Intuitive Proof

[BeHereNow]

Intuition is a method of arriving at direct knowledge, not based on organized, rational thinking, such as logic, deduction or inference, and not based on the evidence available. It is also not a divine revelation, or truth learned from sacred texts.

Because of these things, it is not scientific or religious in nature.
I started studying Zen (Buddhism) many years ago and did not know it at first, but I was studying about Intuitive Proof. It was not until I started studying about Deism that I made connection and started to see the actual reference to intuition as a way of knowing things.
Buddhism is neither atheistic nor theistic, so not inherently religious, although some do adopt one stand or the other. Deism has a belief in god, but none of the trappings of religion, little or no personification of god, and is little more than a form of naturalism. God is part of the natural, the supernatural does not exist. Some will consider Deism a “religion” because it contains the word god, but under classical definitions of religion, Deism falls very short. It is a philosophical world view that does not appeal to Atheists or Theists with strong convictions in these beliefs.

From Deism I investigated the sciences to see if there were a ‘rational’ basis for accepting a non-rational way to truth. I found that there were indeed mathematicians and scientists who accepted and advocated for intuition as a means to truth.

Words in themselves have no meaning. They are arbitrary symbols meant to represent thoughts, concepts, or the existence of actual objects or events.

We give words meaning by mutual agreement of what the symbols represent. Some words have the exact same appearance, but different meanings based on context. The symbols remain the same, the meaning changes.

Words used in this thread will have a particular meaning, applicable to this context, but in other context they may have other meanings.

We will need a common agreement of many words.

The subject of this thread is “Intuitive Proof”, so we will start with defining this one term. This is a term BHN uses, and to my knowledge no one else on this board has supported it or indicated they have prior knowledge of it although everyone has heard the word intuition. Some, such as beto believe the term represents a false belief, so in effect say it does not exist, since it is false. It is up to BHN to define the term and show how there is no evidence it is false, and there is supporting evidence to show it is true. Whether it is convincing evidence will depend on the individual. That is the nature of convincing evidence, it is not universally convincing. I must do this by using words in their commonly accepted meanings, and not creating some truly arbitrary meaning simply to make false statements seem true. In order to do this there has to be a mutual agreement on the meaning of key words in addition to the immediate subject (intuitive proof).

Each word or term can be accepted, rejected, or questionable.
Rejected or questionable meanings will need clarification, with beto stating his objections so BHN can reply and together, arrive at acceptable meanings.
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Naturally this is not a closed debate, so others may challenge the meanings of words and offer their opinions.
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Intuitive Proof is comprised of two words in conjunction. Beto has given us a starting point by offering some dictionary definitions of the individual words. As I mentioned in the thread that spawned this thread, QED taught me years ago that dictionary definitions of words are wonderful for those who do not know the meaning of the words, but for true meaning discussion is needed. I have found dictionaries can be a starting point for those with strong disagreements, so do not object to starting there and incorporating what they offer.

Proof - a: the cogency of evidence that compels acceptance by the mind
of a truth or a fact b: the process or an instance of establishing the
validity of a statement especially by derivation from other statements
in accordance with principles of reasoning

Cogency can have a quality of logic, but this is not acceptable as intuitive proof is not derived from logic. We will take cogency to mean a simple, or clear thought, with elements of plainness, not complex or complicated. Using the first definition of ‘proof’ we have:
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Proof: A clear thought of evidence that compels acceptance of the mind of a truth or fact.
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We can see from this that what is proof to one person (mind) many not be proof to a different person (mind). A proof convinces the mind, but may not convince all minds. This may seem obvious, and yet it may be a point of contention.
There is proof of global warming, yet not all accept the ‘proof’.
There is proof the surge of globing warming we are experiencing is a result of mankind and the burning of fossil fuels, yet not all accept the ‘proof’.
If our measure of proof is that all must accept it, we will find the meaning of ‘proof’ is useless.
There are sane, (otherwise) rational persons who honestly believe NASA never put a man on the moon. For them, there is no proof this happened, only fabricated evidence.
Proof convinces many rational minds, but not everyone always.

Intuition - 1: quick and ready insight
2 a: immediate apprehension or cognition b: knowledge or conviction
gained by intuition c: the power or faculty of attaining to direct
knowledge or cognition without evident rational thought and inference

This last definition (2c) is acceptable when putting meaning to the term ‘intuitive proof’.

So we have:
Intuitive proof: The power of attaining knowledge that is convincing to the mind without evident rational thought or inference, what we can call the tools of science.

By knowledge I mean the accepted meaning of general awareness or possession of information, facts, ideas, truths, or principles.

That which actually exists is truthful. If I identify or describe accurately, a particular planet that orbits a particular star, I have knowledge of that planet.
If a planet orbits a particular star, but I am not aware of it, I have no knowledge of it, yet it still remains a truth that it exists. My lack of awareness does not change a truthful thing into a false thing.
If a law of physics exists, but we have no awareness of it, it is no less a law of physics, it simply has yet to be discovered.

Science is incapable of revealing all true things.
Science may have the potential to reveal any true thing, but this is quite a different admission.

Science has revealed to us that there are other planets orbiting other stars, but I doubt that any of us will see the day science catalogs all of the planets in our galaxy, let alone our universe, and this is a small example.
There are things which are true and science has no knowledge of them.
In some cases, science is so unaware of them, they are not even being investigated. In other cases science is aware of them, but lacks the tools or motivation to investigate them.
By ‘science’ I use the broad meaning of logic, and rational thought applied to material and empirical evidence, which would include the science of math, physics, etc.


Intuitive proofs are not replacements or substitutions for scientific proofs.
Intuitive proofs lead the way for scientific proofs.
Those who accept intuitive proofs can point to much anecdotal evidence for their position.
When a scientist or mathematician says:
“Suddenly it just came to me. . .”
“I had been on the wrong path, when it all became clear. . .”
“I don’t know why it didn’t occur to me sooner that. . .”
“I awoke one night and had to write my thoughts down immediately, before I was fully awake and forgot them.”
There are examples of the anecdotal evidence I am referring to.

Those who object to intuitive proofs point out that any outlandish idea may appear to be true and the results may do great harm if others accept as true what is rubbish.
I should not have to point out that these same charges were leveled against science in the days of Galileo and others.

There is no doubt that by today’s standards science is a safe way of attaining truth, and intuition is like playing with fire in a petroleum refinery.
Caution is the watchword.

Whenever possible, look to the tools of science to support intuitive proofs, because in some cases they are available.

It would be the height of arrogance for any believer of science to say “Science is aware of all true things.” An absence of scientific proof is not proof of non-existence. It is simply an absence of scientific proof, no more.

I would also suggest that for those who argue that science is the only means for discovering truths, they do so with truth they have intuited. The proof that they have the correct approach has been intuited, or is reasoned by scientific means. When scientific means are the rational for accepting only scientific means, we have a belief system built on circular reasoning.

If this is not true, it seems to me science would produce this proof they have that there is no supernatural explanation for any event. (I do not advocate for the supernatural myself, but have friends who do). Certainly there have been tests to demonstrate that some events credited to the supernatural are suspect or even flatly untrue, and continued belief will be based on faith.
Things such as the creation of the universe are beyond scientific testing at this time.

Epistemology is the philosophy that tells us about knowledge, what is knowable and how we know things.
Metaphysics is the philosophy that tells us what is real.

Those of other epistemological or metaphysical beliefs systems can dismiss Intuitive Proofs out of hand, as being contrary to their belief system.
“God tells me everything I need to know.”, is a rebuttal from a different belief system.
Similarly, “Science tells me everything I need to know.”, has different pillars that support their beliefs.
I see both positions to be essentially the same, one is just a little more complicated than the other (stands on shakier ground).

I will point out that if numbers mean anything, it is likely I am wrong.
I have chosen the path less taken, and have found it quite comfortable.

[Beto]

The reader can decide who is being objective and who is being subjective.

That is the whole point, and I trust the readers will be able to take whatever value they can find in our opinions, and use them to objectify their own. I think most of them also recognize how pointless it is to argue with someone that defines words to suit their conclusions.

[BeHereNow]

beto That is the whole point, and I trust the readers will be able to take whatever value they can find in our opinions, and use them to objectify their own. I think most of them also recognize how pointless it is to argue with someone that defines words to suit their conclusions.

My dear beto.

I use a term that you are not familiar with. When google I get over 5000 hits, so please do not argue that this is a contrived term. You have implied that when you say "defines words to suit thier conclusions".

I explain the meaning of the term and you say it is an oxymoron and has no sensible meaning, only a nonsense meaning.

You provide dictionary definitions and challenge me to show how these meanings that you accept can support my position, and the use of my term. Not 'mine' as in I originated it, but 'my term' as in I use it.

I use your accepted meanings and show how they exactly fit my meaning for my term.

You say that is not fair, I should have to use the meanings you accept when using this term.

This term you are not familiar with, and do not like.

Your teacher is lacking more than I first supposed.

[Goat]

beto That is the whole point, and I trust the readers will be able to take whatever value they can find in our opinions, and use them to objectify their own. I think most of them also recognize how pointless it is to argue with someone that defines words to suit their conclusions.

My dear beto.

I use a term that you are not familiar with. When google I get over 5000 hits, so please do not argue that this is a contrived term. You have implied that when you say "defines words to suit thier conclusions".

I explain the meaning of the term and you say it is an oxymoron and has no sensible meaning, only a nonsense meaning.

You provide dictionary definitions and challenge me to show how these meanings that you accept can support my position, and the use of my term. Not 'mine' as in I originated it, but 'my term' as in I use it.

I use your accepted meanings and show how they exactly fit my meaning for my term.

You say that is not fair, I should have to use the meanings you accept when using this term.

This term you are not familiar with, and do not like.

Your teacher is lacking more than I first supposed.

There is a difference between a mathematical concept, and trying to 'prove' any philosophical issues with 'intuitive proofs'. I am sorry if you can't see that, but using the logical fallacy of equivocation is hardly making your point.

[BeHereNow]

goat There is a difference between a mathematical concept, and trying to 'prove' any philosophical issues with 'intuitive proofs'. I am sorry if you can't see that, but using the logical fallacy of equivocation is hardly making your point.

You raise two issues that I see.
One is this particular thread, and the other is the thread that spawned this one.

In this particular thread it is beto who uses the fallacy of equivocation. My term was explained using definitions he offered and applied consistently by me. I did not use the word ‘proof’ in two or more senses, however beto wants to use his particular meaning, to my term. This is ridicules. He offered meanings, I accepted certain ones, and did not deviate. For me to have committed the fallacy of equivocation I would have had to switch meanings mid stream, and I did not do that.
If you see it a different way, please explain as it is certainly not clear.

The other issue is the “burden of proof” thread in science and religion.
That is not so clear.

At issue is the meaning of proof, which I believe is nothing more than a certain amount of evidence. In other word, evidence is the hinge concept. What is acceptable evidence, what is not. This is a philosophical point that can, as I see it, be approached epistemologically or metaphysically. These differences are core belief differences that usually cannot be settled.

In a subject area called “Religion and Science”, it seems to me religion is allowed to present its evidence.

The result is religion cannot prove to science that god exists (because science is not compelled to accept religious evidence). There are those who argue for the existence of god from a scientific position, but in my opinion they fail.

The flip side is science, using its own means, cannot prove god does not exist. An absence of evidence is not evidence. There are many absence of evidence issues (such as the planets I mentioned), and this does not change the truth that those undiscovered planets exist. I do not argue for the supernatural.

Here are the points I am willing to argue, probably in the “Burden of Proof” thread:

I cannot see where science has a closed franchise on what is acceptable knowledge. Epistemological beliefs say otherwise, and it is philosophy that offers methods to attain knowledge, for the individual to choose from.

If the atheist says there is convincing scientific evidence, they are obligated to provide it, and cannot do it concerning the evidence of no-god.

Religion cannot prove the existence of god, except by religious methods that science is not compelled to accept.

What is acceptable evidence is a core belief, and is only disregarded if internally inconsistent. Religious beliefs are core beliefs, which some people will always consider to be supernatural, and beeyond the scope of science. To myself and others they are so improbable as to be disregarded.

Intuition is a core belief, which (at this time) science cannot show is false, and is not internally inconsistent. It is an acceptable epistemological belief, but of course no one is compelled to accept it.

There are probably other points, if beto, goat or others have suggestions for what I might disagree with.

[Beto]

In this particular thread it is beto who uses the fallacy of equivocation.

I could be if I recognized more than one meaning to the word, like you do. You should brush up on logical fallacies.

My term was explained using definitions he offered and applied consistently by me.

Anyone can see you didn't.

I did not use the word ‘proof’ in two or more senses,

That would certainly create an "interesting" conversation.

however beto wants to use his particular meaning, to my term.

This is ridicules.

I'll tell you what's ridiculous.. it's your attempt to take the subjectivity of "intuitive proof" (already ignoring the fact that it's an oxymoron considering normal dictionary definitions, that you by no means agreed to) and attempting to give it a practical use in the exemption of a certain emotion from the rational scrutiny all the others get.

I grow weary of pointing out your straw men. Please don't keep purposefully misrepresenting my position.

[BeHereNow]

Intuition in mathematical proofs is inseparably connected with the originality of mathematical thinking, with creativity while proving. Modern usage of the term“intuition” originates from Descartes. Russian mathematician Steklov (1923) stated
that “the method of discovery and invention is the same for all, one and the same
intuition , because nobody discovers anything with the help of logic; a syllogism maylead other people to the agreement with that or other proof known before, but as atool of invention it is useless… But the heart of the matter is that even in simple cases it is impossible to logically explain all the stages of proof. In invention of practically every step of proof it is intuition that matters and not logic; intuition is higher than any logic”. Independent proofs, thus, can be divided into proofs where intuition is present (the so-called intuitive proofs), and the proofs which will be called logical proofs, i.e. proofs made only with the help of logic, in other words proofs where one uses the method known to a pupil and leading to a purpose though not demanding to put forward new ideas, while the proofs with the use of intuition are necessarily connected with the presence of originality in the ideas proposed by a pupil.

[Beto]

Appeal to Authority doesn't make your case stronger.

Since I don't want to misrepresent your position, I'd like to clarify something:

Please explain how saying: "Intuition is a method of arriving at direct knowledge, not based on organized, rational thinking, such as logic, deduction or inference, and not based on the evidence available" does not imply: "The intuition that drives a scientist to experiment new hypothesis is not related to his knowledge of science or to what he already knows is false".

For example, what would prevent a scientist from having an intuition "telling" him to mix chemical A and B, even though he knows (perhaps by prior experiment) that it will blow up the lab? Or does intuition (rather conveniently) never go against rational thinking, logic, deduction and inference? I hope we don't have multiple meanings for "deduction" and "inference".

[BeHereNow]

goat
I’m waiting for a reply to my rebuttal that you think I used the fallacy of equivocation.
Since I suggest you rethink, do you still believe, or do you see how it is beto who tries to make points by changing the meaning myself and others have used?

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beto Appeal to Authority doesn't make your case stronger.

Well it certainly makes your case weaker, so how can that not my case stronger?
You make the claim that “intuitive proof” is an oxymoron, with only a nonsense meaning. I demonstrate one example among many of how scientists, mathematicians, and philosophers have been using and arguing for the term for a century. These individuals would not do this if your position were correct. If I alone say such things, your case is very strong. The fact that I have not only Zen masters, but those from the sciences as well adds credence to my position and weakens yours.

Since I don't want to misrepresent your position, I'd like to clarify something:

Please explain how saying: "Intuition is a method of arriving at direct knowledge, not based on organized, rational thinking, such as logic, deduction or inference, and not based on the evidence available" does not imply: "The intuition that drives a scientist to experiment new hypothesis is not related to his knowledge of science or to what he already knows is false".
For example, what would prevent a scientist from having an intuition "telling" him to mix chemical A and B, even though he knows (perhaps by prior experiment) that it will blow up the lab?

When you say “knows is false”, I will assume you mean what your words say. Intuition as we are using it leads to truth, not falseness. If she knows something is false, she has proof, since she is a scientist, and only knows those things she can prove, repeatedly. If she truly intuits something, it cannot be something she already knows is false. We of course could use the term “false intuition”, but even that would not apply in this situation. If she has available scientific proof something is false, she cannot intuit it as true. Her mind will not allow this. If she only suspects something is false, different story. If she suspects A and B will blow up the lab, she will test. After all, she is a scientist. She will not ponder the problem for weeks, or months without trying a simple experiment.
It seems you still do not understand that intuition is not a substitution for scientific inquiry. I have pointed this out repeatedly.

Or does intuition (rather conveniently) never go against rational thinking, logic, deduction and inference? I hope we don't have multiple meanings for "deduction" and "inference".

Science sometimes shows that rational thinking, logic, deduction, and inference are incorrect. These things are not absolute proofs, and can be mistaken. That is why our scientists today insist that experimentation be done whenever possible. Of course this was not always the case. There was a time when these things were thought unnecessary. If experimentation cannot be done, then the scientists will look for other supporting evidence that comes from another direction.

If a scientist “knows” something, she has irrefutable scientific proof.

Your clear thinking is being fogged by your attempts to defend your position.
Of course intuition can go against rational thinking, logic, deduction and inference. Actually this is when intuition is most helpful, when it reveals truths hidden by inaccurate evidence.

[Beto]

Appeal to Authority doesn't make your case stronger.

Well it certainly makes your case weaker, so how can that not my case stronger?

I realize I've been giving you far too much credit. Logical fallacies don't make any case stronger in the eyes of those who recognize them. Those who rely on them are either ignorant or dishonest. Either way I have no interest in further discussion.

[QED]

Beto, I think it's out of character for you to be talking in terms of ignorance and dishonesty. Let's just take a deep breath and focus on the arguments.

BeHereNow, I realise that you feel strongly about intuition being metaphysical in some way but many people are familiar with the unconscious processing that our brains are doing all the time. I'm sure you've seen me referring to Malcolm Gladwell's book "Blink" in which he brings together many psychological experiments designed to expose subconscious activity. The point is that our stream of consciousness can be somewhat clumsy when compared with out unconscious operations -- the classic example being running downstairs (don't try consciously thinking about what you're doing!).

This is a very serious point -- Dan Dennett's theory of consciousness likens it to a "virtual machine" implemented on unconscious operations in the same way that Microsoft Windows is implemented on "invisible-to-user" machine-code instructions. Virtual machines are possible over unlimited generations -- thus it is possible to run a Commodore 64 simulation on Windows, and then run a Windows simulation on the virtual Commodore (and so on). At each level the only cost is execution speed -- and Dennett notes the very slow reaction time for conscious action over reflexes.

Going back to the running down stairs example, the accuracy and speed of calculations based on force-feedback are astounding. Other senses and judgements have equally fine-tuned capabilities yet often appear in our conscious thoughts as humble "guesses". Dennett cites "blindsightedness" as a good example of this -- in blindsight cases the usual part of the cortex involved with vision is damaged such that the patient cannot see as we imagine seeing. But the same optical information is shared around other parts of the brain and the person with blindsight will report "guesses" (which can be fully accurate) about certain aspects of vision. Clearly then, there is much that goes on beyond our sphere of direct conscious awareness and typically all kinds of accurate stuff nonetheless "pops up" as guesswork. Knowing this, I think we should not be quite so zealous about recognising intuition as being metaphysical in origin.