a philosophy question : To what extent can u achieve complete certainty in mathematics and science?

Answer 1

Pure mathematics is quite different from the other natural sciences in that it starts from certain given assumptions/ideas/axioms and then takes it from that point on. The assumptions or axioms are just that. They do not represent "truths".

An analogy will make this clear. The game of chess is built on certain rules which everybody agrees on. Then you can analyse what is possible, impossible, stratagies etc within the game. Math is like this.

On the other hand, in say Physics you are always trying to find what the rules of the game are based on observing how it proceeds. Over time humans have discovered rules which are believed to be valid over certain domains of existence. However these rules can be superseded in time by more accurate rules. ie the existing rules are shown to fail in certain contexts.

So complete certainty in mathematics can be in principle and practice be achieved. In the other natural sciences complete certainty over all domains cannot be met but certainty in limited domains or certain general principles can be.

For example, evolution is a general principle which scientifically is certain but not everyone agrees on all the details (the "fine print"). Another example might be laws of mechanics which are certain in the macroscopic world to a great accuracy.

So complete certainty is pretty much the case in math, but that is only because math does not strive to determine universal truths of existence, only truths of mathematics.

Answer 2

Mathematics is an exact science. I could not imagine philosophy without mathematics. Many great philosophers had achieved their status because of mathematics and science. They have semblance in philosophy.

Indeed mathematics had dominated philosophy during the 7th century, giving to the world Descartes, Hobbes, Spinoza, Leibnitz and Pascal.

in the nineteenth century, in Schelling and Schopenhauer, in Spencer and Nietzsche and Bergson, biology was the background of philosophical thought.

Thanks for asking. Have a great day!

Answer 3

Ah yes, I have often thought about this topic. Mathematics is the most certain topic you can get. Using various proofs and theorems, you can prove with certainty different facts of math. Of course, these theorems, etc. had to be established, but they have been set and continue to stay. Science is somewhat more influenced by technology. New discoveries can not only add to our knowledge, but it can also change it, and that makes it different from mathematics in a way.

Hope that answered you question. ;)

Answer 4

If we take your question literally, the answer is zero. Even Mathematics relies on assumptions. If you go back far enough in any proof there is a fundamental assumption that everything else flows from. It may be obvious and common sense, but it is an assumption that cannot be proven. If that assumption is wrong, the rest is a house of cards built on sand.

Look at how many things we have "Known to be True" which have proven wrong over the years.

Answer 5

Certainity is connected truth of the problem.
Truth of any subject is limited by Godel's
incompleteness theorem:

In the 1930s, Austrian mathematician Godel
proved a theorem which became the "Godel
theorem" in cognition theory. It states that
any formalized 'logical' system in principle
cannot be complete in itself. It means that a
statement can always be found that can be
neither disproved nor proved using the means
of that particular system. To discuss about
such a statement, one must go beyond that
very logic system; otherwise nothing but a
vicious circle will result. Psychologists say
that any experience is contingent - it's
opposite is logically possible and hence
should not be treated as contradictory.

http://www.exploratorium.edu/complexity/CompLexicon/godel.html

http://www.search.com/search?q=Godel%27s+incompleteness+theorem

Answer 6

You can't. Mathematics is a language of symbols. It is totally based in the imagination and hypothetical situations.

Answer 7

You cannot fully understand one thing, without fully understanding everything.

~A good friend of mine