“When the only tool you have is a hammer, all problems begin to resemble nails” (Abraham Maslow). Applying the ways of knowing as an alternative of the subject matter of “tools”, this quote suggests that if one looks at the ways of knowing as one group rather than individually, the knowledge that will be gained will not be to the best of the ability of oneself. The four ways of knowing are: reason, language, sense perception, and emotion. We will be determining to what extent is reason more reliable as a way of knowing than the other ways of knowing, in math, natural science, and ethics? 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. Math relies heavily on language as a way of knowing, because math is a language itself. It is used to communicate between mathematicians, students, and teachers, etc. Globally, Math can make statements that are difficult or impossible to make in natural languages, giving it the opportunity to find truth values of statement that can be decided within the system.
Although math heavily relies on language as a way of knowing, it always requires reason. The equation 1+1=2 requires one to logically think; ...
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keeping us at the bottom of the intelligence list of society. In order to expand our knowledge, we need to accept that all ways of knowing are present at all times, each with various strengths and weaknesses. Someone who has not had the same experiences as me might say that you can do without reason in Ethics, or that Math pertains only reason as a way of knowing. Each person has their own opinion, and is entitled to it, just like I am. One day, society may come to a consensus on whether reason is more or less important that the other ways of knowing.
However, I believe that reason is neither reliable or unreliable in general. Depending on the area of knowledge, reason can be the most effective or least effective. In Math, Natural Sciences, and Ethics, reason is relied on heavily, but is not the only way of knowing that is relied on heavily.
The next major theory on how one obtains knowledge comes from David Hume’s Empiricism. Empiricism itself is the idea that all knowledge obtained is done so through senses or experiences throughout life. This theory itself clearly contrasts with rationalism as rationalists believe at no point that they should gain knowledge through senses/experiences. Furthermore, as an empiricist, he does not value anything that is not attained through experience. One of Hume’s beliefs is the idea that everyone is born with a mental “blank slate”. Because all knowledge we gain is thought to be gained through experience (which a newborn would have none at that point) the “slate” starts as blank and will filled in as the person learns through experiences. This
“9x – 7i > 3 (3x – 7u)” and asked to solve for “i”. Any mathematician who has been introduced to algebra would immediately execute the procedures necessary to isolate the “i”. Doing so, I determine the answer to be “i < 3 u”. 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. Different units can be used for the same measurements, but there are always conversions and equations that can be used to determine values for comparison, such as converting a dollar to a Euro or inches to centimeters. Truth in mathematics is approached in a universal manner and concludes that when anyone a...
I also learned that mathematics was more than merely an intellectual activity: it was a necessary tool for getting a grip on all sorts of problems in science and engineering. Without mathematics there is no progress. However, mathematics could also show its nasty face during periods in which problems that seemed so simple at first sight refused to be solved for a long time. Every math student will recognize these periods of frustration and helplessness.
Our knowledge is a key to our success and happiness in our life to give us personal satisfaction. Knowledge is power but not always. Sometimes our self-awareness and growth as an individual gives us negative thoughts that make us want to go back to undo it. Everyone wants to unlearn a part in our life that brought us pain and problems. Good or bad experiences brought by true wisdom can be used for our self-acceptance, self-fulfillment and these experiences would make us stronger as we walk to the road of our so called “life”, but Douglas’s and my experience about knowledge confirmed his belief that “Knowledge is a curse”. Both of us felt frustrated and sad from learning knowledge.
Many seem to think of mathematics as being nothing more than a series of numbers and formulas that they must learn, in order to pass a particular requirement for their college degree. They rarely, if ever, stop to think about the importance of mathematics and how it actually affects them and the people around them. It is ...
The view that some forms of irrationality may serve a useful purpose is being increasingly entertained, despite the disquiet it elicits. The reason for the disquiet isn't difficult to discern, for if the view were made good it might threaten the unqualified normative primacy that rationality enjoys in the evaluation of thoughts, beliefs, intentions, decisions and actions. In terms of the predominant "rational explanation" model, reasons both generate and justify actions, and carrying out the dictates of reason is held up as an ideal. If it can be shown that under some circumstances or for certain types of action irrational elements or procedures would produce "all things considered" better results, this would put these deliberative "ideals" in question.
...dge to one or two of the other forms by suggesting that all three forms of knowledge are logically interdependent. He argues this interdependence through the context of beliefs, and objective truth, and communication. While there is a real-world example of how this theory could falter (i.e. autism), by expanding his theory to address this counterexample, Davidson’s three varieties of knowledge can actually go a long way in explaining how we come to understand the feelings, emotions, and mental states of others.
Is it possible for human beings to rise above the sensory interpretation about the world and become an intellectual? Both Plato’s “The Allegory of the Cave” and René Descartes’ “Cogito, Ergo Sum” examine this issue, and come to the conclusion that it is possible, and from this ascent, to become certain and rational. For each author, though, this is accomplished in different ways. Plato’s allegory points out that we need to look beyond the surface of the knowledge we learn and let the idea of good be our basis in life. Descartes expresses that we need to eliminate doubt in order for us to know certainty and feel comfortable in our knowledge.
"Knowledge, Truth, and Meaning." Cover: Human Knowledge: Foundations and Limits. Web. 17 Feb. 2011. .
Mathematics is everywhere we look, so many things we encounter in our everyday lives have some form of mathematics involved. Mathematics the language of understanding the natural world (Tony Chan, 2009) and is useful to understand the world around us. The Oxford Dictionary defines mathematics as ‘the science of space, number, quantity, and arrangement, whose methods, involve logical reasoning and use of symbolic notation, and which includes geometry, arithmetic, algebra, and analysis of mathematical operations or calculations (Soanes et al, Concise Oxford Dictionary,
Mathematics teachers teach their students a wide range of content strands – geometry, algebra, statistics, and trigonometry – while also teaching their students mathematical skills – logical thinking, formal process, numerical reasoning, and problem solving. In teaching my students, I need to aspire to Skemp’s (1976) description of a “relational understanding” of mathematics (p. 4). Skemp describes two types of understanding: relational understanding and instrumental understanding. In an instrumental understanding, students know how to follow steps and sequential procedures without a true understanding of the mathematical reasons for the processe...
Devlin believes that mathematics has four faces 1) Mathematics is a way to improve thinking as problem solving. 2) Mathematics is a way of knowing. 3) Mathematics is a way to improve creative medium. 4) Mathematics is applications. (Mann, 2005). Because mathematics has very important role in our life, teaching math in basic education is as important as any other subjects. Students should study math to help them how to solve problems and meet the practical needs such as collect, count, and process the data. Mathematics, moreover, is required students to be capable of following and understanding the future. It also helps students to be able to think creativity, logically, and critically (Happy & Listyani, 2011,
To most people English or Language Arts is a creative course and math is just a logical, you get it or you don’t class. My purpose writing this paper is to change your mind. I believe that Math is just as, or more creative than English. I will demonstrate this through a couple of examples.
What is math? If you had asked me that question at the beginning of the semester, then my answer would have been something like: “math is about numbers, letters, and equations.” Now, however, thirteen weeks later, I have come to realize a new definition of what math is. Math includes numbers, letters, and equations, but it is also so much more than that—math is a way of thinking, a method of solving problems and explaining arguments, a foundation upon which modern society is built, a structure that nature is patterned by…and math is everywhere.
- What we know by intuition and deduction, or what we know natively, we could not know through sense experience: reason is