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4th December, 2012:  Tibor Molnar  :  What is Knowledge?   


A fascinating look at what is meant by knowledge and the relationship of knowledge with belief.  




We know many things, and exercise this knowledge every day.  But what does it mean to ‘know', and how does ‘knowledge' relate to evidence, truth, belief, expectation, and mere remembering?  
Plato characterised knowledge as "justified true belief"; but that cannot be the whole story.  For how do we know that we really know?  What is "truth", and how can we be certain that our beliefs are ‘true'?  And further, how can we be certain that our justifications are truly justificatory?  
In this talk I shall disagree with Plato: I shall argue that ‘knowledge' and ‘belief' are different in kind, and show that strictly speaking, philosophers (sadly, myself not excepted) ‘know' almost nothing at all! 

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Some Jargon

Ontology: [Gk: ōn, ont- = being]: the study of existence in the broadest sense - of what there is, of how we know what there is.  However, it is also used more narrowly, to refer only to the inquiry into ‘physical' existence, and to how we infer the nature of the physical world from the phenomena we observe. 

Epistemology: [Gk: epistēmē = knowledge]: the study of knowledge - of how things are known, and of what can and cannot be known.  

Semiotics: [Gk: sēma = mark; sēmeion = sign; sēmeiōtikos = of signs.]: the study of symbolic representation - of signs and symbols, and the grammar of their manipulation. 

Semantics: [Gk: sēma = mark; sēmainō = to signify]: the branch of semiotics concerned with the study of significance and meaning.  What is Knowledge?

According to the late Sir Alfred Jules Ayer [1910-1989], Professor of Philosophy at Oxford from 1959, knowledge is many different things: 
A glance at the dictionary will show that the verb ‘to know' is used in a variety of ways. We can speak of knowing, in the sense of being familiar with, a person or a place, of knowing something in the sense of having had experience of it, as when someone says that he has knowledge of hunger or fear, of knowing in the sense of being able to recognize or distinguish, as when we claim to know an honest man when we see one or to know butter from margarine. I may be said to know my Dickens, if I have read, remember, and can perhaps also quote his writings, to know a subject such as trigonometry, if I have mastered it, to know how to swim or drive a car, to know how to behave myself. Most important of all, perhaps, are the uses for which the dictionary gives the definition of ‘to be aware or apprized of', ‘to apprehend or comprehend as fact or truth', the sense, or senses, in which to have knowledge is to know that something or other is the case. 
Ayer, A.J. (1956): The Problem of Knowledge [Pelican, 1986] p.8(Bolding and italics added.)
What is Knowledge? (cont.)

Indeed, the Concise Oxford Dictionary (6th ed.) lists four definitions for ‘knowledge':
1. familiarity gained through experience (of person, thing or fact); 2. a person's range of information; 3. theoretical or practical understanding (of subject, language, etc.); 4. certain understanding, as opposed to opinion; 
and fully nine definitions for the verb ‘to know':
1. to (be able to) recognise or identify some person, place, event or thing; 2. to be acquainted with/in possession of information (about something); 3. to have personal experience of (fear, poverty, etc.); 4. to be familiar or on intimate terms with (cf. carnal knowledge); 5. to have in mind, to be able to recall, to be aware of; 6. to have learnt (that..., how to..., etc.); 7. to be able to use (language, etc.); 8. to have theoretical or practical understanding of (subject);  and9. to have an idea or suggestion. 
So, it seems that we use the term ‘knowledge' very loosely. What is Knowledge? (cont.)

Naturally, such loose, wide-ranging definitions do not satisfy the philosopher.  As Professor Ayer goes on to explain: 
We may discover the sense of the philosopher's question by seeing what further questions it incorporates, and what sort of statement the attempt to answer it leads him to make. Thus, he may enquire whether the different cases in which we speak of knowing have any one thing in common; whether, for example, they are alike in implying the presence of some special state of mind. He may maintain that there is, on the subjective side, no difference in kind between knowing and believing, or, alternatively, that knowing is a special sort of mental act. If he thinks it correct to speak of acts of knowing, he may go on to enquire into the nature of their objects. Is any limitation to be set upon them? Or, putting it another way, is there anything thinkable that is beyond the reach of human knowledge? Does knowing make a difference to what is known? Is it necessary to distinguish between the sorts of things that can be known directly and those that can be known only indirectly? And, if so, what are the relationships between them? (cont...) What is Knowledge? (cont.)

Perhaps it is misleading to talk of knowing objects at all. It may be possible to show that what appears to be an instance of knowing some object always comes down to knowing that something is the case. What is known, in this sense, must be true, whereas what is believed may very well be false. But it is also possible to believe what is in fact true without knowing it. Is knowledge then to be distinguished by the fact that if one knows that something is so, one cannot be mistaken? And in that case does it follow that what is known is necessarily true, or in some other way indubitable? But, if this does follow, it will lead in its turn to the conclusion that we commonly claim to know much more than we really do; perhaps even to the paradox that we do not know anything at all: for it may be contended that there is no statement whatsoever that is not in itself susceptible to doubt. Yet surely there must be something wrong with an argument that would make knowledge unattainable. Surely some of our claims to knowledge must be capable of being justified. But in what ways can we justify them? In what would the processes of justifying them consist? ibid., pp.9-10
What is Knowledge? (cont.)

To characterise fully the nature of knowledge, Professor Ayer identifies that we must answer at least the following questions (in no particular order): 
Is "knowing" a special sort of mental act, or perhaps a particular ‘state of mind'?
Just what do claims of knowledge entail, and what do they all have in common?
What is the difference between knowing, believing, thinking and mere remembering?
What, if anything, is the difference between things knowable directly and indirectly? 
Is what is known necessarily true?  Can we know anything that is in fact false? 
Is it possible to believe something that is in fact true, without actually knowing it?
If we know for certain that something is so, can we still be mistaken? 
What constitutes a satisfactory justification of a claim of knowledge?
Is there anything ‘thinkable' that is beyond the reach of human knowledge? Who cares?

What does it matter what knowledge is?
Well, it does matter, and we all care!  We base our plans and actions on what we know; and if something "out there" is about to have a major impact on our lives, then we really want (a) to know about it, and (b) to check/ensure whether it's true. 
For example, if I tell you that I'm worried about an asteroid striking the Earth, then you might be inclined, at least initially, to dismiss my anxiety as mere paranoia, or folly.  
Even if I tell you that I'm really concerned that it will happen, you might still be unmoved; and simply refer me, say, to NASA's "Near Earth Objects" website: neo.jpl.nasa.gov/risk/. 
But if I insist that I know that asteroid 2012 DA14 will strike the Earth on 15th February, 2013, you might suddenly become rather more interested... interested in just what I know, how I know it, and why (on what grounds) I claim to know it with such conviction. 
In other words, you would now want to know what I believed to be the case, my justification for believing it, and, ultimately, whether it was true.  Such ‘justified true belief' is precisely the characterisation of knowledge proposed by Plato in his Socratic dialogue entitled "Theaetetus". 
Near Earth Object 2012 DA14

About 45 metres in diameter and weighing about 130,000 metric tons, asteroid 2012 DA14 will pass by the Earth on 15th February, 2013 at a distance of between 27,100 and 52,000 km.  
There is only a 3% cumulative risk that 2012 DA14 will strike the Earth before 2070.  
If/when it does, the energy of the impact will be equivalent to about 2.4 megatons of TNT - about 20% of the energy of the asteroid impact near Tunguska, Siberia in 1908, but still 200 times greater than "Little Boy", the bomb that destroyed Hiroshima. 

      [NASA/JPL Near Earth Object Program Office] What is Knowledge?

So please do not be alarmed, asteroid 2012 DA14 on 15th February, 2013 may knock a satellite or two out of geo-stationary orbit, but it will almost certainly miss the Earth. (See: neo.jpl.nasa.gov/risk/2012DA14.html). 
Nevertheless, this example illustrates that, at least in some cases, knowledge is very important to us, and we care very much about it!  More particularly, we care about it when it is true... so perhaps, at a minimum, we might want to know what constitutes true knowledge, and how to distinguish it from false, or non-knowledge. 
Our dictionary definitions suggest that there are at least four different kinds of knowledge: 
Knowledge as Memory: -  recognising a person, place or thing;   -  recalling a fact or experience; 
Knowledge as Ability: -  knowing how to do something; 
Propositional Knowledge: -  knowing that such-and-such is the case; 
Knowledge as Understanding: -  knowing how or why it occurred/is the case. 
Knowledge as Memory

We know (remember) something when we can recall/reproduce it when required: 
Mary:  "Adam, do you know Michael's phone number?"
However, memory is unreliable: 
Adam:  "Yes, it's 04... 27... umm... er...  Well, I thought I knew it...  I did know it...  Hang on, I have it here in my phone..." 
Whether or not information retrieved from external sources is admitted as ‘knowledge' seems to be largely irrelevant.  The source of the knowledge seems to make little difference when the reference to the ‘knowing' of it is indirect. 
Rachel:  "Mary, do you know Michael's phone number?"
Mary may answer Rachel either way: 
Mary:  "Yes, I'll get it for you..."  (by asking Adam) orMary:  "No, but Adam knows... "  (i.e., he can produce it when required) Knowledge as Memory (cont.)

Thus, at even one remove, it seems not to matter just how Adam knows, just as long as Adam is able to deliver up Michael's phone number upon request.  But, of course, any such ‘external' knowledge depends on the accessibility of the external source: 
Adam: "Um... where's my phone?  Where did I put my phone? ... Ah, here it is... yes, Michael's phone number is 0430-27..." 
Adam is thus perfectly justified in believing that he knows Michael's correct (true) phone number - in fact he called Michael on this number just this very morning!  And so Plato is right: knowledge is "justified true belief"... 
However, in a changing world, knowledge is forever fallible/contingent.  There is always a chance that we are mistaken.  
Mary: "No, that's his old number; he's just bought a new phone." Adam: "Oh!  Well, in that case, I guess I don't know his phone number..." 
So, it turns out that Adam was mistaken.  But, nevertheless, he was fully justified in asserting that he knew Michael's phone number.  He had palpable evidence - how could he have suspected otherwise?   Knowledge as Memory (cont.)

Indeed, until we learn that we are mistaken, how can we ever suspect otherwise?  
This is where Plato's characterisation of knowledge starts to unravel.  Much of what we know (ort at least claim to know) is almost certainly true.  But it's only almost... and most of the time there is nothing more that we can do to prove that it is absolutely certainly true. 
So, if we demand of knowledge that it must be necessarily true - and there is mostly no way of knowing for certain that it is - then much (indeed, most) of what we ‘know' fails to qualify as knowledge.  Most of the time we are not (and cannot be) certain, and despite our various commitments and expectations, we discover the actual truth only serendipitously.  
Thus most of what we know is reduced to just so much informed opinion.  About the only things we are left with are some theorems of logic and mathematics, and a few tautologies... 
Strictly speaking, therefore, we must either refrain from referring to what we know as "knowledge", or weaken Plato's characterisation of knowledge to mere "justified belief".  
It's those dreaded "unknown unknowns"... they get you every time...   Knowledge as Memory (cont.)

[T]here are known knowns; there are things we know we know.  We also know there are known unknowns; that is to say we know there are some things we do not know.  But there are also unknown unknowns - the ones we don't know we don't know.  Donald Rumsfeld, U.S. Defence Secretary, 12th February, 2002

Yes, there are known knowns - they're the things that we know we know.  But are there other kinds of ‘knowns'?  Can we know something without knowing that we know it?  
Quizmaster: "What is the square root of 361?"Elizabeth: "Umm... err...  I don't know..."Quizmaster: "Would you like to have a guess?"Elizabeth: "Umm... OK...  Well, 20 squared is 400... so, umm...  Is it 19?"Quizmaster: "Correct!  It is 19.  See?  You did know it after all!"
But did Elizabeth really know the square root of 361 without knowing that she knew, or did she just come to know now it by working it out?  (Or was it just a lucky guess?)  
Knowledge as Memory (cont.)

I submit that, ultimately, we either know something or we don't; and that to divide what we know into ‘known knowns' and ‘other kinds of knowns' is merely to equivocate on the meaning of the word "know" - to confuse/conflate knowing (in the sense of ‘remembering') with realising (‘noticing') and reasoning (‘working out'). 
Yes, there are things that we know but cannot immediately recall, things that we did know but have forgotten, and things that we don't know but can work out from other things that we do know.  But if knowing something means being able to deliver it up on request, then by definition it is impossible to know something without knowing that we know it. 
So, as there is no actual difference between knowing that we know something and simply knowing it, it follows that there are no unknown knowns.  Even Mr Rumsfeld forgot to mention them... and it's easy to see why: he didn't know there were any! 
And yet... even Plato postulated the existence of unknown knowns.  In his Socratic dialogue entitled "Meno", Socrates claims to have demonstrated to Meno that he actually knows things that he doesn't know he knows.  
But I submit that Plato's argument falls victim to the same equivocations, and that a better title for his Meno dialogue might be the "Me-don't-no" dialogue...  Knowledge as Memory (cont.)

Then there are Mr Rumsfeld's known unknowns - they're the things we know we don't know.  But again the same equivocation appears: for in this case, what we know are those things that enable us to work out that we don't know other things.  The things we know are not the same things as the ones we don't!  
So, just as before, we either know something or we don't; and there is no difference between knowing that we don't know something and simply not knowing it. 
For example, in my own case, a ‘known unknown' is my maternal grandmother's name.  I know that I don't know her name - I've never known it, she died before I was born, and I never thought to ask. 
Anyway, I also know some other things; such as (a) that I had a mother who had a mother; and (b) that mothers, like other people, usually have names. 
And given that I know these other things, I must know that I don't know my maternal grandmother's name (even if she didn't in fact have one).  The only way for me not to know that I don't know her name is for me not to know where babies come from! 
Knowledge as Memory (cont.)

Which brings us to those dreaded ‘unknown unknowns'.  
Here we may ask, just what is Mr Rumsfeld trying to say?  If ‘unknown unknowns' are so unknown that even their' unknownness' is unknown, then how can Mr Rumsfeld say anything about them?  How can he, or indeed anyone, assert even their sheer existence? 
There are clearly many things that Mr Rumsfeld doesn't know (including epistemology, the theory of knowledge); and some number of these Mr Rumsfeld may even know that he doesn't know.  And from this he may rightly infer (by induction from the fact that he now knows things which, at some time in the past, he didn't even know existed) that there might be some more surprises in store in the future - that there might be some things that he doesn't yet know that he doesn't know.
Moreover, as the then US Secretary of Defense, he may even fear those future surprises - those "unknown unknowns" - but nevertheless he cannot at any time know that there are any.  Only with hindsight can we say that there were unknown unknowns.  In the final analysis, unknown unknowns are simply unknown. 
Perhaps we are right to find Mr Rumsfeld's remark amusing: for although what he was trying to say is obvious, there is something not quite right about what he actually said.   Knowledge as Memory (cont.)

But I digress.  Let me summarise the story so far. 
If we take knowledge to mean that which we are able to reproduce or ‘deliver up' on request, then it includes everything (a) that we can remember, work out or look up and (b) that we are fully justified in believing is true (regardless of how it is justified, and regardless of whether or not it is actually true). 
However, if we insist further that knowledge must necessarily be true, then apart from a few theorems of logic/mathematics and some tautologies, we can never be fully justified in believing anything.  On this interpretation, therefore, just about everything that we can remember, work out or look up fails the second condition (b), and we end up knowing almost nothing at all! 
And anyway, there is ultimately no real ‘knowledge' (in the sense of "understanding" or "know-how") in this kind of knowledge - we can either reproduce/deliver it up, or we cannot. 
In short, the characterisation of knowledge as memory is clearly unsatisfactory!  It's part of common usage, and it's part of what we mean by ‘knowledge', but merely remembering something or looking it up cannot be all there is to knowledge.  Knowledge as Ability

If someone were to ask, "Do we know how to ride a bicycle?", we might, perhaps, br able to answer with a "Yes."  We might even demonstrate our answer by hopping on our bicycle and riding away. 
But do we really know how to ride a bike?  Could we operate the controls of a bipedal robot and make it ride a bike by issuing micro-instructions to its hydraulic ‘muscles'?  I doubt that I could... at least not without considerable practice. 
On closer reflection, we see that we don't really know how to ride a bike - we just do it!  Knowing how to ride a bicycle (or swim, or ski, etc.) does not involve knowing anything at all; these are not ‘knowledge-based' or ‘knowledge-bound' activities, they are performance skills.  
And performance skills are not learned or ‘known' in the way that matters of fact are.  When we learn to ride a bicycle (or swim, etc.), we do not acquire ‘knowledge' - just consider how we do not, and indeed could not, learn it from a text-book.  
Rather, we develop performance skill/s somatically - by exercising innate capacities - either sub-consciously through self-discovery (as perhaps in the case of goldfish ‘learning' to swim), or through mimicry, trial-and-error and much training/practice.  Knowledge as Ability (cont.)

And once developed, the further exercise of performance skills does not entail the application of any ‘knowledge' either.  We may be able to describe (approximately) what we do when we're riding a bike, but we don't have to think about riding in order to do it.  
We thus learn to ride and we now ride without knowing how we ride, without knowing how to ride, and even without knowing in full detail how we once learned to ride.  
And, except perhaps for the sheer awareness of the fact "that we can", we ‘know how to' ride a bicycle in just the way that, say, a horse ‘knows how to' trot: once we're trained, we simply get up and do it. 
‘Knowing how to' ride a bike (or swim, or ski, etc.) might thus be more correctly described as ‘being able to' ride (or swim, etc.).  We learn to do these things, not to know them.  
(‘Knowing how to' perform more complex intellectual tasks (such as, say, to play chess) also requires ‘understanding' (about which more later), and is thus more complicated.  But note that such skills are also acquired - at least in part - through mimicry, trial-and-error, practice and experience.) 
Knowledge as Ability (cont.)

So, to say that we know how to ride a bike can mean only: 
a) that we are [familiar with]/[able to describe] what is meant by ‘riding a bike',
b) that we can give a more-or-less vague account of how we ourselves do it, and c) that we are aware of having ridden in the past at least once, and have no reason to suppose that we could not now repeat that performance. 
Beyond that - beyond the sheer fact of knowing the truth/falsity of the proposition "that I can ride", there is ultimately no difference between my ‘knowing how to' ride a bike and my simply ‘being able to' ride.  
Strictly speaking, therefore, there is no real ‘knowledge' involved in ‘knowing how to' ride a bike, or in the holding of performance abilities/skills more generally.  Ultimately, we simply remember being able to perform them.  
Hence the ability to perform a task isn't quite what we mean by knowledge either.  Although it's also common usage, saying that we "know how to" do something is at best a harmless, if mildly misleading, linguistic turn.  Propositional Knowledge

The third kind of knowledge is ‘propositional' knowledge.  In everyday usage, propositional knowledge is what we ‘have' when we know ‘that such-and-such is the case'.
However, we don't actually ‘have' anything when we know it - knowledge is not the kind of thing that can be "had" or "possessed". 
‘Knowledge' is not itself any kind of object, thing, or independently existing substance or "stuff" - neither material "physical-stuff", nor non-physical "mind-stuff".  
There is no disembodied, ‘objective' knowledge - knowledge that is not somehow ‘known' (directly or indirectly) by some or other ‘knower'.  (Indeed, knowledge can disappear without trace when it is universally forgotten.)  
Moreover, ‘knowledge' is not even a property, attribute, or quality of any kind of stuff.  
Being knowledgeable is not like being yellow, or round.  We may say that a ball is round or that it has a round shape.  But a ball isn't ‘bouncy' in the way that it is round: although we sometimes say that it is, a ball isn't ‘bouncy' because it has ‘bounce' - it's bouncy because it does, or is able to, bounce.   Propositional Knowledge (cont.)

Similarly, knowledge is not something that a ‘knower' is or that a ‘knower' has.  A ‘knower' isn't knowledgeable because she is "knowledge-y" or has knowledge; she is knowledgeable because she does know. 
Thus, knowledge is a quantity of ‘knowing' and grammatically speaking, the word "knowledge" is a gerund, not a noun.  
Indeed, we say that a ‘knower' is knowledgeable - i.e., she ‘knows' something - when she produces, or is able to produce, the correct/appropriate response to some-or-other question or command.  
Indeed, to claim that she ‘knows' something is simply to assert that she is able to (and does) respond correctly, and nothing more, just as Professor Ayer observes: 
To have knowledge is to have the power to give a successful performance...
Ayer, A.J. (1956): The Problem of Knowledge [Pelican, 1986] p.15
Propositional Knowledge (cont.)

And Professor Ayer was not alone in thinking that propositional knowledge is reducible to performance skills/abilities.  Here is the view of a fellow Professor of Philosophy at Oxford, Gilbert Ryle [1900-1976]: 
 ‘Know' is a capacity verb, and a capacity verb of that special sort that is used for signifying that the person described can bring things off, or get things right. 
Ryle, G. (1949): The Concept of Mind [Penguin, 1990], pp.128-9
Of course, if propositional knowledge is a capacity - a performance-ability/skill - then a ‘knower' responds as she does not because she knows any particular thing, but simply because she just is the kind of person (or other thing) that responds in just that way when questioned/commanded in just that way. 
The reference to "other things" is significant: for on this interpretation, knowledge is not exclusively the province of self-aware conscious beings.  
We say of ourselves that we know something because we are self-aware - aware that we can respond correctly and appropriately to some enquiry/command.  But just as long as we produce the right responses, does it matter whether we are aware of doing so?  Propositional Knowledge (cont.)

Perhaps not; for we say of other ‘knowers' that they know something (i.e., can respond correctly and appropriately to our enquiries) without particular regard to whether they themselves are aware of what they are doing.  At most, we simply assume that they are.  
However, conscious self-awareness is irrelevant to knowledge - it is entirely incidental to the delivery of appropriate responses.  With access to Googleä and Wikipediaä, say, that's something a sufficiently well-programmed computer can do!
So, to sum up:
We have still not found any ‘thing' that might stand as the essence of ‘knowledge' as such.  At least from without, knowing that something is the case is equivalent to being able to respond appropriately, correctly and consistently to the relevant enquiry - irrespective of what memories, skills and abilities the production/performance of that response might entail.  
And all that is left for ‘knowledge' is the linguistic abstraction - the disembodiment and reification - of that ability.  Which is not a bad first definition, but perhaps there's a little more to it than that.  Knowledge as Understanding

There is more to propositional knowledge than merely recalling that certain propositions are the case, hence the fourth kind of knowledge is comprehension, or "understanding". 
Propositions are usually subjected to extensive processing/manipulation - relation, assembly, synthesis, analysis and interpretation - to produce further propositions about how and/or why they are the case, and about the implications of their being the case.  
In other words, the ‘understanding' of some event or state-of-affairs also involves: 
(1) recalling and recognising the relevance of other data/information about it, and even describing it in terms of other things; 
(2) identifying the various causal mechanisms/motivations that brought it about; 
(3) remembering and applying the laws of Formal Logic to deduce and/or infer relationships between it and other events/states-of-affairs; and(4) apprehending, constructing, reconstructing, and/or explicating the history, purpose, reason, mechanism and/or cause whereby the event or state-of-affairs arose.  Knowledge as Understanding (cont.)

In other words, ‘understanding' or ‘knowing how/why' is the product of a more complicated deliberative process involving memory, reasoning, and other cognitive skills/abilities.  It is the process we call ‘thinking': 

Knowledge as Understanding (cont.)

‘Knowledge' might be regarded as the comprehension and/or higher ‘understanding' produced by this process of ‘thinking' - as those further propositions derived, synthesised, etc., via the complex manipulation, relation and hybridisation of concepts, ideas and relevant memories and abilities. 
For without this kind of ‘deeper' understanding, we have no real knowledge, we have only rote learning and remembering.  We cannot know that which we do not understand.  
For example, if we learn our multiplication tables by rote, do we really ‘know' them?  Do we really know that 2´2=4 if we don't understand multiplication, or don't understand how (and why) two twos combine to produce four?  Or do we merely recall that 2´2=4 because we had committed the equation to memory? 
Similarly, can we really say that we know the Periodic Table of Elements just because we can recognise one when we see one?  Do we know it any better if we can draw/reproduce it but do not understand why it is organised into its particular shape or comprehend/understand the meaning/significance of all the little symbols and numbers? 
Knowledge as Understanding (cont.)

The Periodic Table of Elements  Knowledge as Understanding (cont.)

And further, if we do not understand, say, the meaning of the word "not" (Aristotle's Principle of Negation), or why concepts/propositions cannot be their own opposites (the Principle of Non-Contradiction), do we, can we - indeed could we - really understand or know anything at all? 
This is where Logic comes in.  The axioms and theorems of Set Theory, Formal Logic and even of Mathematics are essential to understanding - for they alone enable us to make sense of our manifold thoughts and experiences: to order them, to organise them, to sort them like with like, and to draw valid conclusions/inferences from them. 
All knowledge is ‘logical' in this way - axiom-based and logical-rule-governed - which means that if we turn out to be wrong about something, then either we've made a wrong assumption/adopted an incorrect axiom, or there's something wrong with our logic.  There is no third alternative.  
And it is this very process of logical organisation, ordering, ‘making sense' and drawing of valid inferences - of ‘thinking' in all its forms - that produces the thoughts and ideas that make up the building blocks out of which we construct knowledge.  Everything else is mere rote learning and memory. 
Knowledge as Understanding (cont.)

A knower's knowledge, then, is that body of propositions that she not only remembers and upholds, but also understands and can substantiate with relevant, plausible and adequate justificatory/empirical evidence, and/or justify/prove via logically valid reasoned argument. 
More briefly, we might say that knowledge vests in the understanding of some fact, and not in the mere remembering of it.  Knowledge requires justification, and the only way to satisfy ourselves that the justification for what we claim to know is valid and sufficient is to understand some or other explanation of it.  
Without understanding, knowledge is reduced to mere identification - to naming and remembering.  For example, without some understanding of optics and the nature of light, all we know about a ‘rainbow' is that it is the name ascribed to a particular kind of visual sensation that sometimes appears in the sky after it rains.  But is that enough for us to say with confidence that we know what a rainbow is?  Do we ‘know' something when all we know about it is its name?  
And if we use "know" in this weaker sense, then how do we distinguish between those knowers who understand things and those who don't? 
Knowledge and Justification

To be accepted as knowledge, therefore, assertions/propositions/knowledge-claims must be justified.  In other words, to assert that some proposition is factually correct (i.e., ‘true'), a knower must simultaneously declare (at least implicitly) that she can, if required, provide both relevant evidence, an account of how she knows it; and justification, an account of why she thinks it is correct/true. 
If the knower is unable to provide such relevant/adequate evidence/justification, then she forfeits the right to claim that her knowledge is factual - or even that she knows it at all - and her audience is justified in treating her assertion as hearsay, opinion, hypothesis or belief.  
Knowledge, therefore, depends crucially on evidence and justification.  Indeed, the difference between knowledge and belief is precisely the presence/absence of such evidence and/or justification.  
For to know something is not only to know that we know - it is to know how and why we know. 
Knowledge and Justification (cont.)

There are at least three different kinds of evidence: experiential, logical, and abstract/mathematical.  Properly applied, they are each useful as justification for knowledge, but the standard rules of evidence apply - relevance, independence, verifiability, etc.  
In other words, not only does a knowledge-claim have to be justified by evidence, but the evidence itself has to be justified.  Justification is regressive in just this way, as yet another Oxford don, Baron Anthony Meredith Quinton [1925-2010], Professor of Philosophy and President of Trinity College Oxford (1978-1987), observes: 
The regress of justification is intended to show that there must be basic statements which do not owe their justification to inference from any other justified statements.  There is an analogous regress argument to show that there must be basic statements of an ostensive rather than intuitive kind which are not introduced into discourse or defined in terms of any other kind of statements - an initial class of statements whose meaning is to be explained not by correlation with other statements but by correlation with the world outside language. 
Quinton, A (1973): The Nature of Things (Routledge and Kegan Paul, 1980) p.126 
Knowledge and Justification (cont.)

‘Knowledge' may be as good as it can be, but it cannot - and does not - come with a "truth"-guarantee.  So, pace Plato, knowledge is not "justified true belief" - that's just how we wish it would be - but at best it is "justified valid belief", the truth of which is [almost] always a contingent matter - contingent as it must be on the validity of the justification and the truth of the premises from which it is derived. 
Indeed, if knowledge were "justified true belief", as Plato suggests, then we could claim to ‘know' only very little - for even when something is justified, how could we be certain that it is true?  What could possibly underwrite our confidence in the truth of some proposition beyond its justification?  There is in principle nothing that could fill that role.  
Knowledge is at best a proposition justified to the point where we believe the uncertainty of the relationship with its dependencies is effectively zero.  
Knowledge and Belief

Accordingly, the Concise Oxford Dictionary defines a belief as an idea, proposition, view or opinion that is held (accepted as true) without regard for justification or evidence.  
  Knowledge and Belief (cont.)

In other words, we know some things and we don't know others; and of the things that we don't know, there are some that we choose to believe anyway.  We believe them - accept/.adopt them "on faith", so to speak - rather than know them, because we have insufficient evidence to claim to know them. 
Hence beliefs are not ‘proven', and may or may not be factually correct.  And there's never any way of telling - for if there were, we would immediately know, rather than believe, what was the case.  It is an explicit property of beliefs that there is insufficient justification/evidence to positively determine them.  
Beliefs are believed (or disbelieved) precisely because they cannot be tested - neither verified/confirmed nor refuted/called into question.  (The contradiction of this condition is precisely the source of the humour in the previous cartoon.) 
And so, at least in this respect, knowledge and beliefs are diametrical opposites!  
Knowledge is not any kind of belief, not even "justified true belief", as Plato said.  A belief cannot in principle be justified - a "justified belief", regardless of whether or not it is true, is a contradiction in terms. 
Knowledge and Belief (cont.)

The provenance of knowledge is through empirical evidence and propositional logic:
Fact  ®  Data  ®  Information  ®  Explanation  ®  Knowledge
rather than emotional commitment: 
Idea  ®  Opinion ®  Belief  ´  Knowledge
This latter ‘sequence', proposed by Plato and still widely upheld, is not a valid continuum. 
It is incorrect - on the ground of insufficient evidence - to claim that we know something when we can only believe it. 
It is misleading - by denying our evidence - to claim that we merely believe something when we actually know it. 
And, pace Plato, it is contradictory to claim that we simultaneously both know something and believe it. 
Knowledge and Belief (cont.)

Returning to our earlier example, do I know that asteroid 2012 DA14 will miss the Earth on 15th February, 2013, or do I merely believe that it will?  (Or even just hope that it will?) 
Does/can anyone really know what the future holds?  If the trajectory of 2012 DA14 is known only approximately and a non-zero value (however small) must be assigned to the probability of an impact with the Earth, can anyone put their hand on their heart and say that they know it won't? 
If not, then we've just arrived at one of Professor Ayer's main concerns: that if we cannot know something without absolute proof - without being fully satisfied that it must be the case - then we end up having to concede that we know almost nothing at all!  
We can but acknowledge the good Professor's worry - for indeed we can know very little with absolute certainty.  We harbour many beliefs and many more expectations, but have precious little certain knowledge! 
Knowledge and Belief (cont.)

And worse... for even when we are fully satisfied - fully convinced - it is still entirely possible that we are mistaken!  While a claim of knowledge may reflect the absolute conviction/commitment of the knower, it does not necessarily entail the truth/accuracy of that which is claimed to be known.  As Professor Ayer observes, 
From the fact that someone is convinced that something is true, however firm his conviction may be, it never follows logically that it is true (except in the rare cases where the truth of the statement in question is a logical condition of its being believed, as in the assertion of one's own existence).[...]
It cannot validly be inferred from this linguistic fact [that by the meaning of the verb ‘to know' one cannot know what is not true] that when someone is considering a statement which he knows to be true, it is his state of mind that guarantees its truth. The statement is true if, and only if, what it states is so, or, in other words, if the situation it describes is as it describes it. And whether the situation really is as it is described is not to be decided merely by examining the attitude which anyone who considers the statement has towards it, not even if the person who considers it knows it to be true."
Ayer, A.J. (1956): The Problem of Knowledge (Pelican, 1986) p.19  Knowledge and Belief (cont.)

Thus, knowledge per se is rarely, if ever, certain; for while an assertion of knowledge assures us that the knower is certain, it does not (necessarily) guarantee that the knowledge itself is certain. 
We may, however, draw a little false comfort from Professor Anthony Quinton:  
It is misleading, though not false, to say that you believe that p when you actually know it.  It is misleading because the weaker assertion suggests that that is all there is to it.  You can also have conclusive reason for believing that p even though p is in fact false.  But if you have conclusive reason for believing that p, you ought to say that you know it.  However, the fact that you ought to say that you know that p does not entail that you really do know it.  You ought to say that you know that p if you honestly think that you do.  When you say this you plainly imply that p is true, though it may not be.  If it is not true then what you said was wrong, in the sense that it was false, but it was the right thing for you to say nevertheless. 
Quinton, A (1973): The Nature of Things (Routledge and Kegan Paul, 1980) p.122 
Knowledge and Belief (cont.)

Indeed, Professor Quinton must be right - if we are almost never certain, then knowledge must of necessity be an expression of conviction, not of certainty.  
It is usually argued that if something is not true, then it doesn't qualify as ‘knowledge' - at least not if knowledge is ‘justified true belief'.  
However, we have already shown that knowledge is not belief, and that it is not even necessarily true.  So let us now re-characterise knowledge as "justified proposition" - or even "proposition/assertion valid/true to the extent that it is justified" - for indeed, that is all it can ever be. 
And on this characterisation, all that remains to be done is to specify the conditions that make a proposition true, and the circumstances under which it is reasonable to consider it justified. 
Knowledge and Truth

Propositions are necessarily about something - there is no proposition that is about nothing.  And if some proposition is ‘true', then it is true because it is about some matter of fact - i.e., because it states/asserts something that is actually the case. 
However, in everyday usage, the meaning of "fact" is ambiguous.  As Professor Alan F. Chalmers [1939-] of Sydney University observes, the term is used variously to refer to: 
1. Actual physical states-of-affairs in the world; 
2. Propositional statements that make claims concerning physical existence and states-of-affairs; 
3. Propositional statements that assert abstract conceptual/logical truths. 
Chalmers, A.F.: What is this thing called Science? 3rd Ed'n (Uni of Qld Press, 2000), p.10)
Rather than argue about which meaning is correct, let us for the sake of clarity adopt the following usage: (1) is a fact; (2) is a factual claim, and (3) is a conceptual or epistemic claim. 
Knowledge and Truth (cont.)

On this interpretation, then, ‘truth' is a property of propositions, not of the physical world; and it describes the relationship of correspondence between the meaning of a proposition and some actual state-of-affairs in the physical world. 
Thus (a) a fact is a way the physical world actually is, regardless of whether we know it or not; (b) a factual claim is true when it correctly represents such a fact - i.e., when its semantic content corresponds to some actual state-of-affairs in the physical world; and (c) an epistemic claim is either logically valid or invalid, but is strictly speaking never ‘true', since it does not correspond to anything in the physical world. 
And on the same interpretation, "a truth" is a true propositional statement (that correctly asserts/corresponds to an actual fact).  In other words, it is a statement that is true in virtue of its correspondence to a fact; but it is not itself a fact. 
It is this last point that is the source of much confusion.  Factual claims are contingent and may always turn out to be false; whereas the facts themselves are not contingent by definition, and can never be false. 
Strictly philosophically speaking this is all very well, but it is not how things are in practice.  Knowledge and Truth (cont.)

In everyday usage, the truth of propositions is asserted in many different ways: 
· by claiming correspondence to some fact· by claiming coherence with other knowledge· by logical entailment/derivation/inference· by declaration as axiomatic· by demonstration· by appeal to higher authority, or revelation· by definition· by tautology
And while only the first of these - correspondence to actual physical facts - constitutes a robust and meaningful assertion of truth (and thereby elevates a proposition to the status of knowledge), in practice, our knowledge is over-determined by too many truth-claims of every description.  
Assertions of truth other than by correspondence to actual facts may be indicative of truth, but their truth is not necessarily assured. 
Knowledge and Truth (cont.)

Claims of coherence with other propositions are only as reliable as the truth of those other propositions -a fully coherent set of propositions may be fully, consistently false. 
Logical entailments, derivations and inferences are likewise indicative of truth, but they remain forever contingent upon (a) the validity of their derivation; (b) the truth of the axioms on which they are based; and (c) the validity of the laws of formal logic. 
Axioms serve to create a valid and consistent system for description and explanation.  However, axioms are never ‘true' - they are epistemic entities and valid by definition. 
Practical demonstrations may also be indicative of truth, but as empirical observations they remain forever uncertain. 
Definitions and appeals to higher authority may be true, but they are not necessarily true. 
And tautologies may serve as true definitions, but they are devoid of meaningful content. 
Knowledge and Truth (cont.)

To sort out the resultant epistemic mess - to work out what is, and what is not, actually the case - is a task not only for scientists, but also for linguists, epistemologists, logicians, mathematicians and analytical philosophers.  
Indeed, Philosophy of Science is principally the study of the methodologies of appraisal for scientific claims and, more particularly, the "logic of justification"; the nature of truth; and the meaning of realism.  
And it is forever a work in progress. 
So, what is Knowledge?

We've shown that while it requires memory, performance abilities and other learned skills, knowledge is not itself any of these things. 
Rather, we've shown that it requires understanding attained through strictly logical reasoning - the systematic organisation, classification, interpretation and correlation of our manifold thoughts and experiences; and the drawing of valid inferences from them. 
We've shown that it is knowledge only to the extent that it is understood rather than believed; and that it is true only to the extent that it is logically valid and/or corresponds to physical facts. 
We've shown that it is only knowledge to the extent that it is justified - substantiated by relevant evidence; and/or proven via logically valid reasoned argument. 
We've also shown that it is not necessarily true, and that it's not even necessarily justified!  It is merely justified as well as we can justify it.
And hence we've shown that Plato's characterisation as "justified true belief" is incorrect, and that knowledge is more correctly characterised as comprising "more-or-less justified propositions".  Not as satisfying, perhaps, but that's as good as it gets.  So, what is Knowledge? (cont.)

Knowledge is often characterised as the firm conviction - dare I say belief? - that we are justified in asserting/maintaining that something is the case.  Moreover, it is described as a belief about which we harbour other beliefs - such as the belief that we are fully justified in claiming that we know it.  
We have shown that knowledge and belief are different in kind, and that this characterisation is confused.  That this erroneous description appears attractive serves only to illustrate just how seldom our knowledge-claims are actually justified. 
Still, if we set the justification ‘bar' too low, we lose the valuable distinction between opinions, beliefs and knowledge.  
And if we set the ‘bar' too high, we end up like Socrates - self-declaredly the wisest man in Athens because he knew that he knew almost nothing at all.  
And look what happened to him! 
What is Knowledge?

Thank you.

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