mathematicians /philosophers

[tali122]

i dont undestand why philosophers are also mathematicians- whats the connection between a area science of determinate calculations and one of subjective thought?
thx

[fo3nix]

first, maths is not an area of science, if that is indeed what you are suggesting.

second, not all mathematicians are philosophers, and not all philosophers are mathematicians.

however, some mathematicians are also philosophers because they, for example, use their interpretation of their maths to try and make sense and form of the world around them.

[mibn2cweus]

There is also the domain of objective thought as found in the Objectivist philosophy. Objectivism asserts that concepts possess a mathematical aspect in the form of measurment which enables knowledge to branch logically from the directly perceived.
For a detailed explanation of this see, "Introduction to Objectivist Epistemology" by Ayn Rand.

[Buenchico]

fo3nix states that 'maths is not an area of science'. He's probably correct but it certainly provides the underlying basis of all the sciences. (However, anyone who's ever been awarded marks for 'elegance' in a mathematical solution knows that mathematics is truly the purest of all the arts).

mibn2cweus has obviously been reading some philosophy texts with lots of big words in them. (And I thought Nietzsche was heavy going!).

As a humble graduate mathematician, with a love of philosophy, might I simply suggest that an ability to analyse and process logical thought is necessary for both mathematics and philosophy?

Chris

[kempie]

Mathematics can be thought of as the "language of science". It is expressed in clear, precise notation to remove misunderstanding or misinterpretation.

It can also be described as a philosophy in itself - link.

[bobjim1705]

There's two opposing schools of thought on the subject of Philosophy of knowledge. One lot, the Empericists, believe that you can only know what you have experienced.
The other lot, the Rationalists (Descartes, for example) believed that you could know everything that there was to know by logically working through things (mathematically, for example) without ever having to leave your room.
The most reliable logic form is maths, and so quite a few Philosophers dabbled in maths in attempt to acquire more knowledge of the world.

[fo3nix]

Buenchico: yes that's totally correct. But still, as i'm very sure you know, maths is not a science. However, anyone serious about physics will endure a lot of maths (as that is currently the best way of expressing the physics), and chemistry is just a big chunk of physics (atomic physics and up, really), and biology at its roots is a large part chemistry.

[can you tell i'm a physicist? ;)]

[mibn2cweus]

Mathematics is a method for measurement based on the application of established units of length; (1 light year = distance light travels in a year, 1 gram = mass (weight) of 1cubic centimeter of water, etc.).
Science is a method for understanding (gaining knowledge about) the nature of the physical world.
Since measurement is involved in virtually all aspects of determining the nature of objects in the physical world, mathematics is a cornerstone of science.
Philosophy is the study of what constitutes knowledge and what its purpose is so all three are different but intimately related.

[kempie]

Following on from mibn2cweus's final sentence, consider the etymology of the word mathematics:

Gr. mathema: knowledge; mathematikos: fond of learning

[fo3nix]

mibn2cweus, I would disagree. Maths is not about measurement. Science is about measurement, that happens to use maths to do it.

[Buenchico]

So, fo3nix is a physicist, eh? That's one of those nasty people who defile mathematics! (Can't you tell that I'm very much a pure mathematician. I absolutely hate it when someone comes along and finds a practical use for a branch of mathematics which has previously only existed as pure theory!).

mibn2cweus has got some very odd ideas about what mathematics is. His wording seems closer to defining arithmetic than mathematics. (Arithmetic, incidentally, has no more to do with Mathematics than handwriting has to do with English). The certificate on my wall says that my degree is in 'mathematics as a double subject' but not one part of my studies ever had anything to do with measurement. (I must assume that mibn2cweus has never come across real mathematics such as set theory, group theory, ring theory, field theory, linear and non-linear analysis, differential and integral calculus, chaos theory, symbolic logic, diophantine equations, etc. None of these branches of mathematics have got anything to do with measurement!).

Despite fo3nix being one of those nasty physicists, I find myself generally agreeing with his view of the relationship between mathematics and science (and totally disagreeing with mibn2cweus!). Pure mathematics, at its finest, is an art form. Applied mathematics is a tool. Measurement does not form an intrinsic part of either of them.

The first thing any mathematician has to, when researching a new area of mathematics, is to determine what may be regarded as axiomatic and what has to be investigated or proved. The same principles apply to the study of philosophy. Maybe that's why philosophers often have an interest in mathematics?

Chris

[Gef]

So fo3nix, if "chemistry is just a big chunk of physics" why are most physicists so crap at it?

[fo3nix]

oh dear, knew that line would get me into trouble!

Gef: most are crap at it because either they do not put much effort into it (instead, learning about other things), or (considering a-levels, etc.) chemistry is much more about learning lots and lots of facts, much like a biology a-level. maybe physicists are generally not as good as this as people only studying biology and chemistry (presumably a lot to become doctors) are? i'm not sure.

but you must agree that Neils Bohr was a physicist, and much of modern chemistry is based on his model of the atom, and subsequent discoveries. J J Thompson, discoverer of the electron (essentially, the particle that is responsible for a lot of important chemical processes), was also a physicist.

Buenchico: it may settle your stomach to learn that I am a theoretical physicist, and thus do appreciate more of the finer qualities of mathematics than some of my straight physics friends.

[mibn2cweus]

First let me proclaim in a loud voice that I have no degrees in mathematics, science, or philosophy! I apologize if I have stepped on a nerve. If you can find it in your heart to forgive me I humbly bow to your professional and honored opinion and ask what would be the proper term to use to describe the process of using quantity of units to measure length, radius, density, temperature, etc? None of the aforementioned exists as objects in the real world. These are, as you say, tools. Science uses these tools to measure (quantify) properties of real physical objects; this is what science does; (ah oh, here come the scientists). My dictionary defines mathematics as the science of measurement, among other things, so if Webster lies and this ain�t math, what is it?

Lord have mercy on me a sinner with �very odd ideas� cast down from the ivory tower!

Oh, by the way, �odd ideas� are not necessarily bad or evil. Relativity and string theory are pretty damn weird to most people.

[Buenchico]

At last! mibn2cweus and I finally agree on something! 'Odd ideas' are, indeed, not necessarily bad or evil. You probably can't be a good pure mathematician unless you're totally happy with embracing some very odd ideas. (It took me a while to get to grips with the concept of n-dimensional space, where n can be any number - big, small, negative, irrational, complex or whatever. It's definitely an 'odd idea' but, for us weird mathematicians, it opens up entirely new vistas).

I'm definitely not looking for a fight with nibn2cweus (who makes many helpful & positive contributions to AB) but since he's asked a question, he deserves an answer:
Q: "...what would be the proper term to use to describe the process of using quantity of units to measure length, radius, density, temperature, etc? "
A: "Metrology"

Chris

[mibn2cweus]

I�ll go along with that for the duration of this thread since the context has been established but for most people, unlike yourself, they would have no idea what we were talking about without it, (or maybe with it) and understanding is what it�s all about; right? Thanks for the response! :~)

[Gef]

fo3nix I do agree with you about Bohr and Thompson. I also agree that the electron is probably the most important particle in chemistry. However, in most fields of chemistry knowledge of electrons is of no importance.

[fo3nix]

yes, this is true. its just a physics thing; we try and say that everything is based on physics.

at the heart of chemistry, and i mean the real heart.. its just physics. explaining why electrons are in subshells, 1s2 and all that stuff is nothing but atomic physics. but yea, lots and lots of chemistry is so far removed from the original physics that it is very loosely physics (hence a different name, "chemistry").

[Gef]

fo3nix, you stick to the physics and I'll stick to the chemistry, lol. Actually it could be argued that the forerunner of chemistry was alchemy and not physics. Oh no, I don't think we want to go there.

Enjoyed the debate and apologies to tali for hijacking the thread.

[einsteinsdog]

Mathematicians have some very difficult philosophical concepts to deal with like zero , infinity, unity and even worse how can we rely on any observation or measurement made by fallible humans

[mibn2cweus]

If it can�t be reduced to evidence you yourself have observed than you have no choice but to evaluate and minimize the risk. When this is the only option I put my money on science every time.