Belief vs Knowledge - The Force

TheDude wrote: If I am to accept knowledge as a subset of truth, then I can only conclude that nobody has knowledge of anything;

You are correct. However you left out one condition. We can never have absolute knowledge of anything. Your right that our perceptions of the universe are inherently flawed and so the old phrase that "seeing is believing" does not hold true. Even justification for such belief can be problematic as in the case of the Gettier problems. That is why knowledge is not a subset of belief. In these cases belief is not actual knowledge, even justified belief. Belief is actually never justified, it is not a step toward knowledge. It begs the question of knowledge and that is why belief is not a factor in any pursuit of actual objective knowledge even though that knowledge is necessarily conditional because of our inability to perfectly perceive the world in all its aspects. There is a difference between the state of knowing and the state of believing. Although they both may carry the same "feeling" the two should not be conflated. Belief may be a condition of knowledge but knowledge is not a condition of belief.

Do you know or do you believe that 1+1=2 is true? You should say that you know this is true. If you say you merely believe this is true it implies you lack the understanding of why this is true. Knowing it is true demonstrates and understanding of why it is true that can be shown to be accurate. Simple belief lacks this ability. The difference is that knowledge can be backed up with consistent familiarity, awareness, and understanding through facts, information, descriptions or skills. Belief can not be.

Kyrin Wyldstar wrote: You are correct. However you left out one condition. We can never have absolute knowledge of anything. Your right that our perceptions of the universe are inherently flawed and so the old phrase that "seeing is believing" does not hold true. Even justification for such belief can be problematic as in the case of the Gettier problems. That is why knowledge is not a subset of belief. In these cases belief is not actual knowledge, even justified belief. Belief is actually never justified, it is not a step toward knowledge. It begs the question of knowledge and that is why belief is not a factor in any pursuit of actual objective knowledge even though that knowledge is necessarily conditional because of our inability to perfectly perceive the world in all its aspects. There is a difference between the state of knowing and the state of believing. Although they both may carry the same "feeling" the two should not be conflated. Belief may be a condition of knowledge but knowledge is not a condition of belief.

Do you know or do you believe that 1+1=2 is true? You should say that you know this is true. If you say you merely believe this is true it implies you lack the understanding of why this is true. Knowing it is true demonstrates and understanding of why it is true that can be shown to be accurate. Simple belief lacks this ability. The difference is that knowledge can be backed up with consistent familiarity, awareness, and understanding through facts, information, descriptions or skills. Belief can not be.

In the case of numbers, I would say that the belief that 1+1=2 is justified on the grounds of the logic of arithmetic. But, as you rightly pointed out, we cannot have absolute knowledge that 1+1=2 any more than we have absolute knowledge of any subject. I still must believe in the legitimacy of logic, rules of inference and deduction, etc. in order to establish that the arithmetic is true. This may not be problematic for you, but I have trouble drawing the line here between absolute knowledge and non-absolute. For, if knowledge is a subset of truth, then what degree of truth is necessary in order to have knowledge? If 50% of the things I believe to be true on a specific, based on logical justification or experimentation, are actually true, then do I "know" that specific?

If I believe "Jimmy brushed his teeth today" and he did, but I have no reason to think he did so, knowledge as a subset of truth would mean that I know Jimmy brushed his teeth today. I don't think that's reasonable, so I'd say that justification is necessary. "Jimmy's teeth are clean, the way a person cleans their teeth is to brush them, Jimmy is a person, so Jimmy must have brushed his teeth today", or something like that. But, as you pointed out, justified beliefs may also be incorrect. Maybe Jimmy didn't brush his teeth, in which case my belief that he did brush his teeth is false while still being justified.

The correlation of justification alongside truth is necessary, but human beings do not have absolute knowledge. Since we do not have absolute knowledge, we can never say "1+1=2 is true", because that is an absolute statement. We can say that "I believe 1+1=2 because of (insert specific laws)", or "it is probably the case that 1+1=2", but to say "I know that 1+1=2" is contradictory to the statement that we cannot have absolute knowledge. For, the law of excluded middle and bivalence both require that the actual answer be either "1+1=2 is true" or "1+1=2 is false", and claiming that we know which one is accurate is essentially to claim absolute knowledge on the subject. If knowledge is a subset of belief, then I can safely say "I know 1+1=2 because of (insert specific laws here)". If it is a subset of truth, I may only say "Either 1+1=2 or 1+1=/=2", but I cannot say "I know that 1+1=2".

TheDude wrote: In the case of numbers, I would say that the belief that 1+1=2 is justified on the grounds of the logic of arithmetic. But, as you rightly pointed out, we cannot have absolute knowledge that 1+1=2 any more than we have absolute knowledge of any subject. I still must believe in the legitimacy of logic, rules of inference and deduction, etc. in order to establish that the arithmetic is true.

The problem I see with this argument is that it is treating truth as some kind of independent standard, "out there" never quite within our reach. What does it mean to say that "rules of inference are true"? I don't understand that. "1+1=2" is not true as a conclusion drawn from any capital-T "true" premises "out there". We put the label "true" on it because we have defined that label such as to be applicable to this and equivalent statements. "True" in this case really means nothing more or less than "equivalent to the tautology by the given logical calculus". Whether this calculus is "true" may well not even be a meaningful question, but under it, and by the way we define the symbols involved in the expression "1+1=2", we know - absolutely - that the statement stands in the specified equivalence relation to the statement we defined as "the tautology". Now, do we know that we know that? No, I suppose technically seeing as we are fallible and may be failing to apply the rules that are being used to evaluate the expression for its truth-value (if it indeed has one), there is a case to be made that, although we do know that 1+1=2 is indeed another way of expressing the tautology, we might not know that we do know it, and we might not have justification to claim that we do, despite it being so.
While I have some passing curiosity for modal logic and am glad there exist people out there who actually go out and do push it all the places it will go under different sets of inference rules (there is for instance a model that includes the axiom by which knowing X implies having knowledge about whether or not one knows X), there rather swiftly comes a point at which one has to question the practical use of it all. The unknown unknowns are just that. There is, in practice, no way around them. The only choice we have is either holding on and staying stuck because of them, or just carrying on worrying about things we can actually do something about. "1+1=2" under the axioms and definitions implicitly assumed between us is true absolutely as far as I can make that judgement and as far as I can tell I do absolutely know that it is, too. There are, at least for me, far more pressing matters to attend to than wasting time pondering whether we can or do indeed know that we know that we know that we don't or that we do... fun though that may be.

Gisteron wrote: The existence and unparalleled success of QFT and QCD in general and the standard model in particular. There are still margins of error but they are so far on the opposite of "great" as to warrant saying something very much like that on the scales relevant in our daily lives the fundamentals are indeed fully understood.
Every bit of my expression there is chosen with care, I should stress. I specified that I'm talking about fundamental principles, because I mean only those and not each and every ever so subtle consequence. I specified relevant resolutions, because there exist open mysteries we already know about that only matter on, say, intergalactic scales, and the riches of which will remain beyond our reach at least until the upcoming heat death of the universe. I'm not saying we know everything, far from it. A lot of work is still ahead of us, by all means, but the basics that matter in practice are something we have covered beyond any reasonable need for worry.
There is no ghost pulling levers, or idling until we let it. The mind (depending on how we define it) is either not actually separable from the body that produces it in which case it makes little sense to speak of it as having power over physiology, or it is and its untapped power resides entirely within the margins of error that are so slim that for all intents and purposes there might as well not be any at all.

Yes, we don't know what we don't know, but we do know what we do know and that puts upper bounds on the maximal magnitude effects we don't yet know about can have on us. We may not know what lies outside of the walls, but we do know that inside the room we are locked in we cannot hear it, so what ever is out there can only be so loud. We would know that something is out there otherwise.

My only issue with this, and you'll hear this metaphor coming from my a lot, is that our understanding of the mind, I think, is still infantile. Feel free to disagree. However, the brain evolved in terms of "hardware" but the evolution of hardware is "software". Instead of using physical commands to do everything (in terms of electricity physically moving through transistors) there is a layer or dimension on top that interacts with the physical but through elaborate shortcuts. It seems like magic because we don't have to think "turn head 15 degrees on the x-axis, 8 degrees on the y-axis". Complex things just happen that if you were to write basic code for it would take weeks or months. We write more complex code and more efficient code and even though the physical processor hasn't changed, the code has and that code allows that physical processor to do more than it could before.

I would agree that the hardware of the brain can only take you so far but that hardware and the neural networking can make the difference between a genius and a simpleton. I don't know and do not profess to know all of what has been studied and to what extent. But there is generally a barrier in which each field of science studies. And perhaps they studied the physical architecture up until the limit of their science, before it crosses over into psychology. But that being said, there is so much psychologists do not know and can only guess because the truth is that every brain is different and therefore every psychology is different. No two brains are wired exactly the same way so I find it difficult to accept that the study of the "mind" rather than saying "brain" has been exhaustive. It is not one aspect of the system alone but all aspects working together, that make the mind capable of all the things that it can do. Am I defending the possibility of super powers by saying this? No. Absolutely not. Like you said, we don't know what we don't know. We don't know what the mind can do until someone does it. And we can't assume that no one can do something simply because no one knows how. While it is unlikely that magic (defying physics) is possible maybe you don't perform magic by directly challenging physics but rather adding some kind of counter balance that makes it physically possible.

For example... I accidentally produced a strong suction that was based on how a tornado works. I set the lid of a pan on the counter top. It had heat and moisture trapped inside. By putting the lid on the counter top I trapped cold dry air underneath and viola! Suction. Could someone (ever) exploit quantum super positioning? I don't know and I don't have enough information to say one way or another. Maybe in the future we'll have some kind of quantum computing chip that rewires our brains to be able to sense and control things we couldn't before. I don't know. And not knowing is good because it allows us to explore uncharted possibilities. After all, It breaks no laws of physics but people have already used technology to control things with their minds which is great for prosthetic limbs. All these things have a long way to go.

TheDude wrote:
In the case of numbers, I would say that the belief that 1+1=2 is justified on the grounds of the logic of arithmetic. But, as you rightly pointed out, we cannot have absolute knowledge that 1+1=2 any more than we have absolute knowledge of any subject. I still must believe in the legitimacy of logic, rules of inference and deduction, etc. in order to establish that the arithmetic is true. This may not be problematic for you, but I have trouble drawing the line here between absolute knowledge and non-absolute. For, if knowledge is a subset of truth, then what degree of truth is necessary in order to have knowledge? If 50% of the things I believe to be true on a specific, based on logical justification or experimentation, are actually true, then do I "know" that specific?

If I believe "Jimmy brushed his teeth today" and he did, but I have no reason to think he did so, knowledge as a subset of truth would mean that I know Jimmy brushed his teeth today. I don't think that's reasonable, so I'd say that justification is necessary. "Jimmy's teeth are clean, the way a person cleans their teeth is to brush them, Jimmy is a person, so Jimmy must have brushed his teeth today", or something like that. But, as you pointed out, justified beliefs may also be incorrect. Maybe Jimmy didn't brush his teeth, in which case my belief that he did brush his teeth is false while still being justified.

The correlation of justification alongside truth is necessary, but human beings do not have absolute knowledge. Since we do not have absolute knowledge, we can never say "1+1=2 is true", because that is an absolute statement. We can say that "I believe 1+1=2 because of (insert specific laws)", or "it is probably the case that 1+1=2", but to say "I know that 1+1=2" is contradictory to the statement that we cannot have absolute knowledge. For, the law of excluded middle and bivalence both require that the actual answer be either "1+1=2 is true" or "1+1=2 is false", and claiming that we know which one is accurate is essentially to claim absolute knowledge on the subject. If knowledge is a subset of belief, then I can safely say "I know 1+1=2 because of (insert specific laws here)". If it is a subset of truth, I may only say "Either 1+1=2 or 1+1=/=2", but I cannot say "I know that 1+1=2".

Yes, 1+1=2 is grounded in the reproducible and verifiable rules of arithmetic. The level of truth that we need for this proof is simply the agreed upon rules of arithmetic and the presupposition that the rules of logic will hold true. i. e. that the universe actually exists as we perceive it. These are conditional, not absolute however because we can never absolutely show them to be true.

It is with inference and deduction that we start to get in trouble. In your tooth brushing example, if jimmy told you he brushed his teeth you could take him at his word or you could go into the bathroom and examine the tooth brush to see its wet and measure the toothpaste to see that there is less than before. All this could cause you to conclude he brushed his teeth and you would have a justified true belief but no actual knowledge. This is because Jimmy could have just run his toothbrush under the water and squirted toothpaste down the drain. You would believe he brushed his teeth and even have justification for this belief but you would still be wrong.

But if you had a video camera that was watching Jimmy and you went back and review that tape and actually saw jimmy going through the act of brushing his teeth you would have verifiable and reproducible evidence of such an event and at that point you would have actual knowledge that he brushed his teeth. Keep in mind however that this knowledge is still conditional and not absolute. You would still have to absolutely prove Jimmy actually exists to brush his teeth and that can never be done, but we can presuppose that Jimmy exists and on that presupposition arrive at a conditional truth that Jimmy brushed his teeth. That is, if jimmy exists, he brushed his teeth. In this case belief is a condition of the actual knowledge you possess but in the other case above it is not.

Kyrin Wyldstar wrote: ... 1+1=2 is grounded in the reproducible and verifiable rules of arithmetic. (emphasis added)

How does one "reproduce" or "verify" rules of arithmetic? What does that even mean?

... that the rules of logic will hold true. i. e. that the universe actually exists as we perceive it.

First of all, no, the existence of any universe, much less one that matches any of our perception, is completely irrelevant to the truthiness of mathematical theorems. 1+1=2 would be true or false based on what ever is meant by it and what ever rules are agreed upon entirely irrespective of whether ot not there is a world out there or what it is like. If tomorrow we found out that we do in fact live in the Matrix, nothing about that equation would need to be called into question because of it.
Secondly, the "i.e." part: No, the existence of any universe or how well it matches our perception is not included in or even entailed by rules of logic, let alone any that'd be required to construct classical arithmetics in particular.

But if you had a video camera that was watching Jimmy and you went back and review that tape and actually saw jimmy going through the act of brushing his teeth you would have verifiable and reproducible evidence of such an event and at that point you would have actual knowledge that he brushed his teeth.

Except the wet brush and the missing bit of tooth paste is "verifiable and reproducible" to the same extent the camera footage is. If Jimmy could have produced the misleading evidence the way you suggested in the paragraph before, why could he not also have prepared fake camera footage to run through to your monitor or edited the one you recovered between its recording and your reviewing it?
This is why I don't like the JTB definition of knowledge. Intuition, a gut feeling can technically count as evidence. Maybe not good evidence by most standards, but evidence nonetheless. It certainly can serve as a justifier, weak though many of us may find it. So can your trust in Jimmy's honesty and his word, so can the wet brush, and so can the camera footage. Likewise, to a sufficiently sceptical, critical subject, all of this can fail to warrant the belief.
You and I may agree that doctoring the camera recording on short notice may be more of a challenge given Jimmy's skill set and available tools and less likely to have happened thusly. We may agree that for this reason the recording is "better" evidence than the wet brush, but this is an agreement between us, little more. When setting all our biases (including past experience) aside and trying to construct an epistemology from scratch, there is nothing to force anyone to agree with you and I on the superior trustworthiness of video recording. Technically almost anything can be enough and almost everything can fail to be.
This might sounds grim or frustrating, and so be it.I am at this point entirely comfortable letting go of any desire to prove or disprove statements about Jimmy and instead say that the footage I have at my avail leads me to the justified belief that he did indeed brush his teeth. Should more evidence surface that contradicts this interpretation, I shall reconsider it all and judge anew. It is neither true nor false that he has. I don't know what that being true or false would even look like. I just have a model that says he did it and the predictions it makes (footage showing him brushing his teeth, wet brush for at least a few hours after the fact, a lighter tube of tooth paste by at least a gram or so) matches observations I make to at least within the specified margins of error.

Gisteron wrote: How does one "reproduce" or "verify" rules of arithmetic? What does that even mean?

By going through the process of executing the rule. Namely adding one and one and showing that it equals two. That is how you verify it and you reproduce that verification by doing it again and showing the same result. One apple added to one apple gives you two apples every time.

Gisteron wrote: First of all, no, the existence of any universe, much less one that matches any of our perception, is completely irrelevant to the truthiness of mathematical theorems. 1+1=2 would be true or false based on what ever is meant by it and what ever rules are agreed upon entirely irrespective of whether ot not there is a world out there or what it is like. If tomorrow we found out that we do in fact live in the Matrix, nothing about that equation would need to be called into question because of it.

You’re getting deeper into the nature of reality than I had originally planned but sure we can go there. This is the problem of where the actual laws of logic come from and why they exist at all. It’s a problem that searches for the most basic underlying nature of existence. This is actually below the nature of reality. Can we even prove the laws of logic are universal? I don’t know if you can but I invite you to try. Beyond that the most basic level of reality that we can agree upon to base a claim of any knowledge on relies on two preconceptions. Those being that the universe does actually exist as we perceive it and that we have the capability to learn something about it.

Gisteron wrote: Except the wet brush and the missing bit of tooth paste is "verifiable and reproducible" to the same extent the camera footage is. If Jimmy could have produced the misleading evidence the way you suggested in the paragraph before, why could he not also have prepared fake camera footage to run through to your monitor or edited the one you recovered between its recording and your reviewing it?

This is a fair point. It could be the case that Jimmy did this. But it relies on the situation and the capabilities of Jimmy. If Jimmy is 5 years old it’s a good bet that he is quite capable of wetting a tooth brush to fool someone but not capable of manipulating the feed of a video camera to do the same thing. So what this comes down to is the level of evidence needed for the claim. Its been said many times that extraordinary evidence requires extraordinary proof. So what level of evidence is needed to fulfill this burden? Well if Jimmy is 5 years old the video evidence is quite sufficient. However if Jimmy is a 25 year old Genius computer video programmer it might not be sufficient evidence and something stronger would need to be put forth. In this case it might take direct evidence like walking into the bathroom and seeing Jimmy with a tooth brush in his mouth brushing away.

So you are right, there are many more factors that go into our accumulation of knowledge than simple evidence or lack thereof. And that is why the preconceived notions for our reality must be in effect in order to further any claims of knowledge. It is also why we will never attain absolute knowledge of anything but we can satisfy our burden that we have accurately attained the correct and accurate conditional knowledge when we apply the parameters of sufficient evidence to fit the claim.

Kyrin Wyldstar wrote:

Gisteron wrote: How does one "reproduce" or "verify" rules of arithmetic? What does that even mean?

By going through the process of executing the rule. Namely adding one and one and showing that it equals two. That is how you verify it and you reproduce that verification by doing it again and showing the same result. One apple added to one apple gives you two apples every time.

One apple isn't "1", and two apples isn't "2". And if you have no apples to play with at all, have you no reason to think that 1+1=2 at all? Besides, that's not the rule anyway. If 1+1=2 was a rule, there would be no need nor a way to prove it at all, it'd be a matter of agreeing to play by it or not. What you are basically saying is that you can verify and reproduce that the chess pawn only ever moves forward by repeatedly moving a wooden one forward, as if the piece of wood itself was the pawn rather than a mere representation of it.

Gisteron wrote: First of all, no, the existence of any universe, much less one that matches any of our perception, is completely irrelevant to the truthiness of mathematical theorems. 1+1=2 would be true or false based on what ever is meant by it and what ever rules are agreed upon entirely irrespective of whether ot not there is a world out there or what it is like. If tomorrow we found out that we do in fact live in the Matrix, nothing about that equation would need to be called into question because of it.

This is the problem of where the actual laws of logic come from and why they exist at all.

No.

It’s a problem that searches for the most basic underlying nature of existence.

Citation needed. What makes you think that the origin or existence of laws of logic has anything at all to do with "the most basic underlying nature of existence", (what ever that is supposed to be)?

This is actually below the nature of reality.

I'd say "beside", not "below", because reality has naught to do with it. Mathematical truths follow under given rules of inference with and without a world for them to apply to. That's why there is no lab out there with people counting apples all day. Mathematics is not a science. It neither requires nor benefits from tests against nature.

Can we even prove the laws of logic are universal? I don’t know if you can but I invite you to try.

What do you mean by "universal" here, and what does that have to do with anything?

Beyond that the most basic level of reality that we can agree upon to base a claim of any knowledge on relies on two preconceptions. Those being that the universe does actually exist as we perceive it and that we have the capability to learn something about it.

I wholeheartedly disagree. I could come to deny both the existence of the universe and my capacity to learn anything about it tomorrow and still rightly claim that I know 1+1=2 afterwards, because I never required a universe to come to know it in the first place, nor would supposing one have aided me in proving it.

... if Jimmy is a 25 year old Genius computer video programmer it might not be sufficient evidence and something stronger would need to be put forth. In this case it might take direct evidence like walking into the bathroom and seeing Jimmy with a tooth brush in his mouth brushing away.

And then there'd still be any chance that your senses were being fooled, by Jimmy or by a third party, or that your recollection of the event now be faulty, or that it was all a dream all along. This is why we don't use mathematical standards when we investigate the world around us. No amount of evidence can prove a statement true or false. It's also why we cannot apples to prove 1+1=2, it just wouldn't work. The claim is just too strong for there to be any amount of scientific inquiry that'd warrant making it.

So when is anyone going to talk about their actual experiences that lead them to know that there is an underlying oneness to our reality?..

This thread is stuck on semantics...