Mathematics & Philosophy
Description of Mathematics & Philosophy;
|| So many People have seen Mathematics and Philosophy are so contradicting and without any relation, and many other people indeed see that philosophy maintains the closest relation to mathematics. So, Who is right? and What are the relations between math and philosophy? In what do they differ and in what are they similar?
As a Definition, Mathematics comes from the greek word "mathema", which means the study of natural quantities, shapes, relationships between n-numbers of things and the variations of things with respect to a variation of a given trait based on a given number of axioms and postulates (which are absolute and do not differ from a mathematical system to another). For example, as expressed mathematically, by the simplest way, y=ax, where any value "y" variates as x times varies for every value of x, where a is a constant coefficient called the slope, (the rate of the change of the whole function).
While Philosophy means the study of basic concepts in general that are related to reality, existence, truth, religions, language based on a rational argument and sense of logic. That it doesn't suffice itself with asking "for example" what is the truth? and answering : It is what really happened and what really should have happened. It goes deep inside the answer and asks, why should it have happened this way? Why should it happen from the first place? Why is this really happened? Of course as mentioned above based on a rational argument and logical axioms, (that may differ from a school of thought to another).
Starting with the similarities between mathematics and philosophy, One could say that math is similar to philosophy in its systematic approach using logic, axioms and definitions besides the fact that both relate things to each other. Like philosophy for example says, The existence would not have existed from nothing, because absolute nothing means that nothing will be found, So if one sees an existence he can imply that something found it". Similarly mathematics says that if y is differentiable then y' is differentiable under some given conditions, if the square has 4-9o degrees, and 4 equal sides, then any similar figure is a square.
That is, Both use the deductive method of answering questions, according to some given basic law.
Mathematics, However, Differ than philosophy in A MAJOR DIFFERENCE, That is, the answers that math gives are absolute and certain and undoubtable because most of them are BASICALLY based on nature and observation and abstract logic. For example, 1+1=2, it s certain and absolute for every two things you put besides each other you will get two things in result. or for example, the integral of x is 1/2 x^2 for any function whatever its name is and for every one linear variable it contained whatever the variable was and whatever the function was(in terms of its naming, as g(x), f(x), h(y), z(q) etc.)
While philosophy gives an uncertain answer that remains for every time a doubtable answer.
Another difference is that, philosophy's axioms that it moves from are not abstract, rational (sometimes) but not abstract. The philosopher moves from what he likes to prove or disprove using arguments that are convincing but are not true some of the times. That s why you see a diversity in the opinions about one philosophical issue like creation and existence, like the mind and its capabilities & etc.
While the fact that mathematics is true and absolute comes from the fact that mathematics as mentioned above moves from given axioms based on natural observation, of course the mathematician being abstract and searching for the truth not for what he likes to prove or disprove but in generalized form. So, in mathematics what is stated as a theorem is absolute and verified for every case. Still sometimes, postulates can be broken but both are true in the given frame of reference, like in differential geometry, when Riemann rejected the fact that space-time is flat and broken the inherited Euclidean Postulates about lines and planes, HOWEVER, BOTH ARE TRUE, EUCLID AND RIEMANN, According to the space you are in.
In Concluding this comparison, We restate the similarities: They are similar in their logical (sometimes in philosophy) approach and search based on axioms and given postulates.
And they differ in: Math is absolute while philosophy is not, it can be still doubted and disproved.
Math is 100% rational and abstract, while philosopher is not, mathematician searches for the truth, philosophers create a truth based on a imagination and make a imagination is a truth based on convincing arguments.
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As a Definition, Mathematics comes from the greek word "mathema", which means the study of natural quantities, shapes, relationships between n-numbers of things and the variations of things with respect to a variation of a given trait based on a given number of axioms and postulates (which are absolute and do not differ from a mathematical system to another). For example, as expressed mathematically, by the simplest way, y=ax, where any value "y" variates as x times varies for every value of x, where a is a constant coefficient called the slope, (the rate of the change of the whole function).
While Philosophy means the study of basic concepts in general that are related to reality, existence, truth, religions, language based on a rational argument and sense of logic. That it doesn't suffice itself with asking "for example" what is the truth? and answering : It is what really happened and what really should have happened. It goes deep inside the answer and asks, why should it have happened this way? Why should it happen from the first place? Why is this really happened? Of course as mentioned above based on a rational argument and logical axioms, (that may differ from a school of thought to another).
Starting with the similarities between mathematics and philosophy, One could say that math is similar to philosophy in its systematic approach using logic, axioms and definitions besides the fact that both relate things to each other. Like philosophy for example says, The existence would not have existed from nothing, because absolute nothing means that nothing will be found, So if one sees an existence he can imply that something found it". Similarly mathematics says that if y is differentiable then y' is differentiable under some given conditions, if the square has 4-9o degrees, and 4 equal sides, then any similar figure is a square.
That is, Both use the deductive method of answering questions, according to some given basic law.
Mathematics, However, Differ than philosophy in A MAJOR DIFFERENCE, That is, the answers that math gives are absolute and certain and undoubtable because most of them are BASICALLY based on nature and observation and abstract logic. For example, 1+1=2, it s certain and absolute for every two things you put besides each other you will get two things in result. or for example, the integral of x is 1/2 x^2 for any function whatever its name is and for every one linear variable it contained whatever the variable was and whatever the function was(in terms of its naming, as g(x), f(x), h(y), z(q) etc.)
While philosophy gives an uncertain answer that remains for every time a doubtable answer.
Another difference is that, philosophy's axioms that it moves from are not abstract, rational (sometimes) but not abstract. The philosopher moves from what he likes to prove or disprove using arguments that are convincing but are not true some of the times. That s why you see a diversity in the opinions about one philosophical issue like creation and existence, like the mind and its capabilities & etc.
While the fact that mathematics is true and absolute comes from the fact that mathematics as mentioned above moves from given axioms based on natural observation, of course the mathematician being abstract and searching for the truth not for what he likes to prove or disprove but in generalized form. So, in mathematics what is stated as a theorem is absolute and verified for every case. Still sometimes, postulates can be broken but both are true in the given frame of reference, like in differential geometry, when Riemann rejected the fact that space-time is flat and broken the inherited Euclidean Postulates about lines and planes, HOWEVER, BOTH ARE TRUE, EUCLID AND RIEMANN, According to the space you are in.
In Concluding this comparison, We restate the similarities: They are similar in their logical (sometimes in philosophy) approach and search based on axioms and given postulates.
And they differ in: Math is absolute while philosophy is not, it can be still doubted and disproved.
Math is 100% rational and abstract, while philosopher is not, mathematician searches for the truth, philosophers create a truth based on a imagination and make a imagination is a truth based on convincing arguments.
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However both Mathematics & Philosophy claim that study reality and nature but in fact they are just fancy Cause they talk about some rubbish thing If u don't suppose any real thing (spatial & Geometrical & Observable) for mathematicals equations all equations will be rubbish. And lots of speeches with lots of defficult words! in philosophy with too many ISM are rubbish cause no relevance between them and reality. lots of ism with lots of different rules and laws to shape your mind means you are not free with philosophy u must be pet of some others people that control and ride you!
Absolute answer of mathematics & doubtable answer of philosophy!
there s no certainty in real world cause Uncertainty principle governs.
and doubtable answers of philosophy means no powerful and strong Idea in philosophy (everyone can have own ism!)
But in Physics, physicists must think and simulate & imagine lots of thing and compare them with observable environments then to summarize their achievements use mathematical equations.
It s Science.
It s Science.
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