Scientific argument for God's existence

[rossum]

This doesn’t prove to me that all axioms are made-up or imaginary.

All axioms are made up. None are imaginary, at least not within the particular axiomatic system that uses them.

For instance in geometry, there are different versions of the parallel axiom: “Given a straight line and a point not on the line there are X lines parallel to the first line and passing through the point.”

X = 0 gives spherical geometry. X = 1 gives Euclidian geometry and X = 2 or more gives hyperbolic (or Lobachevskian) geometry. They are made up because we can pick any of them at will, so long as we remain consistent within the particular axiomatic system. For example, in spherical geometry the angles of a triangle add up to more than 180°, while in hyperbolic geometry they add up to less.

We can make up whatever axioms we want (as long as they are self-consistent). They do not have to conform to the external world.

Mathematicians are happy working in the abstract with any convenient set of axioms. Scientists work with the external world, so they select from the wide range of mathematical axioms available, those axioms which best match the world the scientists study. The good match between scientific mathematics and the world is due to the good selection of axioms to use by scientists. It does not have any deep philosophical significance, just scientists picking the tools that work best from a wide range of different possible tools/axioms.

Scientific mathematics is designed by scientists to match the external world to a high degree of accuracy. Nothing more is needed to explain the observed match.

 

[AlNg]

the existence of this mathematically structured universe does imply the existence of an intelligent and conscious God, conceiving it according to such mathematical structures.

The problem with that is that mathematics is contradictory whereas the mind of God is self consistent. For example, in algebra it is proven that 1 = 1 + 0. But in geometry it is proven that 1 = 1 + 1. The mathematical existence of such an obvious contradiction ( 1 = 1 + 1) argues that the real world is inconsistent, chaotic and has features which cannot be understood using mathematics.
See the BanachTarski paradox.

Banach Tarski Paradox | Brilliant Math & Science Wiki

The Banach-Tarski paradox is a theorem in geometry and set theory which states that a ...

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[Bradskii]

Scientific mathematics is designed by scientists to match the external world to a high degree of accuracy. Nothing more is needed to explain the observed match.

This. …

 

[Wesrock]

IWantGod:

Bradskii:

You could use any symbols and design any equation that reflects that.

It’s not the symbols that are interesting. Obviously the symbols in a book doesn’t mean that the story which those symbols represent are actually real events. What is interesting is that it remains true that 2 irreducible objects + another 2 irreducible objects equals 4 even if those objects don’t exist in the universe or even if we are not imagining them. It is an independent truth insomuch as it is true independently of events.

I agree. But the premise that one plus one equals two is conditional on there actually being two ‘somethings’ that can be counted. It is true when there are those two somethings and it would be true if those somethings were to exist (but currently don’t).

The figures map reality. They only describe it. You can’t describe something if it doesn’t exist or unless you offer a proposition - ‘if such and such conditions apply then one plus one etc’.

Well, that’s the question. Is the proposition meant by the symbols in standard arithmetic 1+1=2 mind independently true?

 

[Wesrock]

Mmarco:

the existence of this mathematically structured universe does imply the existence of an intelligent and conscious God, conceiving it according to such mathematical structures.

The problem with that is that mathematics is contradictory whereas the mind of God is self consistent. For example, in algebra it is proven that 1 = 1 + 0. But in geometry it is proven that 1 = 1 + 1. The mathematical existence of such an obvious contradiction ( 1 = 1 + 1) argues that the real world is inconsistent, chaotic and has features which cannot be understood using mathematics.
See the BanachTarski paradox.
Banach Tarski Paradox | Brilliant Math & Science Wiki

(Please Note: This uploaded content is no longer available.)

That’s not a contradiction it’s just a different operation using the same notation.

 

[AlNg]

That’s not a contradiction it’s just a different operation using the same notation.

1 = 1 + 1.
Subtract 1 from both sides.
0 = 1.
That seems like a contradiction to me. You get something (i.e., 1) from nothing (i.e., 0).

 

[Wesrock]

Wesrock:

That’s not a contradiction it’s just a different operation using the same notation.

1 = 1 + 1.
Subtract 1 from both sides.
0 = 1.
That seems like a contradiction to me. You get something (i.e., 1) from nothing (i.e., 0).

The geometry example isn’t base 10 arithmetic addition. It’s not the same operation. So subtraction isn’t its opposite, either.

 

[Bradskii]

Bradskii:

IWantGod:

Bradskii:

You could use any symbols and design any equation that reflects that.

It’s not the symbols that are interesting. Obviously the symbols in a book doesn’t mean that the story which those symbols represent are actually real events. What is interesting is that it remains true that 2 irreducible objects + another 2 irreducible objects equals 4 even if those objects don’t exist in the universe or even if we are not imagining them. It is an independent truth insomuch as it is true independently of events.

I agree. But the premise that one plus one equals two is conditional on there actually being two ‘somethings’ that can be counted. It is true when there are those two somethings and it would be true if those somethings were to exist (but currently don’t).

The figures map reality. They only describe it. You can’t describe something if it doesn’t exist or unless you offer a proposition - ‘if such and such conditions apply then one plus one etc’.

Well, that’s the question. Is the proposition meant by the symbols in standard arithmetic 1+1=2 mind independently true?

Go back to the time before life began. There is a big rock sitting next to a small rock. I’d say we have two rocks and that 1+1=2 was as true then as it is now.

 

[Mmarco]

I would like to suggest some considerations to those who say that maths is only a description of the universe:

A description does not have a predictive power; for example, we can make a map of a town. The map will describe the town but it will not tell us how the town will become during the next years. The map has no predictive power.

Besides, you can make a map of the town because both the town and the map have a geometrical structure. Could you make a map of a smell? No, it’s absurd, because a smell doesn’t have a geometrical structure. A working model must have a structure similar to the modelled entity.

There is no reason to expect that a mathematical model can be constructed so that it can sistematically predict natural phenomena, if nature didn’t have a rational and mathematical structure.

Quantum mechanics was developped in the first decades of last century, but it has predicted correctly thousands of experiments performed afterwards in different conditions.

Actually completely new phenomena, which had never been observed (and which had never been conceived ) have been discovered as a consequence of the study of the mathematical implications of the laws of phsyics (for example the existence of electromagnetic waves or the existence of antiparticles)

If the laws of physics didn’t describe the intimate structure of matter, these predictions would be to me just an unbelievably lucky series of coincidences.

To those who are discussing about “1+1=2”, I would like to say that “1+1=2” is neither an equation nor a mathematical model, but an identity based on our definition of natural numbers and the definition of sum of natural numbers. In particular the number “2” is BY DEFINITION equal to 1+1.

So the identity 1+1=2 has nothing to do with the much more complex mathematical relations expressed by the differential equations of the laws of physics.

 

[rossum]

I would like to suggest some considerations to those who say that maths is only a description of the universe:

Pure mathematics is not a description of the universe. Take geometry. Euclid started with 2-dimensional geometry. That was later extended to 1-dimensional geometry, -dimensional geometry, 0-dimensional geometry, 3- 4- 5- 6-dimensional geometry etc. Then later fractal geometries were developed: 2.345-dimensional geometry and so on.

That gives an infinite number of possible mathematical geometries. Only some of those many geometries reflect the real world. In classical physics scientists used a mix of 3-dimensional geometry for space and a modified 1-dimensional geometry (you can’t go backwards) for time. Einstein changed that, so now physics uses a 4–dimensional geometry for space-time. Cosmologists are looking at 11-dimensional geometry in some lines of research on the Big Bang.

Only a tiny subset of possible mathematical geometries are used by scientists. That tiny subset is selected by scientists because they provide a good, and useful, description of the universe. Science works to describe the universe, and a chosen subset of mathematics is one of the tools used in that description.

 

[STT]

I would like to suggest some considerations to those who say that maths is only a description of the universe:

As I said before, mathematical equations are foundation of any reality. A reality could look like this or that. That doesn’t prove anything.

 

[Mmarco]

As I said before, mathematical equations are foundation of any reality.

This is a strong assumtion of yours; I disagree .
For example, suppose that you want to build a mathematical equation able to predict exactly all the words I am going to pronounce in the next 24 hours; do you think such an equation may exist?
By the way, we know no equations able to account for consciousness as well as other psychical activities. (actually I think this would be another interesting topic!)

 

[STT]

This is a strong assumtion of yours; I disagree .
For example, suppose that you want to build a mathematical equation able to predict exactly all the words I am going to pronounce in the next 24 hours; do you think such an equation may exist?

No, I cannot because you are a free agent. But you are not supposed to add free agent into the discussion. In fact, I can show that free agent cannot be created. But that is subject of another thread. What I am arguing is that you cannot conclude that there is a creator given the fact that you are assuming that a reality is describable mathematically since any reality, minus free agent, are describable by a set of mathematical equations.

By the way, we know no equations able to account for consciousness as well as other psychical activities. (actually I think this would be another interesting topic!)

True. Consciousness is, in fact, a ability of mind.

 

[Bradskii]

I would like to suggest some considerations to those who say that maths is only a description of the universe:

A description does not have a predictive power;

Indeed. Neither does maths. Because it’s only a description. Even conditionals don’t predIlict. They only describe what happens IF conditions are met.

 

[Mmarco]

Mmarco:

I would like to suggest some considerations to those who say that maths is only a description of the universe:

A description does not have a predictive power;

Indeed. Neither does maths. Because it’s only a description. Even conditionals don’t predIlict. They only describe what happens IF conditions are met.

I am not sure to understand your point: the laws of physics are mathematical equations and they can predict systematically the natural phenomena, in this sense, the have a predictive power becuase they are not used to describe a static situation, such as a map describing a town.

 

[rossum]

I am not sure to understand your point: the laws of physics are mathematical equations and they can predict systematically the natural phenomena, in this sense, the have a predictive power becuase they are not used to describe a static situation, such as a map describing a town.

The laws of thermodynamics say that a gas in a container will fill the whole container, not be confined to one half of the container. That is only true if there are sufficient molecules of gas present. If only one molecule of gas is present then there is always one half of the container with no gas and the other half with all the gas.

Einstein’s General Relativity generally (!) works very well, but it fails in certain extreme situations. Hence the search for a theory of Quantum Gravity to resolve the issues.

A lot of scientific laws have limitations. Their predictive ability is limited, just as Newton’s gravity was limited, being unable to correctly predict the precession of the orbit of Mercury.

 

[Bradskii]

Bradskii:

Mmarco:

I would like to suggest some considerations to those who say that maths is only a description of the universe:

A description does not have a predictive power;

Indeed. Neither does maths. Because it’s only a description. Even conditionals don’t predIlict. They only describe what happens IF conditions are met.

I am not sure to understand your point: the laws of physics are mathematical equations and they can predict systematically the natural phenomena, in this sense, the have a predictive power becuase they are not used to describe a static situation, such as a map describing a town.

IF a planet has a certain mass and IF it is a specific distance from a star and IF that star has a specific mass then one equation will be a description of the planet’s orbit. It doesn’t predict - it describes.

If we’re not talking statistics then the generally accepted definition of a prediction would be ‘an informed guess’.

 

[Mmarco]

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IF a planet has a certain mass and IF it is a specific distance from a star and IF that star has a specific mass then one equation will be a description of the planet’s orbit. It doesn’t predict - it describes.

Let me try to clarify.
The laws of pysics predicts future phenomena; you may use the word “describe” if you like , but it is clear that we are not talking about a static situation. The laws of physics are not a mere description of " already observed phenomena" but they “predict/describe” systematically “not yet observed” phenomena. In order to to this, I think that the laws of physics must be a “description” of the intimate structure of nature, which was my initial point.

 

[Bradskii]

…I think that the laws of physics must be a “description” of the intimate structure of nature, which was my initial point.

Which, unless I am mistaken, is also my point.

A prediction is not generally used to forecast an event that will definitely happen. ‘If you jump out of a tenth floor window then I predict that you will die’. Really?

‘I predict that Liverpool will win the Premier League’.

That’s a reasonable statement based on opinions of squad size, player ability, preparation, strength of other sides etc.

‘Liverpool will win the Premier League IF tbey win more points that anyone else’

There is a simple equation for that statement. Which isn’t available for the first.

 

[Mmarco]

Which, unless I am mistaken, is also my point.

A prediction is not generally used to forecast an event that will definitely happen. ‘If you jump out of a tenth floor window then I predict that you will die’. Really?

At this point I think that the problem is that I am italian and I have used the wrong translation of the italian word “previsione” , which is used also in the case of events that will definitely happen as well as in physics.