Proof, Evidence and Arguments

[WinePusher]

1. Anyone who's taken high school geometry should be acquainted with the concept of a proof. An example of a mathematical proof (from trigonometry) is as follows:

A) secx (cotx) = cscx

B) 1/cosx (cosx/sinx) = cscx by the reciprocal and quotient identity

C) 1/[strike]cosx[/strike] ([strike]cosx[/strike]/sinx) = cscx by the rule that cross products cancel

D) 1/sinx = cscx by the reciprocal identity

A mathematical statement, theorem or postulate can be proven step by step with 100% precision. In otherwords, we are absolutely certain that secx (cotx) = cscx. It doesn't seem that this type of certainty exists anywhere else other than in mathematics.

2) Evidence and Arguments are complementary and tend to go hand in hand. The thing to note is that evidence that is nonmathematical and arguments in general cannot prove anything for certain. When using evidence and arguments the only thing we can establish is the likelihood and probability of an event.

Questions for debate:

1) When discussing issues like the existence of God, or the truth of evolution or the accuracy of the Bible, is it fair to say that none of these issues can be proven with absolute certainty? Will there always be room for doubt when it comes to God's existence and the theory of evolution?

2) Is there any mathematical proof for the existence of God? Does the existence of mathematics itself prove that God exists?

[mwtech]

1) I don't think there is a way to prove either claim right now. There may be a day in the future when there is a scientific explanation for everything, and these explanations are so widely accepted that no one cares to refute them, it might be possible to say we have proven that there is no God. Likewise, if and god(s) made themselves known to the world in a way that was inarguable divine in nature, it would be possible to say there is proof for the existence of that God.

I am convinced that even if there is a scientific explanation for the origin of the universe and how everything works in it, there will still be enough people who don't understand these explanations, and who have been taught about religion their whole lives, that someone will always try to claim that their religion is unarguably the truth.
If there is a time when a god or gods expose themselves to humans in some excellent, miraculous event, after a thousand years, there will be nothing but written record of it, and people will begin to doubt that too.

2) I highly doubt there is any mathematical proof of God. The existence of math absolutely does not prove God's existence. give humans a little credit. We think up all kinds of new things. Obviously, math would have come around a little at a time. Probably starting with simple counting and giving a name for a certain amount of something. The concept of "zero" wasn't even fully developed until the fifth century. But, mathematics evolved in the same way that medicine did. Small, new discoveries built upon one another until we got to where we are now, and it will continue to advance.

[Zzyzx]

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[Replying to post 1 by WinePusher]

1) People who doubt that evolution occurs are typically those who do not know what the term means (and often confuse it with other terms / concepts), the uninformed (have not studied the subject beyond high school / television / sermon level), and/or those who allow their religious beliefs to make them unwilling to accept scientific information that conflicts with their religious beliefs (willfully ignorant).

Some religion defenders concede that evolution does occur -- "but only a little so it doesn't contradict my religious beliefs."

Microbes DO adapt (evolve) to become resistant to antibiotics. That IS genetic change through generations – the exact definition of evolution. Those who deny evolution occurs have the opportunity to determine how microbes become antibiotic resistant without genetic change through generations (evolution) – and become renowned, respected, rich and famous.

The entire scientific / medical community awaits verifiable information to explain antibiotic resistance without evolution. One of the great advantages of scientific study is that there is a constant search for new and novel explanations. However, those explanations (to be taken seriously) must be verifiable by anyone interested and motivated.

"I think so" or "He said so" or "I had an emotional episode" are not considered verification in the real world of scientific study – and are considered humorous, adolescent responses to serious questions.

However, those compose the "proofs" of the existence of "gods" – nothing that can be verified or be shown to be anything more than the product of human imagination.


2) The field of mathematics a product of human intellect and imagination – as are, apparently, all the thousands of proposed "gods" dutifully worshiped, feared, loved, venerated by humans. Some attempt to credit their favorite "god" with creating human intellect; however, their "evidence" is of the "I think so, he said so, I feel it" variety with absolutely no substantiation.

[Divine Insight]

Questions for debate:

1) When discussing issues like the existence of God, or the truth of evolution or the accuracy of the Bible, is it fair to say that none of these issues can be proven with absolute certainty? Will there always be room for doubt when it comes to God's existence and the theory of evolution?

For me personally, the answers to these questions can be highly dependent upon how the "God" is defined.

I personally feel that the Biblical "God" has indeed been totally disproved beyond any shadow of a doubt. And, IMHO, that proof comes directly from the Biblical scriptures with no need to even look beyond them, other than of course, pure common sense and reason.

My reason for saying this is because, IMHO, the Biblical fables of God contradict the very character and essence of what the God is supposed to represent in the first place. (i.e. the Highest form of intelligence, omniscience, and omnipotence)

As far as I can see, the biblical fables simply do not describe such a being. So they are self-defeating.

2) Is there any mathematical proof for the existence of God? Does the existence of mathematics itself prove that God exists?

To begin with, mathematics itself is a logical formalism invented by mankind that is itself based upon unprovable premises. The only reason we can "prove" things in mathematics is precisely because we have already accepted that we must abide by the foundational unprovable premises.

Moreover, we have already seen that we can arbitrarily change those premises if we so choose. For example, in geometry Pi is a constant. However, this is only true if we accept the Euclidean premise of parallel lines. If we toss out that unprovable premise, and instead allow for different axioms we end up with totally different geometries (such as spherical and hyperbolic) where Pi is no longer a constant, and the relationships of trig functions that you had just used as an example earlier don't hold true any longer either.

So even our mathematics is mailable and not absolute in terms of any absolute truths.

In fact, this is a great misunderstanding for many people. Mathematics is not what most people seem to think it is. It does not represent any sort of absolute truth, and therefore it does not prove or even remotely imply the existence of any God.

Mathematics is NOT absolute truth. That itself is a myth that many people have bought into but it simply isn't true. It's a misguided notion that simply doesn't hold the water that people think it does.

[wiploc]

A mathematical statement, theorem or postulate can be proven step by step with 100% precision. In otherwords, we are absolutely certain that secx (cotx) = cscx. It doesn't seem that this type of certainty exists anywhere else other than in mathematics.

People keep saying that. I don't understand why. There are many non-mathematical things that we have complete confidence about. Do you have any doubt at all about whether "round" or "flat" is a better description of the earth's shape, about whether driving drunk at 90 miles an hour with no seat belt could be dangerous, about whether the sky sometimes seems blue to you, about whether homophobia is a thing, about whether some arguments purporting to prove the existence of god are poor, about whether there is a significant correlation between the latitude of one's ancestors and the color of one's skin, about whether tornadoes involve rotation, about whether ice floats, about which side of the road people usually drive on in your country, about whether the world ended yesterday, about where on your body you might find your fingernails?

If you were to adopt a radical skepticism that allowed you to be in doubt about all of the above issues, then how would you maintain your certainty about whether secx (cotx) = cscx?

2) Evidence and Arguments are complementary and tend to go hand in hand. The thing to note is that evidence that is nonmathematical and arguments in general cannot prove anything for certain. When using evidence and arguments the only thing we can establish is the likelihood and probability of an event.

But we can prove that with absolute certainty, right? Aren't you 100% certain that north and south are probably different directions, that Mercator maps probably have more distortion in the higher latitudes, that that you will probably next eat ice cream before you next eat smoked hedgehog, that heat waves probably cause (or are) visual distortion, that diamond is probably harder than glass, that appetizers probably usually come before desert?

Questions for debate:

1) When discussing issues like the existence of God, or the truth of evolution or the accuracy of the Bible, is it fair to say that none of these issues can be proven with absolute certainty?

No. Some religious arguments are wrong, self contradictory, refutable with the same degree of certainty as, for instance, to take a random example, secx (cotx) = cscx.

Will there always be room for doubt when it comes to God's existence and the theory of evolution?

Gods are inherently implausible.

Evolution is a robustly supported fact. The theory of evolution will undoubtedly undergo some tweaking (even as will our understanding of the shape of the earth), but that doesn't mean we have any expectation that it will be significantly contradicted.

Does the existence of mathematics itself prove that God exists?

No.

[Cephus]

People keep saying that. I don't understand why. There are many non-mathematical things that we have complete confidence about. Do you have any doubt at all about whether "round" or "flat" is a better description of the earth's shape, about whether driving drunk at 90 miles an hour with no seat belt could be dangerous, about whether the sky sometimes seems blue to you, about whether homophobia is a thing, about whether some arguments purporting to prove the existence of god are poor, about whether there is a significant correlation between the latitude of one's ancestors and the color of one's skin, about whether tornadoes involve rotation, about whether ice floats, about which side of the road people usually drive on in your country, about whether the world ended yesterday, about where on your body you might find your fingernails?

The earth isn't round or flat, it's a sphere. I'm sure there are plenty of professional drivers who could go 90 miles per hour with no seat belt and be fine and there are lots of people who are color blind and who NEVER see the sky as blue.

We never have absolute certainty about any of those things. The only reason mathematics is absolutely certain is because we defined it that way.

[WinePusher]

1) I don't think there is a way to prove either claim right now. There may be a day in the future when there is a scientific explanation for everything, and these explanations are so widely accepted that no one cares to refute them, it might be possible to say we have proven that there is no God. Likewise, if and god(s) made themselves known to the world in a way that was inarguable divine in nature, it would be possible to say there is proof for the existence of that God.

I am convinced that even if there is a scientific explanation for the origin of the universe and how everything works in it, there will still be enough people who don't understand these explanations, and who have been taught about religion their whole lives, that someone will always try to claim that their religion is unarguably the truth.
If there is a time when a god or gods expose themselves to humans in some excellent, miraculous event, after a thousand years, there will be nothing but written record of it, and people will begin to doubt that too.

I appreciate your well written response, however I don't think your answer necessarily addresses my question. Both theists and nontheists firmly believe in certain things. Theists believe in God and in the infallibility of the Bible while nontheists tend to believe in things like pure naturalism. The point of my topic is that none of these beliefs can be proven with absolute certainty. Absolute certainty only exists in logic and mathematics, and mathematics itself can be seen as an extension of logic.

So, when discussing issues like the existence of God it is inappropriate to ask for proof. The word 'proof' is being grossly misapplied in debates like these. The idea of a formal, definitive proof only exists in mathematics and nowhere else. When discussing God's existence, it is more appropriate to use philosophical argumentation because that's all we can use. And the many people on this forum who constantly complain about how arguments are not proofs are just wrong.

2) I highly doubt there is any mathematical proof of God. The existence of math absolutely does not prove God's existence. give humans a little credit. We think up all kinds of new things. Obviously, math would have come around a little at a time. Probably starting with simple counting and giving a name for a certain amount of something. The concept of "zero" wasn't even fully developed until the fifth century. But, mathematics evolved in the same way that medicine did. Small, new discoveries built upon one another until we got to where we are now, and it will continue to advance.

The question we have to consider concerns the origins of mathematics and logic. Every single other academic field deals with the natural world in some way or another. Chemistry deals with matter, biology deals with life, economics deals with society, etc, and none of these fields would be possible without mathematics. Mathematics is the underlying framework that makes scientific discovery and advancement possible, which is why mathematics is referred to as the queen of science. So where did math (and logic) come from? Is there any natural account for their existence?

You stated that we oughta give humans credit for understanding math, and I agree. You misunderstand my argument if you think I'm saying anything to the contrary. Humans did not invent math in the same way humans invented the wheel or the light bulb, and similarly, the basic unit of math (the number) is not something that exists tangibly. Numbers are considered to be abstract objects. So, while it is true that humans have the cognitive ability to comprehend mathematics, that does not explain why mathematics exists.

[mwtech]

[Replying to post 7 by WinePusher]

I imagine numbers becoming a concept kind of like this.
Guy 1: I need some fish
Guy 2: *brings 3 fish*
Guy 1: I still need fish
Guy 2: How many? (Not these words exactly if there is no possible answer yet, but something to that effect. Same message implied)
Guy 1: we don't have a word for that yet. Let's make one.

And so to start off, math would have just been making up words to fit the concepts of certain punts of a given thing. That is all you need for the evolution of mathematics to begin. In order to better communicate our needs, humans created new words for. A concept that used to be vague.

[Haven]

1. Anyone who's taken high school geometry should be acquainted with the concept of a proof. An example of a mathematical proof (from trigonometry) is as follows:

A) secx (cotx) = cscx

B) 1/cosx (cosx/sinx) = cscx by the reciprocal and quotient identity

C) 1/[strike]cosx[/strike] ([strike]cosx[/strike]/sinx) = cscx by the rule that cross products cancel

D) 1/sinx = cscx by the reciprocal identity

A mathematical statement, theorem or postulate can be proven step by step with 100% precision. In otherwords, we are absolutely certain that secx (cotx) = cscx. It doesn't seem that this type of certainty exists anywhere else other than in mathematics.

2) Evidence and Arguments are complementary and tend to go hand in hand. The thing to note is that evidence that is nonmathematical and arguments in general cannot prove anything for certain. When using evidence and arguments the only thing we can establish is the likelihood and probability of an event.

Questions for debate:

1) When discussing issues like the existence of God, or the truth of evolution or the accuracy of the Bible, is it fair to say that none of these issues can be proven with absolute certainty? Will there always be room for doubt when it comes to God's existence and the theory of evolution?

I'd give you MPG points, but I have none left to give . Excellent post. Far too often I see people -- on both the theist and non-theist sides of the debate -- touting "proof" that god(s) exist/don't exist. This is ridiculous, as there are very few propositions (mathematical statements, tautologies, etc.) that can be known for certain. For everything else (including religious and scientific claims), we must infer to the best explanation using a combination of empirical evidence and rational argument.

Anyone who says "I am certain God exists/doesn't exist" is speaking foolishness.

[Haven]

2) Is there any mathematical proof for the existence of God? Does the existence of mathematics itself prove that God exists?

This question requires a more robust response. I'll address each sub-part separately.

• A. Some theists claim that the scholar Kurt Gödel's ontological proof constitutes mathematical proof for God's (I'll use this spelling of "God" [and the neutral pronoun "it"] from now on, as we are talking about the specific deity concept from classic philosophical theism) existence. Gödel's proof, which uses modal logic, is:
  

  Definitions:
  Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive
  Definition 2: A is an essence of x if and only if for every property B, x has B necessarily if and only if A entails B
  Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified
  
  Axioms:
  Axiom 1: Any property entailed by—i.e., strictly implied by—a positive property is positive
  Axiom 2: A property is positive if and only if its negation is not positive
  Axiom 3: The property of being God-like is positive
  Axiom 4: If a property is positive, then it is necessarily positive
  Axiom 5: Necessary existence is a positive property
  
  Theorems:
  Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.
  Theorem 2: The property of being God-like is consistent.
  Theorem 3: If something is God-like, then the property of being God-like is an essence of that thing.
  Theorem 4: Necessarily, the property of being God-like is exemplified.

  Gödel's proof--like all versions of the ontological argument--fails because it is based upon flawed definitions and axioms. Specifically, his notion of "positive properties" is incoherent because it relies upon a set of purely subjective value judgments. That is, who is to say that, for example, the "positive property" of knowledge is objectively better than the "non-positive property" of ignorance? It is only due to our human subjectivity that we value knowledge over ignorance.
  
  In addition, Axiom 5 is absurd because existence (necessary or otherwise) is not itself a property, but is a precondition for possessing any properties. For some "A" to have any properties, "A" must first exist.
  
  As this (and other very similar proofs like the philosopher Alvin Plantinga's modal ontological argument) is the only attempt at a mathematical case for God's existence, I think it's safe to say that there exists no successful mathematical proof for God's existence.
  
  B. No, the existence of mathematics does not act as evidence for God's existence. As others have mentioned, the human-created mathematical concepts of numbers, ratios, and so on are based on objective properties of the universe. In other words, they are but descriptions of the ways in which the universe behaves. They aren't necessarily true or prescriptive in any sense, but purely descriptive.
  
  One could, for example, devise a precise set of descriptive statements for the functioning of an evolved software program, but that does not imply that the program was created or designed by any mind.