Scientists use mathematical calculations to PROVE the existence of God

[buddhist]

Yes, it is. When you have evidence of something, you have proof of it.

Evidence is proof of the evidence itself. That evidence does not prove any particular theory which attempts to explain it.

For example, Christians often cite love (evidence) as proof of God (their theory). In actuality, love is proof of love. But It does not prove their theory about god.

Or, a shard of pottery with the name "Yeshua" (evidence) proves Christianity (their theory). In actuality, the shard of pottery only proves the existence of itself. It does not prove their religion, nor does it prove my theory (a child name Yeshua graffitied his name) or any other theory.

"Falling" is an object falling towards the surface of the Earth, due to it being stuck in it's gravitational pull. Planetary orbits are a more solid proof, but even that still revolves around smaller objects caught in the gravitational pull of larger/heavier objects (of larger density, .

That's still a theory. There's a theory of an electromagnetic universe, which proposes electromagnetism as that force - not gravity.

 

[Shadow Wolf]

First, let's examine what is meant by modal.

I know what a mode is, as well and the median and mean. None of that proves Godal correct.

 

[beenherebeforeagain]

Sorry, posted that before I was done.

What this study finds is that the usage and arrangement of modal statements set out by Godel are consistent within the system of logic.

 

[james bond]

Further definition from Stanford Encyclopedia.

"A modal is an expression (like ‘necessarily’ or ‘possibly’) that is used to qualify the truth of a judgement. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions ‘it is necessary that’ and ‘it is possible that’. However, the term ‘modal logic’ may be used more broadly for a family of related systems. These include logics for belief, for tense and other temporal expressions, for the deontic (moral) expressions such as ‘it is obligatory that’ and ‘it is permitted that’, and many others. An understanding of modal logic is particularly valuable in the formal analysis of philosophical argument, where expressions from the modal family are both common and confusing. Modal logic also has important applications in computer science."

What is Modal Logic?

"2. Modal Logics
The most familiar logics in the modal family are constructed from a weak logic called K (after Saul Kripke). Under the narrow reading, modal logic concerns necessity and possibility. A variety of different systems may be developed for such logics using K as a foundation. The symbols of K include ‘~’ for ‘not’, ‘→’ for ‘if…then’, and ‘□’ for the modal operator ‘it is necessary that’. (The connectives ‘&’, ‘∨’, and ‘↔’ may be defined from ‘~’ and ‘→’ as is done in propositional logic.) K results from adding the following to the principles of propositional logic.

Necessitation Rule: If A is a theorem of K, then so is □A.

Distribution Axiom: □(A→B) → (□A→□B).

(In these principles we use ‘A’ and ‘B’ as metavariables ranging over formulas of the language.) According to the Necessitation Rule, any theorem of logic is necessary. The Distribution Axiom says that if it is necessary that if A then B, then if necessarily A, then necessarily B.

The operator ◊ (for ‘possibly’) can be defined from □ by letting ◊A = ~□~A. In K, the operators □ and ◊ behave very much like the quantifiers ∀ (all) and ∃ (some). For example, the definition of ◊ from □ mirrors the equivalence of ∀xA with ~∃x~A in predicate logic. Furthermore, □(A&B) entails □A&□B and vice versa; while □A∨□B entails □(A∨B), but not vice versa. This reflects the patterns exhibited by the universal quantifier: ∀x(A&B) entails ∀xA&∀xB and vice versa, while ∀xA ∨ ∀xB entails ∀x(A ∨ B) but not vice versa. Similar parallels between ◊ and ∃ can be drawn. The basis for this correspondence between the modal operators and the quantifiers will emerge more clearly in the section on Possible Worlds Semantics.

The system K is too weak to provide an adequate account of necessity. The following axiom is not provable in K, but it is clearly desirable.

(M) □A→A
(M) claims that whatever is necessary is the case. Notice that (M) would be incorrect were □ to be read ‘it ought to be that’, or ‘it was the case that’. So the presence of axiom (M) distinguishes logics for necessity from other logics in the modal family. A basic modal logic M results from adding (M) to K. (Some authors call this system T.)

Many logicians believe that M is still too weak to correctly formalize the logic of necessity and possibility. They recommend further axioms to govern the iteration, or repetition of modal operators. Here are two of the most famous iteration axioms:

(4) □A→□□A
(5) ◊A→□◊A

S4 is the system that results from adding (4) to M. Similarly S5 is M plus (5). In S4, the sentence □□A is equivalent to □A. As a result, any string of boxes may be replaced by a single box, and the same goes for strings of diamonds. This amounts to the idea that iteration of the modal operators is superfluous. Saying that A is necessarily necessary is considered a uselessly long-winded way of saying that A is necessary. The system S5 has even stronger principles for simplifying strings of modal operators. In S4, a string of operators of the same kind can be replaced for that operator; in S5, strings containing both boxes and diamonds are equivalent to the last operator in the string. So, for example, saying that it is possible that A is necessary is the same as saying that A is necessary. A summary of these features of S4 and S5 follows.

S4: □□…□ = □ and ◊◊…◊ = ◊
S5: 00…□ = □ and 00…◊ = ◊, where each 0 is either □ or ◊

One could engage in endless argument over the correctness or incorrectness of these and other iteration principles for □ and ◊. The controversy can be partly resolved by recognizing that the words ‘necessarily’ and ‘possibly’, have many different uses. So the acceptability of axioms for modal logic depends on which of these uses we have in mind. For this reason, there is no one modal logic, but rather a whole family of systems built around M. The relationship between these systems is diagrammed in Section 8, and their application to different uses of ‘necessarily’ and ‘possibly’ can be more deeply understood by studying their possible world semantics in Section 6.

The system B (for the logician Brouwer) is formed by adding axiom (B) to M.

(B) A→□◊A
It is interesting to note that S5 can be formulated equivalently by adding (B) to S4. The axiom (B) raises an important point about the interpretation of modal formulas. (B) says that if A is the case, then A is necessarily possible. One might argue that (B) should always be adopted in any modal logic, for surely if A is the case, then it is necessary that A is possible. However, there is a problem with this claim that can be exposed by noting that ◊□A→A is provable from (B). So ◊□A→A should be acceptable if (B) is. However, ◊□A→A says that if A is possibly necessary, then A is the case, and this is far from obvious. Why does (B) seem obvious, while one of the things it entails seems not obvious at all? The answer is that there is a dangerous ambiguity in the English interpretation of A→□◊A. We often use the expression ‘If A then necessarily B’ to express that the conditional ‘if A then B’ is necessary. This interpretation corresponds to □(A→B). On other occasions, we mean that if A, then B is necessary: A→□B. In English, ‘necessarily’ is an adverb, and since adverbs are usually placed near verbs, we have no natural way to indicate whether the modal operator applies to the whole conditional, or to its consequent. For these reasons, there is a tendency to confuse (B): A→□◊A with □(A→◊A). But □(A→◊A) is not the same as (B), for □(A→◊A) is already a theorem of M, and (B) is not. One must take special care that our positive reaction to □(A→◊A) does not infect our evaluation of (B). One simple way to protect ourselves is to formulate B in an equivalent way using the axiom: ◊□A→A, where these ambiguities of scope do not arise."

Modal Logic (Stanford Encyclopedia of Philosophy)

 

[Shadow Wolf]

That's still a theory.

So are germs and the combustibility of oxygen. It doesn't make them "still a theory." They are facts, facts that are supported by tons of evidence.

 

[james bond]

I know what a mode is, as well and the median and mean. None of that proves Godal correct.

If you understand that Godel is not correct, then please explain.

 

[Shadow Wolf]

Further definition from Stanford Encyclopedia.

"A modal is an expression (like ‘necessarily’ or ‘possibly’) that is used to qualify the truth of a judgement. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions ‘it is necessary that’ and ‘it is possible that’. However, the term ‘modal logic’ may be used more broadly for a family of related systems. These include logics for belief, for tense and other temporal expressions, for the deontic (moral) expressions such as ‘it is obligatory that’ and ‘it is permitted that’, and many others. An understanding of modal logic is particularly valuable in the formal analysis of philosophical argument, where expressions from the modal family are both common and confusing. Modal logic also has important applications in computer science."

What is Modal Logic?

"2. Modal Logics
The most familiar logics in the modal family are constructed from a weak logic called K (after Saul Kripke). Under the narrow reading, modal logic concerns necessity and possibility. A variety of different systems may be developed for such logics using K as a foundation. The symbols of K include ‘~’ for ‘not’, ‘→’ for ‘if…then’, and ‘□’ for the modal operator ‘it is necessary that’. (The connectives ‘&’, ‘∨’, and ‘↔’ may be defined from ‘~’ and ‘→’ as is done in propositional logic.) K results from adding the following to the principles of propositional logic.

Necessitation Rule: If A is a theorem of K, then so is □A.

Distribution Axiom: □(A→B) → (□A→□B).

(In these principles we use ‘A’ and ‘B’ as metavariables ranging over formulas of the language.) According to the Necessitation Rule, any theorem of logic is necessary. The Distribution Axiom says that if it is necessary that if A then B, then if necessarily A, then necessarily B.

The operator ◊ (for ‘possibly’) can be defined from □ by letting ◊A = ~□~A. In K, the operators □ and ◊ behave very much like the quantifiers ∀ (all) and ∃ (some). For example, the definition of ◊ from □ mirrors the equivalence of ∀xA with ~∃x~A in predicate logic. Furthermore, □(A&B) entails □A&□B and vice versa; while □A∨□B entails □(A∨B), but not vice versa. This reflects the patterns exhibited by the universal quantifier: ∀x(A&B) entails ∀xA&∀xB and vice versa, while ∀xA ∨ ∀xB entails ∀x(A ∨ B) but not vice versa. Similar parallels between ◊ and ∃ can be drawn. The basis for this correspondence between the modal operators and the quantifiers will emerge more clearly in the section on Possible Worlds Semantics.

The system K is too weak to provide an adequate account of necessity. The following axiom is not provable in K, but it is clearly desirable.

(M) □A→A
(M) claims that whatever is necessary is the case. Notice that (M) would be incorrect were □ to be read ‘it ought to be that’, or ‘it was the case that’. So the presence of axiom (M) distinguishes logics for necessity from other logics in the modal family. A basic modal logic M results from adding (M) to K. (Some authors call this system T.)

Many logicians believe that M is still too weak to correctly formalize the logic of necessity and possibility. They recommend further axioms to govern the iteration, or repetition of modal operators. Here are two of the most famous iteration axioms:

(4) □A→□□A
(5) ◊A→□◊A

S4 is the system that results from adding (4) to M. Similarly S5 is M plus (5). In S4, the sentence □□A is equivalent to □A. As a result, any string of boxes may be replaced by a single box, and the same goes for strings of diamonds. This amounts to the idea that iteration of the modal operators is superfluous. Saying that A is necessarily necessary is considered a uselessly long-winded way of saying that A is necessary. The system S5 has even stronger principles for simplifying strings of modal operators. In S4, a string of operators of the same kind can be replaced for that operator; in S5, strings containing both boxes and diamonds are equivalent to the last operator in the string. So, for example, saying that it is possible that A is necessary is the same as saying that A is necessary. A summary of these features of S4 and S5 follows.

S4: □□…□ = □ and ◊◊…◊ = ◊
S5: 00…□ = □ and 00…◊ = ◊, where each 0 is either □ or ◊

One could engage in endless argument over the correctness or incorrectness of these and other iteration principles for □ and ◊. The controversy can be partly resolved by recognizing that the words ‘necessarily’ and ‘possibly’, have many different uses. So the acceptability of axioms for modal logic depends on which of these uses we have in mind. For this reason, there is no one modal logic, but rather a whole family of systems built around M. The relationship between these systems is diagrammed in Section 8, and their application to different uses of ‘necessarily’ and ‘possibly’ can be more deeply understood by studying their possible world semantics in Section 6.

The system B (for the logician Brouwer) is formed by adding axiom (B) to M.

(B) A→□◊A
It is interesting to note that S5 can be formulated equivalently by adding (B) to S4. The axiom (B) raises an important point about the interpretation of modal formulas. (B) says that if A is the case, then A is necessarily possible. One might argue that (B) should always be adopted in any modal logic, for surely if A is the case, then it is necessary that A is possible. However, there is a problem with this claim that can be exposed by noting that ◊□A→A is provable from (B). So ◊□A→A should be acceptable if (B) is. However, ◊□A→A says that if A is possibly necessary, then A is the case, and this is far from obvious. Why does (B) seem obvious, while one of the things it entails seems not obvious at all? The answer is that there is a dangerous ambiguity in the English interpretation of A→□◊A. We often use the expression ‘If A then necessarily B’ to express that the conditional ‘if A then B’ is necessary. This interpretation corresponds to □(A→B). On other occasions, we mean that if A, then B is necessary: A→□B. In English, ‘necessarily’ is an adverb, and since adverbs are usually placed near verbs, we have no natural way to indicate whether the modal operator applies to the whole conditional, or to its consequent. For these reasons, there is a tendency to confuse (B): A→□◊A with □(A→◊A). But □(A→◊A) is not the same as (B), for □(A→◊A) is already a theorem of M, and (B) is not. One must take special care that our positive reaction to □(A→◊A) does not infect our evaluation of (B). One simple way to protect ourselves is to formulate B in an equivalent way using the axiom: ◊□A→A, where these ambiguities of scope do not arise."

Modal Logic (Stanford Encyclopedia of Philosophy)

Can you either summarize or put those in quotations so it isn't taking up so much space?

 

[Shadow Wolf]

If you understand that Godal is not correct, then please explain.

The burden of proof lies in proving that Godal was correct, not in proving him incorrect. Pasteur, for example, couldn't just say spontaneous generation is wrong, he had to prove his ideas correct.

 

[buddhist]

So are germs and the combustibility of oxygen. It doesn't make them "still a theory." They are facts, facts that are supported by tons of evidence.

Yes, germs and oxygen are in and of themselves are facts. But that they are causes for other effects are theories.

 

[beenherebeforeagain]

This particular problem laid out by Godel is still subject to Godel's Incompleteness Theorem...and it is something that the computer program could have come up with on its own, apparently...

It doesn't prove that God exists, only lays out a set of modal conditions that are logically consistent, so that if anyone were ever to supply the evidence to validate the propositions as true, THEN and ONLY THEN would it be an argument that God actually exists...

 

[Reggie Miller]

This particular problem laid out by Godel is still subject to Godel's Incompleteness Theorem...and it is something that the computer program could have come up with on its own, apparently...

It doesn't prove that God exists, only lays out a set of modal conditions that are logically consistent, so that if anyone were ever to supply the evidence to validate the propositions as true, THEN and ONLY THEN would it be an argument that God actually exists...

Thank you. I understand it better after reading that.

 

[beenherebeforeagain]

Thank you. I understand it better after reading that.

Thank you!

This may be a historic day: someone understood something I said! [I hope what I said was really true!]

 

[james bond]

In essence the Austrian was arguing that, by definition, God is that for which no greater can be conceived. And while God exists in the understanding of the concept, we could conceive of him as greater if he existed in reality. Therefore, he must exist.

BTW with the argument by atheists against Godel's use of axioms:

"Definition of axiom

1. 1 : a statement accepted as true as the basis for argument or inference : postulate 1 <one of the axioms of the theory of evolution>"
   

 

[Reggie Miller]

Thank you!

This may be a historic day: someone understood something I said! [I hope what I said was really true!]

I think you explained that entire article rather well. Of course he didn't prove God exists mathematically. If he had he would have surely published it.

Instead he laid the groundwork to make a proof possible. If he had lived long enough maybe he would have made further progress.

Godel was a genius of high degree. We may not have been able to understand it if he had made further progress, though.

 

[james bond]

Which makes the entire article and this thread completely pointless, right?

I'm glad you admitted the TOE is useless ha ha.

 

[james bond]

Only the mathematical validity (strength) of the equation was tested.

The axioms which form the equation have not been proven true, as far as I can tell. The equation remains a mere hypothesis until the 1. axioms can be proven true, and 2. it can be tested via experimentation, and such results are reproducible by others. Then it can be legitimately called a theory.

Even then, a theory is not proof. Scientists take great efforts to disprove theories, and they have frequently.

Are you mixing math and science? According to mathematics, Godel's argument would be proof.

"In mathematics or logic, an axiom is an unprovable rule or first principle accepted as true because it is self-evident or particularly useful. “Nothing can both be and not be at the same time and in the same respect” is an example of an axiom."

 

[Guy Threepwood]

So, since you seem to doubt climatology, astronomy, geology, ecology, physics, etc., why don't you learn how do to the experiments, so you can show everyone where all these good-for-nothing scientists are wrong?

I took enough science classes and learned enough math to be able to tell what is reasonable and unreasonable as far empirical evidence goes. I also realize that as a practical matter, there is no way I, you, or anyone else could actually conduct all these observations and experiments myself...but if you choose to ignore and discount the reports of others as unreliably because you yourself can't/won't go to the trouble to do the studies yourself, I really kinda wonder why you bother to post at all...all you can be arguing is that your clearly limited personal empirical experience doesn't jibe with the experiences and work of others--so we should listen to you exactly WHY?

Likewise, I cannot conduct all these experiments, but I can see ice caps on mars, measure the redshift in a galaxy, demonstrate that light acts as a wave with slits in cardboard, and that plants thrive with increased CO2

There are many wonders of the universe that can be demonstrated empirically,

No such thing for astrology, climatology, ghosts, Darwinism, Big Foot!

Even though 100% of astrologers claim something to be true, I'm not taking their word for it- even if they are the 'experts'

Likewise I don't expect you to take mine, but regarding the topic- I believe there is a logical mathematical basis for God, and also an experiment you can conduct yourself to prove it to yourself firsthand,- which is the best form of proof for anything- was the point...

 

[james bond]

The burden of proof lies in proving that Godal was correct, not in proving him incorrect. Pasteur, for example, couldn't just say spontaneous generation is wrong, he had to prove his ideas correct.

Typicial atheist mumbo jumbo. You're the one who said it was not proof. From what do you base that? Modal logic? If so, then please explain your logic. Just saying Pasteur isn't the same as what we are discussing here.

I'm open because I'm still trying to understand the logical operators. If I left it up to the people in the article who ran the equation and explained it, then it sounds like Godel was correct and it was mathematical proof. However, in the real world and not the math world, we have to show the axioms hold true. That would be where faith comes in.

 

[Revoltingest]

Modal Logic:

Modal logic is a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality. A modal—a word that expresses a modality—qualifies a statement. For example, the statement "John is happy" might be qualified by saying that John is usually happy, in which case the term "usually" is functioning as a modal. The traditional alethic modalities, or modalities of truth, include possibility ("Possibly, p", "It is possible that p"), necessity ("Necessarily, p", "It is necessary that p"), and impossibility ("Impossibly, p", "It is impossible that p").[1] Other modalities that have been formalized in modal logic include temporal modalities, or modalities of time (notably, "It was the case that p", "It has always been that p", "It will be that p", "It will always be that p"),[2][3] deontic modalities (notably, "It is obligatory that p", and "It is permissible that p"), epistemic modalities, or modalities of knowledge ("It is known that p")[4] and doxastic modalities, or modalities of belief ("It is believed that p").[5]

A formal modal logic represents modalities using modal operators. For example, "It might rain today"...(thank you, Wikipedia)
Modal logic - Wikipedia

After reading that, I now know less than I did before.
(Damaged some brain cells in the process.)

 

[beenherebeforeagain]

Likewise, I cannot conduct all these experiments, but I can see ice caps on mars, measure the redshift in a galaxy, demonstrate that light acts as a wave with slits in cardboard, and that plants thrive with increased CO2

There are many wonders of the universe that can be demonstrated empirically,

No such thing for astrology, climatology, ghosts, Darwinism, Big Foot!

Even though 100% of astrologers claim something to be true, I'm not taking their word for it- even if they are the 'experts'

Likewise I don't expect you to take mine, but regarding the topic- I believe there is a logical mathematical basis for God, and also an experiment you can conduct yourself to prove it to yourself firsthand,- which is the best form of proof for anything- was the point...

And what is that "experiment you can conduct yourself to prove it to yourself firsthand?"

And no, it is not "the best form of proof" if it can't be shown that EVERYONE who conducts this same experiment gets the same result...

Your personal experience, my personal experience, other people's personal experiences--those are EXPERIENCES, not empirical evidence...