Mathematical logic

trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.” Math is a language of logic. It is a disciplined, organized way of thinking. There is a right answer; there are rules that must be followed. More than any other subject, math is rigor distilled. Mastering the language of logic helps to embed higher thinking. Reading Journey through Genius helped me understand to open my mind to the expansion of knowledge not just…

functional analysis. Hilbert made great contributions to the mathematic fields in Algebra, Geometry, and Calculus. Hilbert also published these mathematical problems called Hilberts Problems. These were decade defining as they were unsolved mathematical problems. Hilbert was also known as the main father of the infamous proof theory and mathematical logic. Hilbert was the oldest out of his siblings. He was born on January twenty third in eighteen sixty - two in Prussia. His dads name was Otto…

senses for knowledge, Locke proposes that all experience is derived from external objects (Argument of Book IV, Chapter XI, Section 4) and by means of geometric analogy, Locke contends that sensory experience’s reliability is comparable to that of mathematical demonstration (Argument Book IV, Chapter XI, Section 6.2). By demonstrating the necessary input of external stimuli for experience and the reliability of the sensations that subsequently arise, Locke seeks to demonstrate the infallibility…

research field includes a vast domain of unsolved issues and conceptions in development. Well-intended definitions, as suggested by classic positions within the philosophy of mathematics – where logicism describes mathematics as a further development of logic; formalism describes it as a formal game governed by explicitly stated rules; and intuitionism describes mathematics as a particular mental process – might simply be concealing the fact that there are no unifying characteristics of…

of a formal inductive logic proof in Book III, Section 10 of Nicomachean Ethics to conclude, with varying levels of success, that humans who are excessively self-indulgent are no better than animals. Aristotle begins his discussion of moderation by creating his definitions, much like how a logician would define the parameters of their proof. Alluding to his previous definitions of excellence earlier in Book…

argues that one cannot prove we exist or are part of a concrete world. Every aspect of the world found around us could be fabricated. Everything our senses tell us to be true could be a lie. Descartes ideas prove these statements through intriguing logic and convincing hypothesizes. However, there is one argument Descartes, says, can be proven. This is the idea that humans think and have knowledge within their minds. Specifically, that thoughts have to originate from somewhere. Descartes uses…

Aristotle further lengthens his study of syllogism in On Interpretation to study modal logic. Modal logic is phrases that use possibly or necessarily. On Interpretation does bring up a problem about a fixed future. The problem is that what happened in the past either happened or it didn’t, therefor what happens in the future will either happen or it will not. So that brings up the idea of a fixed future. Aristotle rejects this idea of a fixed future and says that what is said about the future…

A seven-year-old child is in a math class learning simple addition and subtraction of single digit numbers. To logically approach this mathematical concept, the instructor employs the analogy of cookies; she asks, “if your mom left four cookies on the table, but your sister took two of the cookies, how many cookies can you eat?”. A smart and logical child raises his hand and says, “I can eat two cookies!” and the teacher rewards him with a lollipop for correctly answering the question. However,…

At times, trying to picture a mathematical problem in the real world is better solved by using abstract math. Ed Yong from National Geographic states that “when learning math, abstract symbols work better than real world examples” due to important logical thinking skills learned (2008). Learning theory is considered how well a person can relate a topic and solve the problem at an understandable quicker rate. According to National Geographic, there was a new study that shows that students who are…

demonstrate how effective use of logos will strengthen arguments. Logos may include the information presented in an argument in a case, the connections between two elements argue given, and the use of mathematical event. Information presented in a case when using logos deals with experts’ opinions or logic. Experts’ opinion may provide evidence to the audience on how relevant they are although these experts’ opinion may be highly acknowledged as proof. For instance, in “Foreign Language Study”,…