When we talk about topics such as Logic and Mathematics, we tend to think of certain, only abstract concepts. The word ‘Logic’ in this title can mean an analysis of a hidden structure associated with syntax of propositions, while the word ‘Mathematics’ can be defined as a specialized kind of abstract language. The title itself follows the concept of opinion and proposition that states both Logic and Mathematics are nothing but specialized linguistic structures, meaning these topics are considered only to be the study of human language, from the sounds and gestures of speech, up to the organization of words, phrases, and meaning. I believe that Logic is not a language itself, but helps to provide a base for all types of languages in the process. …show more content…
It has its own rules of grammar that are quite different from those of the English language and uses the symbolic language, which consists of symbolic expressions written in the way mathematicians traditionally write them. In a real life situation using symbols such as ‘+’, we often use words associated with this symbol such as ‘plus’, ‘add’, ‘increase’, and ‘positive’. This symbol itself can convey multiple messages that are all agreed on by mathematicians to be interpreted one way. Using letters like ‘x’ are considered more of a shorthand for writing values or procedures. 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 …show more content…
Logic and Mathematics are what philosophers call a formal system of knowledge and the foundations of both math and logic are Axioms. By corresponding to reality is implied they fit logically according to what we see and experience, and these perceptions are considered accurate, reliable, and valid. By cohering to reality is implied that `these axioms fit within a larger system of explanation. For example, the right angle or straight lines, or in fact, all of Euclid’s postulates are considered valid, reliable and accurate, and hus cohere within the system of geometry. In math, an axiom's truth is also seen as self-evident, thus it has no, or requires no, proof as they are inherently logical or not logical. You cannot use principles, or the process of deduction, to show that there truth can be demonstrated. Theorems rely on axioms as their starting point, but the theorems truth can be shown by proof based on these. A real life situation connected to this topic is the Pythagorean Theorem, for example, the axiom that all right angles are equal, and the straight line can be drawn from one point to another is an assumption of the Pythagorean Theorem. This theorem also has an extensive proof based on these assumptions within it. But even if Axioms ground our understanding, they may also alter it. To Euclid, an Axiom was just a fact
All languages could be successfully analyzed in terms of mathematical equations. In this sense, language is mathematics. This thesis enables us to explain why languages usually have different word orders, and why any language could be highly flexible.
The logic generally taught to English-speaking students is symbolic logic. How faithful is it when employed as a representation of the connectives they use and will use in their ordinary conversation and in most of their intellectual activity, at least if they are not mathematicians? How fruitful for their education? Is there a logic more faithful and likely to be more fruitful? A conference inviting us to relate philosophy and education makes those questions especially opportune.
“Logic: The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding.”
Since ancient Greece, philosophers have employed logic in their attempts determining what the actual nature of knowledge is and what people can know about it. Logic, as defined by Richard Popkin and Avrum Stroll is “the branch of philosophy that reflects upon the nature of thinking itself,” or the branch of philosophy used to understand the nature of ideas and how they are or are not related to one another (237). Logic can be divided into two major categories, deductive and inductive reasoning, both of which have their merits and limitations. They are both used to arrive at knowledge, which is justified, true, belief. Knowledge is derived with logic with varying degrees of accuracy through various methods.
Logic, as it appears in its everyday form, seems to stand on its own, without any requirements to needed to justify its existence. However, it is commonly overlooked that "logic is the science and means of clear . . . communication." Consequently, many sentences are regarded as logical, which in reality are illogical. It can therefore be found that the language used to communicate this logic must be carefully constructed using a certain format in order to form a logical statement. The requirements in such a sentence include a subject, the verb "to be", a predicate containing information that is relevant to the subject by means of the verb "to be", an adjective, and it must have correct reference numbers. Therefore, logic must consist of sentences of a certain kind, in order to be formatted with the intention of revealing or displaying something. It is because of the former items that a logical sentence cannot exist unless it contains all of the previously mentioned grammatical parts.
Logic is a necessary to learn in order to process the many variables that affect our daily lives such as our beliefs, how to act, and how to judge others with fairness. Without logic one falls victim to many fallacies. According to Copi (1998), "Fallacies are a type of argument that may seem to be correct, but that proves, on examination, not to be so" (p. 690). If you are not able to pickup on fallacies it will affect decisions, actions and attitudes in one's life. Copi (1998) also states, "Logic is the study of the methods and principles used to distinguish correct from incorrect reasoning" (p. 1). By learning logic one is able to become aware of arguments that are flawed because you will involve yourself in assessing reasons. There are several different types of logic; the ones I am referring to are Aristotelian logic and Prepositional logic.
On one hand, it is necessary to discover and investigate correct modes of reasoning in which the property of «truth» is preserved. This task which can be formulated as the question «what is a correct reasoning (proof)?» is considered in Logic. In order to decide this problem, Logic is based upon the concept of «logical form». There is a special syntactical method to deal with this concept—the method of construction of a logical calculus. In this respect, the calculus in question is a «black box» which guarantees the «true» conclusion under the «true» premisses. Thus, Logic (logical form) gives the answer for the question about correct reasoning— «the correct reasoning is a proof». But logical syntax, as a «black box»— calculus, isn’t interested in the real process of derivation building, in studying the question about methods of proof-search, in studying and construction a more manageable and efficient machinery of «truth» preserving. Availability of any method of exhaustive (complete) search, e.g. «British museum algorithm», is quite enough for Logic (logical form).
Ayer's categorization of language places philosophical propositions in a logical system. Wittgenstein had proposed that logical propositions were nonsensical for the reasons that Ayer categorized them as logically significant; they do not correspond to sense data or anything in the world that can be explained by natural sciences. Instead, propositions of philosophy, aesthetics and even the divine lay in the novel formal and material category of logic.
Mathematics is one of the most important subjects of our life. It makes our life orderly and prevents chaos. There are certain qualities that are nurtured by Mathematics. These qualities are power of reasoning, creativity, abstract thinking, critical thinking, problem solving and even effective communication. Informed citizenship demands a good knowledge of Mathematics for such tasks as balancing budget and adjusting expenses for the computation of taxes. It helps an individual to tackle with everyday life problem. Moreover, Mathematics helps individuals for further studies and for better career. It prepares individuals for a wide variety of vocations in a rapidly changing technological world. It can be said that to some extent everybody is
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,
logic is expressed in terms of relations, represented as facts and rules. A computation is initiated by
Mathematical logic is something that has been around for a very long time. Centuries Ago Greek and other logicians tried to make sense out of mathematical proofs. As time went on other people tried to do the same thing but using only symbols and variables. But I will get into detail about that a little later. There is also something called set theory, which is related with this. In mathematical logic a lot of terms are used such as axiom and proofs. A lot of things in math can be proven, but there are still some things that will probably always remain theories or ideas.
Tractatus Logico-Philosophicus evolved as a continuation of and reaction to Bertrand Russell and G Frege’s conceptions of logic, which Russell has left unexplained. Wittgenstein developed a theory of language that was designed to explain the nature of logical necessity. For Wittgenstein, a factual proposition is true or false with no third alternative. He endorses a ‘picture’ theory of meaning: propositions are meaningful insofar as they ‘picture’ facts or states of affairs: if their structure mirrors the structure of the world. The book addresses the central problems of philosophy which deals with the world, language and thought, and proposes a solution to these problems which is grounded in logic and in the nature of representation. Language, thought and reality share a common logical structure, so understanding the structure of the language allows u...
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.
The logic helps me to think coherently and to differentiate between truth and validity. As the mathematical are always valid, there is no possibility that might contradict, as 2 + 2 equals 4 cannot be five. Moreover, he logic helps me to have a good relationship with my coworkers, and I respect that if I get the same respect for them and that leads to a good fellowship.