Proving a Negative

[Oleksandr]

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?

Oh, and on what basis did you come to this conclusion?

[Hieder]

Oh, and on what basis did you come to this conclusion?

Read the rest of my post. I explain how I come to that conclusion very completely. Causality must first be proven to be absolute. We can't prove that.

[Oleksandr]

Oh, and on what basis did you come to this conclusion?

Read the rest of my post. I explain how I come to that conclusion very completely. Causality must first be proven to be absolute. We can't prove that.

What is your standard for a proof?

[musashi]

Oh, and on what basis did you come to this conclusion?

Read the rest of my post. I explain how I come to that conclusion very completely. Causality must first be proven to be absolute. We can't prove that.

What is your standard for a proof?

Aye there’s the rub. How deep is the sea? Or the universe in this instance.

The logical tests I’m familiar with have housekeeping activities associated with asking a question.

What is your standard of proof? (alpha) is one of them. This is the risk of making a false positive conclusion. And while we maybe able to fail to reject a null at 5%, we have less certainty that we’d reject at 1%.

One of the other questions is how certain would you like to be? (beta) This is the risk of making a false negative conclusion. Sometimes they call this the power of a test. Our power of prediction goes up as our sample size increases.

To truly prove a null we’d need to have an alpha of 0% and a sample size of 100%. Both situations are mathematical abstractions similar to infinity.

[Oleksandr]

Statistics have nothing to do with proving anything. They are a way of making the best guess in the cases where you are ignorant of the underlying causal nature.

[Hieder]

The standard for a proof in logic is that the case is completely explained by the given argument. Anything that isn't a complete, bulletproof argument that covers all sides in logical infalably is just evidence to support the case. Making an argument that has been seen to be an explaination for an outcome in all observed cases does not equal a proof because it's just a convienient piece of evidence that presents a possibility. No assumptions can be used. There could still exist a case where the argument does not hold true thus negating the proof quality of the argument, but we cannot assume that this case does not exist. The mechanics underlying the results must first be looked at and fully understood.

We cannot prove that causality is absolute or even that causality is the defining mechanic of the universe because doing so would require infinite observability of all aspects of all situations. If there is even one situation where causality is descovered to not be the governing mechanic then it would mean that causality is not a universal law (sorta redundant), thus it cannot be used to initially describe situations and their outcomes and must first be proven for each individual case to be the governing mechanic. Again requiring infinite observability.

[Oleksandr]

Well, then, there is where we reach the end.

According to you, proving X means proving it in ALL cases, past, present, and future. That means you are demanding omniscience, which logically implies that you have to agree that humans can't know anything with certainty, since humans are not omniscient.

Which means if somebody comes and punches you in the mouth, the only thing you could say is "you might have done something wrong - I can never know since I'm not omniscient." So what is left if logic is thrown out as useless in reaching certainty in knowledge? Emotions, whims, etc.

And that is a death trap.

If men reject logic, then the tie between their mental processes and reality is severed; all cognitive standards are repudiated, and anything goes; any contradiction, on any subject, may be endorsed (and simultaneously rejected) by anyone, as and when he feels like it.

[Leonard Peikoff] http://aynrandlexicon.com/lexicon/logic.html



I'm not going to argue this anymore, but I will point out to those who are interested to know what is the right view on this subject:

Induction.

Induction is the proper method of reaching certianty and it does not require going over every element in the universe (which is not possible for us anyway); it does not require counting white swans until your death and beyond. Explaining the whole theory of Induction is much too difficult of a subject, and I'll leave that to the coming book by Leonard Peikoff [ "Induction in Physics and Philosophy" which comes out in 2011, I believe. He has an audio course on it available already, but it isn't cheap. ]

The only part I will add and quote here is on the topic of certainty.
http://aynrandlexicon.com/lexicon/certainty.html

OPAR has an entire chapter on certainty. I suggest checking that out for details. http://peikoff.com/opar/certainty.htm The book is available in any public library in US.

Idea X is “certain” if, in a given context of knowledge, the evidence for X is conclusive. In such a context, all the evidence supports X and there is no evidence to support any alternative . . . .

http://aynrandlexicon.com/lexicon/certainty.html

[Hieder]

No you are exactly correct and this is the very thing that I am getting at! We are actually in agreement on that point. Inductive reasoning or if an argument contains within itself the evidence that proves the case. This is exactly what foundationalism is. Descartes first philosophy on epistemology was that the only thing he could truely know existed was his mind because the very fact that he was contemplating his own existence must mean that something exists in order to do the contemplating. He was a thinking thing thus proving his own existence. However, these types of proofs only exist in logic.

Math is another thing where the logic to prove certain cases is contained within the situation. I wasn't suggesting that we go with emotional insights to come to conclusions. You jumped to that conclusion (ironically because of emotion perhaps). That would be a stick-man argument no? I was just saying that we cannot come to conclusions if the evidence is not purely conclusive.

But I believe we were getting off track from what I was actually describing which is that things in physical reality cannot be proved since we don't know the nature of physical reality. Perhaps physical reality doesn't work logically and this is also something that Descartes suggested. His ball of wax and the evil demon scenarios. We have no evidence to suggest that causality is a law of the physical universe.

[musashi]

Idea X is “certain” if, in a given context of knowledge, the evidence for X is conclusive. In such a context, all the evidence supports X and there is no evidence to support any alternative.

I often work within this context of no evidence supporting the alternative. Often for the purpose of things like process validations, the most efficient approach towards sampling is to define the acceptance criteria as “Accept on zero failures, Reject on one or more failures”. Any Rand’s definition makes the claim that in any one of these validations if all results pass and no evidence supports the alternative I can be certain in the process.

This certainty is only true to a degree. Again it comes down to those two basic questions.

The first question could be phrased in many different ways

• How perfect is the causality?
• What is the predetermined level of significance (say the alpha value)?
• With is the reliability of the process of system to produce the null condition?
• How do the number of individuals in the sample group compared to the number in the population?

Te second question centers around how confident you’d like to be that with replicate tests we’d reach the same conclusion.

• What confidence interval of the judgement?
• What is the power of the test (beta value)?
• What margin of error for the test?
• How do the number of individuals in the sample group compared to the number in the population?

In my process validations I usually phrase the statement this way…Testing 45 samples (accept on zero reject on one or more), we can have at least a 90% confidence, that the process is 95% reliable. Here’s a nice binomial calculator that helps to do that math. That at least is key, because in reality the process could be far more reliable and or could support a much higher confidence interval.

I do look forward to learning more about inductive logic from Mr. Peikoff’s new book. In some aspects of life induction works very well; like following the rules of the road when driving. Inductive thinking may not provide a judgment framework to prevent all accidents, but induction certainly provides a great benefit in that instance. It would be great to gain more insight about induction.

My difficulty with induction comes when it is used arrive at absolute conclusions about the universe.

[Oleksandr]

. . . Inductive reasoning or if an argument contains within itself the evidence that proves the case. This is exactly what foundationalism is. Descartes first philosophy on epistemology was that the only thing he could truely know existed was his mind because the very fact that he was contemplating his own existence must mean that something exists in order to do the contemplating. He was a thinking thing thus proving his own existence. However, these types of proofs only exist in logic. . . .

I have no idea what you said in your post. I have read it again, and I still have no idea what you said.

And I'm not going to talk about idiot Descartes, if he doubts the world exists, he should go see a doctor.

[Oleksandr]

I do look forward to learning more about inductive logic from Mr. Peikoff’s new book. In some aspects of life induction works very well; like following the rules of the road when driving. Inductive thinking may not provide a judgment framework to prevent all accidents, but induction certainly provides a great benefit in that instance. It would be great to gain more insight about induction.

1. There is no such thing as "inductive thinking." Human mind operates on induction and deduction (which depends on inductive conclusion first!). If you think, you are using induction.

2. Did you read OPAR's chapter on certainty?

Most people today have no concept of contextual certainty. They define absolute statements as something like this:


Leonard Peikoff, OPAR

Many people in our Kantian era think, mistakenly, that absolutism is incompatible with a contextual approach to knowledge. These people define an "absolute" as a principle independent of any other fact or cognition; i.e., as something unaffected by anything else in reality or in human knowledge. Such a principle could come to be known only by revelation. An eloquent example of this approach was offered years ago by a famous relativist, who told his class that airplanes refute the law of gravitation. Gravitation, he explained, means that entities over a certain weight fall to the earth; but an airplane in flight does not. Someone objected that there are many interacting factors in reality, and that gravitation involves an object's falling only if the gravitational pull is not counteracted by an opposing force, as it is in the airplane's case. To which the professor replied: "Precisely. Gravitation is conditional; its operation depends on circumstances; so it is not an absolute." What then would qualify as an absolute? Only a fact that has no relationships to anything (like Hegel's supernatural Absolute). Such a fact would be knowable only "in itself," by mystic insight, without the "contamination" of any "external" context of evidence.

The modern definition of "absolute" represents the rejection of a rational metaphysics and epistemology. It is the inversion of a crucial truth.

[musashi]

Many people in our Kantian era think, mistakenly, that absolutism is incompatible with a contextual approach to knowledge. These people define an "absolute" as a principle independent of any other fact or cognition; i.e., as something unaffected by anything else in reality or in human knowledge. Such a principle could come to be known only by revelation. An eloquent example of this approach was offered years ago by a famous relativist, who told his class that airplanes refute the law of gravitation. Gravitation, he explained, means that entities over a certain weight fall to the earth; but an airplane in flight does not. Someone objected that there are many interacting factors in reality, and that gravitation involves an object's falling only if the gravitational pull is not counteracted by an opposing force, as it is in the airplane's case. To which the professor replied: "Precisely. Gravitation is conditional; its operation depends on circumstances; so it is not an absolute." What then would qualify as an absolute?

This is a great analogy! Flawed, but it works so well. Yeah at first blush scientists like to push orthogonal models – the math is easier. And we always have Occam’s Razor in the back of our minds. That’s not to say that we can’t do interaction of two or more variables; I do it all the time.

I like this analogy because the professor misstated the law of gravitation in both circumstances. The law is F= G((m1m2)/ r^2). And actually in natural science we have very few laws; the law of universal gravitation is one of the few and it has been under siege for hundreds of years.

The first statement Gravitation means that entities over a certain weight fall to the earth. Is incorrect, Objects of any size would have some amount of gravitational attraction to the earth.

The second statement Gravitation is conditional is false as well. The force of gravitation exists independent of other forces acting upon a body.

I like the analogy further because in this instance Peikoff selected it to demonstrate that factors like gravity are not absolute, that outside factors can have an interaction. Yet in this instance the force of gravity is almost completely orthogonal to the lift forces of the wing. In this example gravity is absolute. It is rare when we can catch an error from a great mind like Leonard Peikoff.

[Hieder]

Many people in our Kantian era think, mistakenly, that absolutism is incompatible with a contextual approach to knowledge. These people define an "absolute" as a principle independent of any other fact or cognition; i.e., as something unaffected by anything else in reality or in human knowledge. Such a principle could come to be known only by revelation. An eloquent example of this approach was offered years ago by a famous relativist, who told his class that airplanes refute the law of gravitation. Gravitation, he explained, means that entities over a certain weight fall to the earth; but an airplane in flight does not. Someone objected that there are many interacting factors in reality, and that gravitation involves an object's falling only if the gravitational pull is not counteracted by an opposing force, as it is in the airplane's case. To which the professor replied: "Precisely. Gravitation is conditional; its operation depends on circumstances; so it is not an absolute." What then would qualify as an absolute?

I'm confused. Does Peikoff realize that his chosen example is so weak? If he does then this is how politicians work not philosophers. Playing off of people's emotions.

Physics being affected by a different thing in physics does not equal physics being affected by something else in reality. The very reason its being affected is because the two are related. Cooling is not separate from loss of heat. They are the same thing, though in some minds it may be thought of as different.

Peikoff's paraphrase talks about falling (not gravitation). Things fall unless they are being lifted. An airplane lifts. If this relativist wanted to talk about gravitation he was doing it wrong. It's easy to see this problem in the example, but Peikoff uses it to support his own argument.

A fallable human person's example shouldn't be used to prove a point on logic. It's like saying, "Look at how dumb the opposition is, they say this and this and this, so their position must not be true." Peikoff should develop his own example on this rather than using the weak one he provided.

[Oleksandr]

Peikoff should develop his own example on this rather than using the weak one he provided.

Sigh.

Did you read OPAR book at all? Peikoff develops a whole positive case there page after page after page. So your claim is completely arbitrary, and all because I didn't quote the entire book to you here in this thread.

[Iudicious]

There's a reason why you cannot prove a negative. Proof relies on the fact that something exists, or is true, and if it exists, or is true, it leaves traces of this fact behind. A negative states that something -does not exist-. If it does not exist or is not true, it cannot leave proof of any kind.

As Calderac said earlier, you can show something is false by means of showing that something else is true, but you cannot just out and prove something false, because there can be no proof for a negative.

[S'thiscia]

What a terrific discussion... by way of introduction (instead of a boring old "hi my name is..."), may I suggest a book: "Flatland" It is not technical in any way, but if you are paying attention it implies some wonderfully complex ideas about how perception is limited by dimensionality. It was recommended to me by a mathematician during my undergraduate studies (he is a Logician as a matter of fact).

I am looking forward to finding more interesting discussions like this as I explore these forums

-S'thiscia

[Oleksandr]

Gosh. I looked at the thread again. I need to add another point.


Math =/= Philosophy. Whatever rules and methods you come up in Math has zero application in Philosophy. Math and Philosophy are two vastly different subjects by their very nature of what they do and don't study.

So, please, no more using statistics to try to show some point in philosophy.

[PimpinYourhos]

Gosh. I looked at the thread again. I need to add another point.


Math =/= Philosophy. Whatever rules and methods you come up in Math has zero application in Philosophy. Math and Philosophy are two vastly different subjects by their very nature of what they do and don't study.

So, please, no more using statistics to try to show some point in philosophy.

The ancients believed certain mathematical principles were a subset of philosophy... What say you?

http://en.wikipedia.org/wiki/Philosophy

The main subjects of ancient philosophy are: understanding the fundamental causes and principles of the universe; explaining it in an economical and parsimonious way; the epistemological problem of reconciling the diversity and change of the natural universe, with the possibility of obtaining fixed and certain knowledge about it; questions about things which cannot be perceived by the senses, such as numbers, elements, universals, and gods; the analysis of patterns of reasoning and argument; the nature of the good life and the importance of understanding and knowledge in order to pursue it; the explication of the concept of justice, and its relation to various political systems.

[Oleksandr]

The ancients believed certain mathematical principles were a subset of philosophy... What say you?

I'm not sure what you are asking.

Do you mean that they said that some math principles were a subset of philosophical principles? Or that philosophy defines some of math principles?