Right, it's been a couple of week since I blogged, so it's time to dust the cobwebs off the keyboard and start enlightening everyone with the latest instalment in the world of HCJ. This week's topic will focus on the world according to our good old friend Bertrand Russell and his theories of mathematics and how these numbers can attribute to everyday language.
Mathematics is made up out natural numbers, which are words used to count things and this will then create a category of grouping. Going back to evolution and our primatial cousins they needs only three numbers: one thing, more than one thing and many things. In reality this does make perfect sense as smaller numbers will have different functions than to larger numbers.
Basic mathematical functions, such as add and multiple are empirically plurals of plurals. Creating words and abstract symbols for plurals requires a number-word system and logical syntax, which is then able to combine numbers-words to imply predicates and then these predicates can be analysed.
This can then help determine what is "Analytic Philosophy." It has been determined as the paradigm of analysis and modernism by synthetic German philosophers and shows how language is a vocabulary of symbols, syntax and grammar (predicate). However, there are limits the logical modelling of human intelligence.
Ancient civilisations such as the Egyptians used hieroglyphics for numbers and multiples. The Greeks and Romans system depended on numeric symbols and decided that 0 and 1 were not numbers and in Pythagorean logic, counting started with 2. In India the introduction of Leo came, but it was different as they determined that 0 equaled nothing and something at the same time, which was then adopted by Aristotle as the law of excluded logic.
Modern philosophers of mathematics have asserted 0 as a natural numbers. Number are seen as major and a platonic form with attributed magical properties E.G. 3, 7 and 13. From Greek numbers comes A priori from geometry and aesthetics. Special ratios are shown as the best example of Platonists and Pythagoreans as ratios are perfect and true and this also brought upon the beginning of the now close relationships between music and numbers. Now this is the point in the blog where we stop for our scheduled YouTube video, but instead of a cheesy pop number this week, we will go with something from the left field and with a Latin flavour:
Ok back to the world of mathematics and following Kant, Bertrand Russell believed that numbers and arithmetic were neither platonic ideal forms, nor empirical generalisations, but synthetic A Priori properties, which could in principle be defined logically.
Now after a year and a half of HCJ finally it is time for a brief summary of the life and times of Bertrand Russell. Russell was born in Trellech, Monmouthshire in 1872 into British aristocracy and was one of the first male supporters of the suffragette movement and even stood as an MP for the movement. In 1913 he wrote "Principia Mathematica" in opposition to Einstein's book on his theories of relativity. During World War 1 he was one of few who expressed Pacifist views and these views would lead to his eventual sacking in 1940 from New York University for immolation. He was also a campaigner for nuclear disarmament throughout the 1950's and was very vocal politically until his death in 1970, aged 98.
Russell began his career as a dedicated Hegelian idealist, but he retained some social theories, especially believing scientifically the media was strongly progressive. Maths did appear to be a contradiction of idealism because numbers appear to have objective existence in some cases and their nature is not determined by observation. According to Russell, number can not be understood unless in relation to another number E.G. the questions "What is number?", "What is a number?" and "What is meant by arithmetic?"
Peano showed how numbers van be deduced by the following axioms:
1. The constant 0 is a natural number.
2. X=Y every number has it's own equivalent.
3. Every natural numbers had a successor number.
4. There is no natural number whose successor is 0.
5. If the successor of N is equal to M , then N is equal to M in all number series.
The terms Zero, number and successor were remained undefined by Peano.
Nassau wanted to complete the project by providing objective definitions for zero, number and successor by using class, belonging to a class and similarity. Number is "the class of class similar to a given class."
So, there are number words that numerically corresponding a logical class composed of possible clauses have three members E.G. three cats, three dogs, three students. This will avoid the complication of 3 cats + 4 dogs equals 5 cat dogs. 3 is abstracted because it is from the empirical basis and is purely a logical category. The ultimate basis of the system is empirical observation, therefore platonic idealism is avoided by 3 as "this in itself."
No comments:
Post a Comment