eyes when we go over something new. "We're learning new tricks", he said the other day. I never thought of it that way before, but he is not far from the truth.

The mathematical beauty of music is really neat too. Time signatures, harmony, chords, etc..

It is all very fascinating to me. If I'd only been more interested in it back in high school.:(

Take care,
Sort:)

[MRC_Hans]

To get to the initial question: Is math crucial to understanding?

I think this depends on what you want to understand. It is absolutely crucial if you want to understand how the universe functions, but if you want to understand things like art and human relations, it is of limited or no importance.

To give an example, we could easily imagine som math genius, who can understand Special Relativity, advanced programming, etc. but who is unable to have a sensible relationship to other humans (the example is not random, I have known such a person). On the other hand, it is probably possible to find a person who is lovable, highly moral, with a deep understanding of ethics, but who cannot add up a grocery bill.

Now, for some of the things raised above...

Math handling non-deterministic functions (Whodini): Sure, by probability analysis, and statistics, it is possible to make calculations on non-deterministic events, but isn't the purpose of those methods exactly to handle such events in a deterministic way? If your statisics tell you that en event has 90% probability for a certain outcome, you use this to make a logic decision.

As for logic being deterministic (Franko's argument): Basically, yes. Logic is used, somewhat like probability analysis, to try and reach a deterministic result, but what I said was that logic can handle indeterminism. An example:

Suppose a phosphorescent substance has a half-life of two minutes. On the macro scale, we observe this as a deterministic function; every time we excite a portion of the substance, the resultant glow will be diminshing in such a way that it gets halved every two minutes. Detailed research has proved that this is because individual atoms give up their charge in a non-deterministic way. We can now use logic to infer that if we were to watch a single charged atom, there will always be a 50% probability that it will give up its charge within the next two minutes.

Hans

(Edited for some clarity)

[CWL]

Upchurch,

Your original contention was that mathematics is "crucial to understanding anything, including philosophy."

Not so. There are many things that can be understood and which have very little or nothing to do with mathematics.

My own academic background includes no mathematical studies whatsoever. Yet I still humbly purport to have a certain understanding of the subjects I have studied within the scope of my education (which includes a masters degree in law and in addition thereto two years of university studies of language and other humanities). I would thus like to believe that I have a certain understanding of law, society, history, language and - indeed - philosophy. I have also gained some practical understanding of economics, having practiced as a corporate and commercial lawyer for over six years. All this, I would argue, has not required any advanced mathematical skills.

If you are talking about physics and other related sciences I understand what you are saying. However, your contention does not make any sense if you intended to include understanding as to social sciences and humanities.

[Stimpson J. Cat]

Upchurch,

Mathematics is a formal language for expressing logical statements. It is not the only possible one, either. In that sense, Mathematics can be considered a subset of logic.
--------------------------------------------------------------------------------

True, but I would go one step further and say that it is the most commonly used formal language for expressing logical statements.

--------------------------------------------------------------------------------
In short, intuition is a very useful tool for making educated guesses, but whatever your intuition tells you must be double checked through real logic, before it can be considered to be reliable.
--------------------------------------------------------------------------------

Well, of course. I don't think anyone was suggesting that intuition alone could be used to reach any sort of meaningful understanding. However, I think the point of what was being suggested is that without using intuition to make educated guesses, inquery would reach a stand still. Or, at the very least, be greatly stunted.

I agree on both points.

Dr. Stupid

[hammegk]

Just jumping in without reading the thread -- who has time for that -- have we decided yet if mathematics is monistically materialistic, or monistically idealistic?

If we don't know, is it then dualistic?

[Stimpson J. Cat]

hammegk,

Just jumping in without reading the thread -- who has time for that -- have we decided yet if mathematics is monistically materialistic, or monistically idealistic?

If we don't know, is it then dualistic?

You're making a fool out of yourself again.

Dr. Stupid

[hammegk]

Originally posted by Stimpson J. Cat
hammegk,



You're making a fool out of yourself again.

Dr. Stupid

Yeah, most multi-level statements require understanding at several levels. Most linear thinkers miss the point.

Thanks though for your apparent concern.

[Q-Source]

Originally posted by CWL

Not so. There are many things that can be understood and which have very little or nothing to do with mathematics.

Ummm.... I wonder why you say that they are many. I would say they are the less.


My own academic background includes no mathematical studies whatsoever.

By this, you mean no formal education in Mathematics. But it does not imply that you do not make use of Maths at all in your reasoning and understanding of many subjects.



If you are talking about physics and other related sciences I understand what you are saying. However, your contention does not make any sense if you intended to include understanding as to social sciences and humanities.

Here you are wrong. In the last decades, Social Sciences have been incorporating more and more formal language (mathematics) in order to analyse and understand social problems in a more objective and better way.

Two examples of this revolution are Economics and Sociology. Just look at the history of Economics, at the beggining (with Smith, Ricardo and Marx) it was considered more as a branch of Philosophy and in the last 20 years, it looks like a branch of Mathematics.

Now, it is impossible to understand or analyse some economic problem if you don't translate that problem into a mathematical model. It makes everything more comprehensible.

Q-S

[CWL]

Originally posted by Q-Source
Ummm.... I wonder why you say that they are many. I would say they are the less.

I am not sure what you mean by this. Please elaborate.

By this, you mean no formal education in Mathematics. But it does not imply that you do not make use of Maths at all in your reasoning and understanding of many subjects.

If you mean formal logic, then yes. If you mean formal mathematics, not really (beyond simple application of the four fundamental rules of arithmetic).

Here you are wrong. In the last decades, Social Sciences have been incorporating more and more formal language (mathematics) in order to analyse and understand social problems in a more objective and better way.

Two examples of this revolution are Economics and Sociology. Just look at the history of Economics, at the beggining (with Smith, Ricardo and Marx) it was considered more as a branch of Philosophy and in the last 20 years, it looks like a branch of Mathematics.

Now, it is impossible to understand or analyse some economic problem if you don't translate that problem into a mathematical model. It makes everything more comprehensible.

Q-S

As to some economic problems, yes. I am not disputing this. However, many economic hypothesises (both on the micro and on the macro level) are in reality a part of behavioural science and they can be just as easily understood without the use of mathematics.

The same certainly applies to business economics and management. Let's take accountancy as an example. How much math does one really need (again, beyond basic applications of the four fundamental rules of arithmetic) in order to analyse a balance sheet? Accounting principles (which is really what it is all about) constitute "soft knowledge" which hardly allows itself to be translated into formal mathematics.

Again, I am not disputing that an understanding of mathematics is useful or necessary in many instances - I am disputing the overly generalizing statement that it is "crucial to understanding anything".

[Upchurch]

First, I just wanted to say that I'm really digging this thread.

Second, addressed to CWL, knowing your own legal background, I was tempted to suggest that maybe mathematics is only applicable to understanding of objective "things" (whatever you want to include as "things"). My thinking being that law is determined by society rather than by some over-riding natural law.

But then I thought, sure you could know the letter and the details of the law, but how could you understand everything about how it worked in practice without statistics like conviction rates or demographics of potential jurors? (I'm sure there is probably more, but I'm not familiar enough with the system.)

[scotth]

Originally posted by CWL
Upchurch,

Your original contention was that mathematics is "crucial to understanding anything, including philosophy."

Not so. There are many things that can be understood and which have very little or nothing to do with mathematics.

My own academic background includes no mathematical studies whatsoever. Yet I still humbly purport to have a certain understanding of the subjects I have studied within the scope of my education (which includes a masters degree in law and in addition thereto two years of university studies of language and other humanities). I would thus like to believe that I have a certain understanding of law, society, history, language and - indeed - philosophy. I have also gained some practical understanding of economics, having practiced as a corporate and commercial lawyer for over six years. All this, I would argue, has not required any advanced mathematical skills.


I find this particularly interesting. I am a programmer by profession (and a good one at that). My main talent is in thinking symbolically.

I am also pretty good at digital and analog circuit design. These two things have a very "different" feel to think about. Digital circuit design feels very much like programming mentally. Analog circuit design is more difficult to envision, as relationships are continuous. (How do I make sense of this to someone who has never done it?....) In digital design there is generally only two or maybe three states a circuit can be in and the rest can be ignored. When envisioning analog circuits, I have to keep a "transfer function" in my head for each component as I go.

Anyway..... the point of this (and I probably failed to make it) is that thinking about and trying to solve different types of problems have a distinct mental "feel" to me. I hope someone else has noticed this and can relate to it.

And to the actual point. When I read a SCOTUS decision for example, it exercises my brain in exactly the same way as when I am doing programming or digital circuit design or even a geometric proof for that matter. I enjoy reading many of them. There is a definite beauty of thought in many of them.

It would be my contention that the practice of law is very dependent upon the same types of thinking that is learned is certain branches of mathematics. Probably not linear algebra or calculus, but almost certainly boolean algebra, geometry, arithmetic, and probably set theory as well.

And a further contention would be that learning and practicing these skills could/would sharpen the mind for legal matters as well.

Now that I have put everybody to sleep, a quick note on intuition. My experiences with intuition (concerning the solutions to problems) have been something like this: Even while I am not actively working to find a solution to a stubborn problem, it seems my mind keeps the desire for a solution back there somewhere. As I go through my day, many patterns of logic and/or relationships pass through my mind in dealing with or thinking about other matters. It often feels like there is a kind of static sieve back there that recognizes when one these patterns might be applicable to the stubborn problem I have on hold. When a match happens or maybe happens, that seems to be source of MY eureka moments.

[CWL]

Originally posted by Upchurch
First, I just wanted to say that I'm really digging this thread.

The subject is indeed interesting. I think what it all boils down to is the age old question of the apparent difference between on the one hand natural science and on the other hand the humanities. Your plug may be that mathematics is a necessity - my plug is that natural science and the humanties are in reality inseparable. They are both intertwined and to a great extent dependent on each other. One cannot truly excel in one discipline without having at least some rudimentary grasp of the other.

Second, addressed to CWL, knowing your own legal background, I was tempted to suggest that maybe mathematics is only applicable to understanding of objective "things" (whatever you want to include as "things"). My thinking being that law is determined by society rather than by some over-riding natural law.

But then I thought, sure you could know the letter and the details of the law, but how could you understand everything about how it worked in practice without statistics like conviction rates or demographics of potential jurors? (I'm sure there is probably more, but I'm not familiar enough with the system.)

I think I have partially answered this in statement regarding natural science/the humanities above. You are right of course, statistics are indeed a vital tool in the toolbox of the legislator.

[ahirst]

I've mentioned this book before :'The Problems of Mathematics', by Ian Stewart. Although published in 1987 its still worth seeking out a copy of it.

The entire first chapter is called 'The nature of mathematics'.

Sample quotes:

'One of the biggest problems of mathematics is to explain to everyone else what it is all about. The technical trappings of the subject. its symbolism and formality, its baffling terminology, its apparent delight in lengthy calculations: these tend to obscure its real nature. A musician would be horrified if his art were to be summed up as 'a lot of tadpoles drawn on a row of lines'; but that's all that the untrained eye can see in a page of sheet music.'

'Mathematics is not about symbols and calculations. These are just tools of the trade - quaver, crotchets and five fingered exercises. Mathematics is about IDEAS. In particular the way that different ideas relate to each other. If certain information is known, what else must necessarily follow? The aim of mathematics is to understand such questions by stripping away the inessentials and penetrating to the core of the problem. It is not just a question of getting the right answer; more a matter of understanding why an answer is possible at all, and why it takes the form that it does. Good mathematics has an air of economy and an element of surprise. But above all it has SIGNIFICANCE.'

From chapter 19, 'The limits of computability' :

'At the turn of the [20th] century David Hilbert devised a research programme whose end result was to be a rigorous proof of the consistency of logic and set theory, or equivalently of arithmetic. But before it got going, an unknown called Kurt Gödel threw a spanner in the works and the programme collapsed in ruins. Gödel showed that there are true statements in arithmetic that can never be proved, and that if anyone finds a proof that arithmetic is consistent, then it isn't! Alan Turing was working in mathematical logic, with a view to clarifying the notion of computability. He too discovered that certain very natural questions HAVE NO ANSWER WHATSOEVER. By this I do not mean that nobody is clever enough to find the answer: I mean that it can be shown in all rigour that no answer exists at all!'

'With Gödel's theorems the hope of proving beyond any doubt the unsullied purity of mathematics vanished forever. Mathematics was forced to face an ugly fact that all sciences had come to terms with long before: it is impossible to be absolutely certain that what you are doing is correct.'

(emphases in original)

So that's what its all about then. :confused:

[Franko]

MRC:
Suppose a phosphorescent substance has a half-life of two minutes. On the macro scale, we observe this as a deterministic function; every time we excite a portion of the substance, the resultant glow will be diminshing in such a way that it gets halved every two minutes. Detailed research has proved that this is because individual atoms give up their charge in a non-deterministic way.

Ahhhh, so you have “detailed research” that demonstrates things happen magically?

How do you know for certain that the Uncertainty principle means what you think it means? Why doesn’t this non-determinism manifest in the macroscopic world???

That seems to be a rather glaring contradiction to your claim.

MRC:
We can now use logic to infer that if we were to watch a single charged atom, there will always be a 50% probability that it will give up its charge within the next two minutes.

So how is that Logic handling Non-Determinism??? It looks like the Logic is only involved in the Deterministic part, and the logic can’t touch the Non-deterministic portion AT ALL! If it could, then the Non-deterministic part wouldn’t be non-deterministic – would it?

Here’s what you said:

MRC:
As for logic being deterministic (Franko's argument): Basically, yes. Logic is used, somewhat like probability analysis, to try and reach a deterministic result, but what I said was that logic can handle indeterminism. An example:

So basically you have an entirely deterministic computer program, except a few of your variables have “randomly” generated values. You don’t comprehend the “code” for the random number generating subroutine, but instead of concluding that this subroutine works logically like the rest of your program, you assume it functions magically and completely beyond your comprehension???

Yeah … very “mathematical” and “scientific” of you :rolleyes:

[Franko]

ahirst:
'Mathematics is not about symbols and calculations. These are just tools of the trade - quaver, crotchets and five fingered exercises. Mathematics is about IDEAS.

That’s exactly right. Where: IDEAS = MEMES

In particular the way that different ideas relate to each other.

That’s called entanglement.

If certain information is known, what else must necessarily follow? The aim of mathematics is to understand such questions by stripping away the inessentials and penetrating to the core of the problem.

Don’t tell the A-Theists this; they feel naked if they can’t confuse the issue with Lots and Lots of unnecessary crap. Read any of Upchimp’s posts, you’ll see he is a Master at this.

It is not just a question of getting the right answer; more a matter of understanding why an answer is possible at all, and why it takes the form that it does.

That is rather curious, but most people never think about it.

Good mathematics has an air of economy and an element of surprise. But above all it has SIGNIFICANCE.'

Yep.

Good stuff.

[Q-Source]

CWL,

You said:
There are many things that can be understood and which have very little or nothing to do with mathematics.

I say that those "things" you are talking about, are the less.
Almost all areas of Science require mathematics in one way or another. It is a formal language that makes everything easier to explain and understand.

Originally posted by CWL

As to some economic problems, yes. I am not disputing this. However, many economic hypothesises (both on the micro and on the macro level) are in reality a part of behavioural science and they can be just as easily understood without the use of mathematics.

You must be kidding.

The only posible way to comprehend how economic agents affect micro and macro issues is by modelling their behaviour into mathematical terms. For example, Microeconomics and Rational expectations are only explained in pure Mathematics.

There is no way that we could get reliable conclusions from our intuition or from arithmetics only.



Let's take accountancy as an example. How much math does one really need (again, beyond basic applications of the four fundamental rules of arithmetic) in order to analyse a balance sheet? Accounting principles (which is really what it is all about) constitute "soft knowledge" which hardly allows itself to be translated into formal mathematics.

It depends on how good you are at accounting. :)

If you just fill balance sheets, then you don't need any. If you need to generate the information that you are going to write on your balance sheet, then you will need a lot of differential calculus.

Q-S

I'll bet mathematicians, engineers and programmers are alike in one respect: they feel (correctly) that they are very good at analyzing the world. I think, though, that this is a simple manifestation of the fact that each of these disciplines teaches and enforces a logical way of looking at the world. After enough time, this get ingrained into your thinking patterns.

Certainly a knowledge of mathematics is essential for understanding discussions in almost any of the "hard sciences", and increasingly of the others, as Q-Source pointed out. ("If you can't put a number on it, it's not science.") But for reasoning in general, the underlying logical principles would seem to be far more valuable thinking tools. I might be able to integrate functions all day, but does that mean I thoroughly understand argument and logical fallacies, or recognize an invalid syllogism when I see it?

[hammegk]

Originally posted by Q-Source

... If you need to generate the information that you are going to write on your balance sheet, then you will need a lot of differential calculus.

Q-S

Er, would you provide example of balance sheet data you would generate with differential calculus?

Originally posted by sundog


.....for reasoning in general, the underlying logical principles would seem to be far more valuable thinking tools....

Why do you consider "logical principles" to exist at a more fundamental or deeper level than math?

[Akots]

Originally posted by sundog
I'll bet mathematicians, engineers and programmers are alike in one respect: they feel (correctly) that they are very good at analyzing the world. I think, though, that this is a simple manifestation of the fact that each of these disciplines teaches and enforces a logical way of looking at the world. After enough time, this get ingrained into your thinking patterns.

Certainly a knowledge of mathematics is essential for understanding discussions in almost any of the "hard sciences", and increasingly of the others, as Q-Source pointed out. ("If you can't put a number on it, it's not science.") But for reasoning in general, the underlying logical principles would seem to be far more valuable thinking tools. I might be able to integrate functions all day, but does that mean I thoroughly understand argument and logical fallacies, or recognize an invalid syllogism when I see it?

Spend a few days learning any programming language. The vast avelanche of syntax and logic errors will humble any man or woman. :eek:

Programming certainly taught me that I can be very, very wrong... and no matter how certain I am that it's the computer's fault, it NEVER is. :o

This is likely the first step towards reasoning; admission that you are infallable.

[scotth]

Originally posted by Akots
This is likely the first step towards reasoning; admission that you are infallable.

Now that is a slip.:D

[Akots]

I never said I was infallabubble.

EDIT: Opps! I of course mean Ifailablable. Silly me. :D

Originally posted by Akots


Spend a few days learning any programming language. The vast avelanche of syntax and logic errors will humble any man or woman. :eek:

Programming certainly taught me that I can be very, very wrong... and no matter how certain I am that it's the computer's fault, it NEVER is. :o

This is likely the first step towards reasoning; admission that you are infallable.

An excellent point! But after doing it for twenty years or so, your analytical skills do get better.

Your programs have BUGS? :D

[scotth]

Originally posted by sundog


Your programs have BUGS? :D

Not mine. Mine have unintended features.;)

[Akots]

Originally posted by sundog


An excellent point! But after doing it for twenty years or so, your analytical skills do get better.

Your programs have BUGS? :D

Of course not. I'm infallabubble! :rolleyes:

[MRC_Hans]

I once wrote a fault-free program.:eek:

Hans

[CWL]

Originally posted by Q-Source
I say that those "things" you are talking about, are the less.
Almost all areas of Science require mathematics in one way or another. It is a formal language that makes everything easier to explain and understand.

Would the following disciplines be exemples of those things that are "the less": History, Law, Comparative Literature, Linguistics and - indeed - Philosophy (unless of course you consider formal logic to be "math").

Are the humanities and related subjects not "science" to you?

If "yes", how do you use math as a formal language to "make things easier to understand" within those subjects?

You must be kidding.

The only posible way to comprehend how economic agents affect micro and macro issues is by modelling their behaviour into mathematical terms. For example, Microeconomics and Rational expectations are only explained in pure Mathematics.

There is no way that we could get reliable conclusions from our intuition or from arithmetics only.

I am not kidding. I have a few university credits in economics (micro/macro) and I understand the basic principles just fine without having the slightest idea of how to express them in mathematical terms.

There may be some misunderstanding here however. I think we need to explore what you mean by "pure Mathematics". Would you for instance call a simple graph "pure Mathematics"?

Q-Source, please understand that I have no intention to be contentious here. I agree and understand perfectly find that there can be no deeper insight in macro/micro economics without an understanding of math. Again, what I do not accept is that nothing can be understood without such insight. That would be a disqualification of my own abilities (being a math illiterate). ;)

It depends on how good you are at accounting. :)

Hmmm... well, the auditor of the one company I do the accounting for hasn't complained yet. Of course, he is a friend of mine so that might be the reason why... ;)

If you just fill balance sheets, then you don't need any. If you need to generate the information that you are going to write on your balance sheet, then you will need a lot of differential calculus.

Q-S

Have you ever "generated the information" to be compiled on a balance sheet? I have, and I frankly don't know what differential calculus you are talking about. To the best of my knowledge, nothing in book-keeping requires any mathematical skill beyond the four basic rules of arithmetic (and it's mostly plus and minus). Perhaps you could exemplify?

[Q-Source]

Originally posted by CWL

I am not kidding. I have a few university credits in economics (micro/macro) and I understand the basic principles just fine without having the slightest idea of how to express them in mathematical terms.

Well, I have a whole degree in Economics and I am dead without Maths.
The basic principles, that you learn in the University, don't exist in a vacuum. How do you know that marginal changes in price will cause marginal changes in consumption?.


There may be some misunderstanding here however. I think we need to explore what you mean by "pure Mathematics". Would you for instance call a simple graph "pure Mathematics"?

Of course, no.
I am talking about Econometrics.

Q-Source, please understand that I have no intention to be contentious here. I agree and understand perfectly find that there can be no deeper insight in macro/micro economics without an understanding of math. Again, what I do not accept is that nothing can be understood without such insight. That would be a disqualification of my own abilities (being a math illiterate).

O.K. let's say that there are some areas of humanities where modelling is not neccesary.


Have you ever "generated the information" to be compiled on a balance sheet?

Yes I have


I have, and I frankly don't know what differential calculus you are talking about. To the best of my knowledge, nothing in book-keeping requires any mathematical skill beyond the four basic rules of arithmetic (and it's mostly plus and minus). Perhaps you could exemplify?

In order to fill a balance sheet, let's say that you need to determine your profits. To get profits, you need to determine your income, and then you need prices and costs, and then you need wages, and then you need to determine labour productivity, and so on.

Yeah, you're gonna say that you just apply arithmetics because you just take the market's parameters. Well, in my case (as an economist) and in the case of large companies or monopolies, we have to estimate those parameters.

It is like someone who mentioned that why we should learn Maths if we can use a calculator. He is right, in practice we just take advantage of what it is already done.

Q-S

[Unas]

Originally posted by Franko
Ahhhh, so you have “detailed research” that demonstrates things happen magically?You have again chosen to attribute a viewpoint to another person that was not expressed by that person. Why do you do this, when your tactics are so blatantly obvious?

[CWL]

Originally posted by Q-Source
Well, I have a whole degree in Economics and I am dead without Maths.
The basic principles, that you learn in the University, don't exist in a vacuum. How do you know that marginal changes in price will cause marginal changes in consumption?.

Ultimately that assumption is based on empirical observation, not on math IMHO.

Of course, no.
I am talking about Econometrics.

Fine, I take it we are at least in partial agreement.

O.K. let's say that there are some areas of humanities where modelling is not neccesary.

I take that as a partial concession. I would myself say most areas of the humanities do not require mathematical modelling, nor is mathematical modelling possible in most areas. Again, History, Law, Comparative Literature, Linguistics and to a great extent Philosophy are discplines where this would be true.

Yes I have

In order to fill a balance sheet, let's say that you need to determine your profits. To get profits, you need to determine your income, and then you need prices and costs, and then you need wages, and then you need to determine labour productivity, and so on.

Yeah, you're gonna say that you just apply arithmetics because you just take the market's parameters. Well, in my case (as an economist) and in the case of large companies or monopolies, we have to estimate those parameters.

He he. True, I was going to say that. From this I gather that you get my point.

It is like someone who mentioned that why we should learn Maths if we can use a calculator. He is right, in practice we just take advantage of what it is already done.

You are right of course. Any deeper understanding requires that we go to the source of the knowledge, whether this is based on math or not.

[MRC_Hans]

Originally posted by Franko
Ahhhh, so you have “detailed research” that demonstrates things happen magically?

Only if you choose to label Quantum Mechanics "magic". Since QM is apparantly beyond your comprehension, I concede that it may be indistinguishable from magic to you, but that doesn't make it magic to everybody else.

How do you know for certain that the Uncertainty principle means what you think it means? Why doesn’t this non-determinism manifest in the macroscopic world???

That seems to be a rather glaring contradiction to your claim.

This has nothing to do with the uncertainty principle. The non-determinism I mention does manifest in the macro world. Actually, I just mentioned an example that can be observed in your own home with the unaided eye. If you have another explanation for that phenomenon, feel free to present your evidence (but this is the seventh time I ask you this question, so I'm not holding my breath).

So how is that Logic handling Non-Determinism??? It looks like the Logic is only involved in the Deterministic part, and the logic can’t touch the Non-deterministic portion AT ALL! If it could, then the Non-deterministic part wouldn’t be non-deterministic – would it?

It is logic explaining a non-deterministic function, correlating theory with observation in a logic way.

So basically you have an entirely deterministic computer program, except a few of your variables have “randomly” generated values. You don’t comprehend the “code” for the random number generating subroutine, but instead of concluding that this subroutine works logically like the rest of your program, you assume it functions magically and completely beyond your comprehension???

No, YOU want to believe that the world functions like an entirely deterministic program, but this is contradicted by numerous observations that do not have a deterministic explanation. So, instead of conceeding that the real world does not seem to be deterministic, you claim that those functions must also be deterministic (in order to fit YOUR cosmology). This puts the burden of proof on you, so, again, if you can explain, with compelling evidence, quantum mechanics in a deterministic way, I suggest you do so. Not to me, better publish it in a scientific journal, and sit back and wait for the letter from the Nobel Comitee. :rolleyes:

Hans

Edited to add: Sorry, I see we're getting off topic.

[Q-Source]

Originally posted by CWL


Ultimately that assumption is based on empirical observation, not on math IMHO.

Again, no.



Fine, I take it we are at least in partial agreement.

Yes



I take that as a partial concession. I would myself say most areas of the humanities do not require mathematical modelling, nor is mathematical modelling possible in most areas. Again, History, Law, Comparative Literature, Linguistics and to a great extent Philosophy are discplines where this would be true.

Well, if we strictly speak of mathematical modelling, then you are right.



He he. True, I was going to say that. From this I gather that you get my point.

I also hope that you get my point :eek:


Q-S

[CWL]

Originally posted by Q-Source
Again, no.

Again, why not?

I also hope that you get my point :eek:

I do. My apologies for not expressly admitting that sooner. :)

[Plutarck]

Originally posted by Upchurch

Maybe it'd be more accurate to say that mathematics is crucial to understanding but not sufficient?

I think that is a completely accurate statement:

Mathematics is neccessary, but not sufficient, for understanding.


After all, don't computers do math, to a certain extent, better than humans? Obviously there has to be something else.

Math is, I think, best considered a foundational skill, as well as a building block and mortar knowledge. While often not apparently useful by itself, it can be applied to almost anything to some good effect.

[Plutarck]

Originally posted by Q-Source

In order to fill a balance sheet, let's say that you need to determine your profits. To get profits, you need to determine your income, and then you need prices and costs, and then you need wages, and then you need to determine labour productivity, and so on.


Well, here you are both sorta right and wrong. The Balance Sheet is just largely a collection of data that already exists. Basic arithmetic, at most, is all that is required.

However, it is in the actual operation of the business (Management, not Accounting - Accountants only rarely use anything but basic arithmetic and very simple algebra, excepting Managerial Accounting - must make use of things like Calculus, as well as Economists, of course) that things get complicated. Costing (part of Managerial Accounting) often requires more-than-basic math, as do other such activities, such as setting prices and such.

To sum it all up, everyone needs some math - some people just need alot more of it, and some people need much more advanced levels of it. Not everyone has a use for calculus - but for those who do it is often indespensible.

[Q-Source]

Originally posted by CWL


Again, why not?


Because you were talking about "basic principles" not about "assumptions" :eek:

How do you think we got those principles?

Let's say that we have empirical data, do you think it is useful in the way it is (for example, graphs, figures, and descriptive statistics)?

Empirical data doesn't say much if we don't apply formal language or mathematical tools to extract all the information we can from it.


Q-S

[Q-Source]

Originally posted by Plutarck


Well, here you are both sorta right and wrong. The Balance Sheet is just largely a collection of data that already exists. Basic arithmetic, at most, is all that is required.


This happens in practice. Maybe an accountant doesn't need to know how profits or wages are estimated.

[CWL]

Originally posted by Q-Source


Empirical data doesn't say much if we don't apply formal language or mathematical tools to extract all the information we can from it.

Q-S

Aha! "Formal language"... interesting... and this is not the same as "mathematical tools" you say?

[metacristi]

Is mathematics crucial to understanding?

Our universe is mathematical,to understand it 'mathematical' minds are needed.I've read once an interesting article ('Mathematics invention or discovery?' or something like that) where the author arrive,at some point,at the conclusion that mathematical minds cannot evolve in non mathematical universes (this does not imply the 'reality' of mathematics,in the platonic sense).A very interesting conclusion in the light of evolutionary theory.More or less we are 'forced' by nature to learn some mathematics in order to survive.So that,yes,in my opinion mathematics is crucial to understanding the reality around us.

Sure not all people have outstanding talents at mathematics but exactly how we all (I talk of persons without mental disorders) have 'inbuilt' the capacity to think logically till a certain degree (unfortunately never till the end as the pitfalls of the logical fallacies plenty show) I suppose that we inherit a 'mathematical' brain too.Practically we all have the capacity to learn mathematics at least to the degree to be able to survive in this mathematical universe and to have a basic understanding of how universe 'works'.Remain only to learn mathematics,of course upon everybody's natural maximal capacities (dependent by intelligence).The greater the degree attained the better the understanding of nature (sure in the hypothesis that other sciences are studied in parallel otherwise...).


I've seen that almost all those who posted here consider that mathematics is a subset of logic (logicism).Well this point of view is not shared by all philosophers and (especially) mathematicians.The great (french) mathematician Poincare (representative for the intuitionist current) for example argues that the principle of complete induction cannot be proved using the laws of logic therefore mathematics cannot be 'reduced' at logic (see http://www.utm.edu/research/iep/p/poincare.htm ).
Some others go even further by considering logic as belonging to mathematics (in an extended definition).Personally I agree with this last point of view-logic is a part of mathematics (in an extended definition).

Logical knowledge is impotent without intuition (and vice versa).

[polemos]

This topic seems a little one-sided to me.

The claim that the universe is mathematical is the sort of claim one could not substantiate without reiterating it, but it appears to be meant to do actually work for more than just itself.

But more to the point, the claim that mathematics is necessary/crucial/required for even philosophy I find to be the more culturally contingent of those made. What philosoohy? Whose philosophy?

If the assertion is that standard analytical philosophy as done in the United States requires mathematics or a formal logic syntax, no disagreement there. But if this claim is carried further to say that this style of philosophy is all that there is to philosophy, or that this style of philosophy is all that one can use with our world, then I would heartily disagree.

So, let me ask this, could it be unpacked a little more as to why understanding philosophy or the world requires mathematics? I understand that this topic is meant to do just that, but there were some discussions which seemed to, ah, go aside, and there were other discussions which didn't question the centrality of this premise, this assertion, but instead questioned the trappings of it.

Is it the case that all cultures, all humans, all individuals who aspire to live out their lives and to communicate this life to successive generations, need a mathematics to set them along? Well, if not all humans, then why the ones who do philosophy?

[neutrino_cannon]

Originally posted by Whodini
Logical knowledge is impotent without intuition (and vice versa).

Intuition? Wouldn't that be the same as guessing?

I do not like guessing, and avoid it when possible. I doubt that this practice has emasculated my logical prowess.

[PixyMisa]

Intuition is simply arriving at a conclusion without understanding the process that led to it. It's not necessary for anything; it's just that since we cannot (yet) know the origin of our own thoughts, it's sometimes all we have.

[CWL]

Originally posted by neutrino_cannon


Intuition? Wouldn't that be the same as guessing?

I do not like guessing, and avoid it when possible. I doubt that this practice has emasculated my logical prowess.

Agreed. I would instead propose: logical knowledge is impotent without empirical evidence.

[PixyMisa]

Originally posted by CWL
Agreed. I would instead propose: logical knowledge is impotent without empirical evidence. Absolutely. I pointed this out to Franko some time back, and he reset to "Atoms obey TLOP."

[Rosetta Stone]

You hit on a point that's been bothering me PixyMisa. If the universe is a logical function what makes anyone think it's truth value is decidable? I really can't see how you could know. To me, that question brings the whole house of cards down, but what do I know?

[PixyMisa]

What does it mean to say that the universe is a logical function? What does it mean to talk about its truth value? Does it mean anything at all?

These questions, and more in When Philosophers Attack!

[PixyMisa is on holiday. This is the real me. Sorry about that.]

When Philosophers Attack!


I'm lurking....I'm watching......I'm waiting......One false move and..... :eek:

[Rosetta Stone]

What does it mean to say that the universe is a logical function? What does it mean to talk about its truth value? Does it mean anything at all?That's what I want to know, too. There are those here who say exactly that, and appear to believe that it's self evident, but I don't know what they mean.

I've been reading this stuff for a while now and I'm still clueless.

Originally posted by Rosetta Stone
That's what I want to know, too. There are those here who say exactly that, and appear to believe that it's self evident, but I don't know what they mean.

I've been reading this stuff for a while now and I'm still clueless.

It is the solution to a number of different problems. Think about a mandelbrot set....did Benoit invent it? Or did he just discover it? If he just discovered it, then it must have already existed. This kind of thinking leads to mathematical platonism - self-existing numbers and numerical structures. The physical Universe itself behaves rather like a numerical function or a fractal - which is what led some people to declare that God was a mathematician.

If you're done digesting that lot then think about the problems regarding consciousness and ontology. The legacy of Kant is that we must distinguish between the world as we perceive it (our subjective picture) and the world as it really is, which we can never know the true nature of. But if we consider the world as it really is to be a mathematical function, then not only can it self-exist, but we escape the impossibilities of attempting a materialistic theory of consciousness by positing that the 'material' is really just 'information' and that the solid physical world we perceive is nothing but a mental construction.

I'm sure you'll have a couple of questions to ask.....

:)

Geoff

ps Pixy : If you are going to challenge any of this please try to avoid repeating any of your logically disabled nonsense based on materialism having to be true.

[Rosetta Stone]

It seems like quite the leap from mathematical Platonism to "the universe is a mathematical function". I can't see how anyone can seriously state Mona Lisa is a fractal, but maybe I have no aesthetic sensibility.

I'd settle for the equation that produces the Mona Lisa. Or even one that generates the rust pattern on a 1965 Dodge Dart.

[PixyMisa]

Ah, UCE. Jumping on straw-pixies again, or just lying?

I have never once said that materialism must be true.

I have merely pointed out your countless and repeated errors, not the least of which is that you either deliberately mis-state my position or are simply incapable of reading.

Pixy:


deliberately mis-state my position


You had a position? ;)

Anyhoo....let's see where this thread goes. :)

[PixyMisa]

I am starting to think that my position can be described as:Whatever UndercoverElephant says something is—it is not.Except that I agree - more or less - about Mathematical Platonism.

Originally posted by Rosetta Stone

It seems like quite the leap from mathematical Platonism to "the universe is a mathematical function".


Why?


I can't see how anyone can seriously state Mona Lisa is a fractal, but maybe I have no aesthetic sensibility.


The Mona Lisa is a painting. I am stating that the physical Universe itself is mathematical/fractal-like, not "everything" in it. Just because everything compiled by a C++ compiler was written in C++ it doesn't follow that all the running programs "are C++"

Be careful of using the word "is", by the way - at least make sure you know what you mean when you do use it. Do you mean "identical to", "equates to", "belongs to the category of", "etc....".


I'd settle for the equation that produces the Mona Lisa.


Do you mean "you'd settle for the Universe being the equation?"

Geoff

[CWL]

Originally posted by UndercoverElephant
I am stating that the physical Universe itself is mathematical/fractal-like, not "everything" in it.
Forgive the intrusion, but what in the heck does "mathematical/fractal-like" mean?

CWL


Forgive the intrusion, but what in the heck does "mathematical/fractal-like" mean?


I mean that after 4 centuries of exploring the way the Universe behaves, we can confidently say that it behaves as if it was made of mathematics.....

http://www.hep.upenn.edu/~max/toe_frames.html

Read the New Scientist article linked to from Tegmarks site if you want more info.

surprising connections between number theory and physics (http://www.maths.ex.ac.uk/~mwatkins/zeta/surprising.htm)



The idea of this website is to document all known research which in some way links number theory and physics. Although there have been a few conferences and subsequently-published proceedings on this topic, these were only able to touch on a small part of the overall body of work which has gone on.

The contents of the site should be of interest to both number theorists and physicists. In recent times we have seen, somewhat unexpectedly, number theory being applied by physicists to solve physical problems and, perhaps even more unexpectedly, techniques developed by physicists applied to problems in number theory. Material relevant to all such developments is archived in the sections linked from the upper part of the front page.

There is other 'secondary' material, organised into categories linked from the lower part of the front page. 'Probability and statistics' are not in themselves part of physics, but have been developed in reference to 'events', physical phenomena, and measurements which in some way vary or fluctuate. The fact that they should be applicable to something so profoundly un-physical and unchanging as the theory surrounding the behaviour of the prime numbers is something widely acknowledged as 'curious', 'remarkable', 'surprising', etc. To treat the occurrence of a prime number as a kind of 'random event' is to apply to the pure, eternal world of number a type of thinking inspired by the ever-changing physical world. The section concerning 'fractality' is perhaps less directly physics-related, but a significant part of the content is the work of physicists.

[Franko]

is mathematics crucial to understanding [the Universe/Reality]?

No ... not really. But I guess it depends on "what" specifically you want to understand.

[ahirst]

Further to my previous post on this thread. Here's part of a book review:
---------------------
10. If arithmetic is consistent, then it is incomplete

The most remarkable feature of the universe is that one product of the human mind, mathematics, appears to be the perfect language for elucidating and comprehending it. Einstein wondered at the fact that the most incomprehensible thing about the universe is that it is comprehensible. But what is mathematics, and does it fizzle out when pressed too far? Is mathematics the epitome of abstraction, or is it a tool for mining spacetime for what already exists? If mathematics does fizzle out, then this queen of languages cannot perhaps embrace all the questions we want to ask. Gödel's theorem does indeed circumscribe its potency, so this most abstract of all the sciences - if it is a science - might be limited in what it can reveal about the structure of any formalised system of knowledge.

· Peter Atkins's book, Galileo's Finger: the ten great ideas of science, is published on March 13 by Oxford University Press.
--------------------

Full review at:

http://books.guardian.co.uk/departments/scienceandnature/story/0,6000,912064,00.html

...and no, I have absolutely no connection with the author.


:) :) Cheers.

[CWL]

Originally posted by Franko
is mathematics crucial to understanding [the Universe/Reality]?

No ... not really. But I guess it depends on "what" specifically you want to understand.
Wow.... I actually agree with Franko.

Should I be worried that I may be losing my faith in NO GOD and FREE WILLY? :D

[MRC_Hans]

Originally posted by CWL

Wow.... I actually agree with Franko.

Should I be worried that I may be losing my faith in NO GOD and FREE WILLY? :D

No, I Predict you will Dogmatically and Fanatically Cling to your Weird Magical Reliegious Beliefs, Religious Fanatic.

Jesus, You A-Theists are so Predictable!:rolleyes:



;) Hans ;)

[CWL]

Originally posted by MRC_Hans
No, I Predict you will Dogmatically and Fanatically Cling to your Weird Magical Reliegious Beliefs, Religious Fanatic.
Thanks. I feel Relieved. :D

[amhartley]

Mathematics is based on Logic. Without Logic there is no math.

So obviously LOGIC is more fundamental to understanding reality than Mathamatics.

Furthermore, you haven't even defined what you mean by the term "Mathematics". What makes Math -- Math? Do computer languages (algorithms) count as 'Mathematics" according to you? What's the significant difference between a computer language, and the English language?

Franko,
Was it Bertrand Russell who propagated this idea that math is logic? I know he was the one saying math is a "shorthand way" of doing logic. But in any case have you thought critically about that premise?

In fact, that idea was the reason for the failed attempt last century in the US to teach math using set theory. It got way too confusing, esp. when people ran up against all the paradoxes (Kant would say, "antinomies") concerning unions of infinite numbers of sets. The idea has gotten us into trouble and I thought people had dropped it by now.

Which brings up the question of why anyone would even *want* one way of knowing (math) to be "a part of" or dependent on or reducible to another (logic). I've seen persuasive arguments that such tendencies at root spring from religious assumptions about what in the world is eternal/divine/self-existent.

[rocketdodger]

Mathematics is nothing more than an extension of logic, and if you want you can consider them to be exactly the same.

In any case, anyone who understands anything must do so on the basis of logic. There simply is no other way about it. Thus, one who understands mathematics better is able to understand the world in general better.

Anyone who claims math is not essential is either a rock or doesn't understand that math actually underlies everything they think they know.

[Meffy]

amhartley, you might want to read the dates of the most recent posts before replying to threads. In this case, the previous post was on March 13, 2003, making it unlikely (though not impossible) that the original participant you're responding to will be around. :-) More recent threads will have a much better chance of continuing successfully.

[amhartley]

amhartley, you might want to read the dates of the most recent posts before replying to threads. In this case, the previous post was on March 13, 2003, making it unlikely (though not impossible) that the original participant you're responding to will be around. :-) More recent threads will have a much better chance of continuing successfully.

Meffy, thx for the note; it's just that his post was so intriguing.

[amhartley]

Mathematics is nothing more than an extension of logic, and if you want you can consider them to be exactly the same.

In any case, anyone who understands anything must do so on the basis of logic. There simply is no other way about it. Thus, one who understands mathematics better is able to understand the world in general better.

Anyone who claims math is not essential is either a rock or doesn't understand that math actually underlies everything they think they know.

RD, what is an 'extension of logic'? And, if math is nothing but that, then how can we consider them 'exactly the same?'

Did I seem to be denying the importance of math? Sorry bout that. However, why do you say math "underlies everything [we] think [we] know?" I wouldn't go that far. There are many ways of knowing & experiencing the world: emotional, logical, quantitative, economic, ethical, legal, certitudinal. Are you saying that each of these is reducible to math and/or logic? That they can be understood in purely logical/quantitative terms? You wouldn't be alone (in fact, this was characteristic of the Enlightenment). But I want to understand you aright.

[rocketdodger]

RD, what is an 'extension of logic'? And, if math is nothing but that, then how can we consider them 'exactly the same?'


Uh, I guess I mean something like since all of math is an extension of basic arithmetic, and since the simplest arithmetic seems to be pretty much just an extension of basic logic, then math is just an extension of logic.. I think.



Are you saying that each of these is reducible to math and/or logic? That they can be understood in purely logical/quantitative terms? You wouldn't be alone (in fact, this was characteristic of the Enlightenment). But I want to understand you aright.

Yes this is what I am saying. I don't claim that everything can be understood in such terms, because in fact I think that there are some things that cannot, at least not yet. But for all practical purposes, understanding the immediate universe in order to make our lives better is entirely a mathematical undertaking.