The certainty of mathematics is merely conditional; it rests upon assumptions that cannot be proven within mathematics, but only within the philosophy of mathematics. Exactly the same problem applies with respect to the primary problems of philosophy. We can easily give practical arguments that seem very convincing, but when we analyze these arguments philosophically, we often find that the simple conventions of ordinary argument cannot be regarded as adequate.
While analyzing math, natural science, and ethics, we will see that reason is neither more reliable or unreliable, but plays both as a strength and weakness in different areas of knowing. In math, reason is not the most reliable way of knowing, considering math is mainly about deductive reasoning and logic. Natural science does rely heavily on reason, due to the fact the scientific method is mainly about asking “why” and/or “how” questions. Similar to Natural Sciences, Ethics relies majorly on reason, because of the question “Is this morally right or wrong?” Math is a language. Having an extensive vocabulary, math also touches upon syntax and grammar.
Using various ways of knowing, examples, theories, and ideas both sides are exposed and reveal that they both are supported by plausible evidence and theories. When proving that math was in fact discovered by humans, many turn to occurrences in nature and in the universe as their proo... ... middle of paper ... ...mber of people in a town or how to divide rations equally in a family. Finally, although the question, how do we know if math discovered or invented, still remains unanswered, it is left unanswered with good reason seeing as their does not seem to be a side to the argument stronger than the other. Although both have compelling arguments supported with examples, theories and ideas, neither seems to take precedence over the other. To compromise between the opposing perspectives, it can be concluded that the mathematical relationships already existed, and were then discovered and interpreted through the invented representations such as formulas and equations.
According to mathematical reasoning that is the only true answer, and any mathematician around the world would get the same answer. Mathematics is approached without question or doubt unless another person attempts to solve the problem and arrives at a different answer. At that point, the two mathematicians would closely scrutinize the procedures used by both and eventually, confirm the answer to be “i < 3 u”. No matter where in the world one travels, mathematics is a universal concept. It is a connecting factor for all humans to share knowledge.
Science will never know all the answers; there are just too many questions asked and too many questions that haven’t even been asked yet. For a scientist to be effective in my mind they must be able to present their findings and their hypothesis in a way that doesn’t try to attack other people’s work, is complete with ideas on why and why not their hypothesis is true, and does science for the love of science and learning. I have learned a great deal this year in many of classes about scientists that seem to show these traits. But then again, there are many scientists that stumble upon their work, which is not to say that they don’t fit these qualities as well. Scientists that seem to completely ignore these qualities of good science are those that misuse their work.
Scientists have used this to understand and plot Earth’s elliptical orbit in a mathematical sense. Descartes did not trust anyone he didn’t even trust himself. This caused him to fall in love with math and physics, because of the certainty and truth in the principles. In his Discourse, he explains, “For my notions had made me see that it is possible to reach understandings which are extremely useful for life, and that instead of the speculative philosophy which is taught in the schools, we can find a practical philosophy by which, through understanding the force and actions of fire, air, stars, heavens, and all the other bodies which surround us” (Part 6). Explaining how life is more than the mind and soul, Descartes provides society with the beginning of the laws of nature as well as an introduction of planetary motion.
Math was added to the process with people like Alberti and Da Vinci commented on how math gave value to their works of arts. The process to reach the end now mattered, just like how Francesco Guicciardini, paved way for context to matter when evaluating history. This was an exceedingly important change from the Middle Ages. This ultimately made understanding easier and less oppressive. To learn and to fulfilling one’s potential was one of the great humanistic ideal.
His theorems changed the understanding of various fields of philosophy, particularly to the philosophy of mathematics; they pose prima facie problems for Hilbert's program and directly to logic, to intuitionism and also invites controversial comparisons between the scope of mathematics and the human mind. The extent of the first will be the focus of this essay. I will discuss the efforts of Gödel to unveil a new era of mathematics, in doing so he successfully discovered a flaw in mathematicians reasoning, but whilst his theorems were non-the-less significant, a physical change in mathematics has not been dramatic; the theorems did not over-rule the astounding perfection mathematics has already established. Before we consider such significance, I feel it’s important to confirm a mutual understanding of the theorems and its foundation. Considered to be one of the greatest philosophical mathematicians of a generation David Hilbert published his pursuit of an ideology for a systematic basis for arithmetic; ‘turning every mathematical proposition into a formula…thus recasting mathematical definitions and inferences in such a way that they are unshakeable and... ... middle of paper ... ...ems and to arithmetic.
We would still be in the dark ages if people with a great understanding for math hadn’t been there to invent new things and pull us out of the dark ages and into the techno age. Even though I may not me a mathematical genius, I realize that with out math I would have to write my whole report out on hand instead of a computer. I could not play my video games or chat online with friends if it wasn’t for math and the understanding of it. The study of math is important to society and probably always will be.
Thinking Scientifically to Find the Truth Humanity has been searching for the truth since the beginning of time. This search has produced many things like science, which has greatly advanced the cause that created it. There are many inherent problems in science, and it is not necessary to think scientifically in order to find the truth. There are many types of truth, but the most fascinating one is absolute truth. The basics elements of science, however, make it almost impossible for science alone to find this kind of truth.