I have to say that I've always been a little confused by Descartes' distinction between the 'composite' sciences (physics, astronomy, medicine) and the 'simplest and most general' sciences (arithmetic, geometry, and 'other subjects of this kind').
He clearly wants to make the point that the composite sciences assemble elements of truth and fact--that is, small things that are true, I guess--while the simple-general sciences furnish the list of those elements in the first place. An inelegant paraphrase on my part, I realize, but good enough for now.
But that seems to come apart to the extent that the composite sciences include within them, as proper parts, the simple-general sciences. For instance, what is physics, if you 'remove' the calculus? For that matter, what is biology (surely a composite science) without the systematic description of rates of change of physical factors inherent in ions and all the rest, etc., that characterize the conduction of a nerve signal along an axon? Can science be science without its math?
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I think that there are so many things that we refer to as "science" now that there may be SOME sciences that can be sciences without math, but a majority of them (the real sciences) no, not at all. Without math, we wouldn’t be able to draw conclusions from data or figure out certain coordinates. Science and math go hand in hand.
I have to agree with sandy's comment. That without math we would not be able to make conclusions. I feel like all sciences and maths are intertwined. I am a math major and we do problems involving science alot and I know the same goes for chem involving math( for two examples). Actually, I was talking someone in the education dept. and they told me that I should be certified for science, too, for teaching, because these majors are so similar and involve eachother in all aspects.
I agree with sandy also. You must know mathematics to really understand science. If you think about it, people that do well in math or those who have mathematical mind normally do well in science or visa versa. This is due to the fact that both science and math are interwined.
math and science are concrete subjects. It is in these two subjects that humans have the most consistently proven and reasonable conlusions everytime (if done correctly). 2+2 equals 4. There is no denying that. That's how it is and always will be. Descartes knew that we aren't perfect and that a lot of the things we do or think could be proven wrong. By associating his thought process with a mathematical one, one that has a methodical process, he knew that it would greatly help to add validity to his theories.
I think that some kinds of science can be done with out math, like when you study nature and things like that. But for the most part you cannot make a logical decision without math. You are not able to back up your facts with data, and numbers. So without math most sciences cannot exist.
Math without science and science without math? Impossible? I don't think so... I see a lot of people backing the belief that math is inseparable from science but exact calculations aren't always needed in order to progress in any given science. As far as I know people at the beginning of time weren't given a textbook outlining all things in math, so where did these people start?
Astronomy. For a start people were able to see those things up the sky and able to make shapes of them, hey theres the little dipper! People figured out that once the sun disappears at night, it comes up again in the morning!
Medicine. "Hey, theres an arrow in me, perhaps if I pull it out and put something on it to stop the bleeding it may heal?" Thought obviously a very primitive example, it does show that people carry a natural logic that doesn't require exact math to do things.
Other examples provided that are far too complex for the mind to comprehend without a set of rules and boundaries, i.e. math, do require math to figure out and reach an answer or conclusion.
But remember, mankind had to start somewhere. The creation of math before there was actual "math" must have been an interesting process.
A little different comment, maybe does not belong here, but can't see any right place to put this. As a Biology major, you have concrete answers (for the most part), if you don't know yet, you do experiments, and eventually it will come to light. However, in Philosophy, you can read, analyze, discuss, read again, analyze, get other peoples ideas, and you will never know if you are right (have the same ideas as the author), especially when they are dead. So, Professor, being on both sides of it, I was curious how you made the transition and allowed your mind to go from, relatively concrete answers, to something that offers little clarity into the thoughts of other people writings, especially dead peoples writings??
i agree with most of the comments that are posted here, For the majority of time, you need science and math. Through out high school, i been taking majority of my class in the direction of science and math. For some reason, these two subjects comes really easy for me. And i find that most of my friends who are not good in math also is not doing so well in science. Of course there are exception to the statement. There must be a reason why. If you understand the concept of math, you can pass a lot of subjects in science, which most of the time requires you to do math.
i believe that math and science go together. for the most part, science is not science without math. science has alot of formulas and eqautions to find x. how else would you find the distance of the sun, or the measurement of sound? math has alot do to with science, it's the basic foundation of science. without math, science is not science. one can say that math is involved with everything in life, wheather its science or the simplest thing. we cannot do without math.
I thought D was just getting at what is the most fundamental thing, like the foundations of the house. Perhaps he wasn't trying to make a distinction between them in another way than one is less likely to be corrupted due to human mistakes, as it is more fundamental and thus can't be in as much doubt. He may have originally been getting at like Pythagoras everything is made up of number but then he subverted that with his I think there for I am.
I believe math and science do correlate very closely, and I must also agree with Sandy's comment. For the most part, we need math in order to figure out the answers to formulas and give reasons to why certain things happen. However, certain sciences like Biology for instance need no math. One can say math is a supplement to science to help better explain naturally occuring functions, etc.
i don't believe so. most of science includes experiments and calculations to find proof in a matter. According to Descartes and me agreeing, math or arithmetic is the only concrete proof we actually have no doubt about. So to have one without the other seems almost impossible.
I do believe in many sciences math is a must and even the subjects that you don't think need math in some kind of way math is always included. Im in Human Bio now and in our labs we have to use math to convert numbers and get to the best possible answer. Even if it's not numbers you are using to solve a problem you need some kind of sequence.
Math can exist without anything referencing to it, it is also very universal. Science is based on something real in the world. We use math to prove some of the unknown in sciences.
i dnt agree when andrew said that math isnt needed in biology. i believe math is the bases of all science. like codi said, math is included some how, no matter how small the sciences are.
I think that the composite sciences descartes is talking about is like the testable aspects. The things that can be tested and proven. In science, if a hypothesis is found to be false, they must re-configure the hypothesis so that it is "true" again (until proven false). In science, it is like we assume that things are true based on studies. On things like arithmetic it is understood that 2+2=4. So, D thinks that arithmetic should not be doubted.
Math is used in many didn't types of sciences. Like Sandy said, without math, we would not be able to make conclusions. The two seem to work hand in hand. In science, numbers are involved to make conclusions and for experiments. I personally don't think that science can be science without its math.
Although both subjects are very important, i wouldn't say they go "hand in hand." In pretty much every science, there is math used. Why do you think one of the major courses a Biology major needs to take is Calculus? Without math, you wouldn't be able to compute certain chemical equations in sciences like chemistry. However, the same could not be said vice versa. Rarely, if ever, do you need to know science to be able to accomplish math.
Science cannot be science without math. I can explain this in one simple quote from the movie "Pi". "1. Mathematics is the language of nature. 2. Everything around us can be represented and understood through numbers. 3. If you graph these numbers, patterns emerge. Therefore: There are patterns everywhere in nature." Without these numerical patterns, there is no science.
Most of the comments i agree with. Lately we have been using science for eveything. Now science and math go together. I believe thats the only way to explain certain things. Like my father says the only way to explain a scientifical problem is with math. Decartes is trying to explain us. That is why why he even made that distinction. Everything that decartestries to explain sometimes it does not make sense but relating math with science is actually a good explanation.
I think that math and science relate to each other and they work together. We need math in order to figure scientific problems. Think about when you are doing an experiment and you use math to solve it and coem up with you answer
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