The Importance Of Logic And Mathematics

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.

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

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