Proving a Negative

[Calderac]

There is a discussion going on one of the intro threads about proving a negative. I'm going to move it here so we don't distract from that thread's purpose.

I'm sure most of you have seen this interview Rand did with Donahue, but it touches on the points that were being talked about in the original thread. Rand describes how man cannot be called on to prove a negative, and moreover she specifically addresses the contradictions that were brought up in the earlier thread. Specifically, she's talking about faith vs. reason.

Rand's Faith vs. Reason

Check it out and let me know what you guys think.

[Calderac]

Moved this from original thread...

There are things that can't be proven but solely because it is a negation does not mean it can't be. Observe:

Proposition:
There are no even prime numbers greater than than two.

This is a sufficiently "negative" statement, yes?

Proof:
Assume there was an even prime number greater than two. Since this number is even it can be divided by two with no remainder, but because the number is prime it can't be divided by anything. This brings about a contradiction causing our initial assumption to be false. Therefore there are no prime numbers greater than two.


The ability to prove negatives is rather fundamental to mathematics.

And, uh, sorry for the thread derailment.

Are you not positively proving there are no prime numbers greater than two?

I think philosophical issues may use this application much differently than mathematics.

[Kushan]

I moved this to deep thoughts because it gets more attention. We have a lot of old unused forums we keep around for historical purposes.

[redhotrebel]

From my understanding it sounds like Rand is stating that if the interviewer wants her to believe in god the burden of proof is on him- not her to disprove as it would be irrelevant to her.
She is telling the interviewer IMO that he is using the logical fallacy of Burden of Proof, aka Appeal to Ignorance ("Ad Ignorantiam")

Burden of Proof is a fallacy in which the burden of proof is placed on the wrong side. "Burden of proof" means that someone suggesting a new theory or stating a claim must provide evidence to support it: it is not sufficient to say "you can't disprove this." Specifically, when anyone is making a bold claim, and especially a positive claim, it is not someone else's responsibility to disprove the claim, but is rather the responsibility of the person who is making the bold claim to prove it. In short, X is not proven simply because "not X" cannot be proven.

Anyways- long story short your excerpt does not match your discussion about disproving a negative- only which side holds the responsibility of proving it.

I do find your “reductio ad absurdum” argument intriguing although it might help if you had the entire mathematical principle:
Consider the proposition X is an even prime number greater than 2 that follows the basic laws of mathematics. From that can be derived that:
1. X is not 2 (since it was greater than 2)
2. X is not divisible by any other number than 1 or itself (because it was a prime number)
3. X is not divisible by 2 (follows from 1. and 2.: 2 is not X or 1)
4. but X is divisible by 2 (because X is even)
5. thus X both is and is not divisible by 2

http://en.wikipedia.org/wiki/Burden_of_ ... tive_proof
http://en.wikipedia.org/wiki/Reductio_ad_absurdum

[Thirteen Fish]

There is a discussion going on one of the intro threads about proving a negative. I'm going to move it here so we don't distract from that thread's purpose. I'm sure most of you have seen this interview Rand did with Donahue, but it touches on the points that were being talked about in the original thread. Rand describes how man cannot be called on to prove a negative, and moreover she specifically addresses the contradictions that were brought up in the earlier thread. Specifically, she's talking about faith vs. reason. Rand's Faith vs. Reason Check it out and let me know what you guys think.

Rand states twice in that link that you can't prove negatives but I didn't see that she provided much of her reasoning of that statement in those interviews. Perhaps I am too dense to see it there so if you could kindly guide me to the right part that would be a help.

Alternatively do you have a better source on the reasoning behind Rand's statement of not proving a negative? You can recommend a book, and I will read it if that would help.

Are you not positively proving there are no prime numbers greater than two?

I think philosophical issues may use this application much differently than mathematics.

Yes I am "positively proving" that there are no even prime numbers other than two, but the statement "there are no even prime numbers greater than two" is a negative is it not? And I have proved this negative statement?

Technically, all though I think it is a little silly, logic is generally accepted to be a branch of philosophy and not of mathematics. My example was to show the logic of proving a negative and not the specific mathematics of the nature of prime numbers.


redhotrebel posted after I started composing my post so my response will be short, your burden of proof explanation makes sense. I would accept that.

[reteo]

Let's see if I can explain it...

When we are born, we can only observe the world. We see how things are because we are observing them as we go. As time goes on, we are able to extrapolate principles to those observations, thereby creating abstract frameworks from which we can predict similar events, as they all follow the same principles. Those things that go up will come down. Dogs have wet noses. Frogs hop. birds fly. You get a headache when you eat cold food too quickly.

Once the principles are gained from what we observe and extrapolate from the observation, we then experiment in order to prove them. We throw an apple in the air to see if it comes down. We put a frog down in front of us. We touch our dogs' noses. We watch the birds at the birdhouse. We quickly eat ice cream and greedily gulp our slushees, only to vow never to do so again... until the next slushee. (So I need to learn through continued research... )

In other words, we find the positive principle of reality, and we test it in order to prove it. Yes, there may be things we don't observe, but they will have some affect on the world around us that draws our attention, and therefore, opens new fields of research for us to observe, hypothesize, and test in order to prove.

In all the above, the progress of knowledge has never been about disproving anything, but about finding what's there, proving the principles, and establishing the ability to predict and harness those principles. Because of this, it's in the researcher's best interest to prove what is, not what is not.

And because it's in the researcher's best interest to prove what is, it is the claimant's responsibility to prove the positive, not the skeptic's responsibility to prove the negative, as the latter requires a lot more time and effort for virtually no result, except in cases where the claim directly conflicts with a proven principle.

When you come right down to it, proving the negative quite literally "proves nothing."

Yes I am "positively proving" that there are no even prime numbers other than two, but the statement "there are no even prime numbers greater than two" is a negative is it not? And I have proved this negative statement?

As above, a negative can be proven only if it comes into direct conflict with a positive proof. Even numbers greater than 2 cannot be primes, because the very definition of even is "evenly divisible by 2," which conflicts directly with the definition of a prime number, which is a "natural number that is divisible only by itself and 1." 2 is the exception because it just so happens to be 2.

Technically, all though I think it is a little silly, logic is generally accepted to be a branch of philosophy and not of mathematics. My example was to show the logic of proving a negative and not the specific mathematics of the nature of prime numbers.

Maths can apply to logic, even as logic can apply to maths. Just because they're different disciplines, don't confuse lack of direct relation with a lack of application. You can use one with the other, and still come up with rational results.

[Calderac]

This can be reasoned out.

The onus of proof (or the burden of proof as redhotrebel mentioned) is upon those asserting a positive. Proving a negative cannot be done, however you can prove the positive. If both exist, this leads to a contradiction. Since contradictions do not exist, anything that results in a contradiction and has no proof to support it must necessarily yield to the suppostion that does have proof supporting it.

The first few chapters of this book talk about this in more depth.

In other news, this is what happens when you get bored and the servers go down.

EDIT:
After rereading your post above Thirteen Fish, I thought of one thing to add. In your example, there happens to proof that contradicts your statement. So it happens that the statement is true. However, in a situation such as the existence of God, there is no positive evidence. Thus, the negative cannot be proved.

Just a distinction that I thought should be highlighted.

[JudgeBob]

Quite simply, burden of proof is on the source of the assertion. This is a requirement of logic.

An assertion is that something _is_, not that something _is not_. Negation is an operator applied to assertion, it has no context otherwise.

To turn it on it's head a bit conversationally, to prove that a god does not exist first requires a defined assertion that a god does exist, and so the first step is to evaluate evidence of that assertion.

I believe such evidence does not exist in any amount, and without it there is nothing to "disprove" or even debate. And yet the majority of humans seem not to reason so.

[Lakche]

If there was proof that negatives could not be proven, then the hypothesis "negatives can not be proven" could not be proven, unless the statement was not a negative, and the statement "the statement was not a negative" was not a negative, and the statement "the statement 'the statement was not a negative' was not a negative" was not a negative, and so on.

Ergo, only if all of the statements following that pattern are not negatives and this conclusion is not a negative, can the hypothesis "negatives can not be proven" be proven. From an inductive standpoint, it is a situation where the premise is the only conclusion. Therefor, accepting that negatives can be proven, or that negatives can not be proven and the statement 'things aren't negatives' is not a negatives are both valid ways of thinking, by stoic rules.

Whether stoicism is correct or not is a whole 'nother bag of beans.

[redhotrebel]

Quite simply, burden of proof is on the source of the assertion. This is a requirement of logic.

I'm not sure if you mean "assertion" as the person laying forth a new claim/theory or the person claiming something as "true".

Anyways, I really don't want to get into a "god" argument because that will obfuscate the point, however, one reason why most rational people refuse to try to prove "him" nonexistent is because zealots continuously move the goal post. Also one of the fundamental ideas of a "god" is that their existence can never be proven nor disproven because that would ruin the whole faith thing they have going on.

Anyways, science has proven "negatives" in the past. One such example is the belief that the Earth was held up on the back of a giant turtle. Science said "no there is no magical turtle" and proved a negative. Ofc it is a lot easier once technology advances to a certain stage. We could orbit the Earth- take pictures etc... Another such example is that the universe revolves around planet Earth- Although even science cannot convince some that the universe doesn't revolve around them

Another example is the "young Earth theory". Even when science proves that the Earth is not 6,000 years old but by evidence is billions of years old- you are always going to have a fringe group that refuses to see reason.

Yes it is possible to "prove" a negative.

Long story short: A person who chooses to live a rational life must also choose to live within its rules, one must use inductive thinking, if you throw the apple in the air it will come back down because reason dictates that it will.

[JudgeBob]

Quite simply, burden of proof is on the source of the assertion. This is a requirement of logic.

I'm not sure if you mean "assertion" as the person laying forth a new claim/theory or the person claiming something as "true".

It's irrelevant which. An assertion is an unambiguously defined logical statement that posits something. A negation is not the opposite of an assertion, it is a logical operator. An analogy to math might be that assertions are like numbers, and negation is a mathematical operator such as addition. Assertions have values or meanings, like numbers. Operators do not.

My point is that it's not possible to prove a negative by definition, because a negative does not posit anything, it's a logical operator only. When a person says "prove a negative" the logical meaning is "prove a negated assertion."

Anyways, I really don't want to get into a "god" argument because that will obfuscate the point, however, one reason why most rational people refuse to try to prove "him" nonexistent is because zealots continuously move the goal post. Also one of the fundamental ideas of a "god" is that their existence can never be proven nor disproven because that would ruin the whole faith thing they have going on.

Anyways, science has proven "negatives" in the past. One such example is the belief that the Earth was held up on the back of a giant turtle. Science said "no there is no magical turtle" and proved a negative. Ofc it is a lot easier once technology advances to a certain stage. We could orbit the Earth- take pictures etc... Another such example is that the universe revolves around planet Earth- Although even science cannot convince some that the universe doesn't revolve around them

There is no "proof" that said magic turtle or an earth-centric universe does not exist, only strong evidence for obviously contradictory assertions. This is the root of the uselessness of discussing belief-based nonsense. It's a matter of people not accepting evidence-based logical conclusions and instead favoring some unreasonable interpretation or explanation.

Another example is the "young Earth theory". Even when science proves that the Earth is not 6,000 years old but by evidence is billions of years old- you are always going to have a fringe group that refuses to see reason.

Yes it is possible to "prove" a negative.

Long story short: A person who chooses to live a rational life must also choose to live within its rules, one must use inductive thinking, if you throw the apple in the air it will come back down because reason dictates that it will.

One of the few, but distinct, ways that I find myself in disagreement with Rand: I don't believe reason can be a choice. If one is capable of reason, one cannot "choose" not to use it. To choose so would be to demonstrate one is incapable of reason. By my definition, the capability for reason requires it's use.

The tragedy to me is that the young earth idiots and their ilk don't seem to be a fringe group, at least in the US. Less than half of US citizens accept evolution. The vast majority of voters and political candidates profess to believe in a god. The Texas state board of education deprecates evolution in favor of creationism. Arizona environmental policies are influenced by young-earth lunacy. Astrology horoscopes are found in every newspaper and grocery store. The number of people seeking homeopathic health remedies is increasing. Church attendance and income is big business. It goes on.

It is not possible to prove a negative [assertion]. You can only prove a contradictory assertion, then try to be entertained without getting discouraged by watching an unreasoning fool justify or explain their continued belief. If you haven't read James Randi's book Flim Flam, I recommend it for some fun examples of the lengths people will go to fool themselves and others.

[redhotrebel]

There is no "proof" that said magic turtle or an earth-centric universe does not exist, only strong evidence for obviously contradictory assertions. This is the root of the uselessness of discussing belief-based nonsense. It's a matter of people not accepting evidence-based logical conclusions and instead favoring some unreasonable interpretation or explanation.

Did my brain just stroke off there for a second or am I correct in my reading that you said “there is no ‘proof’ that said magical turtle... does not exist...”?

Humans have seen that there is no turtle, if you cannot believe what is seen (barring schizophrenic illusions) then that is completely irrational thus ending any further argument because the person would have to be clearly insane. Satellites would be unable to orbit the planet due to giant turtle obstructions!!! We cannot call ourselves objectivists if we ignore objective evidence.

Assume for a moment that it is true that a negative statement cannot be proven - since this very rule itself is a negative, how can we ever hope to prove that it's true? The principle is in violation of the Law of Non-Contradiction, which says a thing cannot be both true and false at the same time; that no logical statement can contradict itself. In practice, such a situation is called a paradox, and is automatically false. If the statement 'you can't prove a negative' were ever proven true, it would have to apply to itself, making itself false.

http://www.associatedcontent.com/articl ... html?cat=9

[Calderac]

I think this distinction needs to be made again. Proving a negative is different than proving a positive. One can say that there are no turtles holding us up (the negative assertion). The only way to prove it is to show that there are gravitational forces acting on Earth that determine its position (a positive assertion). One can argue semantics, but the positive assertion was what was proven true. The negative of this was only proven by knowing there can be no contradictions. In order to "prove the negative", a contradiction must be made which means an alternate assertion was what was actually proved. The negative was technically never proved, just shown to be contradictory and thus false.

Take something that has no positive evidence, the existence of a God. This is a negative statement that cannot be proven. Others include that people become spirits when they die, demons exist, telekinesis works, etc... There is no evidence indicating that any of these work. Thus, it is reasonable to say that one does not believe in these without having to prove the negative , which isn't his burden in the first place.

It's a small point but I think we're all dancing around the same idea.

[Lakche]

Assume for a moment that it is true that a negative statement cannot be proven - since this very rule itself is a negative, how can we ever hope to prove that it's true? The principle is in violation of the Law of Non-Contradiction, which says a thing cannot be both true and false at the same time; that no logical statement can contradict itself. In practice, such a situation is called a paradox, and is automatically false. If the statement 'you can't prove a negative' were ever proven true, it would have to apply to itself, making itself false.

http://www.associatedcontent.com/articl ... html?cat=9

What if the statement "you can not prove a negative" was a positive statement? Also, there is a logical invalidity in the link:

Determining that the sun is a ball of Hydrogen automatically rules out the possibility of the sun being made of Cheese Whiz or the souls of flushed gold fish.

If Hydrogen was made of Cheese whiz, or the souls of flushed gold fish, then the sun could be made of either of those things. While the sun may very well not be made of these goods, the reasoning is incorrect. For instance proving that an animal is a cat is not enough to prove it is not also a mammal. In Aristotelian logic, one of the rules for forming valid syllogisms is that a negative conclusion must be based from one positive premise, and one negative premise.

One can say that there are no turtles holding us up (the negative assertion). The only way to prove it is to show that there are gravitational forces acting on Earth that determine its position (a positive assertion)

I disagree that finding an alternative explanation to Earth's movements rules out any others. The selling point of mathematics is that there are multiple explanations to an observation. I could even write one up for the turtle thing.

[TRHaz]

I disagree that finding an alternative explanation to Earth's movements rules out any others. The selling point of mathematics is that there are multiple explanations to an observation. I could even write one up for the turtle thing.

Its seems that the standard of proof here has gotten completely misaligned. When observable objective evidence is present (i.e. not turtles observed holding up earth, observable scientific theories) this is ignored by you as not evidence. However you stating that you can prove that turtles hold up the earth mathematically is evidence. Prove your positive statement before you come in here claiming before objectivists that reality is not objective and that just because a statement is phrased a certain way makes it not provable.

proof |proōf|
noun
1 evidence or argument establishing or helping to establish a fact or the truth of a statement : you will be asked to give proof of your identity | this is not a proof for the existence of God.
• Law the spoken or written evidence in a trial.
• the action or process of establishing the truth of a statement : it shifts the onus of proof in convictions from the police to the public.
• archaic a test or trial.
• a series of stages in the resolution of a mathematical or philosophical problem.

prove |proōv|
verb ( past part. proved or proven |ˈproōvən|)
1 [ trans. ] demonstrate the truth or existence of (something) by evidence or argument : the concept is difficult to prove | [as adj. ] ( proven) a proven ability to work hard.
• [ trans. ] demonstrate by evidence or argument (someone or something) to be : innocent until proven guilty.

While some statements offer evidence, i.e. there is not turtle holding up the world on its back because...

Other statements offer none other than the statement itself Turtles hold up the world on there back.

The negative statement here by dictionary definition has been proven and the positive statement has not.

Now go on throw yourself on the floor scream and shout that you are right and that I am wrong, it will not make you look any less the fool.

[redhotrebel]

The selling point of mathematics is that there are multiple explanations to an observation. I could even write one up for the turtle thing.

Show me. Give me a mathematical or logical explanation that there is a giant turtle holding up the Earth. Don’t piss on my shoes and tell me it's raining, that doesn’t work here. An argument in formal logic is valid if and only if it is not possible for the premises of the argument to be true while the conclusion is false. So any "mathematical" explanation you may have needs to meet that requirement.

In Aristotelian logic, one of the rules for forming valid syllogisms is that a negative conclusion must be based from one positive premise, and one negative premise.

Although it is much easier to prove a positive i.e. the sun is made of hydrogen, it is not as easy to prove the negative because the "negatives" could be infinite, it's not a baseball, it's not a shoe, it's not a cup etc... into infinity. One could postulate that the sun is made of Ethyl Chloride and they could test that theory, but when it doesn’t meet the criteria the theory must change. I suppose the intoned negative could be “not” Ethyl Chloride although it would be irrelevant as one is attempting to show what the sun is rather than what it is not.

Far be it for me to criticize Aristotle, but claiming that a theory must have a negative and postitive side to an argument makes the negative side a possible ad infinitum logical fallacy. The "negative" can become irrelevant (i.e. X or not X versus X or not ABCDEFGHI....). Also in my honest opinion, that statement, however eloquent, does not address the topic directly rather it attempts to convolute the point.

Once again I would like to state that if one wishes to live in a rational world they must live within the rules and boundaries set forth by logic and reason. We do this in part by inductive reasoning to "prove a negative". I cannot prove that god, bigfoot, unicorns or aliens don't exists, but I can use reason to conclude that there is no evidence for their existence. The very nature of an inductive argument is to make a conclusion probable (but not certain) given the truth of the premises.

I feel like I'm just running around in circles now and I do not know of a better way to make this argument. I suppose that personally, I will just have to disagree and leave it at that.

[Lakche]

When observable objective evidence is present (i.e. not turtles observed holding up earth, observable scientific theories) this is ignored by you as not evidence. However you stating that you can prove that turtles hold up the earth mathematically is evidence. Prove your positive statement before you come in here claiming before objectivists that reality is not objective and that just because a statement is phrased a certain way makes it not provable.

The scientific observations lacking any sightings of turtles were based on an invalid premise--specifically that objects have magnitude in no more than 4 perpendicular dimensions colloquially referred to as time and space. Theoretically, there is no falsifiable test to give evidence that no objects anywhere have distance in a fifth, because physics hasn't been developed into an axiom based system; there is no grand unified theory yet. Incidentally, attempts at axiomizing physics takes the route of hypothesizing additional dimensions. M-theory is a popular one these days, and is now up to fully 11 of them, and growing.

A quick explanation of dimensions is due then; people on the roof of a building can bump into each other fairly easily. They can see one another without looking up or down, because they are level. However, in order to see people below them, they must angle their eyes downward. If some unfortunately acrophobic gentlemen who is afraid to look down is situated on this building, he will never see what is below, no matter how much looking he does at eye level. For all he knows, there could be a giant turtle holding the building up, because he has no way of looking downward.

By the same principle, were there a turtle situated adjacent to the earth, but residing also in an additional dimension, we might never see it no matter how many photons we shoot around in the four we're comfortable with. And of course, the only way to angle oneself into this dimension would be to receive some sort of force that originated in this dimension to begin with. You can then safely hypothesize that there 'exists' an infinite integer number of dimensions, and that the distance between everything we know of is 0 in most of them.

Besides being silly, and proving a sticky point, this is actually useful. A model to explain gravity can be envisioned by imagining a metaphorical 2 dimension world, with our friend the turtle holding it up on a 3rd. I'm sure many of you have seen a similar diagram. Here if an object would otherwise proceed linearly, it would instead begin to curve its path in relation to the turtle, and (what do you know it!) that's precisely what our tools in the objective world report happening. Granted today we call them 'gravitational fields' instead of turtles, back in the ol' days they didn't have such fancy words, and relied on metaphors to explain their objective observations.



Since we don't precisely know the cause of gravity, other than mass has something to do with it, the hypothesizing that turtles, chinchillas, gravitons, or even people named Atlas is holding the universe up is all logically acceptable, because to be frank at this level of technology we don't really know. It's enough to simply know how it works instead of why. (Parabolic, like the shell of turtle, f.y.i.)

[redhotrebel]

The scientific observations lacking any sightings of turtles were based on an invalid premise--specifically that objects have magnitude in no more than 4 perpendicular dimensions colloquially referred to as time and space. Theoretically, there is no falsifiable test to give evidence that no objects anywhere have distance in a fifth, because physics hasn't been developed into an axiom based system; there is no grand unified theory yet. Incidentally, attempts at axiomizing physics takes the route of hypothesizing additional dimensions. M-theory is a popular one these days, and is now up to fully 11 of them, and growing...

We do not live in another dimension, we live in this one. Thus we must live objectively by the "rules" this dimension sets forth.

"To introduce into one's consciousness any idea that cannot be so integrated, an idea not derived from reality, not validated by a process of reason, not subject to rational examination or judgment-and worse: an idea that clashes with the rest of one's concepts and understanding of reality- is to sabotage the integrative function of consciousness, to undercut the rest of one's convictions and kill one's capacity to be certain of anything..." Ayn Rand, VoS

we don't precisely know the cause of gravity, other than mass has something to do with it, the hypothesizing that turtles, chinchillas, gravitons, or even people named Atlas is holding the universe up is all logically acceptable, because to be frank at this level of technology we don't really know. It's enough to simply know how it works instead of why. (Parabolic, like the shell of turtle, f.y.i.)

Check your premise.

[Lakche]

We do not live in another dimension, we live in this one. Thus we must live objectively by the "rules" this dimension sets forth.

Something is distorting space/time; all the objective data agrees. Until we find out a way to supercede the effects of gravity, we can only speculate what it is. From what we do objectively know, it is as if the universe (or as an ancient might say, 'the world') is flatly placed on top of a turtle. Via modern lingo, the space/time continuum is distorted in a parabolic shape.

"What senses do we lack that we cannot see and cannot hear another world all around us?" -Frank Herbert

Check your premise.

Still to no avail. I'd even appreciate if you could show which premise is false.

[redhotrebel]

Still to no avail. I'd even appreciate if you could show which premise is false.

...is all logically acceptable, because to be frank at this level of technology we don't really know.

This is the premise I found most disturbing.

[Lakche]

If that premise is false, then there is a known method of collecting information from parallel dimensions that are orthogonal to the parabola of gravitational distortion. (The space where the turtle might be hiding.) Since, as you so succinctly phrased, we live in 'this one,' extracting observations from another is a little tricky... there's some speculative methods on how such a thing might be achieved, such as M-theory, wormholes, and dark matter. The trick is, there has never been the slightest bit of empirical data supporting M-theory, wormholes are unstable, and dark matter has yet to actually be observed. To the best of my knowledge nobody has intentionally achieved magnitude in any greater than 4 dimensions at any given time.

If there is no known method of getting this information however, my premise is true.

[redhotrebel]

Lakche- it is not logical to believe in everything just because it is an unknown. Pascal's wager is an example of that type of backwards thinking. (I'm assuming you know why that line of logic is incorrect.)

[Lakche]

If we accept logic as the condition that true premises never lead to false conclusions, or as you phrased it,

An argument in formal logic is valid if and only if it is not possible for the premises of the argument to be true while the conclusion is false.

then treating unknowns as hypothetical causes for true conclusions is logically valid, because whether the unknowns are true, or false, it doesn't cause the conclusion to be false. This is why "I disagree that finding an alternative explanation to Earth's movements rules out any others." My point was never to prove definitely the turtle thing was the case (amusing as that would be) but rather that given modern calculations, it falls into a range of acceptable possibilities--a thing that's kinda' been hot in physics this last century. It isn't faith based reasoning, and is in fact helpful to show when things are true, as opposed to if, e.g. electron orbits.

Pascal's Wager isn't a parallel case, because it is the conclusion which is unknown, and the premises which can be empirically evaluated. He states that assuming the presence of a god has no cost, and that this unfathomable being would indubitably favor ass kissers who depart from (what he would believe as) their god-given ability to reason. Since reactions in reality tend to always have requirements, which furthermore are costs, the argument is already unsound, unless of course god believing isn't a reaction in reality. So yes, according to Pascal's Wager, you should definitely keep god belief out of the category of things that do happen, because you have nothing to lose and everything to gain.

[Hieder]

Put me in line if I'm being too foundationalist and taking all the fun out of it, but isn't it true that nothing in physical reality can be absolutely proved? I'm often corrected when I use the word "proof" when I should have said "supported". Finding proof in physical reality would require proving causal absolutes; something which cannot be proven. Thus, should not an argument consider alternate possibilities when deducting conclusions based in physical/observable reality?

If my argument becomes "Causality is not absolute" then I am not burdened with having to prove that negative, there is no evidence that it is absolute. I could develop a whole life philosophy based on the idea that there is no evidence for causal absolutes. It then remains in logic's best interest that I consider alternative possibilities and statistical probability when reasoning.

Statistics for a particular case in physics might say 9 out of 10 times a specific outcome will occur. This outcome may be causally understood, but that 10th time a random outcome happens which may be outside of all known understanding. Reasoning using known evidence would suggest that causality in that particular case is not absolute. Reasoning that the evidence has not been fully gathered to understand the situation as being causal would be faith since it has not been proven that this evidence exists. The causal understanding of that 10th outcome must be understood for the case to be causally sound. However, if I am ever tasked with a problem that requires this case as a solution I should calculate that the outcome of it only will follow causal attitudes 90% of the time.

This shows that unproven alternatives must be considered when developing solutions. Also, that physical/empirical reality cannot be used in an argument or example that attempts to prove a negative since doing so would require proving that causality is absolute.

A practical example of this is the existence or non-existence of dark matter. The cause of the problem was not understood so the rules were changed and something that was not causally understood was factored in to make it work.

[musashi]

Statistics for a particular case in physics might say 9 out of 10 times a specific outcome will occur.

Actually the more prevalent acceptance criteria are 19 events supporting the null out of 20 trials (alpha 0.05), but you are on the point.

I choose to think that anything in nature can be questioned. The answer may often come back unchanged, but past results do not guarantee future performance (at least beyond the margin of error in the hypothesis test we are using).