PHILOSOPHY - Epistemology: The Preface Paradox [HD]
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- เผยแพร่เมื่อ 13 ก.ค. 2024
- Everybody has false beliefs, including you. But that means everyone's beliefs are self-contradictory. If we wrote down everything you believe in a book, we'd have to include one more statement in the book's preface: "some of the statements in this book are false". In this Wireless Philosophy video, Jonathan Weisberg (University of Toronto) explains the infamous "Paradox of the Preface", and what it might teach us about belief, reason, and logic.
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Belief is probabilistic.
Well, this could be a contradiction. I mean this belief of yours about belives has a chance to be incorrect right ? but only if you are correct about your believes being probabilistic :D
Of course *I* believe
"Belief is probabilistic" (as Phoenix Fire said)
due to the nature of the difference between belief and knowledge.
I claim to know enough about beliefs and how they are formed to be justified to believe that beliefs about history follow Bayes' Theorem. (See Carrier's book)
+George Steele
the only problem with probability models it relies on random occurrence and that cannot be represented and may lead to a lot a flaws in thought. No model can give a cristal clear 100% chance of something happens even if you need to take that for granted and absolut truth, as logic is logicaly valid, you are alive, because those can only be 1 or 0, there is no space in between.
working in scales of gray instead of seeing black or white seems a good ideia until you realize you cannot see black or white only grays. You need to some how have black, white and gray, but logic only works in black and white and if you try to see the word in scales of gray you will lose the notion of black and white and ultimately will not see any black or white, just a darker gray or a lighter gray. then you can only see / collect information or think!
+António Ricardo Pereira Gonçalves Can you even tell the difference between a really dark gray and black, or a really light gray and white? There's a point where it doesn't really matter anymore.
+Phoenix Fire
If you only admit true black and true white it cannot be gray in any level. because gray colour is made of a % of black and a % of white. Only when one of those % is zero and real zero not a close to zero that is neglected you will get a white or black and trust me when I say that no current probability will give 0%.
the onlt way to obtain a 0% is having without any margin of doubt colected all information related to that subject, and that is impossible since if that would be possible you wouldn't need a probabilitist model in the first place.
Warning: Some of the statements in this book are likely false, given the inherent propensity for statements of fact to sometimes be inaccurate. But if I realize that one of my beliefs is false, I will remove it from my book of beliefs. I can't know which beliefs, if any, are false beyond what I'm representing in my book, but I'm open-minded to new information. So since I don't know which, if any, of my beliefs are false, for each belief, I am forced to stay in the default position of all beliefs, namely "belief".
Instead of probability, use "confidence". I am "very confident" that A. I am a little confident that B. I have just a little confidence in C. I'm not confident in A&B&C. Using "confidence" rather than "probability" points out that the likelihood comes from you and how you feel, not a purported objective probability such as those used in statistics (Like to describe a coin toss). Your confidence in your accuracy is what you're expressing- a "probability" outside of statistics is simply your confidence masked in pseudo-scholarship.
There's also the issue of "unreasonable demands". When people ask you about any fact, they can always respond with "But how do you know?", and after you answer, they can do it again. They can do this forever. The only way to get anything done is to decide that you have enough information and move on, and note that you have enough information to discount other people's claims that none of your information supports (Like Earth being flat). Making unreasonable demands is sort of an argument from ignorance because it demands 100% accuracy before letting you believe something or act because it ends up being a claim that you're wrong because you COULD be wrong. Imagine thinking this way while trying to do anything- maybe by tying your shoes, you'll end up bring the Nazies back from the dead and starting World War III. How do you know that won't happen? Because causality and facts.
A genuinely certain person would be impossible to convince even when presented with what is genuine proof of his/her error. So real certainty is akin to insanity.
The default state of beliefs is disbelief.
+Benjamin Andersen ignorance is not a stare of belief. It is a binary position. Either belief or disbelief. I understand what you are trying to say about human development, and how we develop Skepticism as we age but I am talking about the general state one has on belief.
***** Belief and disbelief is a true dichotomy.
The default position of any argument is disbelief.
Why? Because logic. Let me explain. A stance on belief is equivalent to this example. You can either believe that 1+1=2 or believe that 1+1= not 2. There is no need for a stance of knowledge to decide beliefs. If knowledge is required to make a stance on belief then how would belief establish knowledge since knowledge can be simplified as a justified true belief(keyword simplified I understand the presence of problems with the justified true belief concept in epistemology) .
We just always must be prepared to say, if challenged "So far as I know.", and remain open-minded to reasonable corrections, rather than treat challenges as an unforgivable assault on our world-view.
When a cognitive therapist, rather than telling me how to think, simply pointed out that I held contradictory beliefs, I thanked him for it and voluntarily changed how I thought. It relieved a lot of subconscious tension as a result. I didn't punch him for screwing with my mind, ha-ha!
Why not simply preface with: "To the best of my knowledge"
Don't know whether this is still helpful since I'm a year late. This is not a solution because, for every sentence x the author wrote, the author thinks that x is true to the best of his knowledge (otherwise he shouldn't have written that sentence). So, to the best of his knowledge, every sentence in the book is true. The paradox is back.
You basically summed up my personal perspective on knowledge in this video. I've thought about it a lot. Here's my answer to the question at the end:
True knowledge as we define it is unrealistic. There is no need to reconcile knowledge with uncertainty, we just need to accept that the things we have are not truly knowledge and move on. Saying this is a problem is kind of like saying "I used to use a sponge to clean my car, but then I found out it wasn't actually a sponge at all, but a wash cloth! What should I do?!" It's silly because it somehow implies that a sponge is the only way to solve the problem of a dirty car, which we know is not true because he had been successfully washing his car with the wash cloth all along. Similarly, to say that there is a problem that what we've been working with isn't actually knowledge doesn't change anything about what we've accomplished. The desire to reconcile these two concepts isn't because it is a real problem, it's because we like to believe that we can know things, because it brings certainty, and therefore comfort, to our lives.
found the engineer!
*****
Not really, but thanks, for whatever reason that comes off as praise here!
What about the structure of logic? Do we "know" that? E.g. the law of the excluded middle? Also, isn't it a paradox in the end, that we "know" that we cannot have true knowledge?
Olle Härstedt Logic only functions given premises. Those premises themselves are usually assumptions that either are not the result of logical conclusions, or are extremely basic epistemological principals such as “I exist.” Logic is only foolproof if we assume the premises are true, so the idea that formal logic necessarily produces truth is incorrect. And there is no paradox because I never said that we “know” that we cannot know - we merely have a solid reason to believe it. Same issue all over again (that is, it’s not an issue).
To me it seems interily reasonable to think that I don't know anything for certain. Thing like "the entire universe was created last tuesday" and "the entire universe is a simulation" could always be true and therefore no knowledge I have is certainly true. But at least to me it doesn't really matter.
The entire universe was created last _Wednesday_ and such has always been the case. Personally, I was created last Wednesday with the implant in my brain that there was a last Tuesday, and that I believed on that Tuesday that I was created the Wednesday before.
I think I missed my calling. I could have made it big in philosophy.
+JiveDadson how absurd... God obviously created the universe last Friday.
"This book includes models developed intentionally over time. As time still continues, these models may still develop. As such, assuming an error-free book, anyone reading this book in a time after this book has been written should assume there has been opportunity for modifications to the model presented here. This book, therefore, acts as a powerful snapshot of where the model currently is as well as serves as an excellent presentation of the current model - as of this writing.
"That said, I make more mistakes than the model I'm presenting. For example, this morning I intended to fill my coffee maker with 6 cups of water. In fact, I over filled by over half a cup. The 10% error in my coffee making is substantially more than the (scientifically quantified error) that is believed to be contained in these models. While all effort has been made to minimize both sources of error, rest assured I still had too much coffee this morning and errors found are likely my own and unintentional.
See? I missed the quote at the end. Blast!
This will be the preface of my next book.
This was just another example of philosophers becoming so entangled in their own mental masturbations that they can't see what's obvious anymore.
+Michael Winter : This is great! I'll also steal this for my book, but in return you can have my answer to the stupid "is the glass half full or half empty?" question.
"The quantity of liquid in the glass is approximately 50% of its capacity."
Robin Williams But do you see how oppressive you're being to vessels that are less capacious? They would hold the same amount but be at 51% (or more!) capacity.
Your best bet is to argue that, at this rate of evaporation, the primary premise of the question will be true for so little time as to be insignificant. The more poignant inquiry would be the cost to use ratio.
In America, 4 oz. of clean, potable water costs less than a penny. Now, look at your behavior choices. You're literally pissing it all away.
Michael Winter I know that we're probably both heterosexual males and that we likely live at a big distance from each other and that there is no deep affection between us (yet) and that there's a reasonable chance that there's not all that much chemistry between us anyway, but...
Would you marry me?
To remain balanced, i tend to use the word "may" for "is", thereby introducing the principle of uncertainty, and "guess" for "assume", thereby indicating a lack of reliance on the information being conveyed. "Uncertainty", as opposed to "doubt", which assumes certain knowledge to be correct, is highly underrated.
This is not a paradox. Who said this should have a logical value?
It's just words.
Would you mind elaborating on why you think that this is not a paradox?
To answer the last question: we can know something, without knowing that we know it. It can be knowledge, but only the skeptic would request that we always KNOW that we know.
People think Science "knows stuff" and think Science fails when new knowledge shows old theories partially correct, but Science is an action, not a prescription.
"I wish to thank all of the people who helped me to verify the assertions in this book, so that I am at least 99.99% sure of each one. But there are roughly 20,000 assertions in this book, many of them independent, and I understand probability, so I know it is probable that at least one false assertion slipped past us. This is not a contradiction, just arithmetic. Sorry."
I think he should change the belief "At least one statement in the book is false" to "it is possible that mistakes are in the book" because then he could claim the he doesn't know if mistakes are in the book or not, but still believe them as true.
I think epistemologically one would be a fallibilist or as the late Philosopher Rick Roderick put's it "A fallibilist is someone who passionately believes certain things. Passionately believes certain things, some of them quite bizarre, as you’ll find out as we go along. But about those beliefs, I believe that they could be wrong.".
"I believe some things" and "Some of my beliefs aren't true" isn't a paradox.Those statements make sense when coupled together. For you to think that some of your beliefs might be wrong, first you have to have beliefs.
It would be way more illogical if you said "I don't believe anything" and "Some of my beliefs are wrong"
"I believe that I believe that the Earth is round" is a completely true statement
Certainty is a mood. Knowledge is empirical verification of what is; inherently imperfect and limited - and yet wisdom (that which is loved in philosophy) obtains knowledge. Beliefs can be contradictory, nonsensical, incoherent, etc. and that is the power of the psychological tool no one would make it a single day without: faith.
I have frequent delusions and hallucinations (possibly schizophrenic), and I just YOLO it. Make a hypothesis, assume it's true, try to disprove it, fail or succeed. If successful, make a new hypothesis, if not, assume it's true for practical purposes.
Just admit at least one statement is false. If you do that you can't believe all statements are true, but that's ok.
The problem is that you need to specify which statement is false. You can't believe that each individual statement is 100% accurate without also believing that the combination of those statements is 100% accurate.
But you can belief each statement to be true but possibly false. All statements you belief are true until proven otherwise. No need to specify which one.
Eddie Hill That's correct. However, that's not what you stated in your original post.
here is an approach on the subject: i can believe that each statement is true, but i can also believe that i am fallible. this would nullify the necessity for specifying which is the false statement and replace it with, each statement has a small but equal possibility of having been incorrectly reproduced.
myles swanson That's basically what the video suggested. You're not 100% sure about each individual thing; you're only about 99% sure. So when you add everything together, it's 0.99 x 0.99 x 0.99 ... and so on, until you're close to 0% sure that everything is right.
"For each statement in the book, the author believes that statement to be true, and the author also believes that there is at least one false statement in the book."
In this scenario, the question "Which beliefs should the author change?" can only be answered by an exhaustive exercise of verifying each statement in the book. At which point, the beliefs that need to change are some subset of his individual beliefs of individual statements of the book, and the belief of the extance of mistakes after each false statement in the book is corrected. (note that if the subset is {}, then all required corrections are already made.)
1. The statements in this book are "thought to be true" (as opposed to saying they are true).
2. Some of the statements "thought to be true" are actually false, but it is unknown which are false.
Kinda reminds me of my chemistry professor in the first semester. "A good part of the knowledge I teach you is false. Unfortunately I don't know, which one".
As a human, errors are bound to happen and nothing is ever 100% certain. If someone claims something is 100% certain, he is either delusional about the statement/doesn't know better or lies. That is a fact (not a 100% one, of course :-) ). The only way to confirm something then, is bringing the probability of it being false way down. Yes, it could be wrong that the earth is spherical, but all evidence, observed by hundreds of thousands of people every day, says otherwise. So we have a lot of evidence from a lot of independent people. One is bound to make mistakes, but that all of them actually do the same mistake and so come to the same wrong conclusion is very unlikely.
So I define "knowing" for myself as "seeing the evidence has a very small margin of error".
All you need to do is replace "Some of these statements ARE false" with "these statements MAY be false".
Can't you just say, "It's possible I'm not correct about something or anything. However, I believe I've done as much research as is reasonable to publish this book."?
1. Some people don't care about contradiction to an extent
2. Some people don't believe some of the statements they make for other reasons. Sometimes I lie because it helps me.
As a student of economics, this whole paradox is redundant. From the beginning of the video, I solved the practical application of it by merely multiplying the likelihood of being wrong (q) by the time spent to diminish q, and compare that to the value attributed to diminishing q to you and to the readers. If you are contemplating checking a work a third time, chances are close to bringing these two into equilibrium.
Put more simply, in poker, the "right decision" is merely the decision that has the highest probability of either maximizing profits or minimizing losses, by multiplying the risk by the chance of winning (expected value).
Now you know why most people don't like economists.
There is a difference between what I believe and what I know to be a fact. It's only a paradox if you confuse the two.
Has nobody ever thought they knew something to be a fact, only for it to turn out to be false? The paradox remains.
Except for me it doesn't, because I subscribe to the probabilistic view. We just _act_ as if things are certain, in the interest of pragmatism.
Videojames No. They thought they knew.
Which is the most you can ever do. How would you propose distinguishing between thinking you know something and knowing you know it?
Videojames Socrates did a dialogue on that and even he never settled it.
Your brain only has a shallow understanding of what you think you know about the world; no, unless you can comprehend something in its full ontology, you merely have imperfect perceptions about what you 'claim' to know.
I am almost logically certain of several things, but I accept the small possibility that keeps everything short of 100%: that I'm wrong.
To answer the final question in the video: you don't need to reconcile certainty of knowledge with uncertainty from our fallibility at all. Knowledge doesn't require certainty. I know that I am wearing a white shirt despite also [knowing!] that I am fallible with respect to that belief.
To give an extreme example: on a game show, Billy is asked a hard question that he doesn't know how to answer. The question was "What is the composition of sugar?". He is then offered four options to guess-from, A, B, C, or D. He then looks at "C" (C6H12O6) and thinks "Oh yeah, C rings a bell", so he answers C and is awarded points from the game show for getting the right answer.
Billy did not guess C out of the blue, he felt genuinely drawn to it. This was because his chemistry teacher had taught him about sugar 20 years ago, although Billy can't remember that, nor did he think of it when answering C. In this scenario, Billy was not sure about C, but he still "knew" it, since his predisposition to correctly assent to C is causally related to the fact that C is true, by way of having been told about sugar by a chemistry expert and this casually affecting his psychological disposition to the formula "C6H12O6" facts about sugar.
To make this seem less paradoxical we need merely consider belief on some other subject. For example, if you ask me, "Will you ever die?" I naturally assent to the proposition, "I will die," but if you then proceed to ask me about all the different moments when I may die - "Do you believe you will die in the next moment, T; do you believe you will die in the following moment T2, etc." for all the times when I might die, I will answer "No," to every one. Are my beliefs inconsistent? I don't think anyone is inclined to say so. There is a type of parallel with slippery slope and line-drawing problems. For example, if you ask me another series of questions like, "Did you become bald with the loss of one hair? with the loss of two? the loss of three? etc." I will again answer "No," to each, but I will say that I am quite confident of my baldness nonetheless. So the fact that I cannot stipulate which beliefs are false does not suggest I cannot consistently assume that the aggregate of beliefs contains some that are false.
In Finland, we have this saying: "Nothing is as certain as the uncertain" (Ei mikään ole niin varmaa kuin epävarma).
Belief is probabilistic; we just like rounding 99.9999% confident to 100% confident. Simple. No paradox.
I think the answer is quite simple, separate thought from action. In our thoughts uncertainties are allowed to remain, but when we decide to take action based on those thoughts pragmatism kicks in and we are left with definite yes/no binary choices. Both choices are uncertain but there are ways to make rational choices. First you consider the outcomes, are the outcomes positive, negative or negligible? Then you consider the probabilities; are they high or low? After you make that decision, you can logically deduce which action to take.
For example I will use choices A or B, with positive, negative and negligible outcomes as +/-/0 and simplify probability to 'high' and 'low':
high A+ & high B- => choose A
high A- & low B+ => choose B
... etc
Summary for any probability:
1) A+ & B- => choose A
2) A+ & B0 => choose A
3) A- & B0 = choose B
4) A+ & B+ = You probably win either way
5) A- & B- = You probably lose either way
6) A0 & B0 = Result does not matter
This is basic high/low risk/reward strategies.
Believing something that is wrong is not a contradiction if you don't know it's wrong and willing to correct it once you realize it.
I think he is accepting the possibility of making mistakes in the preface out of convention, courtesy or to show that he is epistemologically humble.
Of the two, the belief which he believes strongly is that he cannot make mistakes.
Do I contradict myself? Very well then I contradict myself. I am large, I contain multitudes.-Walt Whitman
The way we reconcile the difference is simply by determining how uncertain we are. Its not only that we know that a belief is uncertain but we have ways of ascertaining how uncertain it is.
One way to reconcile the original paradox is to think of the brain not as one homogenous belief storage machine, but many many connected parts. We can have contradictory beliefs because these individual parts aren't required to agree. While parts of your brain are certain in what they believe, another part of your brain acting as editor recognizes that the beliefs of the other parts of your brain may be false.
This seems pretty straight forward from the skeptical perspective. The assumption is that ones method for producing belief produces true beliefs. It's not really a contradiction. The preface "paradox" seems to be merely stating the claim that ones belief that something to be true is only true up to the effectiveness of the methodology. The preamble is probably poorly worded to express this notion, which I won't defend, but the argument is over the philosophy not the poetry.
Knowledge is defined as justified true belief. Knowledge is attained by either testimony of others, memory, or sensory experience. Finding that others testimony is sometimes fallible, memory can fail us at times and it's possible to trick our senses, we can never know anything for certain. just saying.
The belief book warning would read "Some of the statements in this book MAY be false". You cannot state truthfully that some ARE false unless you KNOW of at least 1 statement which is false, and if that were the case you would remove it from the book.
I try to acknowledge where I have made an assumption and then, if something shows that assumption to be incorrect, I revise my assumption according to the new information I have gotten about it. It's an estimation of what is and, as long as I remember that the things I believe could be false, then I am open to revising my hypothesis as new information comes in. This leaves me open to the new information but also gives a foundation upon which to operate in and think about the world.
Belief is not the same as knowing.
As Confuscious say, to know that you do not know is the best.
There is no paradox here.
Whatever the author believed, it would include an element of self-doubt (otherwise he/she wouldn't have had the work checked out).
I wonder whether philosophers sometimes deliberately manufacture confusion just so as to give themselves a job.
This "problem" only seems to exist because of the limited definition of "belief" that is being applied here. If you expand the definition the paradox disappears.
In the one case you have a belief about a set of statements, and in the other case you have a set of belief/statement pairs. A belief about a set is not clearly the same kind or category of thing as the various beliefs about each of its members.
I feel a lot of people in the comments are missing the point of what the video is trying to say. Regardless of whether there are two different concepts for "Belief" involved, fact remains that we, as humans, are capable of holding true to two contradictory ideas, while also operating on the idea that there can always be only one "truth" due to our logic system. Even though we program our computers in ways that calculate one "true" possibility, while excluding all others to some extent, we, ourselves, would be unable to function that way, because it would mean always feeling 100% certain about everything, and if we did that, we would never admit our own fallibility. Yet, *because* we are capable of admitting our own fallibility, we're never able to truly say we're "100% certain" about anything, because if we trace our logic back far enough, we'll always find some element in there that we're not 100% certain about, even if that sometimes means going in as deep as to ask "Are we all in the Matrix?".
It's all about how the rules of our logic are all based on a very binary system of Y/N or 0/1 statements, yet we ourselves simply don't work that way. Even Mathematics have uncertainties if you go in deep enough. Just think of Imaginary Numbers.
lol, imaginary numbers are not uncertain. try to make sure you know what you are talking about when you try to argue.
+rillloudmother that's not what I meant, but whatever.
Most of these paradoxes are easily resolved if you realize that most statements have implicit statements of likelihood in them, and you usually omit those qualifiers, but everyone knows they are there. If you simply make them explicit, the seeming paradox is resolved. The hypothetical author mentioned here doesn’t really believe that every single statement he made is true. Implicitly, he meant that every single statement is likely true. But in ordinary language, one omits that qualification. If he simply said, “I’m at least 90% confident in every assertion made in this book.” (which is implied by what he said) then you could easily see that the combined uncertainty adds up to a likelihood of several errors.
You can believe everything you wrote is 100% correct with the information you currently have. If new information is presented it could change. This does not mean that the author "believes at least one statement is false". It simply means that there is a chance that things could be incorrect given more information on the subject and/or simple human mistakes. There is no paradox here.
Here is an idea. "There are many people who have helped fact check and critique this book, without their help this work would never have been published. The author of this book has researched the content of this book extensively and has only included material he believes to be relevant and factual. The author however acknowledges there may be errors in this work and claims full responsibility for anything false or dubious in this work." That should about do it. It covers that the author has researched the heck out of it but human error can sometimes prevail. I also made that formal. Anyone thinking of using that as a preface has to credit me. Here's the wording: "Preface written and composed by DarkLady to whom I give credit and appreciation to".
I've actually thought about this a lot before hearing of what the paradox is called. The answer might be very simple, because as an individual we are largely prone to being wrong but when you count everyone's beliefs as a collective the statistics say that some of us must be right assuming there is a right answer. Therefore the more diversity in beliefs the better the chance of having the right belief and it's safe to assume that anything worth being right about yields positives enough to sway the collective to the right answer.
Change your perception when you find something that is false. By simply asking why over and over again, you will find the truth soon enough. So just because you think something is right, doesn't mean it is. So basically the second statement of saying that everything you know is right is false. Just be sceptical when it comes to things that are contradictory.
This paradox exists only if the preface is considered to not be a part of the book. If, the preface and the book are one, then to state in the preface, that at least one of the statements in the book is false, is not a contradiction. Either, there is at least one false statement in the rest of the book, or the statement in the preface is false.
If there is uncertainty, there is no knowledge.
But if I know that I am uncertain sometimes, then I know that I have no knowledge, and thus I do, because I am certain that I am uncertain.
Well, for the earth being round, there is a very simple way (for most of us) to consider the possibility that it is wrong. Most of us have never conducted an empirical test on it, and wouldn't know where to begin. We are only taking instructions that we are given. Most of us (if we are reasonable) recognize that we don't really _know_ if the world is round. It is just a useful model for our day-to-day life.
But also important, most of us could not compose our own "book of belief." Our beliefs change over time. Even if we were to read through and check off every belief in a purported "book of belief," we would only be able to confirm that we believed each statement at the time we came across it. We could not even confirm that there were no direct contradictions in the book.
Eloquent explanation! Great video!
In some respects we operate like computer models in scientific research. It is the compromise of the two approaches at the end of the video. We make some assumptions that we know under some conditions are wrong, but for the bounds of the model we know they are safe, or at the very least better than never getting an answer at all. We know everything is probabilistic, but using a probabilistic approach with everything is about as useful as the question of whether reality exists. As in stated in the Zen of Python "Now is better than never, Although never is often better than *right* now" :)
Why would you be 100% certain that any one thing you wrote is correct? If you're 99.9% sure on 1000 statements you wrote, you should expect one of those statements to be wrong. How is this a paradox?
If you are using realistic inclinations with natural language, you have to throw out logical conclusions. As Godel proved (very roughly) any language complex enough to make statements like "this statement is false" is internally inconsistent and capable of proving anything, even false things.
To prove something, you have to use finalized language. In natural language we treat beliefs as certainty because that is best for our every day existence, but if you want to formalize it, you have to assign probabilities. Otherwise, you get inconsistencies and false conclusions.
formalized language, not finalized. Autocorrect error.
Yeah I completely agree. This paradox equates two statements which sound the same (because of the language used) but are not. There first is a statement of intent, there isn't any certainty in saying you believe everything in the book is right, it states that to the best of your ability that is what you aimed for. The second is a simple statement of probability. The 'belief' of both statements doesn't form a contradiction, however the language they're framed in would imply they do.
No, he didn't. He proved that any such system would contain well formed "statements" (as you put it) that are undecidable. Those could be reasoned to be both true and false (or neither true nor false) and therefore undecidable.
That doesn't make those statements intrinsically false and provably true as you put it... False statements are false, true ones are true and some statements are possible to construct in the system, but aren't provable within the system.
Yes, that is a much more accurate statement of Godel's theorem. I said I was using Godel roughly, but it really was too rough and not accurate. Sorry about that.
The real point I was trying to make is that the informal language leads to an error. Informal language treats beliefs that you think are likely as though you have 100% certainty. If you formalize the language you will treat the belief, in this context, with some degree of probability. If you are 99% certain about 69 facts, then you've got a better than 50% chance you're wrong about 1 of them. If you have 450 facts and you're 99% certain about each one, you can also be 99% certain that you're wrong about at least 1 of them. Ordinary language doesn't capture the nuance of statistics because it is far older than the development of mathematics and the evolution of our brains are even older than that.
True objective knowledge is simply unattainable. You are, after all, observer, and as such subject to probabilistic behaviours. For instance, you can grow up in a place where everyone has the eye color blue and assume that this is normal.
We can only assign a certain likelihood of truth. Whenever this certainty approaches one (something is very well observed or alternatives can be very well disproved) we can take it as a given, for convenience's sake. This doesn't mean that it can't be false, it just means that it is borderline irrational to think that it would be, given current understanding. It is a human thing, a method of simplification, to think in absolutes, but it helps with modeling reality and making it understandable.
Stating a fact is simply stating that which you find most likely to be true, like the video says. This means that, probability wise, something can be false, and for a big set must be expected to be.
Yes, much of this is said in the video, I just felt it wasn't put forth in a convincing manner.
Sometimes we act with certainty, other times we don't. That's why we go through the day believing many things without question, and we could also at the end of the day write a preface to one of our books saying "I am almost certainly wrong on a least a few statements made in this book." That is one solution to the paradox: examining the psychology of our certainty, which fluctuates depending on the task, subject, kind of beliefs, and amount of beliefs involves, and perhaps a few other things.
Another solution is to deny anyone is ever certain of something, but I think this solution will ultimately crumble into the one given above. I was going to say that if somebody is certain of P, they could never be convinced of the falsity of P, and would instead doubt all auxiliary assumptions, used in arguments and evidence against P, that she finds uncertain. (I am not sure what would happen when, all uncertain assumptions being discarded and only certain assumptions remaining, the argument or evidence still challenged P.) Since people could always in principle change their minds, except perhaps by a few statements such as the existence of other minds (though one person has written to Russell claiming to be a solipsist), it would follow that people are never certain about anything (except very few select statements).
I think this doesn't work because it assumes people are always consistent on their certainty attributions. It could easily and very plausibly be the case that people are certain of something at some times, taking whatever it is for granted, and not on other times, leaving elbow room for (seriously) doubting.
And this is why Philosophers have a reputation of concerning themselves with useless questions...
I've had the same thought, when I was wondering, how "maybe we don't have knowledge" helps anyone. But I think at least we learn something about the word "knowledge".
It's only useless if you think it's useless it's kind of a interesting concept if you aren't a snob.
I don't see why it's hard to reconcile these two things. There are things which I believe to be almost certainly true. Let's say their probability is above 99.99999999. I know that I'm not 100% certain they are true, so there is no logical paradox. However, I also know that the probability of them being false is low enough for me to just ignore it. Therefore, I'll act as if they were true, and use simple logic instead of probability. To put it differently, I don't truly "know" anything with 100% certainty, but there are things which I'm so sure of that I'll just simplify things and say I know they are true.
There you have it, the two points of view are reconciled.
Why can't the author simply believe that he is not perfect but wrote a book to the best of his ability.
See, this is the reason why pure philosophy needs to be tempered by reality. What the author is relating in their book is both observations (facts) and theories (generally agreed-upon beliefs based on facts). What the author is stating in the preface is that, while the facts themselves are completely true, the beliefs based on them are provisional pending further observation. The better authors also state that it is sometimes difficult to tell the difference between a fact and a belief as well, since observation can be colored by belief, and that their relation of the facts and beliefs may contain editing errors. There's no contradiction here, just an acknowledgement in the preface that knowledge is always flawed and incomplete and that humans sometimes make mistakes even in the best of conditions. We needn't make honesty into a paradox.
Without even having watched the video, I could already notice illogic in the description:
"If we wrote down everything you believe in a book, we'd have to include one more statement in the book's preface: 'some of the statements in this book are false'."
This confuses two different ways of thinking as being equivalent. Thinking that there *are* some false statements is not equivalent to thinking that there *might be* some false statements. There's where the error is, resulting in this false conclusion that there necessarily would have to be this "paradox".
Why would an act of replacing "there are some false statements" with "there might be false statements" resolves the paradox?
"Everybody has false beliefs, including you. But that means everyone's beliefs are self-contradictory".
But a person can have a set of beliefs, some of which are false, without the set being self-contradictory.
E.g., { 'The sky is green', 'Denver is the capitol of Colorado' }. These two beliefs are logically consistent, event though one is false.
Hume came up with the idea that belief and knowledge are the same. Also that belief can always be given a probability. Or "degree" of belief.
I'm not sure this is a problem. To believe that a specific one of my beliefs is false entails a contradiction. To believe that the set of my beliefs contains falsehoods isn't a belief about any member of the set, but a belief about the set.
why would you want to? uncertainty is the closest thing to a loving god i'll ever know. it's always there and never surprises me when it surprises me.
it's kinda fun to see this as a paradox, the book and the statement, but it doesn't follow by necessity. it's the difference between deductive reasoning and inductive reasoning. In deductive reasoning, the conclusion is true because the premises are true, by definition. inductive reasoning provides a conclusion with a high probability of truth because the premises are not necessarily true but have a high probability of truth.
Probalistically speaking, the probability that a statement that I believe is true because I think the probability that it is false is low, but with 10000 statements that I believe is true, while P(True(X)) is high, P(True(x1) & True(x2) ... P(True(x10000)) is low if the statements are independent..
What is there to reconcile between these two approaches? Our beliefs are indeed probabilistic, and indeed we also "sometimes think in terms of yes/no answers, to get through the day". That is to say, we get through the day using our beliefs of which we think the probability of them being wrong is negligible (but not zero). (In fact we get through the day on much less certain beliefs, like going for a walk when there's 20% chance of rain!). There's nothing incompatible with this. As for the preface paradox: Each statement in our book we believe with very high certainty. For arguments sake we are very self-assured and believe each of them with 99.9% certainty. However since this is a book of *every* belief we have, say 100,000 of them, we are compelled to believe that the probability of all of them being true is 0.9999 ^ 100,000 = 0.00005. In other words we must believe that its 99.995% true that at least one of our beliefs is wrong! certainly enough to warrant a statement in the preface...
As I see it there is no paradox in the preface - only, well, a badly written preface.
And lack of ability to express oneself precisely hardly constitutes a paradox.
What the author seems to mean is that "a) to the best of my knowledge all statements in my book are true", however, b)statistically I am bound to be wrong in some of my statements."
The real fallacy is that the preface, and the text, cannot be changed in the event of the discovery of a false statement. And thus, the fallacy is the belief that a "contradiction" is permanent. There is a presumption that a paper and ink book is, uh, "written in stone". In the digital age all contradictions, and history itself, God help us, can be edited to correct contradictions, and transmute them into "truth".
The more profound attitude, than questioning one's perceptions and beliefs, but to question one's expectations gleaned therefrom. We act from expectations, not perceptions--however small of a delay there may be between them. We could say that the greater the delay between perception and expectations therefrom, the greater the potential for anxiety experienced.
He showed that:
.99 times .99 is .98.
I think the "unrealistic argument" would say:
The mean of .99 and .99 is .99 (as good as 1).
I think the problem comes from taking knowledge to imply certainty. If we define knowledge as justified true belief, then fallibilism undermines the "true" part. We establish truth through justification. When we believe a proposition, then set out some justifications for it, we can't do anything else to establish the truth of the proposition. At this point, the claim that the proposition is true reduces to the claim that it is justified. This makes the "true" part something that we have to understand in retrospect.
Imagine I believe A, and I use x, y, and z to justify A. From my perspective, no more can be done, and I would have to conclude that I know A. But imaging you know q, which contradicts A. In that case, A is false, and I do not know A. If you told me q (and I believed you), then I might say something like "oh, I thought I knew A, but I really didn't." Now suppose a third party... let's say your mom, knows p, which contradicts q. Now it looks like I was right before, and I really did know A, and that now I'm mistaken. There could always be some additional fact that would reveal the truth or falsity of A, so we can never say that we've "gotten to the bottom of it." So saying that A is "true" doesn't really add anything to my claim of knowledge - really what I'm saying is that "as far as I know, A is justified." Which seems fine...
Mm.. I'm having trouble figuring this out. It seems like we could know lots of things, the problem is knowing that we know it. When it comes to belief, the best we can do is justify. Whether those justified beliefs count as knowledge relies on facts about the world we don't have access to in virtue of the fact of fallibilism.
Uh... hm. Well fuck. I don't know what else to say about it other than that I'm comfortable thinking that I can't know whether my beliefs are true whether they're justified or not, but that I believe (for reasons I have not articulated here) that I should attempt to hold only justified beliefs. Justification seems crucially important here, but truth, while ideal, seems inaccessible. And... so what? That seems fine. IDK, anyone else have anything to add to that?
This video treats all statements are either true or false - which is the classic logical approach. It discusses the idea of the probabilities of the statements being true or false, but stops there.
We know people thought the Earth was flat. Then they thought it was spherical. Now we think it is an oblate spheroid. It is very likely we are wrong, but we are far *less* wrong than before.
For practical purposes we don't need to be perfectly right. Newton was wrong - we now know movement follows Einstein's principles. But for everyday reasoning we apply Newtonian logic, it is much simpler and when driving a car or shooting a gun it gives us results that are entirely satisfactory. We use Relativity calculations for specific tasks that require extreme precision - spacecraft, or particle acceleration, for example.
Thus there is no reason to use probabilistic calculations in everyday statements. I would argue we already do it unconsciously, but that's not the point.
The probabilistic way is less wrong, and should be used when the unrealistic principle does not give us results that are accurate enough.
"Everybody has false beliefs, including you. But that means everyone's beliefs are self-contradictory." An interesting observation, but not a paradox. Our belief system is not a rigorously consistent logical system. We can believe contradictory things, the "but I might be wrong" disclaimer being just one example. Is every contradictory pair of beliefs we hold a paradox?
believing is not knowing
believing something is true according to the information you have gathered, while admitting that the truth might favor otherwise, is not contradictory, but an elementary scientific approach
then there are also unintended errors one might make in his book, but when one claims he believes he made no mistakes, he is saying that he did not intentionally make any;
when he says he believes that unintentional errors might occur in his book, it is not based on his information gathered with respect to the book but rather on previous experience where all books are likely to have some mistakes
This is no paradox at all. Think of it like this - What the author is really
saying is "My beliefs are all supported by knowledge which gives me 51%
or greater certainty. However, it is likely that there is some knowledge
unavailable to me at the present time which would overturn at least one
of those beliefs if i had access to it."
As for the other side of things, 51% certainty is as good as 100% for all practical purposes since as far as you know nothing may exceed it. Eventually you may be proven wrong on some point in which case you'll simply change your mind and go on being just as certain as you ever were.
The real question is how certain are you really? If you haven't done sufficient research you'd be lying to say you were certain in the first place. If you are an expert you have epistemological warrant to believe the thing even if it is later shown to be an exceptional case.
Human language is an imperfect artificial construct laid over the integrated systems of Nature. This language we use on a daily basis obfuscates the clarity that is otherwise present. Human language is still evolving, and is in the process of correcting itself, as indicated in the video.
For example, the common concept that the earth is 'round' is mentioned at least twice in the video. 'Roundess' is two-dimensional and its use indicates flatness, a fundamental geometric error in this case. The earth is a spheroid, indicating three-dimensionality. Even though there appears to be an error, listeners understand what is meant by the word 'round' as opposed to 'flat'. Logic is not the only consideration for the preface paradox. Experience and use of language packs within each set of words many meanings not indicated in the presentation of the words. The mind must 'add' these associations.
I think that in an effort to quantify all that exists, humans have invented systems that negate other potential causes, introducing fundamental errors as discussed in the video.
The author does NOT believe "each statement in the book is true".
The author has a set of beliefs, which they believe are true. The author attempted to write statements reflecting those beliefs. But, the statement in the book is not the author's belief, it's a reflection of it and may contain an error. That's what a "mistake" is in this case, a translation error between a belief and a statement.
I think the probabilistic answer works fine. I think it's probably true that there's nothing we can know with 100% certainty, but that some things are more likely to be true than others.
If the author believes there are mistakes, then he doesn't believe everything in the book is true. He believes that a percentage of the things he wrote are inevitably false because he understands he is fallible.
Truth is not something we reach. It is something we approach.
If the author changed his belief from being absolutely certain each statement is correct to a probability, say 99.9% correct then his beliefs do not contradict. After many many statements the probability of at least one of them being false changes to a almost certainty.
Edit: Ah ha i called it, it does go to probability.
Although people model beliefs as probabilistic it may not be the case that persons are doing any work with the probability. It was suggested to me that there could be a model where what persons are doing is more like (dis)confirming their beliefs (modeled as credence). I am awaiting for a former professor to finish a book he is a co-writer on dealing with these sorts of question. So I'd advise people who are interested in scholarly work about this to look out for Coherence by Branden Fitelson, Kenny Easwaran, and David McCarthy. I am not a coherentist myself, but Bayesianism does sound a good start to these sorts of issues.
Obviously, the answer is that for computation reasons there is cutoff for approximating something to 1 or 0. Prepositional logic works well with a priori knowledge because of computational efficiency, but probabilistic is how we think of the world. I don't see this idea anywhere epistemology is discussed. It's not a particularly revolutionary idea. Knowledge in the colloquial sense does not need to be 100% certain.
The statement "some of this book content may not be accurate" is a believe itself that's because there is nothing as wrong or right for a point of view it depends on the frame of thinking it's still one of believes so the whole book is 100% correct for the author
that's why people can't be changed unless they did it
I think that's a bad example. The author believes what is in his mind, not what is written, as there could have been typos etc. He also believes some of his believes, which might have ended up in the book, could be false. We are humans, we dont have access to infinite knowledge, so we sometimes have false beliefs. A false belief may or may not affect another belief, but it will hardly ruin everything
The answer is no brainer, it's called the scientific method, in simplistic terms I create observable experiments with repeatable results. At some point a philosopher has to stop siting in his/her room thinking about the world and actually go out an start interacting with the world, to prove for himself/herself that the world is truly round.
However I do admit that not everything can be made into and observable experiment and therefore I would recommend creating some type of scale or index of probability or certainty for such cases. But at the same time keeping in mind that such an scale or index is more than likely arbitrary. Such is the nature of the regress argument of skepticism.
I would recommend the author of the history book to add to the disclaimer that the book was created from knowledge derived from the historical evidence currently available at the time of writing the book and new evidence found later may change what is currently known. Really that's a no brainer.
It seems somewhat obvious to say that, while we may 'know' that any one of out beliefs might be false, however unlikely individually, we still must *act* as though they are certain, unless presented with sufficient experience to deny them. In the form of the Preface Paradox - We may acknowledge that we believe with a high degree of confidence each individual fact, and may acknowledge that the book as a whole is likely to contain at least one error; but it is not contradictory to then -act- as though the book contains no errors, until and unless we receive specific credible counter-information.
It seems as though, in large part, this argument commits a fallacy of ambiguity of terms. It demands that we use a form of logic that only permits certainty, while stating as a premise that each statement is only probabilistic - that is the origin of the contradiction. That we, in daily life, use 'simplified' logic based on true/false certainty is only a model for a more complex system that has shown to work well enough in most circumstances (much like Newtonian physics works extremely well in day to day experience, but in more extreme situations you need more exact and careful systems).
If you define knowledge as involving certainty, then yes, we -can't- have knowledge. But that isn't a very useful definition of knowledge, in that case, as it relies on Simplified logic - we would need a definition that relies on the system of logic we -are- using, which is itself at least approximately consistent with Simplified Logic for the uses to which we put Simplified Logic.
Consider a grocery list - a set of statements "We need eggs." "We need bread." etc. We have no reason to doubt each of those items as we go to the store - it's possible that we made an error and don't need one of those items, but the number of items is small enough that the total probability of an error is low and we can use Simplified Logic to treat it as though it were a simple certainty. It is only when we collect ever larger numbers of statement that we reach the point where Simplified Logic's approximation doesn't line up with reality.
Our brains are not equipped to constantly think in Full Probability Mode in day to day situations, because that is resource intensive, but we -can- do it, given sufficient reason. We can say that we have 'knowledge' of a thing, meaningfully, in the Simplified System, and determine our Confidence in that knowledge if and when necessary for places where Simplified Logic is insufficient.
Because knowledge itself is probabilistic based on the majority of objective evidence found to support or deny claims made. Evidence can change the outlook of knowledge in some situations....for example, words have different meanings through history, calling someone "tall" is a fuzzy logic statement, or the idea of the atomic model allowed us to stop believing in the "elements" (wind, water, fire, etc.) for the most part. Knowing that things could change or that flaws are apparent, allows forgiveness for the transference of knowledge through speech and text, but it's better to know false claims and prove them wrong than to force everyone to start from scratch in order to prove their personal objectivity correct (highly inefficient for a society to grow and become smarter).
One more reason inductive reasoning has gone so much further than deductive. Some things are certain, unfortunately highly unlikely beliefs such as stars forming from gas in a vacuum which is impossible, being presented as facts by so many people makes for confusion.
I really like these videos. Very nice popcorn philosophy for those who don't intend to take a college course but are still interested in educational bites.
I just wanted to say, there is a growing group of people who do believe the earth is flat. They have their own internal logic and evidence.
Also, though it's reasonable to change ones beliefs when you find a contradiction, this is not often true. People will tend to find new ways of holding the belief and/or struggle with the belief until they can no longer believe it.
the thing about all these paradox's is that we have imperfect reasoning and logic
The author believes what they wrote is true, but is still open to the possibility of being wrong when presented with new information, or simply due to human error. This is not a logical paradox at all.
We could do the following: we could agree upon a probabililty such that any belief which has this probability or greater of being true is considered to be absolutely true. If, at a later point, new information is provided to lower the initial probability below the threshold, we consider it to be totally probabilistic.
Pragmatic assumption: The world is as it appears to me, and all my beliefs are correct in the absence of evidence against them.
I will probably encounter evidence against specific beliefs during my life, in which case I will modify my beliefs accordingly and then get on with my life, believing that my beliefs as a whole are now correct.
Sure, I'll also believe that some of my beliefs are not correct, but in the absence of evidence to resolve the contradiction, I'll just continue to believe the contradiction. Which just leaves me with 5 more to find, and then I can have breakfast...
Jonathan is 100% certain that he cannot be 100% certain of anything.