A New Proof for the Existence of God

[Peter_Plato]

Peter, this makes it appear that you don’t know the difference between a priori and a posteriori, between deduction and induction, between analytic and synthetic. I’m guessing you do, just saying it makes it look like you don’t.

I see you haven’t lost your “Dance like a bee, sting like a butterfly,” Mohammad Ali style savoir faire.

 

[Oreoracle]

Legislated laws are no different in that respect. Legislated laws don’t just appear to be laws. They are laws, and whoever disobeys them will be subject to the consequences.

Legislated laws are different in this respect, actually. I can break a legislated law, but not a law of physics. In fact, with sufficient skill, one can break a legislated law without consequences. So legislated laws are more prescriptive in nature, whereas laws of physics are descriptive.
Charlemagne III:

The apparent theoretical conflict in laws (relativity versus quantum physics) cannot be an actual conflict in nature. Einstein was convinced of this. His take was that we simply do not understand how to reconcile the two systems of physics. After all, it may well be that the human mind is following a law of its own; that is, a physical law that says you are wired to understand so much, but not more.

that is only if you accept the Copenhagen interpretation of QM, which Einstein did not.

Although it is admirable to defend Einstein, he was quite wrong when it came to quantum mechanics. Einstein flat out rejected quantum mechanics for most of his life and refused to do any work in the field. (He spent the last of his career trying to unify classical theories of physics while completely ignoring the development of quantum mechanics.) Only near the end of his life did he give the new theory any credit at all. He conceded that it was useful, but he still doubted its truth.

His interpretation, as Tomdstone suggests, is that the laws only appear to be probabilistic because we have incomplete information. This is simply not true. One can look at the Wikipedia article over Heisenberg’s Uncertainty Principle for an example. The uncertainty is inherent in nature. The uncertainty is not a reflection of our ignorance as Einstein so desperately wanted to believe.

Probabilistic formulations may indicate a lack of knowledge about all the variables involved, such as for example.

This interpretation is called a “local hidden variable theory”. This has been disproven by Bell’s Theorem, which also has a Wikipedia article dedicated to it.

 

[Oreoracle]

I don’t believe that is true. That is an unwarranted assumption with nothing to back it up. Take for example, the parallel postulate in Euclidean geometry. That exists because of our perception of the real world as Euclidean. However, later on, it was found that there are spherical and hyperbolic possibilities in reality and Euclidean geometry was expanded to include these possibilities.

Actually, a little research on your part would reveal that these geometries were developed before any application of them was even known to exist. They were invented because mathematicians wanted to know whether the Parallel Postulate was independent of the other axioms of Euclidean geometry. The fact that other consistent geometries could be made by replacing the postulate affirms that it is indeed independent.

Checking the consistency of an axiomatic system is a logical problem, not an empirical problem. It can be done without appealing to the “real world”.

Further, relativity theory resulted in further developments in mathematical theory. All of these developments were confirmed by constraints and observations in the real world.

Interestingly enough, General Relativity made use of differential geometry, which had begun at least 150 years earlier and was largely useless in terms of practical applications until then. Face it, math often develops independently of its uses.

If you changed your mathematics and said that 1+1=3, you would be wrong. You can’t change mathematics to be an inconsistent science and be credible at the same time.

False. Again, there are nice Wikipedia articles over these matters if you care to look them up. There are plenty of consistent ways of doing algebra that differ from the standard field of real numbers. For example, in some fields, powers distribute over addition.

As a simple example that has nothing to do with fancy algebraic notions, consider differing number systems. 1+1=10 in binary. That is mostly a matter of notation, but it illustrates the point.

 

[Peter_Plato]

Checking the consistency of an axiomatic system is a logical problem, not an empirical problem. It can be done without appealing to the “real world”.

Unless, of course, the axioms of an axiomatic system are accurate depictions of the empirical world, then the logical problem becomes one where an appeal to the “real world” is inherent in the axiomatic system.

While it may be true that checking the consistency of an axiomatic system CAN be done without appealing to the “real world” that does not mean the real world CANNOT be appealed to or, perhaps, even must be appealed to as a requirement to check the adequacy - if not the consistency - of some axiomatic systems.

 

[Oreoracle]

While it may be true that checking the consistency of an axiomatic system CAN be done without appealing to the “real world” that does not mean the real world CANNOT be appealed to or, perhaps, even must be appealed to as a requirement to check the adequacy - if not the consistency - of some axiomatic systems.

I mostly agree, except when you say that it may be necessary to appeal to the real world to check for consistency. Even if we were omniscient with respect to the physical world, this would not demonstrate the consistency of the mathematics of our physical theories or the underlying logic of that math.

Proving consistency is harder than demonstrating “adequacy” (as you call it), because one must be sure that the axiomatic system is consistent for all of its possible uses, not just the practical ones that are likely to show up in real world affairs. In fact, Gödel’s work shows that consistency is impossible to prove for sufficiently complicated systems unless one assumes an even more complex system beforehand.

 

[Tomdstone]

Their brains have neurons, just as ours do. They have consciousness and memory.

They lack the ability to do physics or metaphysics.

However, I believe that they can do elementary arithmetic.

 

[Tomdstone]

Not according to the Borde-Guth-Vilenkin (BGV) Theorem which states that “any universe, which has, on average, a rate of expansion greater 0 that system had to have a finite beginning.”

There are four possible exceptions to a finite universe, but the conditions for the exceptions to obtain are untenable.

Not according to Anthony Aguirre who says that a geodesically incomplete region grafted onto a spacetime region which is not eternally inflating may extend infinitely into the past.
arxiv.org/abs/gr-qc/0301042
“We develop our recent suggestion that inflation may be made past eternal, so that there is no initial cosmological singularity or “beginning of time”.”

 

[Tomdstone]

Actually, False. Again, there are nice Wikipedia articles over these matters if you care to look them up. There are plenty of consistent ways of doing algebra that differ from the standard field of real numbers. For example, in some fields, powers distribute over addition.

As a simple example that has nothing to do with fancy algebraic notions, consider differing number systems. 1+1=10 in binary. That is mostly a matter of notation, but it illustrates the point.

Sorry, but I claim that you are wrong. You cannot have a consistent non-trivial mathematics which states that 1+1=3 in the decimal system. Give us a reference to some mathematician who says so. Your example that 1+1 = 10 in the binary system is completely equivalent to 1+1=2 in the decimal system. (10)_binary base = (2)_base 10. So your example in no way contradicts my statement that you cannot have 1+1=3 in the decimal system. That 1+1 = 3 is impossible can be easily proven. Simply subtract 2 from both sides and you are left with 0=1. I challenge you to find one mathematician in the entire world who says that 0=1 is consistent and can lead to non-trivial mathematics.

 

[Tomdstone]

In fact, Gödel’s work shows that consistency is impossible to prove for sufficiently complicated systems unless one assumes an even more complex system beforehand.

Not true, because Gerhard Gentzen proved the consistency of Peano arithmetic using ordinal analysis.
gdz.sub.uni-goettingen.de/dms/load/img/?PPN=GDZPPN002278391&IDDOC=37344

 

[Charlemagne_III]

However, I believe that they can do elementary arithmetic.

Yes, I expect they will be drawn to the bigger clump of bananas rather than the smaller clump.

 

[Oreoracle]

Sorry, but I claim that you are wrong. You cannot have a consistent non-trivial mathematics which states that 1+1=3 in the decimal system.

If you want an example of genuinely conflicting axiomatic systems, look no further than Euclidean geometry vs. hyperbolic geometry. If you adopt the view that there is some “absolute truth” floating out there somewhere, then one of them must be “right” and the other “wrong”.

But you cannot decide which is right or wrong because you can’t compare two axiomatic systems with different axioms. There’s no way to decide which axioms are right. If you could decide such a thing, you could prove those axioms.

Some other examples of mathematical ideas that are counterintuitive or contentious:

1. Pretty much any expansion of the real number system was fought every step of the way, such as the complex number system and the hyperreal number system. So if you ask something like “Does x^2+1=0 have a solution?” the answer will depend on the axioms you’ve chosen.
2. Some mathematicians to this day still dislike the inclusion of the Axiom of Choice in set theory.

Some arithmetical examples:

1. You may have heard of floating point arithmetic, which deals with formal ways of approximating tedious calculations. It is a common joke that 2+2 could equal 5 in floating point arithmetic because of rounding errors.
2. Some versions of arithmetic are uninterested in equality and look at weaker relations, such as congruence. Modular arithmetic lets you choose a modulus and regard two numbers as equivalent provided that their difference is a multiple of the modulus.
3. I’ve already given the example of the zero ring, where 1+1=0. You can dismiss this as trivial, but it’s simply meant to illustrate that there are other consistent ways of defining addition and multiplication. I’m sure we could dream up more interesting examples. If we couldn’t, abstract algebra would hardly be worth the time as a subject, no? Another example: In fields of characteristic 2, we get the nice formula (x+y)^2=x^2+y^2

Not true, because Gerhard Gentzen proved the consistency of Peano arithmetic using ordinal analysis.
gdz.sub.uni-goettingen.de/dms/load/img/?PPN=GDZPPN002278391&IDDOC=37344

I should have known that I would have to quote the theorem for you since you can’t be bothered to look it up. Here is Gödel’s second incompleteness theorem: “For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent.”

In plain English, sufficiently complicated axiomatic systems cannot be used to demonstrate their own consistency. You cite Peano arithmetic as an example, but that isn’t sufficiently complicated. Peano arithmetic is only a first-order theory. For heavy-duty mathematics to get off the ground, that isn’t enough. For example, you can’t prove that the natural numbers are countably infinite using only first-order logic. Basically, you can only talk about individuals of sets with first-order logic, not the sets themselves.

 

[Charlemagne_III]

If you want an example of genuinely conflicting axiomatic systems, look no further than Euclidean geometry vs. hyperbolic geometry. If you adopt the view that there is some “absolute truth” floating out there somewhere, then one of them must be “right” and the other “wrong”.

But you cannot decide which is right or wrong because you can’t compare two axiomatic systems with different axioms. There’s no way to decide which axioms are right. If you could decide such a thing, you could prove those axioms.

Some other examples of mathematical ideas that are counterintuitive or contentious:

1. Pretty much any expansion of the real number system was fought every step of the way, such as the complex number system and the hyperreal number system. So if you ask something like “Does x^2+1=0 have a solution?” the answer will depend on the axioms you’ve chosen.
2. Some mathematicians to this day still dislike the inclusion of the Axiom of Choice in set theory.

Some arithmetical examples:

1. You may have heard of floating point arithmetic, which deals with formal ways of approximating tedious calculations. It is a common joke that 2+2 could equal 5 in floating point arithmetic because of rounding errors.
2. Some versions of arithmetic are uninterested in equality and look at weaker relations, such as congruence. Modular arithmetic lets you choose a modulus and regard two numbers as equivalent provided that their difference is a multiple of the modulus.
3. I’ve already given the example of the zero ring, where 1+1=0. You can dismiss this as trivial, but it’s simply meant to illustrate that there are other consistent ways of defining addition and multiplication. I’m sure we could dream up more interesting examples. If we couldn’t, abstract algebra would hardly be worth the time as a subject, no? Another example: In fields of characteristic 2, we get the nice formula (x+y)^2=x^2+y^2

I should have known that I would have to quote the theorem for you since you can’t be bothered to look it up. Here is Gödel’s second incompleteness theorem: “For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent.”

In plain English, sufficiently complicated axiomatic systems cannot be used to demonstrate their own consistency. You cite Peano arithmetic as an example, but that isn’t sufficiently complicated. Peano arithmetic is only a first-order theory. For heavy-duty mathematics to get off the ground, that isn’t enough. For example, you can’t prove that the natural numbers are countably infinite using only first-order logic. Basically, you can only talk about individuals of sets with first-order logic, not the sets themselves.

Will someone kindly explain to me what any of this has to do with a new proof for the existence of God?

 

[Oreoracle]

Will someone kindly explain to me what any of this has to do with a new proof for the existence of God?

I could summarize the issue, but I don’t want to risk oversimplifying it and having someone make a strawman of my position. Fortunately, we are on a forum, so the posts stay in place for you to read through and discover for yourself why certain topics have arisen.

 

[Charlemagne_III]

I could summarize the issue, but I don’t want to risk oversimplifying it and having someone make a strawman of my position. Fortunately, we are on a forum, so the posts stay in place for you to read through and discover for yourself why certain topics have arisen.

Sorry, I just don’t see any connection between your post on mathematics and post #1.

 

[Charlemagne_III]

If you want an example of genuinely conflicting axiomatic systems, look no further than Euclidean geometry vs. hyperbolic geometry. If you adopt the view that there is some “absolute truth” floating out there somewhere, then one of them must be “right” and the other “wrong”.

But you cannot decide which is right or wrong because you can’t compare two axiomatic systems with different axioms. There’s no way to decide which axioms are right. If you could decide such a thing, you could prove those axioms.

Since this is not a mathematics forum, but rather a religious forum, let us transfer your discussion of mathematical axioms to moral axioms.

Are there no absolute moral axioms that everyone worldwide agrees upon as a fundamental axiom?

Can you not think of just one?

 

[Charlemagne_III]

O.K., since I realize I am changing the subject of this thread, I have started a new thread here:

forums.catholic-questions.org/showthread.php?p=12186098#post12186098

Please join me if you are interested in talking about absolute moral axioms.

 

[Oreoracle]

Since this is not a mathematics forum, but rather a religious forum, let us transfer your discussion of mathematical axioms to moral axioms.

You seem to have this misconception that moral axioms are somehow different from mathematical axioms. They are the same as far as logic is concerned–axioms are axioms. Math is just as good of an example of the application of logic as anything else.

As for why I prefer to use math as the example and not morality, it’s because math can be discussed more objectively. People aren’t very passionate about numbers and shapes, so they can think clearly about them and without bias. They don’t have to run and hide behind ambiguous language because they fear scary implications. If you understand axiomatic systems properly, you should have no trouble applying your reasoning to math.

 

[Charlemagne_III]

As for why I prefer to use math as the example and not morality, it’s because math can be discussed more objectively. People aren’t very passionate about numbers and shapes, so they can think clearly about them and without bias. They don’t have to run and hide behind ambiguous language because they fear scary implications. If you understand axiomatic systems properly, you should have no trouble applying your reasoning to math.

If you have no problem discussing moral axioms, you should be comfortable in this forum discussing them.

There are perhaps few people in this forum who would be comfortable discussing mathematical axioms.

I will not be back at this thread. I see you have joined the other one. See you there.

 

[ChainBreaker]

Please see post #15.

I decline.

 

[Tomdstone]

If you want an example of genuinely conflicting axiomatic systems, look no further than Euclidean geometry vs. hyperbolic geometry. If you adopt the view that there is some “absolute truth” floating out there somewhere, then one of them must be “right” and the other “wrong”.

But you cannot decide which is right or wrong because you can’t compare two axiomatic systems with different axioms. There’s no way to decide which axioms are right. If you could decide such a thing, you could prove those axioms.

Some other examples of mathematical ideas that are counterintuitive or contentious:

1. Pretty much any expansion of the real number system was fought every step of the way, such as the complex number system and the hyperreal number system. So if you ask something like “Does x^2+1=0 have a solution?” the answer will depend on the axioms you’ve chosen.
2. Some mathematicians to this day still dislike the inclusion of the Axiom of Choice in set theory.

Some arithmetical examples:

1. You may have heard of floating point arithmetic, which deals with formal ways of approximating tedious calculations. It is a common joke that 2+2 could equal 5 in floating point arithmetic because of rounding errors.
2. Some versions of arithmetic are uninterested in equality and look at weaker relations, such as congruence. Modular arithmetic lets you choose a modulus and regard two numbers as equivalent provided that their difference is a multiple of the modulus.
   .

Regardless of the axiom of choice or of complex numbers or of modular arithmetic or of playfair’s axiom, I continue to claim that you cannot have 1+1 = 3 in a non-trivial system.