Like I've often said, “I think, therefore I am.” We can continue building on our certainties using rationa... ... middle of paper ... ...e knowledge. Watson: I agree with Pascal on his view of the capabilities of reason. We are feeble, misled creatures in the midst of a reality which we cannot know. Descartes was correct in his attempt to use mathematical logic to get rid of uncertain assumptions and find truth, but he needs to realize that most truth is beyond our reach. We, as thinking humans, do have the remarkable ability to study ourselves.
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.
Instead, this school of thought maintains that because the world that we experience through our sense is in a state of constant change it can, therefore, not be relied upon in deriving distinct and reliable truths, also known as absolute truths. Rene Descartes, a seventeenth-century mathematician, was one of the most influential philosophers in rationalism. Descartes, like all rationalists, rely on the absolute truths found only in mathematics and logic, and place ultimate value in analytic statements. "An analytic statement attributes a property to something, and that property is already implicit in the definition of that object or concept". (White & Rauhut, pg.72) Descartes introduced the idea of "radical doubt", as we... ... middle of paper ... ...lank state", provide us with a logical explanatory argument against rationalism.
Reason is used most, if not all the time to formulate valid arguments and to prove points using logic. It allows people to understand and form judgments about certain topics. In mathematics, this is used extensively as all math propositions are proven using theorems and postulates as the arguments until a conclusion is formulated. The other ways of knowing don’t feature as prominently in this area of knowledge. Ethics also involves reason substantially.
Using ‘x’ as an example, is a shortened way of saying it is just an unknown constant value. In fact, many could argue that mathematics can be directly translated to English or any other language due to the definitive meanings behind the symbols like ‘x’ and ‘+’. Needless to say, math certainly does fulfill the requirements of being a specialized linguistic structure. ‘Math can only be used to describe certain abstract concepts’ is a statement that can be debated because I believe maybe there is more uses to Math than that. Maybe Mathematical language has to relate to a broad part of life, for example English can be used to talk about a wide range of topics, whereas the language of math can also be used to describe or predict phenomena that are not perceivable such as plants that are not
This is also often the case with ethics where our morals, and our views of other people are based upon intuition and Perception rather than evidence. In the area of knowledge of mathematics, language allows us to generalize words, equations and ideas to make knowledge in math universal, rather than dependent on opinion person to person, and therefore relies on facts in order for theories to be formulated. Mathematics greatly requires the use of reason and logic. Reason is a way of knowing, which by the use of known facts and logic, extends our knowledge. There are two forms of logic in reasoning: deductive and inductive.
“The basic strategy of Descartes’ method of doubt is to defeat scepticism on its own ground. Begin by doubting the truth of everything—not only the evidence of the senses and the more extravagant cultural presuppositions, but even the fundamental process of reasoning itself.”( Kemerling). Descartes believed that science should be rested on solid foundations. But, these foundations should come from the mind and not from our senses, since we can be deceived by our senses. “Above all I enjoyed mathematics, because of the certainty and self evidence of its reasonings, but I did not yet see its true use and, thinking that it was only useful only for the mechanical arts, I was astonished that on such firm and solid foundations nothing more exalted had been built, while on the other hand I compared the moral writings of the ancient pagans to the most proud and magnificent palaces built on nothing but sand and mud.”(31).
Starting with Descartes’ vision of a philosophy with a mathematical certainty, rationalists claimed to have grasped a rather large portion of reality, including the world, God, consciousness, and whatever falls in-between. As empiricists argued, most of this "knowledge" was in effect assumed, a habit, as it had no representation in the real world. The rationalists’ notorious abstractness and their disregard for the seeming discrepancy between their proofs and the real world have been the main reasons for the fearsome opposition and caricature they faced: even Voltaire, though influenced to a great extent by Leibniz’s philosophy, ridicules it in his masterpiece Candide in the form of ludicrously optimistic Pangloss. . Kant, especially, has put a rather impressive dent in the hull of rationalist philosophy, branding it dogmatic metaphysics.
Hence “To what extent various types and methods of gaining of truth are different in mathematics, art and ethics” Most of mathematicians claim that mathematics’ truth was an absolute truth. How we can gain truth in mathematics actually it is from logic as one of the ways. We can say this statement easily from adding numbers because when we add a number to another number it will get an absolute number. Peano axioms are the evidence for this claim. As example if we plus one with one the outcome can’t be other number except two.
The concepts can only be accepted to be true by using the skills to process and generate information and belief. The use of the skills as an “exercise” with no meaning or understanding is not critical thinking however. It is always believed that the area of a right triangle is one half the base times the height. Reasoning can be used through the drawing of a grid to prove this formula to be true. Therefore, mathematics uses critical thinking as a way of known skills to guide behavior based on intellectual commit... ... middle of paper ... ...been generated over time through develops in technology, scientific advancements as well as advancements in math and the arts.