The Limits of Science

[KBCid]

Exact Sciences use Logic every day to reach to conclusions.
Logic cannot prove anything, as prove by Godel.
PS. If mathematicians are not scientists, what are they?

Einstein - General relativety rationalised by mathematical model backed by scientific method.

"at the age of sixteen Einstein had discovered a paradox by considering what would happen if one could follow a beam of light a the speed of light -- the result being 'a spatially oscillatory electromagnetic field at rest.'"
For nine years he quietly worked on this insight and others and in 1904 at the age of 25 he had his ideas on paper. In 1905 he published them. One of the papers was theory of relativity that revolutionized the view of the universe. On of the other papers was used for his Nobel Prize years later.
He did not have a doctorate or even an advanced degree. He was not at a university working with others. He was alone.
http://www.tparents.org/library/unifica ... tein1a.htm

Being scientific does not require a degree to prove someone is a scientist. When you follow the scientific method then you have become a scientist. Those who practice the scientific method are scientist who submit their concepts and methods for backing by others who can produce or reproduce them.

The funny part in our time is that people with degrees in science tend to go beyond the scientific method depending on the degree to give their word a sense of real meaning. Strangely it seems to work when you see the many 'sheep'le who reference such people and their concepts to rationalise reality.

Everything can be explained by the undirected actions of natural forces...
Abiogenesis...
All life originates from a single common ancestor...
Life evolved / s ....
String theory....
Multiple universes...
The universe (Time and space) has a beginning...
The speed of light is static...
matter can come from nothing...
Intelligence resulted from chance occurances...
Thought is dictated by chemical interaction...
etc. etc.

[skakos]

If you're referring to Godel's incompleteness theorem, you should note that this only applies to certain axiomatic sets not all. For instance, if you take addition, identity, and some other basic axioms across the natural numbers, every true statement will be accounted for in this set by the axioms. First-order logic is likewise sound and complete for all possible propositions. You can't assert that every set of axioms is incomplete, that's very brash and is based on a misunderstanding of his incompleteness theorem. Further, science doesn't rely on a set of axioms in the way that mathematics does, it simply uses models and explanations. It doesn't try to account for all knowledge, it only tries to provide some knowledge on a more top-down level, and this isn't necessarily a problem. Using this can't disprove the accuracy of a model nor the explanatory power of a theory.

Why can't we say that incompleteness theorem applies to all theories based on a set of axioms?
I did not see any "disclaimer" of that kind in the theorem.

[skakos]

Exact Sciences use Logic every day to reach to conclusions.
Logic cannot prove anything, as prove by Godel.
PS. If mathematicians are not scientists, what are they?

Einstein - General relativety rationalised by mathematical model backed by scientific method.

"at the age of sixteen Einstein had discovered a paradox by considering what would happen if one could follow a beam of light a the speed of light -- the result being 'a spatially oscillatory electromagnetic field at rest.'"
For nine years he quietly worked on this insight and others and in 1904 at the age of 25 he had his ideas on paper. In 1905 he published them. One of the papers was theory of relativity that revolutionized the view of the universe. On of the other papers was used for his Nobel Prize years later.
He did not have a doctorate or even an advanced degree. He was not at a university working with others. He was alone.
http://www.tparents.org/library/unifica ... tein1a.htm

Being scientific does not require a degree to prove someone is a scientist. When you follow the scientific method then you have become a scientist. Those who practice the scientific method are scientist who submit their concepts and methods for backing by others who can produce or reproduce them.

The funny part in our time is that people with degrees in science tend to go beyond the scientific method depending on the degree to give their word a sense of real meaning. Strangely it seems to work when you see the many 'sheep'le who reference such people and their concepts to rationalise reality.

Everything can be explained by the undirected actions of natural forces...
Abiogenesis...
All life originates from a single common ancestor...
Life evolved / s ....
String theory....
Multiple universes...
The universe (Time and space) has a beginning...
The speed of light is static...
matter can come from nothing...
Intelligence resulted from chance occurances...
Thought is dictated by chemical interaction...
etc. etc.

I would agree that many scientists today use specific conclusions of very limited-scope theories to promote philosophical ideas of a much greater scope...

Materialism has taken over modern science and it is really hard to find spirit anywhere if you start with the AXIOM that all that exists is "matter"...

[Beanybag]

If you're referring to Godel's incompleteness theorem, you should note that this only applies to certain axiomatic sets not all. For instance, if you take addition, identity, and some other basic axioms across the natural numbers, every true statement will be accounted for in this set by the axioms. First-order logic is likewise sound and complete for all possible propositions. You can't assert that every set of axioms is incomplete, that's very brash and is based on a misunderstanding of his incompleteness theorem. Further, science doesn't rely on a set of axioms in the way that mathematics does, it simply uses models and explanations. It doesn't try to account for all knowledge, it only tries to provide some knowledge on a more top-down level, and this isn't necessarily a problem. Using this can't disprove the accuracy of a model nor the explanatory power of a theory.

Why can't we say that incompleteness theorem applies to all theories based on a set of axioms?
I did not see any "disclaimer" of that kind in the theorem.

Quoted from: http://en.wikipedia.org/wiki/G%C3%B6del ... s_theorems

Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic.

In other words, it only applies to arithmetic sets of axioms such as Peano Arithmetic. It likely has far reaching impacts on other axiomatic systems, but it must be shown on a case by case basis generally. I'm pretty sure that an incompleteness general algorithm will be undecidable, so I don't think there's a general rule.

So, in other words the incompleteness theorem doesn't apply for two reasons. 1) Science isn't an arithmetic system and 2) Science is not establishing a set of axioms.

[skakos]

Mathematics is the most pure of sciences.
If mathematics cannot prove "everything" within the scope of their axioms, the same applies for other less pure sciences which ALSO RELY ON AXIOMS. (and which also rely ypon logical methods, e.g. induction, to reach to conclusions based on premises.

The logic is the same. And so are the limitations.

Like physics for example...
If physics is based on the axiom "only matter exists" then it cannot certainly go any further that the tip of its nose in explaining humans...

[Beanybag]

Mathematics is the most pure of sciences.

That's quite a thing to say. The only mathematics that even approaches the ambiguity of science would be maybe probabilistic reasoning. Computer science is a science in name only as proofs are still used. Nothing in science is proven. Everything in mathematics is. A scientist might look at the Reimann hypothesis and conclude its validity through induction, since we know it is valid for the first 10^10^10 billion integers, or so. But a mathematician would never accept such a 'proof'.

If mathematics cannot prove "everything" within the scope of their axioms, the same applies for other less pure sciences which ALSO RELY ON AXIOMS. (and which also rely ypon logical methods, e.g. induction, to reach to conclusions based on premises.

Science is more akin to a philosophy. If you want to try and prove that all of math reduces to logic, so that logic and math are the same, be my guest. That would be a revolutionary proof indeed. But science is not math and vice versa. They are distinct, even if science sometimes uses mathematics. Also, the 'axioms' of science lack much of the rigor of axiomatic mathematical systems. Laws are hardly comparable to axioms. Your point may still stand (that the knowledge science can ascertain is limited) but using mathematical tenets to get there is not working.

[1over137]

How can science study phenomena which happen only ONCE? (e.g. the creation of the Universe) How can it study things which cannot be reproduced?

Science can study such phenomena. But depends on what you mean by studying it. There may be leftovers for example.

[1over137]

Exact Sciences use Logic every day to reach to conclusions.
Logic cannot prove anything, as prove by Godel.

PS. If mathematicians are not scientists, what are they?

I'm really not sure what you're talking about, Godel proved no such thing. Mathematics is wholly and entirely seperated from science. Logic is also possibly very different than mathematics. Math and logic are used heavily in science, but models are not necessarily dependent on either philisophically.

Mathematics separated from science. What?

[skakos]

How can science study phenomena which happen only ONCE? (e.g. the creation of the Universe) How can it study things which cannot be reproduced?

Science can study such phenomena. But depends on what you mean by studying it. There may be leftovers for example.

These "leftovers" could be important though...

[Sam1995]

How can science study phenomena which happen only ONCE? (e.g. the creation of the Universe) How can it study things which cannot be reproduced?

Science can study such phenomena. But depends on what you mean by studying it. There may be leftovers for example.

These "leftovers" could be important though...

Part of the reason why science will always leave left overs is because if there were NO leftovers, then we would have a logical, intelligible and correct way to explain the origin of the universe, the origin of life, the origin of morality, whether or not life has a purpose, etc.

Where I'm going with this is this, if science can answer EVERYTHING, then where does God fit in?

[PaulSacramento]

Science can ONLY comment on the observable world.

[GreyDeSilvisanctis]

Where I'm going with this is this, if science can answer EVERYTHING, then where does God fit in?

So follow up question on your question:
Is He the answer?
Well, I believe He is.

Science can ONLY comment on the observable world.

Yes, quite so. I think observation is the epitome of science and nothing more, nothing less.

~Grey

[Sam1995]

Where I'm going with this is this, if science can answer EVERYTHING, then where does God fit in?

So follow up question on your question:
Is He the answer?
Well, I believe He is.

~Grey

Exaclty, there's my point.
If science could explain the universe away without a need for God (which is cannot currently do) then one of two things would be happening:

a) God is deceiving us with His creation because it can be explained without a need for His existence
b) God doesn't exist

Doesn't seem like very good set of options, if I'm honest.

SB

[Byblos]

Where I'm going with this is this, if science can answer EVERYTHING, then where does God fit in?

So follow up question on your question:
Is He the answer?
Well, I believe He is.

~Grey

Exaclty, there's my point.
If science could explain the universe away without a need for God (which is cannot currently do) then one of two things would be happening:

a) God is deceiving us with His creation because it can be explained without a need for His existence
b) God doesn't exist

Doesn't seem like very good set of options, if I'm honest.

SB

Can science ever answer for itself?

[Sam1995]

Where I'm going with this is this, if science can answer EVERYTHING, then where does God fit in?

So follow up question on your question:
Is He the answer?
Well, I believe He is.

~Grey

Exaclty, there's my point.
If science could explain the universe away without a need for God (which is cannot currently do) then one of two things would be happening:

a) God is deceiving us with His creation because it can be explained without a need for His existence
b) God doesn't exist

Doesn't seem like very good set of options, if I'm honest.

SB

Can science ever answer for itself?

What do you mean exactly? Because my immediate response would be that if we look at chemistry, for example, we can see how different chemicals react with each other and produce certain results, here science answers for itself without the need for any other input, but I'm not totally clear that's what you meant!

SB