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The Nature of Knowledge(1)

Know - "(1) to perceive or understand clearly and with certainty; to have in the mind or memory as
the result of experience, learning, or information; to understand and be able to use; to have
personal experience of; (2) to feel certain."

Knowledge - "(1) acquaintance with fact truth or principles, as from study or investigation;
acquaintance or familiarity gained by sight, experience or report; (2) the fact or state of knowing;
clear and certain perception of fact or truth; (3) that which is or may be known; (4) the body of
truths or facts accumulated by mankind in the course of time."

Opinion - "a belief or judgment that rests on grounds insufficient to produce certainty; (2) the
expression of a personal attitude or judgment."

Certainty - "The state of being certain."

Belief - "Trust or confidence (in); acceptance (of thing, fact, statement, etc.) as true or existing."

Certain - "(1) free from doubt or reservation; (2) established as true or sure; unquestionable; (3)
that may be depended on." Information - "items of knowledge."

 Datum - "(1) thing known or granted, assumption or premise from which inferences may be
drawn. (2) facts or information, especially as the basis for inference."

We are all interested in figuring out what is the best thing to do.   We are all interested in learning the
answers to our questions.   But to choose between alternative things to do, we have to make some forecasts
as to the likely consequences of each alternative, and evaluate the desirability of those consequences on
some scale of better or worse.   And to make use of the answers we find to the questions we ask, we have to
judge how dependable our informants are.  

If you and I want to discuss what it is we each judge to be what we think is the best thing to do, or what we
claim is the correct answer to the question, then we need to understand the words that we use.   We each
support our judgements and claims by offering reasons.   And when we offer these reasons, we describe
them as "things that we know".   So, in order to remove one potential source of conflict between us, it is
advantageous for us together to agree on just what it means to "know" something.   For this reason,
exploring the meaning of our concept of "knowledge" has become fundamental to the western philosophical
tradition.  

Whether it is you or I, John or Jane, when we claim to know something, what is it that we mean by that
claim?   What is the best way to Larissa?   Where does the tiger lurk?   Should Jack and Jill go up the hill or
down the dale to find water?   Why is knowing the answer to these questions so much more desirable than
simply believing the answer?   So, if we place so much store in someone who claims to "know", just what
does it mean to claim "I know" something?   Under what circumstances is such a claim proper and valid?  
Under what conditions would we say that such a claim is invalid or cheating?

Contents

1 Introduction
   1.1 Why the Interest in Knowledge
   1.2 Why is Knowledge Valuable
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2 What is "Knowledge"?
   2.1 Different Kinds of Knowledge
   2.2 How to Define "Knowledge"
3 The Traditional Definition of "Knowledge"
   3.1 The Justified True Belief Model
   3.2 The Belief Condition
   3.3 The Truth Condition
   3.4 The Justification Condition
      3.4.1 The 1st Person vs 3rd Person Sense of "Justification"
      3.4.2 "Prior-Grounding" versus "Default and Challenge"
4 The Gettier Problem
   4.1 The Problem
   4.2 The Solutions
      4.2.1 Infallibilism
      4.2.2 Defeasible Evidence
      4.2.3 No False Inference
      4.2.4 Contextual Decomposition
      4.2.5 Global Justification Externalism
      4.2.6 Causal Chain
      4.2.7 Reliablism
5 The "Sceptical" Problem
   5.1 Kinds of Sceptical Challenges
   5.2 Agrippan Scepticism
   5.3 Cartesian Scepticism
      5.3.1 An Overview
      5.3.2 The "Brain in a Vat" Argument
      5.3.3 The "Epistemic Closure Principle"
      5.3.4 Hillary Putnam's Brain-in-a-Vat
6 Alternatives to the Traditional Definition of "Knowledge"
   6.1 Foundationalism
   6.1.1 The Problem of the Foundation
   6.1.2 The Problem of the Structure
   6.2 Coherentism
      6.2.1 The Nature of "Coherence"
      6.2.2 Truth Tracking
   6.3 Reliablism
   6.4 Causal & Law-Like Theories
   6.5 Contextualism
      6.5.1 Default and Challenge Justification
      6.5.2 Two Variants of Contextualism
      6.5.3 Inferential Contextualism
   6.6 Truth-Tracking Theory
   6.7 Deontological Theory
   6.8 Performative Theory
7 Sources of Knowledge
   7.1 Knowledge from Testimony
      7.1.1 Language Use
      7.1.2 Risk Assessment
      7.1.3 Default and Challenge Justification

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      7.1.4 Truth Tracking

      7.1.5 Conclusion
   7.2 Knowledge from Perception
      7.2.1 Perceiving to Believing
      7.2.2 Believing to Knowing
      7.2.3 The Role of Truth / Three Theories of Perception
      7.2.4 Conclusion
   7.3 Knowledge from Introspection
   7.4 Knowledge from Memory
   7.5 Knowledge from Reason
Footnotes
Bibliography

1 Introduction

1.1 Why the Interest in Knowledge?

Unlike a "mere" belief, something that we "know" isn't just a psychological or mental state that cannot be
challenged.   To offer as a reason something that we "know" is to offer a reason with a special normative
status -- a belief that merits a special kind of positive evaluation.   Consider the following series of
statements:

I think that there is a God. I believe that there is a God. I know that there is a God.
I think that there is no God. I believe that there is no God. I know that there is no God.
I think that there are UFOs. I believe that there are UFOs. I know that there are UFOs.
I think that she is my friend. I believe that she is my friend. I know that she is my friend.
I think the tiger is I believe that the tiger is I know that the tiger is
behind that tree over there. behind that tree over there. behind that tree over there.

As we go from think to believe to know, the degree of assurance that the statement broadcasts increases.  
An assertion that is couched in terms of "think" or "believe" allows for a large degree of doubt in the truth of
the statement.   Whereas an assertion that claims to be something that we "know" communicates a much
higher degree of assurance.  

No direct evidence, A lot of positive

Some evidence to
No evidence either but some related Adequate justification evidence, and no
support the truth of
way.   P is as likely reasons for suspecting for guaranteeing the contrary evidence.  
P, with no contrary
to be true as false. the truth of P, and no truth of P to others. Or, no logically
evidence.
contrary reasons. possible alternative.
"Silly Wild-Assed
"I think" "I believe" "I know" "Certain Knowledge"
Guess"
I think there is
I believe that she is I know that London is I am certain that
There is a God. extraterrestrial life out
my friend. in England. 2+2=4.
there.

Whether what we believe counts as "knowledge" is ultimately a subjective evaluation.   Along that continuum
between "silly wild-assed guess" and "certain knowledge", will be a line drawn.   To one side, we maintain
that our belief has inadequate epistemic grounding, and to the other side we maintain that our belief qualifies

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as "knowledge".   Close to the line, we will be uncertain which is which.   Further from the line, we will have a
great deal of confidence in which is which.   But the choice of where a particular belief falls along that
continuum relative to the location of that line, is largely a subjective evaluation.

Science and our western philosophical tradition began when our attempts to understand the world around us
was decoupled from myth and tradition.   Beginning in ancient Greece (perhaps with Thales of Miletos, circa
624-546 B.C., but certainly by the time of Plato circa 428-347 B.C.), western philosophical tradition has been
one of analysis and criticism - a detailed examination of the elements or structure of something, the
separation of something into its constituent elements, and the judging of and explaining the importance and
meaning of other people's writings.   Myth and traditions are "taken on faith", "taken as given", are deemed
true because someone or something (usually "the Gods") says so.   Myths and traditions simply are.   They
are the words of "Authority" and as such, they cannot be analyzed or challenged.   They cannot be
understood in any greater depth.   They can sometimes be interpreted and re-interpreted, but they cannot be
critically examined, and cannot be compared with alternatives.   Reasoned argument cannot, therefore, be
used to distinguish between alternatives.   Reasoned argument, analysis and criticism, can only be used to
distinguish between alternatives if the reasons that justify those beliefs can be explored.   Scientific and
(western) philosophical thinking demands reasons, justification, rationales.   When it comes to questions
about Nature and the origins of the Universe, what separates myth and tradition from scientific and (western)
philosophical thought is the demand for, and existence of, some form of warrant.   And we can not explore
reasons and their warrants unless we understand the words we use to describe them.

"Knowledge", then, is a species of belief.   It is clearly an honorific title bestowed upon only some beliefs.   It
promises a positive normative evaluation that separates some beliefs from others -- it promises some kind of
sanction, authorization, guarantee, security, ground, justification, confirmation, proof.   It is a success-state
for beliefs.   The question is why we have this distinction between things we believe, and things we believe
so strongly that we call them by a separate name -- "knowledge".   And, of course, just what are the success
criteria that qualify a belief as knowledge?

1.2 Why is Knowledge Valuable?

When it comes to our struggle for survival, it pays (on average, and in the long run) to know (ie. have some
credible assurance) behind which tree the tiger lurks.   To base our survival on an unwarranted (ie.
unassured) belief is to run a greater risk of becoming lunch rather than enjoying lunch.   We have the
concept "knowledge" to distinguish those beliefs that are somehow more likely to be useful -- more likely to
be true -- more likely to yield the expected results when relied upon -- more likely to offer a survival
advantage.   To know behind which tree the tiger lurks is therefore to have some form of warrant for the
belief -- to have some special factors that render the belief more likely to be true than other unwarranted
beliefs.   And it pays to demand that warrant from others.

Knowledge is power.   The ancient Greek philosophers considered knowledge to be power over oneself.  
But to modern man, knowledge is power over the world.   Knowledge is the power to control and manipulate
our environment.   If you need to build a bridge across a stream, it is more likely to be a successful rather
than a fatal undertaking if you rely on some knowledge about the best ways to build it rather than some
unwarranted beliefs on how to do it.   Which bridge builder are you going to trust with your life when you want
to get across the gorge?   The one who says he thinks the span is strong enough, the one who says he
believes the span is strong enough, or the one who says he knows the span is strong enough?

2 What is "Knowledge"?

2.1 Different Kinds of Knowledge

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We begin with the task of clarification.   There are several ways in which we describe cases of knowledge.  
To each of these ways there might correspond a theory of that kind of knowledge -

              (i) Acquaintance

              (ii) Competence

              (iii) Recognition of information as being correct

The first sense of meaning is exemplified by such statements as "I know John", "I know the answer when I
see it", or "I know New York".   This sense of the word "know" implies a degree of acquaintance or familiarity
with the object of the verb, and an ability to recognize it again on re-encounter.   This is "knowledge of ".  
Acquaintance knowledge implies a certain degree of skill or ability, and is relative in nature.   It also implies
that you have encountered the known thing before.   I can know John or New York more or less than you do,
or than I did or will.   And I can know or not know depending on whose standards of acquaintanceship is to
be applied.   Over time, my level of knowledge can increase or decrease.   To someone who is not familiar
with New York, I can claim to know New York.   But to someone who is more familiar than I with New York,
perhaps I can not properly claim to know New York.  

How do I determine whether or not I "know" any particular thing in this sense?   The key is that I must be able
to recognize the object upon re-encounter with some degree of accuracy.   If I have never encountered the
object before, I cannot claim to have any acquaintance with it.   If I am not sufficiently familiar with the object
to meet the required standard of re-recognition, then I cannot be said to have the knowledge in question.  
Knowledge by acquaintance has a long association with philosophical enquiry.   It formed the core of Plato's
theory of knowledge.   And has occupied the attention of numerous philosophers since, including Bertrand
Russell and A.J.Ayer.   But this sense of the concept "to know" is not the subject of this essay.

The second sense of meaning is exemplified by such examples as "I know the violin", or (again) "I know New
York".   This is "knowledge how  . . ." and implies a much higher degree of skill or ability in the topic that is
the object of the verb.   The sense of the word in this context implies some special skill or ability, not merely
re-recognition upon re-acquaintance.   I can claim to know the violin not because I can recognize a violin
when I see one, but because I can play the violin to some standard.   Or I can claim to know New York if I
can find most obscure landmarks or restaurants in (say) Greenwich Village or Chinatown.   Ability knowledge
is also relative in nature, and can change over time or according to whose standards are to be applied.  

How do I determine whether or not I can properly claim to "know" any particular thing in this sense?   The key
is that I must be able to employ my special skill or ability to some much higher standard.   Thus, if I can play
the violin to my mother's standards, then to her I can say that "I know the violin".   But if I cannot play well
enough to satisfy anyone else, then I cannot say to them that "I know the violin".   As you can see, like
acquintance knowledge, whether or not I "know" something in this sense is dependent upon the standards
that are being applied.   And these standards can vary, depending upon the audience for my statement.   But
this second sense of the concept "to know" also is not the subject of this essay.

It is the third sense of meaning that is the focus of this essay.   It is "knowledge that   . . .", or propositional
knowledge.   This is the kind of knowledge that appears in statements that have the general format "S knows
that P", where "S" is any subject of interest, and "P" is any truth statement or proposition.   I introduced a
sample of such statements above in that little table.   To "know that   . . ." is the same kind of mental
construct as "think that   . . ." and "believe that   . . .".   Each involves a statement or other assertion about the
world around us.   And each expresses something about the truth of that statement.   But to "know that   . . ."
adds something special over and above "believe that   . . .".

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As you can see, the propositional sense of the concept of "knowledge" differs quite dramatically from the
previous two.   The most significant difference is that the use of the concept is not relative.   The knowledge
possessed by S either does or does not include P.   One cannot say I know P more today than I did
yesterday, or that you know P better than I do.   S either knows or does not know that P.   So how do we
determine whether or not "S knows that P"?   Or, alternatively, how do we determine whether the knowledge
possessed by S does or does not include P?   Equivalently, how do I determine whether I can properly claim
to know that P?

For example, consider the statements "John knows that the ball is red", or "I know that P the Sun will come
up tomorrow", or "The teacher knows that one of her three students gave her the apple", or "I know there is a
God", or "I know there is no God", or "I know there are UFOs", or "I know that she is my friend", or "I know
that the tiger is behind that tree over there".  

In each case, if I state that I know that P, am I expressing an opinion, a thought, a belief, or do I have the
knowledge?   And if it is more than a belief, is it knowledge?   Just what is the difference between a person's
belief that the ball is red, and a person's knowledge that the ball is red.   What has to be added to the belief
in order to qualify it as "knowledge"?   What conditions does the belief have to meet in order to qualify for the
special honorific of "knowledge"?

Notice that knowledge-how (ability) and knowledge-of (acquaintance) are not completely independent of
knowledge-that.   Acquaintance and ability knowledge both involve significant amounts of propositional
knowledge.   And on some understandings of knowledge-that, it involves a significant amount of knowledge-
how -- how to discriminate one thing from another.

2.2 How to Define "Knowledge"

In order compile a "philosophical" (as opposed to an ostensive or dictionary) definition philosophers analyze
the common usage of the words "knowledge" and "know".   Obviously, in common practice we mark the
distinction between a belief and knowledge by how we use these words.   We already have an ability-
knowledge of how to use the word (and concept) "know".   We all readily employ the concept of knowledge in
our communications with other people, and even when talking to ourselves.   And we each readily correct the
way other people use the concept.   Because language is a social convention, we must all therefore employ
the concept with a reasonable degree of consensus and consistency.   So our intuitive reactions as to which
hypothetical scenarios involve knowledge rather than beliefs, and vice versa, can be used as a guide in
discovering what the conditions are that we are employing.

The process of determining just what the difference is between S believing that P and S knowing that P,
therefore, involves identifying the conditions that are severally necessary and jointly sufficient to warrant a
claim to knowledge.   By "severally necessary" we mean that all the conditions we identify are required to
make some belief qualify as knowledge.   And by "jointly sufficient" we mean that when all the conditions we
identify are fulfilled, then the belief at issue qualifies as knowledge.

Among philosophers, from Plato to the present, there has been more or less complete consensus that a valid
claim to knowledge excludes three things:  

 (i) Ignorance -- if you lack the information, you cannot claim to know.

 (ii) Error -- if you are wrong about the matter, you cannot claim to know.

 (iii) Opinion -- if you have no special grounds, you cannot claim to know.

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But saying that does not really help us understand just what it is that separates a belief from knowledge.  
From the above three exclusions, all we can conclude is that in order to be knowledge, your belief must
involve the appropriate information, not be wrong, and be based on appropriate grounds.   But these limited
conclusions have been recognized from the time of Plato.   Since that time, the epistemological study of
knowledge has exploded the search for necessary and sufficient conditions into a number of more detailed
problems:

The analytic problem -- Just what are those necessary and sufficient conditions that differentiate belief
and mere opinion from knowledge?   What started initially as the whole problem as evolved into just
one part of a larger series of questions.   However, it is the analytic problem that will be the primary
focus of this essay.
The sceptical problem -- Is knowledge possible at all, in view of the sceptical challenges?   It has been
the sceptical problem that has been the impetus behind much of the development in the theory of
knowledge ever since Rene Descartes (1596-1650) and David Hume (1711-1776).   How to deal with
scepticism has motivated much of the thinking in response to the analytic problem.
The method problem -- Are there different methods of acquiring knowledge, or just one?   Can we
improve our ways of seeking knowledge?   Are there (and if there are, what are the) distinctly rational
methods of inquiry or of forming beliefs, or of forming knowledge?   I will be dealing with the three main
answers to this problem at the end of this essay.
The demarcation problem - What sorts of things might we reasonably expect to know about?   What
are the scope and limits of human knowledge?   Are there different kinds of propositional knowledge --
can we draw categorical distinctions between such things as (say) a priori versus a posteriori
knowledge?   Do the analytic/synthetic and necessary/contingent dichotomies have any meaning?  
And if so, what do they contribute to our understanding of knowledge?

In order to begin addressing these problems, it is best to present the "Traditional" theory of what knowledge
is.  

3.0 The Traditional Definition of "Knowledge"

The most widely recognized theory of knowledge is what is called the "Tri-Partite" or "Justified True Belief"
(JTB) theory.   Its first documented appearance was in Plato's Theaetetus dialogue.   All of the other theories
of what knowledge is, and most philosophical discussion of just how the other problems just described are to
be addressed, derive from the various problems and questions that surround "standard" or arch-typical
understanding of what knowledge is.

3.1 The Justified-True-Belief Model

The Traditional or "Standard" JTB theory posits three conditions that are severally necessary and jointly
sufficient for S to know that P, mirroring the three things that are almost universally recognized as being
excluded from knowledge -- ignorance, error, and opinion.   (The phrase "severally necessary and jointly
sufficient" is usually translated as "if and only if" -- abbreviated as "iff".)

  (JTB)    S knows that P iff   (1) P is true;

        (2) S believes that P; and
        (3) S is justified in believing that P.

The first condition for knowledge within the standard JTB theory is that the statement "P" itself must be true.  
This condition excludes all those beliefs that are in error.   Obviously, it is possible that I might believe some
proposition that is not in fact true.   But it would certainly be counter intuitive for me to claim to know things

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that are not in fact the case.   Or more correctly, since I undoubtedly do believe many things that are not in
fact true, it would be an improper   use of "know" for me to claim to know things that are not true.   It is
common practice to expect that for me to claim to know that London is in England, it would be necessary that
London is in fact in England.   If I were to claim to know that London is, instead in Ireland, most people would
claim that I am mistaken in my belief, and that I do not in fact know that.   If the statement is not true (in other
words, the ball is not in fact red) then we do not say "John knows" that the ball is red.   We say instead that
John merely believes that the ball is red, and that belief is not in accordance with the facts.   By the way we
commonly use the words, a belief can be false, but knowledge cannot.   However, I will have more to say
about the "Truth Condition" below.

The second condition for knowledge within the standard JTB theory is that S must believe that P is true.  
Again, it would be an improper   use of "know" for me to claim to know something that I do not believe is the
case.   The teacher is not said to "know" that one of her students gave her the apple, unless she firmly
believes that one of them did, in fact, give her the apple.   If John believes that the ball is blue, then we do
not say "John knows the ball is red", even if the ball is in fact red.   We employ the concept of "belief" here in
its stronger sense of "internalized operating basis", rather than its weaker sense of "pragmatically adopting
an unproved thesis".   Thus S must believe that P in the sense that S makes behavioural choices on the
basis that P, rather than in the sense that S merely does not dispute that P.   So if S does not believe,
accept, and operate on the basis that P, then rather than saying "S knows that P" we instead say "S accepts
that P".

The third criterion for knowledge within the standard JTB theory involves justification.   It is the role of
justification to separate knowledge from ignorance, and accident.   There are many propositions that I might
believe on a whim, that just happen to be accidentally true.   No one would accept my claim to know any of
these propositions.   Something extra is clearly required.   Not only must John believe that the ball is red, and
the ball must in fact be red, but John must be justified in his belief.   If John had no information other than his
guess that the ball is red, then regardless of the fact that the ball is indeed red, we would not say that "John
knows the ball is red".   We would instead say that John thinks the ball is red, but does not know the ball is
red.   There must be some evidence that John is aware of, some reason, some justification, to justify John's
belief that the ball is red.  

However, it is the issue of just what constitutes justification, just what this "justification" actually means, that
has occupied epistemologists at least since the time of Plato's dialogue between Socrates and Meno.   There
are many different theories of just what "justification" means in the context of the extra condition that needs
to be added to true beliefs to warrant calling them knowledge, and to successfully exclude ignorance and
accident.   Investigating the various possible alternatives for the meaning of justification, and their inevitable
consequences, will form the bulk of this essay

As a result of all of these (and other) issues, the standard JTB definition of knowledge offered above is no
longer considered an adequate definition of knowledge.   Firstly, there are some well respected theories of
knowledge that would deny that "knowing that P" involves a "justified true belief", or that it requires S to
believe that P, or that it involves anything like "justification".   I will be exploring some of the more well known
of these alternative theories later in the essay.   Secondly, even accepting the premises of the "Justified True
Belief" theory of knowledge, these three conditions as stated do not provide an adequate understanding of
just what is meant by either "true" or "justified".   Different philosophers have offered different interpretations
of both of these concepts.   And I will be exploring some of those alternatives below.   Thirdly, however
"truth" and "justification" are to be understood, there are three additional challenges that are not adequately
addressed by this simple model.   These challenges are Agrippan Scepticism, Cartesian Scepticism, and the
"Gettier Problem" (after Edmund Gettier who first explored this issue in 1963)(a).   I will deal with each of
these challenges in some detail.
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For the time being, however, we'll maintain the standard JTB model of knowledge, with all of its problems,
and examine two of its three conditions in greater detail.

3.2 The Belief Condition

I said above that it would be an improper   use of "know" for me to claim to know something that I do not
believe is the case.   And the JTB theory of knowledge is based on just that intuition.   But there have been
challenges to that intuition.   The first of these is typified by a scenario called the "Diffident Scholar".  

The diffident scholar studies some subject thoroughly, and answers exam questions on that subject correctly
-- say that the mass of the tau neutrino is 18.2 MeV.   However, because of nerves or pressure, he does not
believe that he knows the answer and thinks that he is only guessing.   The answer of 18.2 MeV "looks right",
but he can bring to mind no reasons to support that intuition.   He is guessing, but does not believe that the
mass of the tau neutrino is 18.2 MeV.   If asked, he would say that he does not believe that he gave the
correct answer.   It is argued from this example that there are adequate grounds to claim that, contrary to the
subject's own claim, he does actually know the correct answer, despite the missing belief.  

This example highlights the distinction between the first and third person sense of having reasons for one's
beliefs.   And it suggests that there are two kinds of answers as to what constitutes "good reasons" for one's
beliefs.   One can say that the diffident scholar is not in fact aware of any good reasons for his hunch about
the mass of the tau neutrino, and hence very properly does not claim to know the answer to the exam
question.   And in fact he is so bereft of reasons in support of that hunch that he does not even believe the
answer he has provided is correct.   On the other hand, we who have access to information that the diffident
scholar has forgotten, do have sufficient reasons for believing that he has provided the correct answer.   So
we can very properly claim to know that the mass of the tau neutrino is 18.2 Mev.   But can we say that the
diffident scholar actually knows the right answer even though he does not believe it, and even though he
does not have any good reasons for believing it?   Most people would say no, but some philosophers have
argued that he does.

The other way of dealing with scenarios like the diffident scholar, is to argue that belief has nothing to do with
knowledge.   Down this road we find the theories of knowledge that fall outside of the JTB family of theories.  
And I will address a few of those later.

3.3 The Truth Condition

Knowledge requires judgements -- thoughts or beliefs that can be true or false.   But that simple statement
leaves open the questions of just what that is supposed to mean.   We are looking for a state of affairs, which
can be recognized when it obtains (or recognized at least some of the time -- this is up for debate) in which S
believes that P and has good justification for believing that P but, in our view, is wrong about P.   That is how
we are able to say things like, "S thinks she knows, but she's wrong'.

In order to explore the significance of the truth condition further, we need to consider the ramifications of a
theory of knowledge that omits this truth condition.   For this hypothetical model of knowledge we would then
have --

  (JB)    S knows that P iff   (a) S believes that P; and

       (b) S is justified in believing that P.

Given the context of an investigation into the necessity of the truth condition, we can temporarily ignore any
questions relating to S believing that P, or the detailed nature of the "justification" involved.   However,
because we are ignoring the details, it does need to be made clear that the following discussion will assume
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that those details of justification that we are passing over are not so stringent that it is not logically possible
for a claim to be suitably justified and yet false.   There are some approaches to justification that demand just
such infallibility (see below).   If one does choose to adopt an "infalliblist" model of justification, then the JTB
and the JB models are logically equivalent, since "proper" justification for the belief that P would guarantee
the truth of P.   For the purposes of this section of the essay, therefore, I will assume that the justification
involved in both the JTB model and the JB model are "fallibilist.

The JTB model's truth condition is usually understood from a truth-realist perspective, where the truth of P is
evidence transcendent in an absolute sense.   However, the position of truth-anti-realism is that there is no
such thing as evidence transcendent truth.   The anti-realist truth-status of P is determined by the evidence.  
If P is beyond any evidence then its truth-status is undefined.   This might initially appear to make the truth-
condition of the JTB model superfluous, with the presumption that the evidence that dictates the anti-realist
truth-status of P would be properly contained within the details of the justification condition.   But this is
generally not so.   Both the JB and the JTB models of knowledge are specific to a single claim to knowledge.
  Only the most subjectivist (solipsistic?) of the truth-anti-realist theories would maintain that it is each
individual's evidence that dictates the truth-status of P (for S).   The rest of the truth-anti-realist theories
stipulate that it is the coherence of the evidence available (in practice, or in principle, or at some limit) to
some relevant population that dictates the truth-status of P (for that population).   So only for the most
subjectivist of truth-anti-realists would JB be logically equivalent to JTB.   For all other truth-anti-realist
theories, the truth of P will be as evidence transcendent for S as it would be for any truth-realist theorist.  
Therefore, for the purposes of this section of the essay, I will treat the truth condition in a manner neutral
between truth-realism and truth-anti-realism, while specifically excluding extreme subjectivist truth-anti-
realism.

Given that clarification of context, the first thing notable about JB as a theory of knowledge is that it perfectly
captures the point of view of S when S makes a claim to know that P.   It is usually assumed within the JTB
theory of knowledge that whether P is true or not is evidence transcendent (at least with respect to the
evidence available to S then and there).   In other words, in the JTB model of knowledge, the epistemological
status of S with regards to P does not determine the truth status of P.   Therefore, from the perspective of S,
all that S has epistemologically available is the belief that P, and any justifying rationale that P.   On that
foundation alone is based any claim by S to know that P.   The actual truth-status of P is not available to S.  
If this is the case from the perspective of S, what purpose does the truth-condition serve?   What function, if
any, does the truth condition of JTB contribute to our understanding of "knowledge" that is not satisfied by
JB?  

Suppose Alice tells me she knows that Bob is in the kitchen.   From that and JB, I can infer that Alice
believes that Bob is in the kitchen, and the Alice has judged that she has adequate justification for that belief
to qualify as knowledge.   From the JTB model I could also infer that it is true that Bob is in the kitchen.   But
what additional information have I gained from that last inference?   Especially when I must consider the fact
that whether or not Bob is in truth in the kitchen is an evidence transcendent fact for me as well as Alice.  
Alice could believe Bob is in the kitchen, and (in her judgement) have thoroughly adequate justification for
that belief, and yet never-the-less be wrong about it.   And so could I, even if I went and looked.   (It is
actually not Bob that Alice and I see in the kitchen when we look.   It is his identical twin brother Ben.   And
neither Alice nor I am aware that Bob has an identical twin brother.)   So by either definition of knowledge, if
Alice tells me Bob is in the kitchen, I am in exactly the same predicament.   Assuming that I do not go and
look for myself, I can only claim to know that Bob is in the kitchen if I trust Alice's judgement about her own
justification.   In a single person scenario, therefore, from the perspective of S, the truth condition adds
nothing meaningful to our understanding of knowledge.   I can properly claim to know only what I believe,
and judge that I have adequate justification for believing.   I, myself have no access to the truth-status of P.  
Likewise, in a two person scenario, the truth condition also adds nothing meaningful to our understanding.   I
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am fully aware that Alice can properly claim to know only what she believes, and judges that she has
adequate justification for believing.   Neither of us have access to the truth-status of P.

Which brings us to the second thing notable about JB as a definition of knowledge - it is a purely internalist
construct.   Only Alice can tell whether or not she believes that Bob is in the kitchen.   All I can do is observe
her behaviour and speech.   I can infer from these the likelihood that she believes what she tells me, but it
remains possible that she is intentionally misleading me.   I have no basis of authority from which to
challenge her claim to believe that Bob is in the kitchen.   Similarly, only Alice can judge whether or not her
justification for a claim to knowledge is sufficient or not.   I am not (under normal circumstances) party to the
details that she uses to justify her belief.   I cannot, for example, see Bob in the kitchen from my location, and
have only her claim to justify a belief that she can and does see Bob in the kitchen.   So I am forced to take
any claim by Alice to know something at face value.   I have no basis of authority from which to challenge the
adequacy of her justification.   By JB, therefore, any claim of S to know that P is necessarily infallible and
unchallengeable.  

Now, of course, this is not completely absolute.   Depending on those passed over details on the nature of
justification, it remains quite possible that for a JB claim to knowledge to be "properly" justified, Alice must be
able to offer supporting rationales that I can examine and challenge.   But again, depending on those details,
not necessarily.   If her supporting justification is perceptual evidence, for example, not being able to share
her perceptions I cannot challenge her perceptual judgements.   Barring a lengthy (and energy expensive)
conversational exploration of her supporting rationales and criteria of judgement, therefore, I am likely going
to be forced to take her word that she has the necessary sufficiency of justification.   I am not normally going
to be in a position to challenge her claim.   Which means that, in general, under a JB model of knowledge,
any claim of S to know that P must be considered infallible and unchallengeable -- in practice at least, if not
in principle.

In order to address the (more or less) unchallengeable nature of JB claims to knowledge, what the JTB
model adds is a thoroughly "externalist" condition on S's claim to know that P.   By design, it is not a
condition that S has any access to.   But it is a condition that the rest of the population can impose on S.  
This externalist nature of the truth condition only starts to make a contribution to matters when claims to
knowledge are considered in multi-party iterative over-time scenarios.   The truth-status of P, while evidence-
transcendent for any one party, is asymptotically approachable by a multitude over time (in either truth-realist
or truth-anti-realist terms).(2)

The truth-condition of the JTB model is intended to capture this asymptotically approachable limit.   The
difference between Alice's claim to know that Bob is in the kitchen therefore takes on greater significance
when considered under JTB compared to JB.   Under JTB, Alice's claim is not just that she has judged her
justification sufficient for a claim to knowledge, but she has also warranted that as the asymptotic limit of
evidence is approached by a relevant population over time, she will not be proved wrong.   This is the key
additional feature that the JTB model's truth condition adds over the JB model -- a warrant (an assurance)
that despite the fallibility of justification, the claim is none the less true, and will never be proved wrong.

While this additional warrant contributes little of meaning in one or two party single interactions, it becomes
significant under more populous and interaction-iterative scenarios.   Because under these extended
conditions, it is not just the justification of the knowledge claimant that matters, it is the coherence of the
entire accumulated body of knowledge of the population involved.   In other words, in the case of the JTB
model, not only must S believe that P, and have personally adequate justification to qualify that belief as
knowledge, but that belief must properly cohere with the entire body of knowledge of the relevant population.
  This is a significant addition because it expands the scope of justification from the claimant's personal
judgement, to the entire population's collective judgement.   By thus raising the bar of justification, it makes

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more likely that S is not ultimately proved wrong in his claim that P.   And that is where the truth-condition
pays its way.  

In the normal course of events, it might not make much difference whether Alice is ultimately proved wrong in
her claim to know that Bob is in the kitchen.   But if Alice is claiming to know behind which bush lurks the
tiger, it becomes of vital importance to the tiger's intended lunch whether she is ultimately proved wrong in
her claim or not.   Under such evolutionary survival conditions, the extra warrant that a JTB claim to
knowledge offers, over a less assured JB claim, is significant and worth having.   Under a JB claim to
knowledge, no one else who might have some input on the location of the tiger can properly raise any timely
objections to Alice's claim to know where it lurks.   Under a JB model of knowledge, Alice believes the tiger is
over there, and she judges that she has sufficient justification to qualify that belief as knowledge.   No one
else can challenge her claim without a time and energy expensive investigation of her rationales and
judgement criteria.   But under a JTB claim to knowledge, if anyone within influence of her claim has any
contradictory information, they can immediately (and much less expensively) challenge her claim to know
where the tiger lurks.   If my survival depends on the validity of that claim, if I am the tiger's intended lunch,
then I want the additional assurance that the JTB model of knowledge offers.   I want the expectation that
others will feel free to judge the accuracy of Alice's claim to know where the tiger lurks.

The difference between the JB and JTB models of knowledge is sufficiently meaningful that the English
language has provided separate words for what they define.   The JTB model defines what we call
"knowledge", and the JB model defines what we call "opinion".   Without the truth-condition, JB claims are
reduced to opinions.   One's opinions are one's opinions, infallible and unchallengeable, and whether they
are true or not is largely irrelevant.   One cannot properly challenge another's opinions as invalid, improperly
formed, or inadequately justified.   One can only challenge them as being right (true) or wrong (not-true).  
And that, of course, is an appeal to the truth-condition.   If our opinions are right (i.e. true), and suitably
justified, then we elevate their status to that of "knowledge".   We can conclude therefore, that (with the
exception of extreme subjectivist truth-anti-realists) the truth of P (in either truth-realist or truth-anti-realist
terms) is indeed necessary for S to know that P.   A claim to know that P is a freely challengeable warrant
that P will not ultimately be proved not-true.

3.4 The Justification Condition

3.4.1 The First Person versus Third Person Sense of "Justification"

In thinking about what it means for a belief to be "justified", we first need to address just what it is that is
supposed to be justified:   S's believing that P, or the proposition that P.   The former is first-person
justification (also referred to as "personal justification", or "epistemic responsibility").   If it is S's believing that
P that is justified, that means that S is aware of the grounds that justify his belief that P.   The latter is third-
person justification (also referred to as "general justification" or "epistemic grounding").   If it is P that is
justified, that means that there exists adequate grounds for a belief that P, whether or not the believer is
aware of those grounds.

In the first-person sense, for S to be justified in believing that P, S must live up to certain "epistemic
standards" of behaviour.   Epistemic responsibility is an essential component of rationality.   The point of
setting standards for epistemic responsibility is to reduce the risk of error.   For example, the subject must be
aware of some evidence that suggests that P is more likely, and must not ignore any evidence that suggests
that P is less likely.   In the first-person sense, the subject can tell whether or not he has lived up to the
appropriate epistemic standards.   In the third-person sense, S is judged by someone else to be justified in
believing that P if there exists enough supporting evidence that makes P more likely, and no defeater

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evidence that makes P less likely.   In the third-person sense, the subject cannot tell whether there exists
adequate grounds for his belief.  

The distinction is relevant because all theories of knowledge that admit that knowledge involves beliefs (as I
mentioned above, not all do) grant that there must be proper epistemic grounding (third-person sense of
justification) for the belief that P.   However, the various theories of knowledge that have been proposed can
be divided according to whether they place their emphasis on the first-person "epistemic responsibility"
sense of justification, or on the third-person "epistemic grounding" sense of justification.   Internalist theories,
like the family of Justified True Belief theories, focus on the "epistemic responsibility" sense of justification.,
and would argue that knowledge requires one to have (be aware of) good reasons for one's beliefs.  
Externalist theories, on the other hand, focus on the epistemic grounding sense of justification, often to point
of excluding entirely the first person sense.   While all justification-externalist theories would agree that for
knowledge there must be good reasons for one's beliefs, a pure externalist theory of knowledge would
maintain further that knowledge does not involve one having good reasons for one's beliefs.  

However, from the perspective of the traditional JTB model, one is epistemically responsible in believing
some proposition only if one's belief is based on having adequate evidence.   This requirement makes the
first-person sense of evidential justification in the traditional JTB model so fundamental that it tends to mask
any distinction between the two senses of justification.

So, in order to capture these two separate senses in which P can be justified, and keep the distinction clear
for the duration of the following discussion, the traditional JTB definition of knowledge really should be
expanded to:

  (JTB*)    S knows that P iff   (1) P is true;

        (2) S believes that P; and
        (3p) S is personally justified in believing that P; and
      (3g) S's belief that P is based on adequate grounding.

3.4.2 "Prior Grounding" versus "Default and Challenge"

Whether justification is considered in the first-person sense or the third person sense, there are two models
of understanding what constitutes "proper" or "adequate" or "sufficient" justification.   There is the "prior
grounding" model and the "default and challenge" model.  

The "prior grounding" model of justification demands that S be aware of (or at least have access to) the
reasons that constitute his justification for believing that P in order to validly claim to know that P.   The prior-
grounding model is therefore thoroughly internalist.

The Prior Grounding model of justification includes four mutually reinforcing principles:-

1. Evidentialism.   Grounds are evidence: propositions that count in favour of the truth of the proposition
believed.   To be knowledge, there must exist for that belief a solid epistemic grounding.   The evidence
must exist.
2. Priority Principle.   It is never epistemically responsible to believe a proposition true when the third-
person epistemic grounds for believing it true are less than adequate.   In other words, the third-person
epistemic grounding sense of justification has priority over the first-person epistemic responsibility
sense.   Regardless of the reasons you might have for claiming to know that P, your claim is not valid if

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there is not in fact good third-person grounding for that belief.   False beliefs about the evidence, the
existence of defeater evidence, or the adequacy of the evidence cannot properly count as reasons.
3. No Free Lunch.   Epistemic entitlement - personal justification - does not just accrue to us: it must be
earned by epistemically responsible behaviour.   A person fulfills his epistemic responsibility if he has
gained adequate awareness of that grounding.   You cannot properly claim to know without also
knowing the reasons that elevate your belief to knowledge.   You cannot claim to know P without also
knowing that you know P.   You cannot judge that you have adequate reasons for believing that P,
without also having adequate reasons for believing that you have adequate reasons for believing that
P.
4. Possession Principle.   For S's belief to be adequately grounded, it is not sufficient for there merely to
exist appropriate evidence for it.   Rather, S must possess (and make proper use of) sufficient evidence
to make the proposition believed (very) likely to be true.   The possession principle is the key principle
that separates the Prior Grounding model of justification from the alternative Default and Challenge
model.

A consequence of the Prior-Grounding model of justification is that any claim by S to know that P can be
subject to an open-ended challenge for the reasons S has for believing that P -- for the epistemic grounding
of which S is aware.   Since a claim to knowledge, on this model of justification, is a claim to be aware of the
adequate grounding for the belief, it is an open invitation to be asked for that grounding, and an open
promise that when asked the grounding can be provided.

The "default and challenge" model, on the other hand, takes an entirely different approach.   It grants default
warrant to some beliefs until and unless challenged.   It places the priority on epistemic responsibility, and
incorporates epistemic grounding only when, and to the extent that, the claim to know that P is specifically
challenged.   So, in terms of this model of knowledge, one does not necessarily have to have (be consciously
aware of) good reasons for one's beliefs to qualify them as knowledge.   Although the epistemic grounding
must never-the-less exist.

A consequence of the default and challenge model, and a key difference with respect to the prior grounding
model, is that you can claim to know P without also knowing that you know P.   You can judge that you have
proper default reasons for believing that P, without also being aware of all the reasons that exist for believing
that P.

From the default and challenge model of justification, in claiming knowledge we are not supposing ourselves
to have access to an impossible God's Eye view of the informational environment.   Rather, we are issuing a
strong and open-ended guarantee of the correctness of what we believe.   We are stating that we have
sufficient confidence in the truth of our belief to guarantee that we will not be eventually proved wrong.   We
are betting that there is no non-misleading counter evidence to our belief.

Consequently, from the basis of the default and challenge model of justification, a claim by S to know that P
is not subject to the same kind of an open-ended challenge as it would be under the prior grounding model.  
Under the default and challenge model, the reasons S may have for believing that P -- for the epistemic
grounding of which S is aware -- may consist of reasons why a default belief is sufficient.   Since a claim to
knowledge, on this model of justification, is a claim that a default belief is not defeated, one need be aware
only of the absence of defeaters.   It is, then, not an open invitation to be asked for the grounding of one's
belief, but merely an open promise that the grounding exists.

4 The "Gettier" Problem

It is intuitively obvious that an accidentally true belief cannot be knowledge, but it is less than obvious what
makes a belief not accidentally true.   The study of the Gettier Problem is the study of how the various
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suggested definitions of knowledge fall short of our common use of the word.

In preparing a definition for a term like "knowledge", philosophers generally employ a process that combines
a suggestion for the conditions that are individually necessary and jointly sufficient to warrant the claim to
knowledge, with a search for counter-examples where the definition is at odds with the common use of the
concept.   It turns out that it is relatively easy to compile scenarios where the definition of knowledge as a
"justified true belief" runs counter to our intuitive understanding of how we employ the concept of
"knowledge".

Edmund L. Gettier, in a 1963 article(a), argued that the JTB definition of knowledge has a serious problem.  
If we do have knowledge in ordinary cases, then we must have appropriate justification in ordinary cases.  
But then there can be cases in which we appear to have suitable justification but the proposition we believe
is only true "by coincidence" or "accidentally".   These cases will be Justified-True-Beliefs that are not
generally considered knowledge.  

4.1 The Problem

Regardless of the particular model of justification that is brought to the standard JTB theory of knowledge,
there is always the possibility that the three conditions for a "justified true belief" are satisfied, but satisfied in
a way that is not generally accepted as knowledge.   It is possible that P could be true, that S believe that P,
and that S is considered properly justified (however that is to be understood) in believing that P.   Yet the
satisfaction of these three conditions together might be totally accidental.   All the evidence (or other beliefs)
that are considered by S to support the truth of P might not be supportive of P at all.  

Edmund Gettier, along with many philosophers who have studied the problem, have framed numerous
ingenious examples.   Here is one of them.   Consider the case of Fred's Ford.   John believes that Fred
owns a Ford.   In fact, Fred does indeed own a Ford (a Ford Explorer, actually).   Yet all of the evidence that
John has that suggests to him that Fred owns a Ford, is derived from John's observations of Fred and a
particular Ford Mustang.   John concludes from the evidence that Fred owns a Ford.   But actually the
evidence equally supports the alternative that Fred has borrowed his sister's Ford Mustang.   It is generally
acknowledged that John does not actually know that Fred owns a Ford because John's belief that Fred owns
a Ford is quite unjustified.   It is just "epistemic luck" that Fred does in truth own a Ford.   Without changing
any of the justifying reasons that John has for his belief about Fred and this particular Ford Mustang, Fred
could actually not own a car at all, or might own any other kind of car besides a Ford.

Gettier scenarios in general share a few key characteristics.   In each case, a subject holds a belief that P
that the proposed scenario stipulates is well justified, yet is supposedly generally acknowledged as not
knowledge.   The justification that is described in the example strongly suggests that P is true, but is not
conclusive proof that it is, and is in fact defeated.   Each example contains the key element of luck (called, in
this context "epistemic luck").   Each case is constructed so that it is pure chance that P is true, because the
evidence that justifies the belief that P is also consistent with not-P.   The challenge that the Gettier problem
presents to the justified-true-belief definitions of knowledge is to identify the additional (fourth) factor that
must be added to a "justified true belief" to render the intuitively more correct judgement of whether the belief
in question is knowledge.

4.2 The Solutions

There have been many different attempts to "de-Gettierize" the standard Justified-True-Belief theory of
knowledge by adding what is termed a "fourth condition".   Unfortunately, despite this, the Gettier problem
remains an unresolved issue.   As each new idea has been presented to the philosophical community,
someone has come up with an alleged counter example.   Here are some of the attempted solutions:
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4.2.1 Infallibilism

Notice that the Gettier Problem only arises because we were trying to say that Fred could know that
someone owns a Ford on the basis of evidence that falls short of certainty.   If we demand that knowledge
requires absolutely certain or infallible evidence, then it would be clear why Fred is not in a position to know
that someone owns a Ford.   Fred doesn't have infallible evidence that someone owns a Ford.  

Fallibilism about the justification of knowledge acknowledges that there are ways in which belief-forming
processes can go wrong, but it accepts that these sources of error are themselves part of the normal course
of events.   The Gettier problem presupposes fallibilism about justified belief, since otherwise a belief could
not be both true and justified without being an instance of knowledge.   A Gettier example is a belief which,
even though it is justified, is lucky to be true, in the same way that an unjustified belief is lucky to be true.  
For example, it is not out of the ordinary to misremember that one left one's glasses on one's desk rather
than on the sink.   But it is rather extraordinary both to misremember this and to be right about their
whereabouts anyway, because someone moved them from the sink to the desk.  

For justified beliefs, error is normal as compared to accidental truth.   Most of our beliefs are not knowledge.  
Short of being knowledge, justified beliefs are more likely to be false than to be accidentally true.   An
ordinary justified false belief is unlucky not to be true because it has what it normally takes to be true.   One
is steered wrong on grounds of the same sort on which one is normally steered right.   In a Gettier situation
the justification, though adequate, is defeated.

However, infallibilism, as a solution to the Gettier problem, limits the concept of "knowledge" to those beliefs
for which we have sufficient evidence to rule out any logically possible alternative.   Since neither induction
(generalization from a series of examples) nor abduction (inference to the best explanation) can give rise to
inferences with sufficient certainty for this approach, infallibilism limits valid claims to knowledge to beliefs
arrived at by deductive inference.  

However, most of our beliefs are formed on the basis of induction or abduction (or perhaps directly from our
sensory experiences).   Hence, most normal knowledge claims (assuming they are valid cases of knowledge)
are only defeasibly justified, although their justifications are not in fact defeated.   As a matter of contingent
fact and normally acceptable common usage, our justifying reasons for claiming knowledge are usually far
from sufficient to rule out any logically possible alternative.   Most of the time our justifying reasons are just
barely sufficient to rule out the more likely alternatives.  

The problem with infallibilism is that it rules out most of what we normally refer to as knowledge.   Infallibilism
is implausibly restrictive, therefore, because it entails that beliefs which are less than maximally justified do
not qualify as knowledge.   While it should be noted in passing that one response to an offered Gettier
example is to deny the premise that the belief in question is in fact properly to be called knowledge,
infallibilism is so at odds with the generally accepted usage of the term "knowledge" that it is no longer a
seriously proposed solution.  

4.2.2 Defeasible Evidence

This approach demands that the evidence the subject draws upon to justify his belief that P not be opposed
by any evidence to the contrary.   There are two degrees of this approach, reflecting the first and third
persons sense of justification.   The weaker condition is that the subject himself cannot be aware of any
defeating evidence -- the first-person epistemic responsibility sense of justification.   However, it is unclear
that this approach will resolve many of the proposed Gettier examples.   In the example cited above, John is
not aware of any evidence that might defeat his belief that Fred owns a Ford.   Yet it is generally accepted
that in this case John does not know that Fred owns a Ford.  
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The stronger variant of this approach is that there must not exist any defeating evidence, whether or not the
subject is aware of it -- the third-person epistemic grounding sense of justification.   This would resolve the
case of Fred's Ford.   But there have been counter examples designed for this suggestion.   Consider what
has been called the "Assassination" scenario.  

Jill reads in her favourite newspaper that the president of her country has been assassinated.   In fact, this
story is true.   However, the president's associates have mounted a campaign to suppress the story, and
they've been broadcasting false reports on all the television stations that the president is OK, the assassin
actually only killed a bodyguard.   Jill is blissfully unaware of all this misleading evidence.   The newspaper
she read happens to be the only news source that's reporting the true events.   All of Jill's peers, on the other
hand, have heard the misleading TV reports and aren't sure whether or not the president was really killed.   It
is suggested that Jill has a justified true belief that the president was assassinated, but she doesn't have
knowledge, because there is all this misleading evidence abroad in her community, which she has only
managed to avoid by sheer luck.

There is no valid evidence that does in fact defeat Jill's belief, but there is a lot of false evidence that, if
believed, would be considered defeating.   So even though there is in fact no defeating evidence, the
presence of the false evidence is supposedly sufficient to withhold the label of knowledge.   Most
philosophers would agree that in this scenario, Jill does not in fact know that the President has been
assassinated.   Such examples demonstrate that this approach, while promising, is not a complete solution.

4.2.3 No False Inference

This approach demands that S include no false inferences when justifying a belief that P.   In the example of
Fred's Ford, John employs the false inference that the Ford Mustang that all his evidence is about actually
belongs to Fred.   But like all other proposed Gettier solutions, counter-examples have been offered for this
one as well.   The Assassination scenario offered above is one of them   Jill does not employ any false
inferences in supporting her belief, yet it is generally agreed that she does not know that the president has
been assassinated.   Consider also the "Barn County" scenario.(3)

Suppose there is a county in the Midwest with the following peculiar feature.   The landscape next to the road
leading through that county is peppered with barn-facades: structures that from the road look exactly like
barns.   Observation from any other viewpoint would immediately reveal these structures to be fakes: devices
erected for the purpose of fooling unsuspecting motorists into believing in the presence of barns.   Suppose
Henry is driving along the road that leads through Barn County.   Naturally, he will on numerous occasions
form a false belief in the presence of a barn-facade.   Since Henry has no reason to suspect that he is the
victim of organized deception, his belief that these facades are barns is justified -- they do look just like
barns.   Now suppose further that, on one of those occasions when he believes he is looking at a barn, he
happens to be looking at the one and only real barn in the county.   This time, his belief is justified, and true,
and not based on any false inference.   But its truth is the result of epistemic luck, and thus his belief is not
generally accepted as an instance of knowledge.   So the No-False-Inference approach can be defeated.

4.2.4 Contextual Decomposition

There is, however, a variation of the No-False-Inference approach that I believe is proof against counter-
examples.   It focuses on context specific judgements about the knowledge claim.   Examine S's belief that P
and focus on the concepts that S employs rather than the words used to describe the scenario.   If one then
decomposes S's belief that P into S's "atomic beliefs" (which is easily doable from the context provided by
each example), then it seems to me that either S's false inference becomes obvious, or it becomes obvious

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that we are mixing S's first-person judgement about the knowledge claim with our own more informationally
rich third-person judgement about that claim.

In the case of Fred's Ford, John's belief is based on a lot of evidence having to do with a Ford Mustang.   To
decompose this belief into its conceptual context is to render it as "Fred owns that particular Ford Mustang
for which I have all this evidence".   John's belief that Fred owns a Ford is not the basic belief for which John
has al his evidence.   It is rather a derived belief -- derived from the belief about Fred and that Ford Mustang.
  (And in fact, it is derived on the basis of the Epistemic Closure Principle -- a principle that we will see later
does not actually hold for knowledge.)   It is clear from this contextual decomposition, therefore, that John is
falsely inferring that Fred owns the Mustang.  

In the case of Barn County, the knowledge claim that is offered in the scenario is Henry's "I see a barn".   But
conceptual decomposition renders this as either Henry's "What I see over there is a barn" or our own "What
Henry sees over there is a barn".   In the former case, I would actually disagree with Goldman.   It is true that
there is some potentially defeating information available "out there" that Henry is unaware of.   But does this
render unacceptable his judgement that his belief is sufficiently justified to qualify as knowledge?   I think not.
  I think that Henry can validly claim to knowin this case that what he is looking at is a barn.   He has
adequately fulfilled his epistemic responsibility, and there does exist adequate grounds to justify his belief.  
Of course, where he was looking at a barn-facade, he cannot validly claim to know it is a barn he is seeing,
because it is not a barn.  

On the other hand, if we treat the questionable knowledge claim as our own "What Henry sees over there is
a barn", however, I think it is obvious that the answer comes down the other way.   We can not properly claim
this as knowledge because we are in possession of the defeating additional information about the existence
of barn-facades.   We can further conclude that in our own judgement, on the basis of our additional
knowledge, Henry's belief is not knowledge.   Even though we can admit that from Henry's context, his
knowledge claim is valid and proper.

The assassination scenario is handled the say way as the barn county scenario.   If we are discussing Jill's
claim to knowledge, then I disagree with the general position that the false and misleading counter evidence
negates Jill's claim to knowledge.   She is not aware of that false evidence, and thus does indeed have
adequate justification for her claim to knowledge.   But we, who are aware of that false and misleading
evidence, cannot claim to know that the president has been assassinated.   Contextually, there is a
fundamental difference between first-person knowledge judgements and third-person knowledge
judgements.  

This distinction between perspectives highlights the fact that knowledge claims involve a judgement and a
confidence scale for belief.   Henry is sufficiently confident in his belief (because he believes he has sufficient
justification and is not aware of the counter evidence) that he claims to know it is a barn.   Jill is sufficiently
confident in her belief (because she believes she has sufficient justification, and is not aware of the
misleading false counter evidence) that she claims to know the president has been assassinated.   And from
their first-person contexts, their claims are right and proper.   We, on the other hand, in possession of more
information, see that their confidence is misplaced and properly conclude that they do not know what it is
they claim to know.   And from our third-person contexts, our claims are right and proper.   If knowledge
claims are seen as context sensitive, not absolutely objective as most philosophers would insist, then we can
conclude that Henry and Jill and we can all be correct in our respective judgements while contradicting each
other.

(To see how Contextual Decomposition treats other Gettier and similar scenarios, click on Gettier Cases.)

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The no-false-belief approach, if combined with an internalist conception of justification (without contextual
decomposition), can easily suffer from "creeping scepticism".   The scepticism arises because it is never
clear from the inside when some particular supporting belief we are using in the justification of our belief that
P is actually or even likely false.   We are none of us infallible.   At any given time, it is always possible that
some of our beliefs are in fact false.   If that is the case, then it is possible that we don't know what we think
we do.   Contextual decomposition prevents this creep to scepticism by making it clear, even to the subject,
which belief is the unjustified one.  

The no-false-belief approach combined with an externalist conception of justification (without contextual
decomposition), quickly devolves into the next offered solution.

4.2.5 Global Justification Externalism

Like the strong defeasible evidence variant mentioned above in Section 4.2.2, this approach demands that
there must not exist any defeating evidence, and considers it irrelevant whether or not the subject is aware of
it.   But it goes further than the defeasible evidence approach by examining all the potential evidence
(practically available or not) and considers how that evidence impacts the third-person (God's Eye) process
of justification.   This approach nicely deals with all of the Gettier examples because it considers, from a
global omniscience perspective, all of the evidence provided in those scenarios.  

The problem that this approach faces is that it makes the concept of knowledge something that is
determinable only externally by an omniscient intellect, or at least by an outside observer.   It provides no
guidance to us fallible and limited individual knowers on whether any claim to knowledge is properly justified.
  Like with the strong version of defeasible evidence, global justification externalism is at odds with many
philosophers' preference for the alternative of justification internalism.

4.2.6 Causal Chain

This approach demands that the subject's belief that P be caused in "an appropriate way" by the fact that P.  
Furthermore, the subject's justification for the belief must include the logic by which the truth of P caused the
belief that P.   This nicely rules out all of those Gettier examples where the truth of P is not the cause of the
subject's belief that P.   In the example of Fred's Ford, John's belief that Fred owns a Ford is not caused by
the fact that Fred owns a Ford Explorer.   But it remains vulnerable to examples where the causal chain is
intact, but there is actual or false defeater evidence available -- like the assassination or barn county
examples.   In such scenarios, the belief that P is suitably caused by the fact that P, but the real or false
defeater evidence is not provided a role.

The additional challenge faced by this theory, is that it is difficult to specify exactly how the truth of P can
cause a belief that P without recourse to the very concept of knowledge that is being defined.   So this
approach also is demonstrated to be less than satisfying.

4.2.7 Reliablism

This is perhaps the most popular of the alternatives to the standard conception of knowledge as an
intellectual exercise.   Reliablism is the thesis that propositional knowledge consists of a true belief that is
arrived at through some reliable (albeit fallible) process.   It is an externalist theory because the subject is not
in a position to determine whether the processes involved are reliable.   Although the approach can be
somewhat internalized by considering our beliefs about the reliability of our belief-forming processes.  

The advantage of reliablism as an approach to the Gettier problems, is that a reliable process need be only
more reliable than not.   The Reliablist approach takes Fallibilism seriously, responding to the Gettier

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Problem by simply accepting a certain low-level rate of errors.   A reliablist conception of knowledge permits
subjects to err in their claims to knowledge.   Jill and Henry may properly claim to know about assassinations
and barns, and yet be mistaken in their claims.   We, with more information, can reach a different reliable
conclusion.   Likewise, our common employment of the concept of "knowledge" need not be totally precise.  
We need only be more correct than not.   So instances of an incorrect granting or withholding of the warrant
of "knowledge" can be quite acceptable as long as it is not too often.   A definition consisting of necessary
and sufficient conditions to properly cover all conceivable scenarios is not required.   Some slack is tolerable,
and unlikely Gettier counter-examples can be ignored.

5.0 The "Sceptical" Problem

In addition to the Gettier Problem described above, the traditional JTB definition of knowledge suffers from
the problem of scepticism.   The fundamental claim of Scepticism is that there is nothing contradictory in the
suggestion that our belief that P may be well and properly justified, yet P might none-the-less be false.   In
the standard understanding of the JTB definition of knowledge, there is a gap between justified belief and
truth (assuming a fallibilist understanding of justification).   The sceptic claims that this gap cannot be bridged
and that therefore none of our beliefs are sufficiently justified to qualify as knowledge.  

5.1 Kinds of Sceptical Challenges

Sceptical challenges to the JTB theory of knowledge comes in various forms --

Local versus Global.   While granting that knowledge is possible in other areas, the local sceptic brings
to the discussion particular arguments that purport to show that knowledge in some restricted field is
impossible.   The typical example is that of moral or ethical knowledge.   Within the restricted field, the
sceptic claims that there exist no epistemic grounds to justify any beliefs as knowledge because there
are no facts of the matter to function as grounds.   Hence the moral sceptic will claim that there are no
moral facts of the matter.   Global scepticism takes this position as a general one.   A global sceptic
denies that there are such things as "facts of the matter", and hence that knowledge is impossible in
principle.   Global scepticism is the greater threat to the standard JTB theory of knowledge because of
its claim that we can never achieve sufficient justification for the warrant of knowledge.   It is always
possible that P might be false.
Evidential Standards.   Some sceptical arguments maintain that while knowledge is theoretically
possible, it is not in practice possible.   Such sceptical arguments maintain that the standards for
evidential support or justification for any claim to knowledge is so high that in practice it is impossible to
satisfy.   And hence in practice knowledge is impossible to obtain.   Such sceptics maintain that our
claims to practical knowledge are like our claims that something is "round".   A circle is a mathematical
concept that is never obtainable in practice.   No matter how finely we grind the ball, it will inevitably
depart from the mathematical ideal of "round" to some extent.   "Knowledge" then is an "error claim" -- a
claim that is not in fact ever true in practice, but is accepted as "true enough" in some practical
circumstances.
Understanding.   Most sceptical arguments attempt to deprive us of knowledge while still allowing that
we understand the truth of the propositions that we are no longer allowed to know.   Other sceptical
arguments challenge the very notion that we can even understand those propositions.   They maintain
that the reason we do not know whether these propositions are true is because we do not understand
what these propositions mean.  

The universe of sceptical arguments can also be divided along more historical lines.   The early sceptical
arguments drew upon what is now generally called "Agrippan Scepticism".   The more recent sceptical
arguments draw upon what is now generally called "Cartesian Scepticism" or "Brain-in-a-Vat Scepticism".

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5.2 Agrippan Scepticism

This form of sceptical challenge is known as Agrippan (or Ancient Greek) Scepticism after the Five Modes of
Agrippa identified by Sextus Empiricus.(4)  

Most theories of knowledge, like the JTB family of theories, are classed as "internalist" because their concept
of justification is based solely or primarily on things that are directly available to the knower.   Internalist
theories of knowledge and justification focus on the way we employ reasons to support conclusions from the
evidence.   When you list all the reasons you believe justify your belief that P, what you are listing is other
beliefs, along with the associated second-order beliefs that the supporting evidence actually does imply P, or
make P more probable.  

However, if your knowledge is justified on the basis of other beliefs, and those are in turn justified based on
further beliefs, it is easy to see that an infinite regress quickly develops.   A similar infinite regress occurs with
the second-order beliefs that the evidence supports the likelihood of P.   The sceptical challenge is that when
asked to provide the reasons that justify any particular belief, you have only one of three options:

1)  Keep providing some new supporting reason -- i.e. embark on an infinite regress of reasons;  
or

2)   At some point, repeat yourself -- i.e. reason in a circle; or

3)   At some point give up, and fall back on some basic dogmatic (and hence unjustified)
assumption.

The Agrippan Sceptic argues that none of these three alternatives is acceptable as a proper justification for
your beliefs.   Therefore, none of your beliefs are justified.   Hence knowledge (conceived as justified true
belief) is impossible to attain.

The two most well known alternatives within the family of JTB theories of knowledge and justification are
distinguished by how they attempt to resolve this challenge of Agrippan Skepticism.   Foundationalism
responds to the Agrippan sceptic by adopting the premise that there are some "foundational" beliefs that are
non-inferentially justified -- intrinsically credible by virtue of the kind of belief they are.   Foundationalism
therefore argues that Agrippa missed one alternative on that list of three -- that there are beliefs that are not
justified by other beliefs.  

Coherentism, on the other hand, responds to the Agrippan sceptic by adopting the premise that beliefs can
be mutually supporting.   Coherentism argues that reasoning in a circle does not have to be circular
reasoning.   Coherentism is justification internalism without foundational beliefs.   The hypothesis is that
one's belief that P is justified if and only if one's belief that P coheres with the rest of what one believes.  
Unlike foundationalism, the coherence concept of justification is holistic rather than linear or hierarchical.

I will expand on both of these theories of knowledge once I have discussed Cartesian Scepticism.

5.3 Cartesian Scepticism

5.3.1 An Overview

This is a very famous radical sceptical challenge to knowledge.   It is known by various names.   Most
famously it is called "Cartesian Scepticism", after Rene Descartes who initiated modern sceptical thought
with his "method of doubt".   He hypothesized that for all he knew, all of his experiences might be deceptions
provided by an evil demon.   More recently, drawing upon the popularity of science fiction and technology,
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Descartes' evil demon has been replaced by evil scientists or ingenious aliens who steal your brain and place
it in a vat of nutrients.   In this scenario all of your experiences are provided by a super computer wired to the
sensory nerves of your brain.   By hypothesis, no experience that we might possibly have can discern
whether or not we are a brain in a vat.   (Star Trek episodes and the Matrix trilogy of movies have
popularized this scenario.)   Hence the popular name for this kind of scepticism is "The Brain-in-a-Vat
Argument".   It is also known as "The Problem of Under-Determination" or "The Problem of the External
World".  

The sceptic argues that all of our beliefs about the existence of an external world are unjustified because all
of the evidence (perceptual experience) we have in support of those beliefs cannot rule out the sceptical
alternative that we are a brain in a vat or being deceived by Rene Descartes demon.   All of our experiences
are fully compatible with both the hypothesis of an external world and the sceptical alternative that we are but
a brain in a vat.   Hence our beliefs about the external world are unjustified.   And since all our beliefs about
the external world are unjustified, none can qualify for the honour of "knowledge".

In detail, these arguments can be group into three general approaches:

1. Argument from Error:  We have been known to make errors in similar situations.   So it is always
possible that we might be making an error this time as well.   Even in unique situations, it is always
logically possible that things are not as they seem.   Our knowledge claims are always inductive in
nature.   More evidence might undermine the justification of our beliefs.   This kind of sceptical
challenge demands if not total infallibilism then at least less-than-usual fallibilism about knowledge.   It
claims that justificatory standards cannot be so high as to eliminate the possibility that we are in error.  
If they are raised high enough to eliminate error, then you are reduced to infallibilism.   If they are low
enough to allow most usual claims to knowledge, then they are not immune from error.   Hence we
cannot properly claim to know anything.  
2. Argument from Dreams:  This is the argument made famous by Descartes.   It is always possible, it is
argued, that we could be dreaming, hallucinating, or under the control of an "Evil Demon".   Or be a
"Brain in a Vat".   The sceptic argues that his alternative hypothesis is as likely to be true as what we
ordinarily believe.   All of the available evidence is equally consistent with either alternative.   And no
amount of information about the course of experience will ever logically entail that the world is one way
rather than another.   Therefore, none of the evidence we bring to bear as justification for our beliefs is
sufficient to rule out the possibility that we are dreaming or are a brain in a vat.   None of our beliefs are
sufficiently justified to warrant a claim to knowledge.   Hence we cannot properly claim to know
anything.
3. Argument from Under-Determination:  All our reasoning is based on the hypothesis that the future will
be like the past.   (Or, alternatively, that Nature is consistent.)   As Hume famously pointed out(5), there
is no justification for this hypothesis.   I only have reason to believe that my experiences make some
proposition probable if I have reason to believe quite generally that events which I have not observed
were similar (or are going to be similar) to events which I have observed.   Hume's point is that it is
impossible to have any reason for this last belief without assuming the belief as a premise.

Note that these challenges are not directed against justified beliefs.   It is, rather, a claim that our beliefs can
be justified and yet still not qualify as knowledge.   The Cartesian sceptical challenge is based on the
premise of metaphysical realism.   How things are (truth) may be different from how they seem (perception).  
The sceptic concludes that no one is ever sufficiently justified in their beliefs to warrant the honorific of
knowledge, so knowledge is not possible.   This conclusion applies to personal justification (first-person
justification, epistemic responsibility) as well as general justification (third-person, adequate grounding).  

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However, it needs to be emphasized that the sceptic's arguments only show that there are limits to our
abilities to give reasons or cite evidence.   Cartesian Scepticism is an argument about adequate grounding.  
To get from what he argues to what he concludes, the sceptic needs to assume the prior grounding model of
justification -- that no belief is responsibly held unless it is based on citable evidence.   More precisely, he
needs the dependence principle of the prior grounding model of justification to link epistemic responsibility
with adequate grounding.   And he needs strong justification internalism to identify grounding with the ability
to cite the evidence.   It is the Cartesian Sceptic's claim that no amount of epistemological responsibility can
guarantee adequate epistemological grounding.  

Be that as it may, the various externalist, non-JTB theories of knowledge and justification owe their genesis
to different notions of how to counter the kinds of sceptical arguments presented by Cartesian Scepticism.  
These theories, like reliablism and the causal theory, posit direct links between knowledge and epistemic
grounding, bypassing the first-person sense of justification that is epistemic responsibility.

But before exploring some of the alternatives to the traditional JTB theory of knowledge, I need to explore the
"Brain in a Vat" argument in greater detail.   The form of the argument, and the premises upon which it is
based, will provide important input into the following discussions of the various alternatives theories of
knowledge.

5.3.2 The "Brain in a Vat" Argument

(i)    If I am a Brain in a Vat, then I do not have two hands.

(ii)   I cannot tell whether or not I am a Brain in a Vat.
(iii)  Therefore, I can not know that I am not a Brain in a Vat.
(iv)  Therefore, I can not know that I have two hands.

This sceptical argument depends for its impact on its apparent paradox -- the argument seems intuitively
reasonable, yet at the same time intuitively false.   It seems quite obvious that we do in fact have a lot of
knowledge about the external world.   It seems quite unproblematic for me to claim to know that I have two
hands.   Yet it also seems obvious that the sceptical argument is at least comprehensible.   Once the
possibility is pointed out, it seems quite reasonable and unproblematic to suppose that I can't in fact know
that I am not a brain in a vat.   And it also seems reasonable to conclude from this that I therefore don't know
what I think I know -- that I have two hands.   To see where the problem lies, we need to examine the
argument in greater depth.  

In order to be comprehensible, the short-form argument provided above requires the necessary addition of a
number of premises that are normally hidden.   Some of these are rather obvious additions required to turn
the argument into a valid deductive format.   But some of these necessary additional premises are well
buried.   Both the obvious and hidden missing premises open up opportunities for responding to the sceptic,
either by negating his argument or by demonstrating that his argument is incoherent.   Making clear what
these unmentioned premises are makes clear that the sceptical argument is not as intuitively reasonable as
first supposed.   Thus, at the very least, dissolving the apparent paradox.

To begin with, a more formally framed version of the Brain-in-a-Vat argument proceeds as follows:

(BIV)   (a)   If      (I know things about the external world), and  
         (I know that knowing things about the external world implies that I am
not a BIV),
    then  (I know that I am not a BIV).  [Closure Principle]
  (b)   Things may not really be as they appear.

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    (c)   Despite appearances, I may really be a BIV.   [From (b)]

  (d)   I cannot prove, and hence I do not know, that I am not a BIV.  [From (c)]
  Thus    
    (e)   I do not know things about the external world.  [From (a) and (d)]

Now let's explore some of the implications of the necessary missing premises -

(1)   Things may not be as they appear.  This is the basic Cartesian sceptical premise of
metaphysical realism.   This premise is necessary in order to separate the way that things appear
from the way that things are in fact.   If there is no such separation (metaphysical idealism), then I
could prove that I am not a BIV by simply observing that it does not appear to me that I am a BIV.
  In order for the sceptical argument to have any force, therefore, it must assume that it is possible
that I might in truth be a BIV despite the fact that it does not appear to me that I am.   "Folk"
philosophy comes freighted with the baggage of Cartesian mind/body dualism, so it is natural for
us to expect that there is a gap between how our minds "see" things, and how they really are.  
Hence, from the perspective of folk philosophy, it is quite intuitively acceptable that things may not
be as they appear.  

One way to challenge the BIV argument, therefore, is the adoption of either metaphysical idealism or a direct
realist theory of perception.   Both alternatives would deny the Cartesian premise that things might not be as
they appear.   Another way to mount the same sort of challenge is the alternative of an (extreme) anti-realist
conception of truth.   Truth-anti-realism (when taken to the extreme) would also deny the premise that things
might not be as they appear.

(2)   An infallibilist model of knowledge.  In order to move from the mere suggestion of the BIV
alternative to the conclusion that I therefore do not know (because I cannot prove) that I am not a
BIV, the sceptical reasoning must demand that my justification for my beliefs about whether or not
I am a BIV rule out all potential defeaters, including the BIV hypothesis.   In other words, the BIV
argument is based on the assumption that the justification required to make my belief (that I am
not a BIV) into knowledge must be much closer to being infallible than usually expected.   This
infallibilist premise is reinforced by the particular form in which I expanded the BIV argument
above.   The expanded version asserts the premise that "I cannot prove that I am not a brain in a
vat".   Employing the word "prove" reinforces the presumption of infallibilism, since "prove" in
contexts such as this is usually understood to imply something like "logical proof", or "deductive
proof" -- a sense of guaranteeing the truth of, rather than simply providing evidence in support of.
  This is nicely consistent with the common "folk philosophy" understanding of knowledge as a
belief about which we are "certain".   Hence the infallibist assumption appears quite reasonable
and is usually not recognized for what it is.  

The way to challenge the BIV argument here is the alternative of a fallibilist conception of knowledge.   A
fallibilist conception of knowledge would allow that I could know a lot of things about the external world
because those beliefs are adequately justified, and yet never-the-less that justification might be mistaken
about the truth of those beliefs.   The justification required for my beliefs to qualify for the honorific
"knowledge" would not have to rule out all logically possible alternatives.   The process of justification could
permit some errors.   It is possible (if I am indeed a BIV) that I do not in fact know anything about the external
world.   But the fact that I cannot prove that I am not a BIV is not a defeater for any of my claims to have such
knowledge.   Fallibilism draws upon the distinction between a first-person (internal, epistemic responsibility)
view of justification, and a third-person (external or God's Eye", adequate grounding) view of justification.

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(3) A foundationalist model of knowledge.  The BIV argument is based on the premise that
knowledge is to be understood from a foundationalist perspective.   The reasoning is based on
the premise that experiential awareness of perceptual evidence has some form of intrinsic
epistemic priority.   The justification necessary to elevate beliefs into knowledge has to be
fundamentally based on perceptual knowledge, not on other beliefs.   Otherwise, the required
possibility that things might not be as they appear would have no epistemic weight.   On some
alternative theories of knowledge, my belief that I am not a BIV (and my beliefs about the external
world) would be sufficiently justified (proven) by the coherence of a set of beliefs.   Similarly for
the various externalist models of knowledge, my beliefs about the external world could qualify as
knowledge without my even considering the BIV alternative -- let alone proving that I am not a
BIV.   But we are all intuitive empiricists, so we naturally feel quite comfortable with the
assumption that perceptual/evidentiary propositions have some special epistemic status -- the
basis of foundationalism.  

As a result, any of the non-foundationalist models of knowledge would provide a way to challenge the BIV
argument.   As a matter of historical fact, they have been specifically constructed to do so.   The two most
well-known are also members of the JTB family of theories -- Coherentism and Contextualism.

(4) A prior grounding model of justification.  As a consequence of the premises that assume that
knowledge demands an infallible foundationalist justification of one's beliefs, the BIV argument
can also be seen to require the "prior grounding" model of justification.   The BIV argument
demands that the subject be aware of the "proof" that infallibly justifies the belief that one is not a
BIV before allowing that one knows that one is not a BIV.   The sceptic cannot admit either (a) the
possibility that I might in fact be appropriately justified and yet not be aware of that fact; or (b) the
possibility that some of my beliefs about the external world might be default justified.   Otherwise,
I might properly be said to know that I am not a BIV without being able to prove it.   When folk
philosophy thinks about "knowledge", it normally thinks in terms of asking and giving reasons for
one's beliefs.   So it is natural to fee comfortable with a "prior grounding" model of justification.  
Knowing that one is not a BIV is usually understood to mean having good reasons for believing
that one is not a BIV.   Which, of course, the BIV argument denies is possible ex hypothesi.

There are two kinds of alternative way of challenging the BIV argument here, or rather two ways in which one
can adopt a non-prior-grounding model of justification.   One is to adopt an externalist theory of knowledge
that denies that knowledge involves justification at all (such as pure reliablism, a causal theory, or Nozick's
truth-tracking theory).   The other option is to adopt the "default and challenge" model of justification (as is
incorporated in the contextualist theory of knowledge, for example).   From this latter alternative, I am prima
facie justified in believing all sorts of things about the external world until and unless the sceptic can provide
a context that challenges that default justification.   Since the mere mention of the BIV alternative does not
provide the necessary context, the burden is shifted to the sceptic to provide justification for believing the BIV
alternative.   With a default prima facie justification in play, it is irrelevant that I cannot prove that I am not a
BIV.

(5)   Knowledge is closed under known entailment.   This is the "epistemic closure principle"
employed in step (a).   This is a complex topic in itself, and I will explore this premise in much
further detail in the next section of this essay.

When the hidden premises behind the apparent intuitive reasonableness of the sceptic's argument are made
clear, it becomes obvious that the BIV argument relies for its comprehensibility on a concatenation of highly
questionable premises about the nature of knowledge.   Each of those premises has been challenged by
criticisms presented by many philosophers.   There are numerous theories of knowledge available in the

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literature that provide alternatives for each premise.   While the image of "knowledge" that underlies the
seeming reasonableness of the BIV sceptical argument might be recognized as the "traditional" or
"paradigmatic" JTB theory, for many reasons, some of which we have seen already, it is no longer
considered the "best" model of knowledge available.

5.3.3 The "Epistemic Closure Principle"

The "closure principle" or the "principle of known entailment" (or known implication) when applied to
knowledge posits that -

If     (1) S knows that P

and  (2) S knows that P entails (implies) Q
then (3) S knows that Q.

It is easy to see the intuitive appeal of this principle.   If I know that this tomato is red, and I know that a red
tomato implies that it is ripe, then I know that this tomato is ripe.   If John knows that Fred owns this particular
Ford Mustang, and John knows that this implies that Fred owns a Ford, then John knows that Fred owns a
Ford.   Logical implication is a form of deductive argument.   And as such, given true premises it guarantees
that the conclusion is also true.   So -

If      (1) if it is true that P

and   (2) it is true that P entails (implies) Q
then  (3) it is guaranteed to be true that Q.

This seems to be a ery good justification for believing that Q.   We use reasoning of this sort all the time.  
Thus it is reasonable to assume that for a "Justified True Belief" model of knowledge, the principle of known
implication is simply documenting the fact that logical entailment, a deductive argument generally, is a
sufficient reason for justifying the conclusion.   This is perhaps easier to see if we focus in on the justification
aspect of knowing.   A more interesting variation of the closure principle (for reasons you will see in a
moment) is whether justified belief is closed under known implication.   In this form, the "closure principle"
posits that -

If      (1) S has a justified belief that P

and   (2) S has a justified belief that P entails (implies) Q
then  (3) S is justified in believing that Q.

Or alternatively, drawing upon the JTB definition of knowledge one can, without losing the sense of the
above, mix the two forms as -

If      (1) S knows that P

and   (2) S knows that P entails (implies) Q
then  (3) S is justified in believing that Q.

And it really seems quite counter intuitive to not believe something that one is fully justified in believing.  
When phrased in terms of justified beliefs, it would initially seem as if all of the JTB theories of knowledge
would have to agree that justified belief is indeed closed under known entailment.  

For the externalist alternatives to the JTB family of theories, however, the situation is a little more complex.  
For each particular theory it would depend on whether or not logical entailment is encompassed within the
details of whatever reliable, causative, or law-like connection might be posited.   Nozick's "truth tracking" or
"subjunctive conditional" theory of knowledge is, however, an example of an externalist theory of knowledge

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that would specifically deny that justified belief is closed under known implication -- mostly because Nozick's
theory does not treat knowledge as a question of a belief justified by other beliefs.

The closure principle has gained its significance because of its employment in the Brain-In-a-Vat   arguments
of Cartesian Scepticism as described above in the previous section.   In order to reason from the very
reasonable sounding premise (BIV-d) that "I cannot prove that I am not a BIV" to the problematic conclusion
(BIV-e) that "I do not know that I have two hands", the sceptic is drawing upon premise (BIV-a) that
knowledge is closed under known implication.   The sceptic depends upon a modus tollens deductive
argument that proceeds from the premise "I know that P" (I know that I have two hands) through the closure
principle (if I know that P, and I know that P implies Q, then I know that Q), to the interim conclusion "I know
that Q" (I know that I am not a BIV), and then denying this interim conclusion (I do not know that I am not a
BIV) to reach the ultimate objective of denying P (I do not know that I have two hands).   We are all familiar
with deductive reasoning, and the closure principle for knowledge seems to be a simple matter of deductive
logic and therefore seems obviously true.

Unfortunately for the Cartesian sceptic, and fortunately for we who know that we have two hands, the closure
principle does not in fact hold as a matter of necessity for most theories of knowledge.   So the Brain-in-a-Vat
argument fails at step (BIV-a).   And John's reasoning from his basic belief about Fred and a certain Ford
Mustang, to a less specific belief about Fred and Fords generally, also fails.   Even if the closure principle is
framed instead in terms of justified belief, then it is step (BIV-d) that trips up the sceptic.   In terms of justified
belief, step (BIV-d) would have to be phrased as "I do not have a justified belief that I am not a BIV".   But of
course, it is now obvious that I do indeed have a very well justified belief that I am not a BIV.   My belief might
in fact be false (if the sceptic's hypothesis is true and I am indeed a BIV).   But I none-the-less have a
justified belief that I am not a BIV.   Its not an infallibly justified belief, but it is a well justified none-the-less.

There are two reasons why the closure principle fails for knowledge.   The first is the question of belief, and
the second is the question of justification.   Given the traditional JTB definition of knowledge, it is obvious that
with the closure principle, the truth condition is satisfied.   It is stipulated that P is true.   And the deductive
reasoning of logical implication appears to ensure that Q is true.   But it is the belief condition in the JTB
concept of knowledge that trips matters up.   Knowledge as a justified true belief is not closed under known
implication because belief is not necessarily closed under known implication.   Assuredly it often is closed as
a matter of contingent fact.   We do often believe what we have adequate justification to believe.   We even
often believe what we do not have adequate justification to believe.   But it is also entirely possible that I
might know that P, and know that P implies Q and yet not believe (for whatever reason) that Q.   Perhaps I
also believe (falsely) that Q is inconsistent with some other (also possibly false) beliefs that I hold.   Or
perhaps I have just been cognitively lazy, and while knowing when I think about it that P entails Q, have not
taken the trouble to acknowledge, and hence believe, that Q.   Advising me that I have very good justification
for believing that Q does not necessitate that I will believe that Q.   Belief as a mental state does not follow
logical rules.

Here are two examples of situations where belief in Q does not follow:

Lottery Paradox -- I believe that individually each ticket of a lottery is a loosing ticket.   Believing
that individually each lottery ticket is a loosing ticket (P), entails that collectively all lottery tickets
are loosing tickets (Q).   Yet I also believe that one ticket will be a winning ticket (not-Q).   This is
a rationally justified belief based on the rules of lotteries.

Preface Paradox -- I believe that individually each proposition in this essay is true.   Believing that
individually each proposition is true (P) entails that I believe that all propositions are true (Q).   Yet
I also believe that at least one proposition in the essay is false (not-Q).   This is rational belief
based on the observation that I am not infallible, and do make mistakes.   Hence it is highly likely,
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to the point of certainty, that I have made an error in at least one of the many propositions that I
believe individually are true.

Most theories of knowledge, because they rely on the condition that S believe that Q before S can know that
Q, would therefore fall into that group of theories for which knowledge is not closed under known entailment.
  The group would include foundationalism, coherentism, contextualism, reliablism, the causal and law-like
connection theories, and Nozick's "truth-tracking" or subjunctive-conditional theory to mention just the more
readily recognizable.  

But there are also a few theories that do not incorporate this second condition on knowledge that S believe
that Q.   The performative theory, as one example, would however also deny that knowledge is closed under
known implication because it maintains that "to know" is performance verb that has nothing to do with beliefs
or justification.   And while most deontological theories fall into the JTB family of theories (and hence deny
the closure principle for knowledge) it is possible to frame a deontological theory in terms of S having a right
or duty to believe that Q (when properly justified), rather than in terms of S actually believing that Q.   And for
this variation, knowledge would indeed be closed under known implication.   By dropping the requirement
that S believes that Q, similar variations can be created out of some of the other theories as well

This brings us to the reason discussed by Fred Dretske for denying that knowledge is closed under known
implication.   Dretske's argument is that accepting Q could nullify all the justification one has for knowing that
P.   And hence one could not accept the extension of knowledge from P to Q, even if one accepted that P
implied Q.  

The example that Dretske provides is that of the zebras at the city zoo.(6)   If one visits the city zoo and sees
what looks to all appearances as zebras in a pen, along with a posted sign explaining that these are zebras
in the pen, and one knows of no reasons for doubting this information, then one is justified in believing that
there are zebras in that pen.   But there being zebras in the pen logically implies that what you are seeing are
not mules cleverly disguised as zebras.   Dretske argues that you are not justified in believing that what you
are seeing in the pen is not mules cleverly disguised as zebras because you are no longer justified in
believing they are zebras.

The problem with Dretske's reasoning as a basis of denying the closure principle, is that it simply doesn't
work at the level he intends.   Dretske's reasoning is based on the traditional JTB model of knowledge.   But
the logical extension through the implication to Q only works if P is true.   If S knows that P, then by
definition, P is true.   In other words, if I know that I am seeing zebras, then it is true that I am seeing zebras.
  (If it is not true that I am seeing zebras, I cannot by definition know that I am seeing zebras.)   Then if I know
that P (I am seeing zebras) implies Q (they are not cleverly disguised mules), I am completely justified in
believing that they are not cleverly disguised mules.   Dretske's argument that the possibility that they might
be cleverly disguised mule

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