Is strict deductive reasoning to mathematics what the scientfic method is to science?
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No.  The scientific method is to try to think of a rule or equation which will fit the observed data you already have, and apply it mathematically to predict the result of observations or experiments you have not made yet.  When you make them, and get the predicted results, the rule or equation is more likely, but it is never completely certain.\n\nThe mathematical method is as old as Euclid (about 500 BC).  From axioms, we deduce theorems which are at least as true as the axioms, and from these theorems we deduce more theorems.  All the way along, if the axioms are true, then the theorems are true too.
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One of the things that is amazing to me, as a scientist, is that partly because of philosophers and their need to create a "philosophy of science", the scientific method is supposed to have a number of rigid steps that are followed like a formula.\n\nI can tell you, working scientists do not do this. \n\nScience has basically two main features:\n\n1. data, from observations or the results of experiments\n2. theories, which attempt to explain the data\n\nAnd all of the scientific method is concerned with either getting the data, or making up theories. That is it. Others make it much more complicated and hard to understand and in fact, boring. \n\nThere are some other features of science that are important, such as:\n\n1. observations and experiments should be repeatable, at different times and by different people, to be trusted\n\n2. theories are discarded and superceded when a new theory comes along that explains the data better\n\n3. science is a trial and error process\n\n4. theories can be used to make predictions, which can then be verified by data if it is a good theory\n\n5. Some areas like chemistry are amenable to experiments,and some are more appropriate for observations, like astronomy. After all, you cant really make a star in your lab to perform experiments on.\n \nThere are many stages to producing data and theories, however. Some people call these the scientific method. Often scientists will specialize in one or more areas, and as science has become more complicated and involved, science has become more of a collaborative process. \n\nFor example, scientists might specialize in:\n\nexperimental design\nobservational design\ndesigning experimental equipment\ndesigning observation technology\nbuilding equipment\ndata collection \nfield work\nlaboratory experiments\ndata reduction and processing\ndata analysis\nmodeling the data\nmathematical and statistical techniques for data analysis and modeling\nproducing theories\nanalyzing theories\nmaking predictions based on theories\nverifying predictions\nmathematical and statistical methods for analyzing theories\n\nand so on\n\nSome of these activities overlap with things that engineers do or statisticians do, or with mathematicians or people in other fields.
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Logic is the study of reason, that is, of rational ways of drawing or establishing conclusions. \nLogic is for constructing proofs which give us reliable confirmation of the truth of the proven proposition.
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The scientific method is the process a scientist uses to collect accurate information from the environment.  It is designed to take care of personal bias and human error as much as possible. A scientist's work is supposed to be open to scrutiny by his peers and others so his work must be clearly set out showing his hypothesis or the question he is trying to answer, the methods he used, the observations or results he got and the conclusions he/she draws from it.  These must be set out clearly enough so that if anyone else goes through the same procedure, the one should arrive at the same results and conclusions. If this does not happen then there may be some error or bias somewhere.  The link below is a good introduction to the scientific method.
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what type of disease are you trying to diagnose? you need to be specific..if you are asking for the mechanism itself, you better start with the classical symptoms presented by the patient. hypothetico-deductive reasoning is the best pathway you can use to deduce the patient's pathophysiological state.
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Someone once told me that Science is a branch of Philosophy.  It employs the scientific method to test an hypothesis.  Seems to me, this Alternative category belongs here under Science and Mathematics, just as much as any other branch of Science and Higher Math.\n\nNot all scientists are narrow-minded in nature.  They do not want to exclude the extensive research and testing done in the fields of Paranormal Phenomena, and Paranormal Psychology.  They challenge the alternatives and test the impossible in order to better understand the world around us.\n\nOther "scientists" need to limit themselves to "normal" phenomena only.  Anything out of the ordinary is quickly dismissed. These people live in a thin plane of existence, where all the rules have to be neat and understandable.  They wish to concentrate on what they know, and can explain, and exclude the rest.\n\nAnd being the most vocal group, and most willing to spend their energy getting labels exactly how they like them, YA will most certainly cave in and move the category.  \n\nAfter the category is changed, I hope they all take a moment to tell NASA to stop looking for alien life, stop worrying about UFO's, and stop exploring the unknown, since we already know all there is to know on the subject, and what they are doing is not considered Science.  Also write to police agencies around the world and implore them to stop seeking the assistance of "Intuitives" as this should be unacceptable in police investigation work, no matter how many crimes have been solved using this kind of help as a tool.
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Do you mean the belief in science?  The basis of Science is proof.  Every scientific theory has to be proven and re-proven before it is excepted by the scientific community and eventually by (most) people.  That's why they call it scientific fact.\n\nOccasionally certain things are proven wrong and a new theory replaces it and is tested and proved to replace the old.  But to call the whole thing a load of balls is rediculous.\n\nWhat do you know of what you speak?
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Science is the study of anything through application of what is known as The Scientific Method.  The Scientific Method consists of certain principles and procedures for the systematic pursuit of knowledge.  This involves the recognition of the problem and careful description of it in order to understand exactly what you are studying.  This is followed by collection of data by experimentation and observation of the thing under study.  From this gathering of data, you than are able to formulate  hypotheses and test them.
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using the scientific method of forming a hypothesis, testing the hypothesis and interpreting the results
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Science (from Latin scientifko - knowledge)
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postulates are geometric concepts that we accept as true. Theorems must be deductively proven as true.  The problem is, what one geometry book offers as a postulate, another book may have as a theorem.\n\nSee your geometry teacher for some extra help, that's what the teacher is there for. Good luck.
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Yes. Lets define science\nsci·ence (sns)\nn.\n   1. The observation, identification, description, experimental investigation, and theoretical explanation of phenomena.\n   2. Such activities restricted to explaining a limitied class of natural phenomena.\n   3. Such activities applied to an object of inquiry or study.\n   4. Knowledge, especially that gained through experience.\nBy the definition itself. Feng Sui is science. Isn't it that science have many branches?
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sci·ence (sī'əns) \nn.\n\nThe observation, identification, description, experimental investigation, and theoretical explanation of phenomena.\nSuch activities restricted to a class of natural phenomena.\nSuch activities applied to an object of inquiry or study.\nMethodological activity, discipline, or study: I've got packing a suitcase down to a science.\nAn activity that appears to require study and method: the science of purchasing.\nKnowledge, especially that gained through experience\n\n\nACCOUNTING:\n\n\nThe bookkeeping methods involved in making a financial record of business transactions and in the preparation of statements concerning the assets, liabilities, and operating results of a business.
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The real world contains minute details that can never be measured with total accuracy. But even though we can't do better than approximations, the unnatural precision in our made-up math enables us to at least better our understanding of things, as we better our approximations.\n\nI'm not sure what you mean by suggesting that math is "flawed". For one, math is not really all about numbers, it is about logic--the logic that first led us to reason that there existed transcendental numbers (also not sure what you mean by "unresolved"). I think part of the problem is that you've been led to a mistaken belief about what math purports to be. Math is not science--at least, it is certainly not a science of the natural world because a lot of real mathematics considers situations that are not considered to necessarily exist in reality. If anything, math is a science of ideas, and even that is waxing poetic a bit. As far as natural science is concerned, math is a conceptual tool--it can form the backbone of scientific theories but it is not science.\n\nExplaining the universe through math is "no more accurate than our explanations of god(s)"? How can you possibly hope to justify such a statement? Are you saying that theology, in the complete absence of math, could enable us to correctly land probes on distant planets, or design electronic computers, etc.?
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Mathematics\nA science (or group of related sciences) dealing with the logic of quantity and shape and arrangement\n\nStatistics\n\nA branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of various theories to estimate and interpret.\n\n\nhttp://www.schoolingkids.com/\nhttp://www.futureaccountant.com/
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weezy is on the right track, that glow1989 is on the right track.  For everyone who thinks that writing 1+1=2 is so obvious that it constitutes a self-contained proof of itself(!)... if you undertake a serious study of mathematical proof, you might find that 357 pages is a good length for a quick introduction to the ideas that are involved in considering questions in this area.  Of course, I am talking about actually UNDERSTANDING something - very different to simply passing an exam, regardless of the 'level' of maths you are enrolled in.\n\nYes, as you mentioned, this is a hard question.  'Proving' that 1+1=2 is not as simple as it sounds, because of the inherent question of what we mean by 'prove'.  You might have noticed that some proofs you have used depend on other proofs, which in turn depend on other proofs, ... which ultimately rest on a handful of axioms.  It is the nature of operations that are allowed by any axiomatic system, that determine the characteristics of mathematical problems that can be said to be SOLVABLE.  It is no small task to understand the axioms that underlie our systems of mathematics.  For example, maths students learn: that division by zero is undefined; that any object raised to a null power is equal to unity; some differences between rational and irrational numbers; what we mean when we consider objects to exist in 'sets'; and so on.  Those who consider themselves to be excellent students are usually able to list these rules in rapid-fire style.  But if we are asked to 'prove' why those rules are the way they are, the questions start to seem fuzzy, and you typically run out of convenient formulas to rely on.  You could easily write 357 pages just to explain what you actually MEAN by the numbers 1 or 2, without worrying about the definition of the addition operation!  As usual, people might do better to stop and consider what the question is asking before booting in a smug answer.\n\nLook into Hilbert's Problem (David Hilbert - German mathematician), which was a more workable and compact form of a proposal by Russell and Whitehead to formalise mathematics on a general basis, according to well-established axioms and procedures.\n\nOther notable mathematicians to work in this area were Alan Turing, Alonzo Church (look for Church's Lambda Calculus), Emil Post, and the brilliant Kurt Gödel.  In more recent decades, look for Gandy (1988) and of course many others.\n\nLol, molawby is spot-on.  I wish he'd posted b4 me... would've saved me a bit of typing.  If all you need to do is learn to sing the right song, to pass your exams and get the job that stipulates that you need to have completed such-and-such a course, then you don't have to worry about any of this.  Of course, that doesn't mean you have to dismiss it either.  But if you are chasing a deeper understanding, it probably does take the 20 yrs, and you won't necessarily get paid for it, heheheh.\n\nFor bedside reading, I suggest Roger Penrose etc...
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The Deduction Theorem states that if a formula F is deducible from E then the implication E → F is demonstrable (i.e. it is "deducible" from the empty set)