Is the Unification of Sciences Possible?

[evagelos]

What is your opinion that every different science, physics, mathematics, phychology are different views of the same thing. For example boundaries in physics speed of light, boundaries in mathematics (godel principle) or in phychology (the unexplained of the personality) exist and try to explain the world from a different prism.

 

[CRGreathouse]

My opinion is that physics, mathematics, psychology are not different views of the same thing.

 

[HallsofIvy]

You can certainly say that they are different ways to explain the world but that does not make them "different views of the same thing" unless you are going to say they are different views of the world, which is trivial. So are history, art, and literature. There is nothing but "the world" (in the general sense- the entire universe which appears to be how you are using the word) and everything we do is dealing with it.

 

[Focus]

I am sorry to bring this up but mathematics is not a science. Oxford dictionary says science is "the intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment". Maths has no experiments (or observations for that matter, except for statistics which isn't really maths). The limitations in these fields are compleately different in my opinion. The limitations get weaker. Godels Incompleateness is a very strong limitation compared to speed of light (I do not know any psychology but I imagine its limitations are even weaker), as speed of light is a scientific theory and most of them seem to be proven wrong or improved on over the years due to the assumptions underlying a theory. The assumptions of mathematical theories are universal, which are the axioms. In my opinion Godels theorems are a limitation of the human knowladge, basically saying, humans can't know everything, and it is very simular to sciences in the manner that it also says that the assumptions on which scientific theories are based will never be compleate and consistent.

Sorry for the long cranky sounding reply, I'm not cranky really. :)

 

[peos69]

When you are trying to find out how much a bird can count,isn't that an mathematical experiment?? For example it is well known the experiment with the suspicious crow.

 

[CRGreathouse]

When you are trying to find out how much a bird can count,isn't that an mathematical experiment?? For example it is well known the experiment with the suspicious crow.

I think that there are mathematical experiments, but I don't count the above as such. Those would be experiments in biology, or something. I think of http://expmath.org/ as mathematical experimentation.

 

[HallsofIvy]

I am sorry to bring this up but mathematics is not a science. Oxford dictionary says science is "the intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment". Maths has no experiments (or observations for that matter, except for statistics which isn't really maths). The limitations in these fields are compleately different in my opinion. The limitations get weaker. Godels Incompleateness is a very strong limitation compared to speed of light (I do not know any psychology but I imagine its limitations are even weaker), as speed of light is a scientific theory and most of them seem to be proven wrong or improved on over the years due to the assumptions underlying a theory. The assumptions of mathematical theories are universal, which are the axioms. In my opinion Godels theorems are a limitation of the human knowladge, basically saying, humans can't know everything, and it is very simular to sciences in the manner that it also says that the assumptions on which scientific theories are based will never be compleate and consistent.

Sorry for the long cranky sounding reply, I'm not cranky really. :)

Not at all cranky- exactly right. Mathematics is NOT a "science" in the strict sense of adhering to the scientific method. I would go further- the philosophy underlying any science is necessarily "realist" (in the Philosophical sense) since the test of truth for a scientific theory is its confirmation by experiment- its correspondence to the "real world". Mathematics, on the other hand determines the truth (or better validity) of a theory by its consistency and so is necessarily based on "idealist" philosophy.

 

[evagelos]

well, ok mathematics is not science with the strict meaning, however who can say in a similar way that physics is a science? because of the experiments? well if we follow a idealistic philoshopy nothing is science. But the hard matter here is the following. The godel's theorem says that if we can set a group of axioms there will be always a truth that can not be validated by this axiom system. Well, the same boundary exist in physics or in phychology. I feel that these boundaries has something more to tell us. I can mention more similarities on this subject. These similarities has something to tell us. The world is not a mix of diferent parts. In such a way we loose the "important". The main issue.

 

[Focus]

Not at all cranky- exactly right. Mathematics is NOT a "science" in the strict sense of adhering to the scientific method. I would go further- the philosophy underlying any science is necessarily "realist" (in the Philosophical sense) since the test of truth for a scientific theory is its confirmation by experiment- its correspondence to the "real world". Mathematics, on the other hand determines the truth (or better validity) of a theory by its consistency and so is necessarily based on "idealist" philosophy.

Nice to see some pure mathematicians here. I thought most would be applied. The stuff we get taught is in no way a science, it doesn't even have any real life applications. Mathematics in my opinion is about proving that an answer or a solution exists (or not), it is up to scientists to determine what that is (which we call trivial :D). That is why I find it beautiful.

 

[peos69]

well, ok mathematics is not science with the strict meaning, however who can say in a similar way that physics is a science? because of the experiments? well if we follow a idealistic philoshopy nothing is science. But the hard matter here is the following. The godel's theorem says that if we can set a group of axioms there will be always a truth that can not be validated by this axiom system. Well, the same boundary exist in physics or in phychology. I feel that these boundaries has something more to tell us. I can mention more similarities on this subject. These similarities has something to tell us. The world is not a mix of diferent parts. In such a way we loose the "important". The main issue.

Evagelos my cousin just walked in and informed me that THERE EXISTS a group of axioms that it is complete and consistent too he calls it the propositional calculus,isn't that correct?

 

[Focus]

Evagelos my cousin just walked in and informed me that THERE EXISTS a group of axioms that it is complete and consistent too he calls it the propositional calculus,isn't that correct?

Those aren't axioms. Don't let the name (or your cousin) fool you, propositional calculus is not calculus like in maths, its a logical formal system. Axioms are added to propositional calculus to make it into a formal system. First order logic is consistent and complete. These are all a set of interference (?) rules. Any non-trivial set of axioms will lead to incompleteness or inconsistency.

 

[peos69]

So there DOES NOT EXIST a set of axioms which is complete and consintet ,tru or not?

 

[peos69]

And another thing everywhere I search in this forum the Godel guy is popping up.
CAN someone write here and now the theorems that the guy discovered word by word
PLEASE

 

[Focus]

So there DOES NOT EXIST a set of axioms which is complete and consintet ,tru or not?

Not, read my previous post.

And another thing everywhere I search in this forum the Godel guy is popping up.
CAN someone write here and now the theorems that the guy discovered word by word
PLEASE

Godels original work may be a little too formal for non-logicians. At the crust of the argument is that in any formal system with non-trivial axioms one can always construct a statement that says "I am not provable". If you can prove it, the system is inconsistent, if you can't its incomplete. If you really want to read his work, its in God Created Integers by Steven Hawking, which is an awesome book (has a lot of original publications). Before that you really should do a lot (I mean a lot) of reading on logic. Wikipedia won't help you much on this.

 

[peos69]

Are you a logician yourself?
By what you wrote above you implying:
1)mathematicians must become logicians to just read not to prove Godels theorems
2) integers and logic are inseparable
But anyway just write down those theorems not the proof

 

[peos69]

Godels original work may be a little too formal for non-logicians. At the crust of the argument is that in any formal system with non-trivial axioms one can always construct a statement that says "I am not provable". If you can prove it, the system is inconsistent, if you can't its incomplete..[/QUOTE]

I GET nothing out of it

 

[Focus]

Are you a logician yourself?
By what you wrote above you implying:
1)mathematicians must become logicians to just read not to prove Godels theorems
2) integers and logic are inseparable
But anyway just write down those theorems not the proof

1) Mathematics and logic are separate things, logic is not just some basic thing that everyone can learn, it is quite complex.
2) Logic is a tool for applying on various fields, they are separable.

No I am not a logician, I did take courses on logic though and read various books on the subject and discussed them with my logic lecturer. By no means am I able to comprehend Godels work nor would I consider myself a reliable source on the subject.

Please be a bit more patient and trust my word that even the statement of the theorems requires deep understanding of logic (Godel numberings, recursive functions, formal systems ect..). If you wish to read on Godels work please make your own research or buy the book I suggested.

 

[D H]

well, ok mathematics is not science with the strict meaning, however who can say in a similar way that physics is a science? because of the experiments?

Mathematics is not science, period, because it does not use the scientific method. It is grounded to axioms and production rules. If you don't like the axioms you are free to make your own. For example, say you aren't thrilled with the parallel postulate. In mathematics, are free to make up a new postulate. You can then generate new mathematical theorems from this new set of axioms. If these theorems are useful your new mathematical system will thrive. Of course, if a logical contradiction pops up out of your new set of axioms your new system is toast. (Mathematicians loathe contradictions for the simple reason that one can prove anything if a statement and its negation are both true.)

Science, unlike mathematics, is grounded in reality. Science uses mathematics and logic to explain reality, but the ultimate goal is to explain reality. While mathematicians are free to make up a new version of mathematics, scientists are not free to make up a new version of reality. Science uses a different kind of reasoning than mathematics, and this scientific reasoning is essentially invalid logically. Every observation of a black crow serves as confirming evidence of the scientific theory that all crows are black.

Notice the difference in terminology: Science is based on theories while mathematics is based on theorems. There is a huge difference between the two. Mathematical theorems can be proven to be true, and once proven true they remain true forever. Scientific theories can be proven to be false, and once proven false they remain false forever.

 

[peos69]

No definitely not ,write down those theorems otherwise i will do it tomorrow
So conclusion is that nearly every day nearly by every body in nearly every instant Godel is mentioned to solve things out and yet nobody understands his work.
How about Mathematical logic .IS it separated from maths?

 

[peos69]

OK dh tomorrow i got to ask a couple of questions

 

[HallsofIvy]

well, ok mathematics is not science with the strict meaning, however who can say in a similar way that physics is a science? because of the experiments? well if we follow a idealistic philoshopy nothing is science.

I get the impression you are repeating words that you do not understand. I mentioned "idealist philosophy" but I certainly did not imply anything like that. I don't see how you say "if we follow a idealistic philoshopy nothing is science" unless, of course, you really have no idea what an"idealist philosophy" is.
Oh, and we can say "in a similar way" that physics is a science because we know what the scientific method is and know that physics follows it.

But the hard matter here is the following. The godel's theorem says that if we can set a group of axioms there will be always a truth that can not be validated by this axiom system.

No, Godel's theorem (actually he had many but I think I know which you mean) said nothing of the sort.

Well, the same boundary exist in physics or in phychology. I feel that these boundaries has something more to tell us.

What "boundaries" are you talking about? You mention Godel's theorem but it says nothing about a "boundary".

I can mention more similarities on this subject. These similarities has something to tell us. The world is not a mix of diferent parts. In such a way we loose the "important". The main issue.

The main issue is learning what words mean before you use them.

 

[evagelos]

I get the impression you are repeating words that you do not understand. I mentioned "idealist philosophy" but I certainly did not imply anything like that. I don't see how you say "if we follow a idealistic philoshopy nothing is science" unless, of course, you really have no idea what an"idealist philosophy" is.
Oh, and we can say "in a similar way" that physics is a science because we know what the scientific method is and know that physics follows it.


No, Godel's theorem (actually he had many but I think I know which you mean) said nothing of the sort.

What "boundaries" are you talking about? You mention Godel's theorem but it says nothing about a "boundary".


The main issue is learning what words mean before you use them.

well, i will talk about boundaries, recall quantum mechanics and heinseberg inequalities.
if we notice a smal particle, measuring the exact position we do not know or having idea about the momentum. This is analogus to the axiom of choice in mathematics. When i choose a particle in a wide meaning of the word, this is a choice and this choice introduces human into the science. The same does the axiopm of choice. If there is not somenone to use this choice in the set theory, all the analyis falls to pieces. So the unification in the wide meaning of word has to make more humble and not to trust proud dictionaries.

 

[D H]

if we notice a smal particle, measuring the exact position we do not know or having idea about the momentum. This is analogus to the axiom of choice in mathematics. When i choose a particle in a wide meaning of the word, this is a choice and this choice introduces human into the science. The same does the axiopm of choice. If there is not somenone to use this choice in the set theory, all the analyis falls to pieces.

No, your analysis falls to pieces. You really do need to follow Hall's advice and learn the meaning of concepts before you start talking about them.

 

[peos69]

The same does the axiom of choice. If there is not someone to use this choice in the set theory, all the analysis falls to pieces. .

This the only truthful statement i come across this Forum

 

[peos69]

Who really in this Forum understands the meaning of the concepts that she/he uses in their arguments??

 

[matticus]

mathematics is a priori and physical sciences are a posteriori. i think this difference is a very big one and big enough at least to say they're not the same things.

 

[Focus]

This the only truthful statement i come across this Forum

Godel proved that Axiom of Choice does not make the system any more or less consistent or complete.

What is yellow, sour and a bit like the Axiom of Choice?
Zorns lemon :D

 

[peos69]

nice

 

[evagelos]

No, your analysis falls to pieces. You really do need to follow Hall's advice and learn the meaning of concepts before you start talking about them.

I know the concepts, however, i would like you to stay in the analogies between physics and mathematics. Just observe these analogies. There is something more than the obvious...

Easy answers from an extra specialised view can not combine the whole.

 

[evagelos]

Another example is that in modern string theory about the genesis of cosmos, the continuity of space can not be prooved due to the fact that dimensions are not even four. Therefore the unification of sciences can not be assesed in a logistical manner.
Hence, the present meaning of concepts may loose their power and may you find yourselves on the wrong side of events.