Is knowledge justified true belief?

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An Enraged Platypus
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Re: Is knowledge justified true belief?

Postby An Enraged Platypus » Wed Aug 24, 2011 9:56 pm UTC

Katrex wrote:If you can't understand the argument, and the simple logic of it there's no helping you. If you don't understand you wont agree, that's fine. If you're capable of understanding it you will agree.
I know that sounds arrogant but its just one of those things either you get it or you don't. You think just because it might be written in some book will make it more valid than if not?
Regardless it's self consistent, and no ones been able to find a fault in it yet. Having no citations makes no difference to it's validity. Look at the evidence, try to think up a scenarios where it's not true and decide for yourself, not because some overrated philosopher said it was the case.

Of course if you're religious and/or hold unjustified beliefs to be "TRUE" then will not fit in with your world theory, but if you "believe" in logic and evidence it is a very good definition on knowledge.


I really couldn't disagree more. Claiming to have fixed a major problem in philosophy in a couple of paragraphs without consideration of, disagreement with, or building upon named predecessors is stupendously unlikely to be correct. Let's say that you do have a fully worked out system, radically different from everything before, with complete internal justification and minimal reliance on outside sources for substantive content. Let's see it, the magnum opus, with every angle worked out by baby steps. Heidegger did it, and if you're serious about your argument so will you. In the meantime, let's expand on what I meant by "citation needed":

Justified true belief is a nice easy definition, but that's not what knowledge is.

Knowledge doesn't have to be "true" the definition most people have of it anyway. Hard to parse, sloppy grammar.To go with a pure science approach , Define "pure science" clearly, preferably with a precedent citation.

Knowledge is the belief that accurately explains all the evidence. What kind of evidence? What is belief in this context? Again, which literature does this base itself upon?
Truth requires no evidence. It is true that 2+2 is 4. Says who?

the only Truths with a capital T are provable. This is an assertion, again with no supporting citation and or heavy duty exposition.
Everything else is meaningless use of language and confusing ourselves. The extension of this phrase is not clear. The rest of the discourse on truth is meaningless? All utterances or inscriptions putatively about things not apodictially true are a waste of breath?

The statements, this knowledge is true, this knowledge is false are meaningless, as knowledge is our best explanation. If it's not our best explanation, then it's just less justified belief. Conclusion from undefended or weak premises (see above comments).

Take the question "How can the universe have always existed? How can it have had a beginning" These questions are meaningless, You can't prove them mathematically and there is no evidence to use that could allow us to come up with theory to explain. They are meaningless abstract statements. All we know is the evidence suggests the universe had a beginning, that's it. It might be incomprehensible, but that is all it comes down to. It had a beginning end of. You're missing a meta-metaphysical premise here relating to the impossibility of logically proving ontological statements or a precise ontological statement about the universe.

You'll find half the questions in philosophy aren't provable and have no evidence either way. They are meaningless and that's why no one ever comes up with a real answer. People confuse matters by trying to find meaning. I tend to agree, but then again a broken clock is correct twice a day. There's no such thing as meaning, it's a human invention so that the concept of human existence doesn't destroy us.


EDIT: copy-pasted wrong material from word into the fora first time round.
Last edited by An Enraged Platypus on Wed Aug 24, 2011 10:45 pm UTC, edited 1 time in total.
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Re: Is knowledge justified true belief?

Postby Katrex » Wed Aug 24, 2011 10:40 pm UTC

Knowledge doesn't have to be "true" the definition most people have of it anyway.

Hard to parse, sloppy grammar.

To go with a pure science approach ,

Define "pure science" clearly, preferably with a precedent citation.

What I mean is to go with an aproach that will make sense when looked at from a scientists viewpoint.

"Knowledge is the belief that accurately explains all the evidence."

What kind of evidence? What is belief in this context? Again, which literature does this base itself upon?

First off, all the evidence, means ALL the evidence. All the information we receive through our sense data.

We create a theory that explains the information we receive as sense data. If that theory explains ALL the sense data we receive accurately, that is what I define as knowledge.
Truth in the way most people think about it is an abstract idea, because it is unknowable. For example. Magellan was the first person to sail around the earth. That statement most would argue to be true. I disagree, that statement is knowledge, the evidence sugests he was the first person to sail round the world, because therefore we believe it. However somebody else COULD have done it before, but we have no way of knowing. Therefore Magellan sailed round the world is knowledge that might be true.

So yes, something out there are True with a capital T but since we'll never know it's just a useless part of language. So I say to make things clearer and better defined. Define truth as something that is provable. And those "Truths" that are not provable as meaningless

I hope this has explained my definition a little better. Its mostly about utility and keeping language and understanding less abstract. But it works.

**back to the Magellan thing. I simplified. There is a lack of any evidence of anyone doing it before Magellan. It is unlikely that people could have done this before proper sailing ships with large crews and supplies etc (but not impossible). And we have good records of the voyages people made with said sailing ships. So we say Magellan did it, it's unlikely anyone did it before, therefore Magellan was probably the first. Since it's our most probable answer that adequately explains the evidence it is knowledge. It might not be true though, regardless its still knowlege

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Re: Is knowledge justified true belief?

Postby mward » Thu Aug 25, 2011 11:42 am UTC

Katrex wrote:
the only Truths with a capital T are provable.


Provable from what?

Proof means starting with axioms and applying inference rules to derive results.

Are your axioms true? In which case, according to your assertion, they must be provable:
therefore they are not axioms but theorems.

What about the rules of inference? Are they true? If so, then, according to your assertion, they must be provable: presumably from other rules of inference. But this leads either to an infinite regress, or to a circular argument: and an infinite regress or a circular argument is not a valid proof of anything.

Chesterton wrote:
Briefly, you can only find truth with logic if you have already found truth without it.


Pascal wrote:
We have to know when to doubt, when to affirm what is certain, and when
to submit. Anyone who acts otherwise does not understand the force
of reason. There are some who break all three of these principals,
either affirming that everything can be proved, because they know
nothing about proofs, or doubting everything because they do not know
when to submit, or always submitting because they do not know when they
must use their judgment. . . . The last step that reason must take
is to recognize that there are an infinite number of things beyond it.
It is merely feeble if it does not go so far as to grasp this reality.
If natural things are beyond it, what can we say about the supernatural?


In conclusion: if there are any truths at all, then there are truths which are not provable.

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Re: Is knowledge justified true belief?

Postby Whimsical Eloquence » Thu Aug 25, 2011 12:26 pm UTC

Katrex wrote:Knowledge is the belief that accurately explains all the evidence.
Truth requires no evidence. It is true that 2+2 is 4.


It seems to require assumptions though. Namely about the nature of that opperator, "+", those quantities and the meaning of that is (do you mean equals?). Mathematics is tautologous, systems relying on axioms - indeed I can derive different truths dependent on my assumptions. There are multiple, conflicting systems of geometry out there you know. This doesn't seem very much like "Truth" to me; not the one you speak of anyway.
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Re: Is knowledge justified true belief?

Postby TrlstanC » Thu Aug 25, 2011 1:40 pm UTC

Whimsical Eloquence wrote:It seems to require assumptions though...


I'd agree, I think any knowledge requires some assumptions. I was actually thinking about that with regards to the "logical true belief" definition, which I think makes it clear that assumptions need to be made. However, I think that there are a couple assumptions that are so important to our understanding of knowledge that they should be integrated in to the definition. The most important being "I can trust my conscious observations." By that I don't mean "this looks like a rose, therefore it is a rose" (that would be "my observations are true") instead it means that my observations aren't hallucinations or dreams, ect. This is obviously not true all the time, but I believe it's also impossible to consciously know anything without assuming that first, so including it as part of the definition makes sense. Also, we accept that it's possible to know something from an appeal to authority, so that should be included somehow as well. But ultimately accepting an expert's opinion on something is just a combination of different observations and conclusions - observing facts that can be used to conclude that someone's an expert, and observing them in some way (listening to them, reading something they wrote, ect), so we can include our assumption that an appeal to authority can be a source of knowledge as just a continuation of observation plus logic.

If include these assumptions as part of the definition, it actually simplifies it a bit (which is probably good) and makes it a bit more intuitive as well, we end up with:

We can say that S knows p if and only if p is a Logical True Belief such that:

1. p is true
2. S believes p
3. p can be logically concluded from S's true observations


By including a couple assumptions, a couple of different requirements collapse down, and by explicitly recognizing that we're judging trueness in 1 and 3, we don't need to include the assumption that we have perfect information. If we want to use perfect information to judge trueness (for hypothetical situations), we can use it for both, and if we want to use more realistic judgments of trueness, we can use that same level information for 1 and 3 as well.*

I believe this definition will work in all everyday situations, and will also work in all hypothetical situations including the Gettier, and Gettier-like examples. If anyone can think of an example that doesn't seem to work, please post it. Hopefully an apparent counter-examples will be due to issues outside the definition, such as misunderstood assumptions or other definitions (such as the definition of what a barn is), but I'm also definitely open to twerking this further.

The one weakness I see is that by making assumptions about how humans know things part of the definition it may not work in possible situations where we want to judge, for example, if a thinking machine knows something - what counts as an observation or a belief for a machine could be very different than what we're assuming it is for a human.




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*Depending on our understanding of how human consciousness works it might make sense to explicitly state #2 as "S truly believes p" to avoid situations where S thinks they believe p, but doesn't actually.

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Re: Is knowledge justified true belief?

Postby Katrex » Thu Aug 25, 2011 4:02 pm UTC

Yes, I was a little vague on the maths front. Indeed maths requires axioms, Such as If a+b = c then b + a = c. My main point to put it simply is this.

Knowledge doesn't have to be true. It just needs to explain out sense data.
The only "Truths" of value are attainable through logic.
If something has neither evidence nor can be logically concluded it is meaningless and not worth thinking about. (eg. there exists an invisible teapot that we can not perceive through any means)

It can't be logically concluded and it has no evidence sporting it therefore it's meaningless. There are lots of things in philosophy that come in to this category/. I think my definition just makes it easier to dismiss them and discuss something important instead.




Where this definition gets grey is where something has some evidence in favor but not all. So i use the following definitions to make the grey area clearer.
I differentiate between personal knowledge and public knowledge and paradigmatic knowledge .

For example, my friend she "Experiences" god, to her that counts as evidence, her mother prophesies and other weird things happen in her life. To her "God exists" is knowledge. But it's personal knowledge because it relies on personal evidence.

If she could make her evidence public, show the world her mother is prophetic and show some of the weird things that happen in church then her belief would be public knowledge. Public knowledge is a combination of personal evidence and public evidence, where the personal evidence tips the scales in favor of your belief over the paradigmatic knowledge. (doesn't mean she's being logical)

It's only at the point where ALL of her evidence for believing something becomes public that it CAN become paradigmatic knowledge, however now that it's all public it's subject to scrutiny from everybody and if her conclusion isn't valid (because she hasn't looked at all the evidence etc) it still won't become the paradigm. However if the evidence all holds up and her belief is judged by the majority to be the best explanation of all the evidence then it becomes the new paradigm.

Wow that ended up being a lot more long winded than I thought. The paradigm tends to be defined by science, given that it does look at all the evidence, only considers reliable evidence and systematically tries to eliminate bias. Anyway that's they way I explain other peoples an my own beliefs. If i believe something other than the paradigm i can explain what personal evidence i have that explains why i believe differently. I can end an argument by making the point that the person has too much personal evidence for it to change my mind, etc etc. It's been very useful in having healthy constructive stimulating debates.

This i think teaches people that knowlege isn't certain or set in stone it's just the best explanation we have.

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Re: Is knowledge justified true belief?

Postby TrlstanC » Thu Aug 25, 2011 4:37 pm UTC

Katrex wrote:Knowledge doesn't have to be true. It just needs to explain out sense data.

...

This i think teaches people that knowlege isn't certain or set in stone it's just the best explanation we have.


I think that knowledge does have to be true – at least in some sense of the word, we just have to accept that in our everyday usage, we can never determine perfectly if something is absolutely true. We have to accept a less strict version of "true" for everyday usage, which is basically "true as far as we can tell." We can also use an individual definition of truth or "true as far as I can tell." We should accept that people use, and there are, different possible ways to use the word "true."

The Logical True Belief definition of knowledge allows us to apply whatever usage of "true" we want to use (or have to use), and it will give us a definition of knowledge that matches up with our expectations about the amount of information we have about the world. In everyday usage we can still use this definition to say that "Smith knows p" with a less then perfect judgment of what's true instead of say "we can never judge truth perfectly therefore we have to abandon our idea of knowledge."

We can also create hypothetical situations where we have perfect information, can judge truth perfectly, and we can still use this definition of knowledge to absolutely say whether "Smith knows p" or not. And I think there is value in being able to explore ideas philosophically, there is a point in thinking about things that we lack evidence to prove. Saying things are meaningless just because we don't currently have the ability to prove them perfectly with the evidence available misses out on some important tools we have available to us to understand the how the universe works.

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Re: Is knowledge justified true belief?

Postby Katrex » Fri Aug 26, 2011 7:34 am UTC

I guess that is where we fundamentally differ. I appreciate and understand you point but, i discarded philosophy that doesn't give us certainty in our answers. There are so many things that we don't know and can find out. Maybe one day we'll know all that and it will be time to hypothetical explore the meaningless, but until then rather just try and understand what we can.

Thank you for sharing your belief, unlike the sarcasm of some of the other poster's it was enlightening. I hope to discuss other things with you again some time.
Kat

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Re: Is knowledge justified true belief?

Postby TrlstanC » Fri Aug 26, 2011 2:16 pm UTC

Kat,

That's true, philosophy certainly isn't for everyone. And if we all sat around philosophizing all day and no one was ever driven to go do some experiments or research we wouldn’t make much progress. In fact, we can tackle a lot of difficult questions, like how to put a man on the moon (or mars) without thinking about philosophy. (Although some of that science probably does rest on a foundation that was built partly by philosophers).

Does it matter in our everyday life if knowledge is justified true belief? Probably not, if someone wants to call knowledge justified belief that would work out fine. As long as we don’t just call it a belief, otherwise, what’s the point of having two words? Does it matter if defining knowledge as logical true belief solves Gettier problems? Most of the time it doesn’t.

But we also shouldn’t assume that our brains are just like computers, that they just chug away on problems, and spending time (or cycles) on unsolvable or hypothetical questions is a waste. Our brains change depending on how we use them, they don’t just store new information and results, they also rewire themselves depending on the problems we face. Think it about it like doing pushups. You could say “I would rather spend my time out in the real world actually lifting things” but when I run in to a really big box, all that preparation doing pushups might help me push it around a little more. We could even extend the metaphor, and say philosophy is like yoga, not only does it strength our bodies, but it also improves our flexibility and helps us learn about how our bodies work and what our limits are.

I certainly appreciate the chance to take a break during the day and come stretch my brain a bit on these forums.

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Re: Is knowledge justified true belief?

Postby TrlstanC » Sun Aug 28, 2011 4:10 am UTC

I just finished putting all these thoughts down together on one page, something a little easier to follow, here: http://consciousthoughts.net/otherpapers.php

This is still an early draft, so any thoughts or critiques, let me know.

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Re: Is knowledge justified true belief?

Postby TheGrammarBolshevik » Thu Sep 01, 2011 12:25 am UTC

TrlstanC wrote:To summarize the requirements I’m suggesting, in their latest, most clearly stated form, we can judge that “S knows p” if and only if:

1. S believes p
2. p is true
3. Given S’s assumptions it's possible to logically conclude p
4. S’s assumptions are logical true beliefs

OK. So you believe that no belief can be knowledge if it is not produced by logical deduction? In particular, I'm looking for you to clarify what you mean by "logically conclude."
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Re: Is knowledge justified true belief?

Postby TrlstanC » Thu Sep 01, 2011 1:58 am UTC

TheGrammarBolshevik wrote:OK. So you believe that no belief can be knowledge if it is not produced by logical deduction? In particular, I'm looking for you to clarify what you mean by "logically conclude."


No, the definition doesn't make any requirement to how the knowledge is produced, only that it could be produced logically. I actually rewrote the requirements again recently (on the page I linked to, but forgot to repost them here). THe underlying idea is the same, but this takes in to account a couple assumption that I hoped would simplify it and make it more intuitive to apply:

[/quote]We can say that S knows p if and only if:
S believes p
p is true
It’s possible to logically conclude p from all of S’s true observations[/quote]

As far what "logically conclude" means, I believe the common understanding is that given some premises, we can apply rules of inference to make conclusions. In this case the premises would be "S's true observations" and the conclusion (if it's possible to conclude) would be p.

Of course this means that the 2nd requirement is redundant, if we can conclude p from true premises, then it must also be true. But I thought it was an important enough requirement that stating it explicitly was worth a little redundancy. The definition also makes some assumptions about how humans come to know things, and what it means for someone to believe something, so it's probably not perfectly suited if we wanted to draw conclusions about learning machines or something like that.

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Re: Is knowledge justified true belief?

Postby TheGrammarBolshevik » Thu Sep 01, 2011 3:28 am UTC

TrlstanC wrote:It’s possible to logically conclude p from all of S’s true observations

That's… far from sufficient. If I show a trigonometry problem to a fifth grader and she happens to guess the right answer (perhaps she even has some invalid reasoning, so that she is expressing a genuine belief as opposed to a hypothesis), she doesn't know the answer.

It's also far from necessary. If a dog must be an organic being rather than a robot, I would have to perform an autopsy to logically conclude that something is a dog. But I don't need to do this in order to know it.

Finally, what do you mean by "true observation"? As I originally argued, it seems to most people that when I look at what looks like a barn and say "That's a barn," I'm observing that it's a barn. And if it turns out that it is in fact a barn, then my belief would be knowledge on your definition. But by your previous statements (and in accordance with the Gettier argument), you want to rule out knowledge from at least some cases like this. So what is the ingredient that prevents such judgments from being counted as observations?
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Re: Is knowledge justified true belief?

Postby Zamfir » Thu Sep 01, 2011 9:09 am UTC

TrlstanC wrote:As far what "logically conclude" means, I believe the common understanding is that given some premises, we can apply rules of inference to make conclusions. In this case the premises would be "S's true observations" and the conclusion (if it's possible to conclude) would be p.

Trouble is, logic works excellent in math or electric circuits. There you can apply fairly simple, universal and definitely very hard principles to derive conclusions from premises.

But in most situations, the process from premises to conclusions is inherently somewhat uncertain, somewhat incomplete, and definitely very context-dependent. You could call still it logic (or inductive logic, as opposed to deductive logic), but then logic is no longer the clear and water-tight beast of Fortran or of Socrates-is-a-mortal examples.

So by putting "logically conclude" in there, you might be begging the question. If someone has indeed a watertight 'logical' argument for their beliefs, then surely they 'know'. But then the problem remains, when is an argument about the world really logically sound, watertight? That's about as difficult a question as there is.

On the other hand, you could use "logically conclude" in a way that doesn't imply the certainties of mathematical logic, just the normal standard of evidence we use in day-to-day affairs. But that leaves you wide open to Gettier problems. Those rely on the fact that you can make acceptable, reasonable, convincing arguments to support a belief, while still being wrong, or right for the wrong reasons.

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Re: Is knowledge justified true belief?

Postby TrlstanC » Thu Sep 01, 2011 1:57 pm UTC

I’ve copied the full paper I posted on consciousthoughts.net at the bottom in spoiler tages to make it easier to reference, this should be a good summary of the steps used to get from “justified true belief” to “logical true belief.” I think that in most cases justified true belief works well as a definition, especially in our everyday usage. I just think that “justified” is a difficult term to use because it inherently includes the possibility the someone is using false information to make justifications, and also, different people can have slightly different understandings about what’s justified or not. The “logical true belief definition” should come to the same judgment about knowledge as JTB in just about all cases, it just keeps false information out, and spells out clearly the last requirement – at least that’s the goal.

TheGrammarBolshevik wrote:
TrlstanC wrote:It’s possible to logically conclude p from all of S’s true observations

That's… far from sufficient.

I disagree, but I’ll try to make it clear why with a couple examples.

TheGrammarBolshevik wrote: If I show a trigonometry problem to a fifth grader and she happens to guess the right answer (perhaps she even has some invalid reasoning, so that she is expressing a genuine belief as opposed to a hypothesis), she doesn't know the answer.

I’d agree here, and I’d also say that the “logical true belief” definition would come to the same conclusion. That’s good because it’s a fairly straightforward case, and one that JTB handles easily as well. So, let’s see why. It would fail the JTB test because we don’t think she’s justified in her belief, and why’s that? I think most people would say because the fifth grader doesn’t know and hasn’t studied trigonometry, which I’d agree with. And this wouldn’t pass the “logical” test either because she doesn’t have sufficient true observations to solve the problem logically – she hasn’t studied trig.

Now a more interesting question would come up if we could claim that all of trigonometry is derivable logically from first principles. Then would it be possible to logically conclude the answer? I still don’t think so because without any information about trig at all (without any true observations) then the fifth grader doesn’t know what the symbols and notation means. Without knowing what the question is it’s impossible to come to the answer logically.

An even more interesting question might be: In the same situation what if we explained all the symbols and notation to her, but didn’t teach her any trigonometry, what then? I think one of the strengths of the “logical true belief” definition is it allows us to get to interesting questions like this, it doesn’t get hung up on different ideas of what justified means, of stuck on obviously false information, it forces us to get in to the assumptions that these questions rest on. And hopefully that will lead us to further study how humans actually acquire knowledge, the actual physical process going on in our brains to see if we’re making the right assumptions. In this case, I’d say she still doesn’t know the answer since you can’t teach someone what all the symbols and notation of trig mean without also teaching them enough trig to use them. But that’s a discussion I think would be worth having, one that might not have a simple answer.



TheGrammarBolshevik wrote:It's also far from necessary. If a dog must be an organic being rather than a robot, I would have to perform an autopsy to logically conclude that something is a dog. But I don't need to do this in order to know it.

Again, I believe LTB and JTB would come to the same conclusion, if you’re petting a robot dog and think it’s a real dog, you don’t know that it’s a real –organic- dog. If the assumption is that the only way to know if a dog is organic or not is to cut it, then any definition is going to be bound by that assumption.

TheGrammarBolshevik wrote:Finally, what do you mean by "true observation"? As I originally argued, it seems to most people that when I look at what looks like a barn and say "That's a barn," I'm observing that it's a barn. And if it turns out that it is in fact a barn, then my belief would be knowledge on your definition. But by your previous statements (and in accordance with the Gettier argument), you want to rule out knowledge from at least some cases like this. So what is the ingredient that prevents such judgments from being counted as observations?

By true observation I mean an observation which is of true information. I’m not saying a true observation is “this looks like a rose therefore it is a rose” I’m saying “this looks like a rose, I’m not dreaming or hallucinating, therefore that’s something that looks like a rose.” And in the barn country example I’d say that looking at a barn and concluding that the thing is a barn is a false conclusion (people make them all the time). A barn is defined by what its function is, not by what it looks like. Just from looking at the exterior of a barn (or a picture of a barn) the best you can logically conclude is “that’s something that looks like a barn.” However, if all the “fake” barns were incredibly realistic fakes that included real tractors and animals and farmers, and they all appeared to be using the barn (but were maybe just pretending to farm) it would be a worthwhile question to ask if the barns are actually real barns or not.

Zamfir wrote:Trouble is, logic works excellent in math or electric circuits. There you can apply fairly simple, universal and definitely very hard principles to derive conclusions from premises.

But in most situations, the process from premises to conclusions is inherently somewhat uncertain, somewhat incomplete, and definitely very context-dependent. You could call still it logic (or inductive logic, as opposed to deductive logic), but then logic is no longer the clear and water-tight beast of Fortran or of Socrates-is-a-mortal examples.

I’m working under the assumption that under formal logic it’s possible to express any statement as a preposition using the appropriate syntax, and apply appropriate rules of logic to decide if the conclusion is valid or not. If there are true statements, which are possible to believe and we agree people can know, but that are impossible to logically conclude then this definition would fail in that instance, but I can’t think of a situation that would fit that example.



Zamfir wrote:So by putting "logically conclude" in there, you might be begging the question. If someone has indeed a watertight 'logical' argument for their beliefs, then surely they 'know'. But then the problem remains, when is an argument about the world really logically sound, watertight? That's about as difficult a question as there is.

On the other hand, you could use "logically conclude" in a way that doesn't imply the certainties of mathematical logic, just the normal standard of evidence we use in day-to-day affairs. But that leaves you wide open to Gettier problems. Those rely on the fact that you can make acceptable, reasonable, convincing arguments to support a belief, while still being wrong, or right for the wrong reasons.


I think it’s possible for people to use the certainties of logic, but use false assumptions, and come to false conclusions. It may not even be obvious initially what the false assumption is, but if the definition forces us to inspect all of the assumptions to see if they’re true or false before deciding if a belief is knowledge, then I think that’s a good thing. And if we run in to a situation where someone can have true assumptions, perfect logic, and have a belief which isn’t knowledge that would be a problem. But I think it’s more likely that we’d run in to a situation where we run in to a limit of our understanding of how humans learn, observe and process information. A situation where we can’t definitely say that a person “believes p” or even that they have definitely “observed x” – for example, what if they saw x, but formed no short term (or long term) memories. What id they only observed it unconsciously? I think these are good limitations to have because they point us to the areas we need to learn more about.


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Full text of LTB definition
Spoiler:
The classical definition of knowledge is that of a “justified true belief.” This definition works well in most everyday cases, but there are situations where these conditions fail. A definition should, in all cases, agree with our usage of the term such that whenever we would say S knows p all the requirements of the definition would be true, and vice versa. Gettier problems, and Gettier style problems, point out cases where the usage of the term, and the “justified true belief” definition don’t line up.# The classical definition can be stated succinctly as:

We can say that S knows p if and only if:

S believes p
p is true
S is justified in believing p


There have been alternative proposals on how to adjust the definition of knowledge to account for Gettier problems, most of them involving adding a new fourth condition to the definition. However I believe that there is a conflict inherent in the justified true belief conditions, and that addressing this conflict is the best way to bring the definition on knowledge in line with our usage of the term. The conflict is between the “true” and the “justified” requirements.# When we judge if something is true, this is an absolute judgment, which makes use of all available information. For example, in hypothetical situations we can define certain facts as true or false, and judge them to be true or false for this requirement with access to perfect information. In general usage, it’s easier to say if something is true or false with access to more information, and we’ll have more confidence in our judgment the more people are in agreement. For this requirement we make use of the maximum amount of information, and as many perspectives, as are available. The “justified” requirement has another specific set of requirements, and we recognize a different amount of information in making the judgment. A possible definition of justified is:

We can say that S is justified in believing p if: p can be logically concluded from all of S’s observations and/or appeals to authority that they believe are true.

Inherent in that definition are two limitations. One is that we’re relying on only the information available to S, as opposed to our judgment of “true” where we make access of all available information. The other critical limitation is that we accept that S can make use of false or incomplete information if they believe it’s true, we are explicitly allowing false information to be used in making the judgment. Many proposals to avoid Gettier style problems will add a condition such as “no false premises” or “causality” which attempt to avoid this issue. However, I think that as long as the definition of knowledge includes a justification requirement there will be conflicts with at least one other requirement, adding additional requirements won’t resolve the issue.

The first step therefore is to remove the “justified” requirement, but we’ll have to add back in a requirement that captures the important features we’re now missing. We should also make note of several assumptions we’re making. One, that S can use their observations, and that they can trust their observations. Allowing access to observations should be fairly easy to accept as that is the primary way we gain knowledge about the world.# The other assumption, that we can trust our observations, shouldn’t be understood as “that looks like a rose, therefore it is a rose” but as “that looks like a rose, I’m not dreaming or hallucinating, therefore that’s something that looks like a rose.” We also assume that we can make use of experts or authorities, but once we accept the other two assumptions this one is no longer explicitly necessary. An appeal to authority can be understood as “observing that someone is an expert” and “observing them” for example by listening to them, or reading something they wrote. An appeal to authority is therefore just a different kind of observation.

Taking these assumptions in to consideration we can simplify the “justified” requirement as a “logical” requirement, so that we have a definition of knowledge as a “logical true belief.”

We can say that S knows p if and only if:

S believes p
p is true
It’s possible to logically conclude p from all of S’s true observations


This change removes two key problems. First, by recognizing that we’re only going to use true observations we allow ourselves access to the same information for the “logical” requirement that we allow ourselves for the “true” requirement. Two, we’re also recognizing that while it’s S’s observations we’re judging, we’re not relying on their perspective to judge if they’re true. This means that the definition avoids any conflicts of the amount of information available between the different requirements. If we create a hypothetical situation, and allow ourselves perfect information we can make a perfect judgment if a fact is true or not for both requirements.# This should avoid any Gettier or Gettier style problems. For example#:

Case 1

“Smith has applied for a job, but, it is claimed, has a justified belief that "Jones will get the job". He also has a justified belief that "Jones has 10 coins in his pocket". Smith therefore (justifiably) concludes (by the rule of the transitivity of identity) that "the man who will get the job has 10 coins in his pocket".



In fact, Jones does not get the job. Instead, Smith does. However, as it happens, Smith (unknowingly and by sheer chance) also had 10 coins in his pocket. So his belief that "the man who will get the job has 10 coins in his pocket" was justified and true. But it does not appear to be knowledge.”

However, the justified belief that “Jones will get the job” cannot be logically concluded from true observations, and therefore any conclusions based on it would not count as knowledge under the new definition.

Case 2

“ Matthew drives through an area that appears to have many barns. In fact it contains a great many realistic barn facades, perhaps made to help shoot a Hollywood movie 'on location'. When Matthew looks at the one real barn along his route, he forms the allegedly justified true belief, 'There's a barn over there.' But if he follows the strong requirement for justified belief, then his thought process will follow the previous mentioned steps exactly.”


However, the justified true belief “There’s a barn over there” cannot be logically concluded from the true observation “that looks like a barn.” Barns aren’t defined by what they look like, they are defined by how they’re used. Therefore it would not count as knowledge under the new definition either. It would be possible to conclude: “that looks like a barn” which would be judged correctly as knowledge. Or to inspect the barn carefully to see how it’s used, and conclude that “this is a barn since it’s used like a barn” which would also be accepted as knowledge.

In both cases the “logical true belief” definition of knowledge not only avoids calling something knowledge which we wouldn’t ordinarily call knowledge, it also makes it easier to see exactly where the gap in knowledge is, where the information available falls short of allowing us to know a certain fact.

This definition also works well in everyday usage when we accept that we won’t always be able to perfectly judge if something is true or not. By making it clear when we need to judge the truth of something it also makes clear what limitations we have to know things absolutely, or what assumptions we have to make to allow ourselves to accurately say we have knowledge.

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Re: Is knowledge justified true belief?

Postby TheGrammarBolshevik » Thu Sep 01, 2011 8:04 pm UTC

Let's ditch the trig example for a clearer one. In 1990, the assumptions required for the proof of Fermat's Last Theorem published in 1995 were already well-known. A mathematician who understood ZFC could wildly guess that Fermat's Last Theorem is true and have a true belief borne out by her true observations (if we can't describe mathematical axioms as such, then we can't have mathematical knowledge, which would be an even bigger problem for your analysis). But such wild guessing fails both the justified belief test and our intuitions. It is not knowledge.

TrlstanC wrote:Again, I believe LTB and JTB would come to the same conclusion, if you’re petting a robot dog and think it’s a real dog, you don’t know that it’s a real –organic- dog.

My example is a situation where I'm petting a real dog. By your standard, I can never know that I'm petting a real dog just by inferring that its insides are likely enough to be real. You leave no room for knowledge that can't be deduced.
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Re: Is knowledge justified true belief?

Postby TrlstanC » Thu Sep 01, 2011 9:10 pm UTC

TheGrammarBolshevik wrote:Let's ditch the trig example for a clearer one.
I don't think this is a clearer example, if anything, since I don't think anyone here has a really good grasp of all the number theory that was required to prove Fermat's Last Theorem, it's significantly more difficult to understand.
The trig example was pretty clear, and as far as I can tell, the "logical true belief" definition would come to the same conclusion as anyone who was correctly applying the term "knowledge" - which should be the goal of a definition. The fact that a simple and clear example raised interesting questions, or that we could modify a simple example to investigate other areas of inquiry, should be taken as a strength of the LTB definition - it lets us stop talking about the definition and start talking about how people come to know things.

TheGrammarBolshevik wrote:In 1990, the assumptions required for the proof of Fermat's Last Theorem published in 1995 were already well-known. A mathematician who understood ZFC could wildly guess that Fermat's Last Theorem is true and have a true belief borne out by her true observations (if we can't describe mathematical axioms as such, then we can't have mathematical knowledge, which would be an even bigger problem for your analysis). But such wild guessing fails both the justified belief test and our intuitions. It is not knowledge.
If a mathematician just flipped a coin and guessed that the theorem was true, then I don't think anyone would think they "knew" it was true. Does the LTB definition say the same thing? To make that judgment I think we would have to know a lot about exactly what was going on in the head of our hypothetical mathematician. If however, we assume that she is at the cutting edge of number theory, and has done the months (or years) of research necessary to truly understand all of the information that's necessary to prove the theorem, and then decides that "yes, it's true" - without consciously doing the logical calculations needed to get to that conclusion. Well, in that case I could see the argument that she knows that the answer is yes. Again, it's such a complicated subject that without knowing exactly what's going on in the mathematicians brain, I would be hard pressed to judge either way.

But I don't see how this is more clear then the trigonometry example, which seems pretty clear cut. There's a math problem, if you've been taught enough to answer a question and you come up with the answer then everyone (and the LTB) would say you knew the answer. If you haven't been learned enough to solve the problem, everyone (and the LTB) would say you didn't know the answer if you happened to guess it correctly. The Fermat's last theorem example is exactly the same, but substitute "incredibly complex number theory that very few people in the entire world fully understand" for "trigonometry."

TheGrammarBolshevik wrote:My example is a situation where I'm petting a real dog. By your standard, I can never know that I'm petting a real dog just by inferring that its insides are likely enough to be real. You leave no room for knowledge that can't be deduced.


Let's spell out your example more clearly, and more generally:

1. You're petting something X, so you can see it, smell it, hear it, and are touching it.
2. X is a "real dog", all you have to do here is define what a real dog is, call that definition p.
3. If you can logically conclude p from your observations (we'll assume they're all true, ie. you're not hallucinating) then we can conclude that you know that you're petting a real dog, if not, then we can't. Obviously you'd have to believe it as well.

Again, the LTB definition lets us ask the important question in this example, which is "what does it mean for something to be a real dog as opposed to a fake dog?"

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Re: Is knowledge justified true belief?

Postby TheGrammarBolshevik » Thu Sep 01, 2011 9:21 pm UTC

TrlstanC wrote:I don't think this is a clearer example, if anything, since I don't think anyone here has a really good grasp of all the number theory that was required to prove Fermat's Last Theorem, it's significantly more difficult to understand.

You don't need to know any number theory to understand the example. You just have to know that FLT is true, and follows from ZFC (you don't even have to know what FLT and ZFC are, really).

TrlstanC wrote:If a mathematician just flipped a coin and guessed that the theorem was true, then I don't think anyone would think they "knew" it was true. Does the LTB definition say the same thing? To make that judgment I think we would have to know a lot about exactly what was going on in the head of our hypothetical mathematician.

The only thing your definition says about what's going on inside a subject's head is that she has true assumptions that logically entail her knowledge. If she understands and believes ZFC, then she does. Whether or not she's actually used ZFC — let alone used it properly — is irrelevant to your definition as presently stated.

Concerning the dog example, I've simply stipulated that internal organs are part of what it means to be a dog. If you don't like that stipulation, I can simply change the knowledge-candidate to the belief that I'm petting an organic dog. You're still left with the problem that your definition doesn't allow me to non-deductively infer this from experience.
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Re: Is knowledge justified true belief?

Postby TrlstanC » Fri Sep 02, 2011 1:49 am UTC

TheGrammarBolshevik wrote:You don't need to know any number theory to understand the example. You just have to know that FLT is true, and follows from ZFC (you don't even have to know what FLT and ZFC are, really).

Ahh, good that does make things a lot simpler to deal with. If A implies B, and a person has only ever observed A, but has a belief that B is true, then I would say that they know B is true.

TheGrammarBolshevik wrote:The only thing your definition says about what's going on inside a subject's head is that she has true assumptions that logically entail her knowledge. If she understands and believes ZFC, then she does. Whether or not she's actually used ZFC — let alone used it properly — is irrelevant to your definition as presently stated.

Correct. I don't think we know enough about how our brains actually process information to make that distinction. The more complicated an example we make, the more other terms the judgment of whether S knows p starts to rely on. At some point, we'd have to have a perfect definition for terms like "understand" and "believes", or "observes" which are probably even trickier than "knowledge." We would have to specify what process the brain goes through to make a logical judgement, to see if it's "correct" or not. I don't think the "logical true belief" definition is the perfect definition that will work forever. When we're dealing with a subject like how the brain processes information and learns things, we're going to have to accept we currently don't have a very good idea how things work. In addition, topics like machine learning or intelligent machines are going to change the way we understand information processing. We don't even know how the information we're aware of creates or interacts with our consciousness. This creates a lot of limitations when dealing with complicated scenarios, especially hypothetical situations. A definition of a word is supposed to spell out the conditions under which we use it. If we create a hypothetical situation like "a mathematician understands all the information and is capable of coming to a correct logical conclusion, but comes to the conclusion a different way, is that still knowledge?" Not only are we not sure if the situation is even possible, but asking whether the definition of the term knowledge is correct in that situation implies that there would be a consensus as to whether we would agree it's knowledge or not. I personally don't know whether I think that's knowledge or not, I find myself wanting to know a lot more details before saying for certain. The LTB belief would appear, with the information available, to say that it is knowledge. Since the definition seems to work well in every logically consistent and believable situation I can imagine, I'd be willing to accept that. If it doesn't work for you, I think that you could probably come up with a 4th condition (an "except" condition) that would take care of situations like this. I think there's an assumption that the internal definitions we use to determine whether a judgment of something like "knowledge" is correct or not are simple and straightforward, I doubt that's the case, at least not for everyone.

Concerning the dog example, I've simply stipulated that internal organs are part of what it means to be a dog. If you don't like that stipulation, I can simply change the knowledge-candidate to the belief that I'm petting an organic dog. You're still left with the problem that your definition doesn't allow me to non-deductively infer this from experience.[/quote][/quote]
No, I was just saying that if the definition of a dog includes the fact that "it has to have internal organs" and you can get to that conclusion with true observations, then the LTB definition would come to the same conclusion you do. An example:

1. This looks like a dog, is breathing, and is warm. (the important observations)
2. Things that are breathing and warm are alive and have internal organs
3. No one has the capability to create a fake dog that looks like a warm, breathing, dog.
4. Therefore this is a real dog I'm petting.

I'm sure there's a shorter or more concise, or cleaver way to get there, but I was trying to guess what would be fairly close to the actual steps someone would use (if not their actual order or importance).

-----------------------------------------
Edit: Thought of a couple examples to highlight the "making hypothetical questions excessively complicated can make it difficult to judge simple ideas" and "the definition of a word is just a tool to let us understand how we use it" points I was trying to make above.

1. Someone asks me what 20 times 15 is and I think that "Oh, 20 is twice as big as 15, and 20 times 10 is 200, so 20 times 15 is 300" and say "it's 300". Two things should be stated, one, that I actually do know how to do simple multiplication, I understand the concepts and can apply them logically. Two, I made an error in my internal logic, or at least the conscious stream of my thoughts, and still came to the correct answer. If you couldn't read my thoughts, everyone would say that I know what 20 times 15 is. If you could hear my thoughts, would the answer be different? I would think that most people would still say that I know what 20 times 15 is. And it's even possible that if we could scan my brain while I was thinking, then we would see that while I was thinking one thing consciously, my brain was actually making the correct calculation "in the background."

2. Someone asks me if I know where I live, and I say "yes." Then they ask me my address, and I can't remember. They conclude that I don't know where I live, or at the very least, I don't know the address of where I live. However, after a few moments of quiet contemplation, and without using any new information, I remember my address. Now suppose that instead of not remembering originally, I gave the wrong answer, and then remembered the correct address.

I hope these are relatively straightforward, and realistic examples, that get at the heart of the points I was trying to make. And I'd be interested to know what everyone's personal judgment of whether I "knew" the facts in these examples, and whether you think that everyone would agree with you.

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Re: Is knowledge justified true belief?

Postby TheGrammarBolshevik » Fri Sep 02, 2011 2:33 am UTC

TrlstanC wrote:Ahh, good that does make things a lot simpler to deal with. If A implies B, and a person has only ever observed A, but has a belief that B is true, then I would say that they know B is true.

The problem is that nobody else would say this. And that means that you're not analyzing a concept; you're making up a new definition to apply to a word that already has a different meaning.

TrlstanC wrote:2. Things that are breathing and warm are alive and have internal organs
3. No one has the capability to create a fake dog that looks like a warm, breathing, dog.

How can one observe such universal claims?

TrlstanC wrote:I would think that most people would still say that I know what 20 times 15 is.

Really? You don't think that most people accept that justification is necessary for knowledge? Do you have a citation for that?
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Re: Is knowledge justified true belief?

Postby TrlstanC » Fri Sep 02, 2011 12:03 pm UTC

TheGrammarBolshevik wrote:
TrlstanC wrote:3. No one has the capability to create a fake dog that looks like a warm, breathing, dog.

How can one observe such universal claims?

Statements like this usually aren't direct observations, they're the conclusions of lots of other observations. If I honestly had to go back and document all the observations I've made in my life that would lead me to the conclusion that a fake dog is impossible right now, it would probably end up being a very long list of observations, conclusions and additional observations and conclusions based on those. Basically though, I think it would boil down to "every technology described or hypothesized for a fake dog is far beyond any technology that anyone has demonstrated, or would be possible given our development." Again, describing such a complex process (likely covering a number of years) in one sentence is going to be quite a summary, but that's the way it is with being human, we collect a lot of information, and it's not always easy to summarize that information succinctly.

Do you believe that " No one has the capability to create a fake dog that looks like a warm, breathing, dog" is true? If so, how did you come to that belief?


TheGrammarBolshevik wrote:
TrlstanC wrote:Ahh, good that does make things a lot simpler to deal with. If A implies B, and a person has only ever observed A, but has a belief that B is true, then I would say that they know B is true.

The problem is that nobody else would say this. And that means that you're not analyzing a concept; you're making up a new definition to apply to a word that already has a different meaning.

That may be true (I'm not sure exactly who would and wouldn't believe it, but many or at least some people probably don't). But if these requirements come to a conclusion that's the same as a person's intuitive judgment then the definition is functionally equivalent, and it can therefore be a useful tool. I guess if in some situations two people (or some large percentage of people) disagree as to whether something is known or not, does that mean a definition is impossible? Or does it mean that some people are using the wrong definition? If some people are, and assuming everyone's definition is at least logically consistent, how do we know who's wrong?

TrlstanC wrote:I would think that most people would still say that I know what 20 times 15 is.
TheGrammarBolshevik wrote:Really? You don't think that most people accept that justification is necessary for knowledge? Do you have a citation for that?


I think that the traditional "justification" requirements and the "logical" requirement will come to the same conclusion in a vast majority of cases, and that in these cases, something being "logical based on observations" will be the same as justified.

And I actually do think that most people would think that even if I made a logical mistake once, I still "knew" the answer, I think they would still think I was justified. I could of course be wrong here (interestingly, I didn't say I "knew" that's what most people would say because I didn't base it on observations). It would be interesting to see a study of how people judge this kind of situation. I had assumed most people would say there was knowledge in that case, but I could certainly be wrong. I guess if most people thought there wasn't knowledge, then the correct definition, at least for them, would include the requirement "S can logically conclude p from all of their true observations."

Edit: If we make use of the observation that "we don't consciously know everything going on in our brains" then we should be able to accept the statement that "it's not possible to know if we can make a logically consistent conclusion from true premises using only processes that include faulty logic." Under that assumption the two different definitions would be indistinguishable; there would be no case where we could say one was correct while the other was wrong. So, that in everyday usage both versions of the LTB definition should work and be equivalent in all situations. And in hypotheticals one or the other should work in all situations, depending on the assumptions being made.

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Re: Is knowledge justified true belief?

Postby TheGrammarBolshevik » Sat Sep 10, 2011 6:25 pm UTC

TrlstanC wrote:Do you believe that " No one has the capability to create a fake dog that looks like a warm, breathing, dog" is true? If so, how did you come to that belief?

By induction. But this is not a logical basis in any clear sense — that is, if you regard induction as "logical," then you need to be more clear about what you mean by logical. I certainly didn't come to this belief by purely deductive reasoning, which is usually what is meant by logical inference: if I were to discover a robot dog, my previous observations and reasoning would not be contradicted.

TrlstanC wrote:That may be true (I'm not sure exactly who would and wouldn't believe it, but many or at least some people probably don't). But if these requirements come to a conclusion that's the same as a person's intuitive judgment then the definition is functionally equivalent, and it can therefore be a useful tool. I guess if in some situations two people (or some large percentage of people) disagree as to whether something is known or not, does that mean a definition is impossible? Or does it mean that some people are using the wrong definition? If some people are, and assuming everyone's definition is at least logically consistent, how do we know who's wrong?

It's not a matter of right or wrong; people can use the word "knowledge" to describe different concepts. But the issue is that you're not really solving the Gettier problem if your solution is an analysis of a concept different from the one that the Gettier problem problematizes.
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Re: Is knowledge justified true belief?

Postby TrlstanC » Sun Sep 11, 2011 1:30 pm UTC

Edit: After some more thought I realized that it's possible to also make different assumption about how humans process information, I think this is a much more important point to make, so I put the originally reply in spoiler tags at the bottom, and left this point up here, I think this really gets to the heart of the issue.

We have very little information about how the brain works, a lot of our beliefs about ourselves are just assumptions. The LTB definition makes several explicit assumptions about how humans process information, but there are a huge amount that haven't been stated clearly (since that may not be reasonable or possible). A key one is that we are not consciously aware of everything our brain is doing. We don't know every little piece of sensory data that comes in through our nerves, and don't know all the processing that happens before it enters our consciousness, and even once it's in our consciousness it's entirely possible for us to not understand what's going on, and in fact a lot of our consciousness might be just an attempt to explain "after the fact" how we came to our beliefs. A key assumption I'm making is that there is a lot (maybe the vast majority) going on in our brain that we're not aware of. For example I think that once we're able to understand this process a little better it will be clearer to say that part of knowing is "truly believing" as opposed to "thinking we believe." Right now that doesn't make a lot of sense, but with an improved ability to understand what's going on in the brain I think the distinction will be worthwhile. Also, I think that defining knowledge will change drastically at some point when we have a much better understanding of what's actually happening in the brain, it will become something more like "a pattern reflected in neurons that matches a true pattern interacted with previously" or something similarly concrete and biological.

For now, however, I'm assuming that all that processing we're not aware of is part of the "observation" step since we can't describe exactly what's going on. And in fact even the parts we claim to be aware of, or in control of, may actually be happening somewhere else and we're just mistakenly believing it's primarily a conscious process. I'm not saying that we don't do any actually thinking or deducing, but instead that the ratio of "unrealized" to "realized" information processing in the brain is probably skewed wayyy to the unrealized side, much more then we normally expect or think about. So, we definitely come to some conclusions consciously (and sometimes also through flawed reasoning) but there are lots of conclusions we make unconsciously, including the vast majority of our judgments about what the world is like, and I think it's fair to make those all part of the "observations" test and allow ourselves to judge if those observations are true or not.

For example instead of imagining a robot dog in the park, instead imagine that it's a lamb. You're sitting on the bench and a lamb comes and sits next to you on the ground, you see it out of the corner of your eye, pet it, and come to the belief that it's your dog. Obviously this is a case of not knowing, but I wouldn't say that you observed it was a lamb and concluded it was your dog. I would say that you observed it was a dog, and concluded it was your dog. If we accept the second, then it's clear it would fail the LTB test because it relies on false observations. If instead we assume that first is the correct way to think about how the brain works (I don't think it is) the LTB test would fail because the belief would be based on true observations (and some kind of undisclosed logic). At this point in our understanding of how the brain works we have to make a lot of assumptions about what's actually going on. Since we can't know for sure what's actually happening, instead of trying to judge the process I think it makes more sense to make all that processing part of the "observation" requirement and then just have to judge if the observation is true or not.

If however, we want to assume that observations are more like "pure" data and we do all our data processing consciously, we can do that, but it will require us to spell out a lot of information and processing (that we're not sure we understand) explicitly, especially in hypothetical situations. I'm not sure this is a useful assumption given our current understanding of how the brain works. More thoughts about assumptions like this below in the original response, basically, we have to be very clear about the assumptions we're making in hypothetical situations, especially with regards to what we're assuming is going on in the brain.


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Orignal response (this is mostly "nuts and bolts" thoughts about what's possible in hypothetical situations, and the need to be clear. Also, that the LTB definition can be used with different amounts of information, and will yield different results.)
Spoiler:
One of the benefits of describing knowledge as a logical true belief is that it makes clear the definition will apply differently depending on what information we have available to us. But this also means that we're going to be able to define different things as knowledge depending on the information we have, running the full scale from "only what I personally have access to" all the way up to "perfectly described hypothetical world." This is going to result in lots of contradictions if we use mixed information, for example our everyday usage of the term "to know" or "what a dog is" in hypothetical situations. And that's only the start of the problems because in any definition people are going to be able to disagree about the underlying terms. For example, what's "an observation" or "a belief" and there's certainly different definitions for what "logic" is. Spelling out each term is absolute clarity is only a possibility in mathematical definitions - or in hypothetical situations.

I don't know if "logical true belief" is the internal definition everyone is using when they use the term "to know" - in fact, I would assume not. But, I do believe that the logical true belief definition will come to the same conclusion in all everyday usages that are possible to consider correct. In everyday usage I think it's functionally equivalent to the "true" definition. Why? Because we know things, and how do we know things? Well, it has to be through a combination of observing things and making conclusions using some kind of logic. In the real world it's not possible to spell out all the observations and conclusions that are used to know everything, but in a hypothetical situation it is. We can create a hypothetical situation with fake barns, or robot dogs, or a man with 10 coins in his pocket, but when we do, we also have to state explicitly every observation that we're interested in, and any beliefs, what can be logically concluded and what's true and false. If we go through all those steps and in our hypothetical situation we don't agree that "S knows p" and "S has a logical true belief about p" then there are three conclusions we can draw

1. The LTB definition isn't correct
2. We are using different internal definitions of "to know" (it would be interesting if you could try and spell out what definition you're using, or if you just don't think it's possible to define, and why. As far as I can tell the definition I use is equivalent to LTB.)
3. We have come to different understandings of the assumptions in the hypothetical situation, we need to be more clear in stating our assumptions
4. We have created a hypothetical situation which is so unrealistic or so complicated that it's not a useful tool

The way I understand it, if you are petting a dog, and through the observations, logic and beliefs you have available you can conclude that it's a dog then you are correct in saying you know you're petting a dog if it is a dog and all your observations are true. If we change the world slightly so that there's a perfectly realistic robotic dog in it, we also have to be able to asume that such a world is possible without affecting any of the observations you've made in your lifetime that support your belief that you're petting a dog. This would seem to be possible, and I think most reasonable people would agree that if you're petting a real dog you know it's a real dog, and if you're petting a robot dog you've made a mistake and you don't know it's a dog. If however we modify the world in such a way that robot dogs are possible, but allowing them requires for either 1. you to be deceived about some of your observations 2. you to make incorrect observations then most people would agree that you never know if you're petting a dog or not. The same goes for the Gettier problems. Depending on what we assume for observations we can either conclude that Smith is incorrect in thinking he knows that "the man who will get the job has 10 coins in his pocket" or it may be possible that he could never know that "the man who will get the job has 10 coins in his pocket."

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Re: Is knowledge justified true belief?

Postby TheGrammarBolshevik » Mon Sep 12, 2011 7:53 pm UTC

TrlstanC wrote:For now, however, I'm assuming that all that processing we're not aware of is part of the "observation" step since we can't describe exactly what's going on. … So, we definitely come to some conclusions consciously (and sometimes also through flawed reasoning) but there are lots of conclusions we make unconsciously, including the vast majority of our judgments about what the world is like, and I think it's fair to make those all part of the "observations" test and allow ourselves to judge if those observations are true or not.

So anything that we believe without conscious reason counts as an observation?
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Re: Is knowledge justified true belief?

Postby TrlstanC » Mon Sep 12, 2011 8:04 pm UTC

TheGrammarBolshevik wrote:
TrlstanC wrote:For now, however, I'm assuming that all that processing we're not aware of is part of the "observation" step since we can't describe exactly what's going on. … So, we definitely come to some conclusions consciously (and sometimes also through flawed reasoning) but there are lots of conclusions we make unconsciously, including the vast majority of our judgments about what the world is like, and I think it's fair to make those all part of the "observations" test and allow ourselves to judge if those observations are true or not.

So anything that we believe without conscious reason counts as an observation?


As long as it's also true and logically consistent with our other true observations then I think so.

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Re: Is knowledge justified true belief?

Postby TheGrammarBolshevik » Mon Sep 12, 2011 8:06 pm UTC

So if I form a belief, can't give any conscious reason for it, and I turn out to be right, that's knowledge?
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Re: Is knowledge justified true belief?

Postby TrlstanC » Mon Sep 12, 2011 8:19 pm UTC

TheGrammarBolshevik wrote:So if I form a belief, can't give any conscious reason for it, and I turn out to be right, that's knowledge?


As long as it's also logically consistent with your other true observations, then I think so.

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Re: Is knowledge justified true belief?

Postby gmalivuk » Tue Sep 13, 2011 4:55 am UTC

TrlstanC wrote:But if these requirements come to a conclusion that's the same as a person's intuitive judgment then the definition is functionally equivalent, and it can therefore be a useful tool.
But that was the point: they absolutely don't come to the same conclusions. Because mathematicians didn't know FLT was true until it was proven. And furthermore they knew that they didn't know FLT was true.

TrlstanC wrote:
TheGrammarBolshevik wrote:So if I form a belief, can't give any conscious reason for it, and I turn out to be right, that's knowledge?
As long as it's also logically consistent with your other true observations, then I think so.
And again, you've just proven that you're talking about a different concept, rather than the one people generally refer to with the word "knowledge".
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Re: Is knowledge justified true belief?

Postby TrlstanC » Tue Sep 13, 2011 11:57 am UTC

gmalivuk wrote:
TrlstanC wrote:But if these requirements come to a conclusion that's the same as a person's intuitive judgment then the definition is functionally equivalent, and it can therefore be a useful tool.
But that was the point: they absolutely don't come to the same conclusions. Because mathematicians didn't know FLT was true until it was proven. And furthermore they knew that they didn't know FLT was true.

If the assumption being made is that at least one, and maybe more mathematicians had a perfect understanding of every concept needed to prove FLT, and yet still thought that they didn't know FLT was true, then I would say that that is a very big assumption to make. To claim that we can state definitely the inner workings of someone else's brain, and how well they understood such difficult concepts, seems to be an unreasonable assumption. Especially since we could explain the same situation with a possible example like: between many different mathematicians the information needed to prove FLT was true was understood, but not until one of them was able to come to a full understanding of all the concepts did he know that FLT was true.

Also, I think that this example is needlessly complex, and the same point can be made using trigonometry or geometry or arithmetic. That "just because you fully understand the concepts doesn't imply you know the conclusions." Although, again I would argue that we're making a big assumption assuming someone fully understands a concept before they can use it to come to a conclusion.

And again, I believe that when I, personally, use the term "know" I would include cases where a person could logically come to a belief, but appears to have illogically come to the belief, see my arithmetic example above. I think many people would make the same judgment since we can't know what's actually happening in someone else's mind. If, however, we create a hypothetical situation where we assume perfect knowledge about someone's mind, and they come to a true belief illogically (that they could have come to logically) and most people would say that that isn't knowledge, then we can just change the third requirement of the definition to "3. S logically concluded p from their true observations." Which would be equivalent in all day to day cases (since we don't know the workings of someone's mind) and would match people's judgements in hypothetical cases as well.

Of course, once we do understand how our brains work, this definition probably won't seem very accurate either. But assuming we know how they work, and because of that assume something that would make this definition false seems to be a mistake to me. Especially since it seems to work in all common usage, which makes sense because it's based on the JTB definition which works in most common usage. The only difference being that LTB takes the "justified" requirement and modifies it so that we can make better judgments about whether the observations used are true or not.

gmalivuk wrote:
TrlstanC wrote:
TheGrammarBolshevik wrote:So if I form a belief, can't give any conscious reason for it, and I turn out to be right, that's knowledge?
As long as it's also logically consistent with your other true observations, then I think so.
And again, you've just proven that you're talking about a different concept, rather than the one people generally refer to with the word "knowledge".


Again, I think this counter example is relying on a false assumption that we know how the brain works. In particular it's assuming that it's possible to come to a belief "out of nowhere." I would argue that every belief someone has is based on their experience, even if they're not conscious of it. Also I would think that if we ruled out every piece of knowledge that we didn't create consciously then we'd be ruling out a lot of knowledge that we take for granted everyday. We may be able to look back and say "I came to this belief because I consciously concluded it was true." But that statement should really be understood as "Now that I look at it, I think that I consciously concluded it was true." If there's any doubt about how much trust we should put in people's recollections just look at the body of evidence showing how unreliable witness statements are.

Also, I think that people may be using different understandings of the term "observation." I don't think that an observation is the same as sensory data. Otherwise when someone asked you for your observations you couldn't say "I saw a man running down the street" you would have to say something like "I saw colored shapes moving in a predictable pattern through an area" or similar. I also don't think that all observations are true, otherwise the idea of a "false observation" wouldn't make sense. An observation can be thought of as a judgment of fact based on sensory information and experience (and "experience" is just a different kind of sensory information). And in particular I wouldn't claim that we make all observations consciously, or that we understand the exact process by which we make these judgments. Although, I think that defining an observation as "a statistical judgment of fact" at least for the time being would work, as long as we feel it's safe to assume that 1. all judgments are based on sensory information and 2. the brain is using something similar to a statistical process, weighting different experiences to come to a conclusion. Of course, we don't have to assume that, or use that definition, as long as we can agree that 1. observations can be false and 2. we don't have a perfect understanding of how observations are created.

And it might make the discussion easier to follow if anyone has a definition of knowledge (or observation, or consciousness) that they're using which conflicts with the LTB definition to spell it out, so we can see where it conflicts. Or, if you just believe that a definition is impossible, it would be interesting to hear why.

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Re: Is knowledge justified true belief?

Postby gmalivuk » Tue Sep 13, 2011 9:13 pm UTC

TrlstanC wrote:If the assumption being made is that at least one, and maybe more mathematicians had a perfect understanding of every concept needed to prove FLT, and yet still thought that they didn't know FLT was true, then I would say that that is a very big assumption to make.
A number of mathematicians understand the rules of logic and the axioms of ZFC and how integers are defined. FLT is logically implied by those things. Therefore by your account, all of those mathematicians "knew" FLT was true, and yet at the same time all of those mathematicians would have told you that they were certain they didn't know whether FLT was true, though they did believe it (and were somewhat justified in believing it, and it turned out to be true).

To claim that we can state definitely the inner workings of someone else's brain, and how well they understood such difficult concepts, seems to be an unreasonable assumption.
Yes, but also it's an assumption that no one is making. I don't need to understand the inner workings of your brain to determine whether you understand the axioms of set theory. And if you think "understanding" something requires knowing in full detail all of its logical consequences, all that means is that I've found another word you're redefining to mean something no one else means when they say it.

gmalivuk wrote:
TrlstanC wrote:
TheGrammarBolshevik wrote:So if I form a belief, can't give any conscious reason for it, and I turn out to be right, that's knowledge?
As long as it's also logically consistent with your other true observations, then I think so.
And again, you've just proven that you're talking about a different concept, rather than the one people generally refer to with the word "knowledge".
Again, I think this counter example is relying on a false assumption that we know how the brain works. In particular it's assuming that it's possible to come to a belief "out of nowhere."
No, it's absolutely not relying on anything of the kind. TGB simply posited not being able to give any *conscious* reason for it. Which isn't even a little bit like the same thing as the belief coming out of nowhere.

Ask people if they think it will rain tomorrow, and many of them will express beliefs on the issue. Many of those beliefs will be consistent with all their other true observations. Are you honestly going to say that whichever people turned out to be correct in their belief *knew* whether it would rain?
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Re: Is knowledge justified true belief?

Postby TrlstanC » Tue Sep 13, 2011 10:07 pm UTC

gmalivuk wrote:
TrlstanC wrote:If the assumption being made is that at least one, and maybe more mathematicians had a perfect understanding of every concept needed to prove FLT, and yet still thought that they didn't know FLT was true, then I would say that that is a very big assumption to make.
A number of mathematicians understand the rules of logic and the axioms of ZFC and how integers are defined. FLT is logically implied by those things. Therefore by your account, all of those mathematicians "knew" FLT was true, and yet at the same time all of those mathematicians would have told you that they were certain they didn't know whether FLT was true, though they did believe it (and were somewhat justified in believing it, and it turned out to be true).


That may be, and this might be a case that doesn't fit with the definition I proposed, in which case maybe we could work on coming up with a definition that does work. Or perhaps someone does have a definition that they believe works, and hasn't shared it, or maybe people just believe that a definition is impossible, and haven't shared a reason why they believe. However, I can honestly say that I don't understand what ZFT is, or have more then the most minimal understanding of how FLT was proved true. It would be great if a different example could be used, for example, trigonometry or arithmetic. I assume that this point isn't just confined to FLT? Of course, if the key point is that the belief has to be logically concluded (instead of just possibly logically concluded) then we can just change the definition. I was just trying to have the definition line up with the way I use "knowledge" which may be different then other people's - the differences are hard to detect when examples only come up rarely.

gmalivuk wrote:
To claim that we can state definitely the inner workings of someone else's brain, and how well they understood such difficult concepts, seems to be an unreasonable assumption.
Yes, but also it's an assumption that no one is making. I don't need to understand the inner workings of your brain to determine whether you understand the axioms of set theory. And if you think "understanding" something requires knowing in full detail all of its logical consequences, all that means is that I've found another word you're redefining to mean something no one else means when they say it.

I'm not implying a different meaning for "understanding" I'm just saying that if I don't understand the hypothetical situation (or if maybe very few people have a complete understanding of the proof) then we may have to assume a lot about what types of things people know to figure out what's going on.

gmalivuk wrote:Ask people if they think it will rain tomorrow, and many of them will express beliefs on the issue. Many of those beliefs will be consistent with all their other true observations. Are you honestly going to say that whichever people turned out to be correct in their belief *knew* whether it would rain?

At least this is a very straight forward example that we can all wrap our heads around easily, and it shouldn't present any difficulties in judging if people actually know whether it will rain, or whether the LTB would conclude that people know it will rain (I believe it concludes they don't). In fact, we don't even need to use that proposed definition, we can just rely on the regular justified true belief definition, which has some problems, but which should work here, and conclude that people don't know it will rain.

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Re: Is knowledge justified true belief?

Postby gmalivuk » Wed Sep 14, 2011 12:15 am UTC

TrlstanC wrote:
gmalivuk wrote:Ask people if they think it will rain tomorrow, and many of them will express beliefs on the issue. Many of those beliefs will be consistent with all their other true observations. Are you honestly going to say that whichever people turned out to be correct in their belief *knew* whether it would rain?
At least this is a very straight forward example that we can all wrap our heads around easily, and it shouldn't present any difficulties in judging if people actually know whether it will rain, or whether the LTB would conclude that people know it will rain (I believe it concludes they don't). In fact, we don't even need to use that proposed definition, we can just rely on the regular justified true belief definition, which has some problems, but which should work here, and conclude that people don't know it will rain.
What? But you just said that if a person believes something, which happens to be true, and which is logically consistent with all their other true observations, then they know it. But clearly they don't know whether it will rain tomorrow, despite having a believe on the matter which is logically consistent with all their other true observations.
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Re: Is knowledge justified true belief?

Postby TrlstanC » Wed Sep 14, 2011 12:52 am UTC

Do you think that it's possible for people to have a justified true belief that it will rain tomorrow, which would be knowledge? What about a JTB that isn't logically consistent with true observations?

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Re: Is knowledge justified true belief?

Postby TheGrammarBolshevik » Wed Sep 14, 2011 3:22 am UTC

TrlstanC wrote:At least this is a very straight forward example that we can all wrap our heads around easily, and it shouldn't present any difficulties in judging if people actually know whether it will rain, or whether the LTB would conclude that people know it will rain (I believe it concludes they don't).

Why? Show us why. So many of your sentences begin with "I believe" or "I think" or "I assume," but so rarely do you show us the reasoning behind those thoughts. Walk us through the LTB analysis as applied to this case. Which criterion does not apply to the example?

TrlstanC wrote:In fact, we don't even need to use that proposed definition, we can just rely on the regular justified true belief definition, which has some problems, but which should work here, and conclude that people don't know it will rain.

Of course it does that. But it's not a matter of whether we need to use your analysis. It's a matter of whether we can use your analysis in all situations.
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Re: Is knowledge justified true belief?

Postby gmalivuk » Wed Sep 14, 2011 11:58 am UTC

TrlstanC wrote:Do you think that it's possible for people to have a justified true belief that it will rain tomorrow, which would be knowledge? What about a JTB that isn't logically consistent with true observations?
No, of course not. I'm the one saying they *don't* know whether it will rain tomorrow. You're the one whose account of knowledge implies that they *do*.
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Re: Is knowledge justified true belief?

Postby TheGrammarBolshevik » Wed Sep 14, 2011 12:33 pm UTC

(I do think that people could have a justified true belief that it will rain tomorrow if they're meteorologists or they've checked a reliable weather report. I suspect gmal would agree with this as well. But, perversely, your LTB account fails to count this as knowledge (since the observations that meteorologists make don't logically entail rain), while it does count random suppositions (since you count those as observations).)
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Re: Is knowledge justified true belief?

Postby TrlstanC » Wed Sep 14, 2011 1:06 pm UTC

I've assumed that a person can jusitify a belief by appealing to "obervations, an authority or logical deductions based on one or both." And further assumed that an appeal to authority is just a certain kind of observation. Have I assumed too much? Is there a different usage of the term "justify" that's contradictory with this usage?
Last edited by TrlstanC on Wed Sep 14, 2011 3:07 pm UTC, edited 1 time in total.

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Re: Is knowledge justified true belief?

Postby gmalivuk » Wed Sep 14, 2011 1:50 pm UTC

The thing we are talking about is this claim by you:
TrlstanC wrote:
TheGrammarBolshevik wrote:So if I form a belief, can't give any conscious reason for it, and I turn out to be right, that's knowledge?
As long as it's also logically consistent with your other true observations, then I think so.
You aren't requiring any ability to consciously justify a true belief. You're only requiring that it be consistent with other true observations.

And you're further arguing that yours is a *better* account that JTB, which means it should solve some of the problems with JTB, not lead to even more. (In other words, there should be cases we wouldn't intuitively call knowledge, but that JTB incorrectly does call knowledge, which your account correctly says aren't knowledge.)

So either you face a situation with the weather where people know the future even when they themselves would deny that their belief is knowledge, or you have to explain why this isn't knowledge even when your account seems to say it is.
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Re: Is knowledge justified true belief?

Postby TrlstanC » Wed Sep 14, 2011 2:21 pm UTC

gmalivuk wrote: You're only requiring that it be consistent with other true observations.
I know, but if we think that JTB works in most cases (leaving aside Gettier style problems for now) and that LTB would come to a different conclusion in some of those cases, I'm trying to figure out where the difference comes from by looking at the steps I used to get there from JTB. So, If we:
TrlstanC wrote:assumed that a person can jusitify a belief by appealing to "obervations, an authority or logical deductions based on one or both." And further assumed that an appeal to authority is just a certain kind of observation.
Then we should be able to replace the "justified" requirement in JTB (S is justified in believing p) with a "logical" requirement such that S can logically conclude p based on observations. This should just be a re-wording of JTB at this point, and should be equivalent in all cases. If it's not, then one of the assumptions is wrong, or I've just made a linguistic error. Either of which we should be able to fix.

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Re: Is knowledge justified true belief?

Postby gmalivuk » Wed Sep 14, 2011 2:31 pm UTC

TrlstanC wrote:if we think that JTB works in most cases (leaving aside Gettier style problems for now) and that LTB would come to a different conclusion in some of those cases, I'm trying to figure out where the difference comes from by looking at the steps I used to get there from JTB.
Well for one thing, you seem to be jumping between someone's prior observations logically implying P, and someone's prior observations merely being consistent with P.

Which is it, precisely, that you mean by "logically conclude"?
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