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Tuesday
May 3, 2005

The Veridicality of Conceptual Discernment by Ed Thompson

[Editor's note - I post this one unedited, & without comment. Linz]

Knowledge is often signified by "justified true belief." It is this author's opinion that another signification would better help those seeking truth and understanding--and the value which flows from them. In this short essay, I will explore some past thinking errors (about knowledge and certainty) and offer productive solutions to these errors.

Being able to distinguish something from all other known entities (veridical conceptual discernment) is what "knowledge" is. (Read more...)
Discuss this Article (98 messages)

Post 20

Wednesday, May 4, 2005 - 7:01pm

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Jeff:

A few thoughts on the pi example:

Ed Thompson wrote:

We don't know "pi" (3.1415926 ... ), because it's a simple sign for a complex number, and we don't know this complex number in its entirety (down to the last digit).

We do "know" pi in the sense that we know it's 'that numerical value which is the ratio of a circle's diameter to its circumference.' In fact, we know this because it's the definition of pi.

Jeff wrote:

Minor point in the philosophy of mathematics. We do, in fact, know 'the last number' of pi.

It is: pi.

You are apparently using "number" differently than Ed's "digit". You are saying pi IS a number (and that when you say 'pi' you are knowing and saying the ENTIRE number).

But what is the conceptual content of that use? Absolutely nothing beyond the definition. We know only that it's A number, some number, a ratio between two things apparently fixed by the nature of circles whatever their size, but nothing more. Certainly not the numerical value, absent computation of some portion of that number.

I.e. it is the felt (and unnecessary) need to force all numbers into a decimal form that creates such pseudo-problems.

But there IS a need to express pi in a numerical form--whatever the number base--if 'pi' is to have more conceptual content than 'the ratio of ...'

We can assert that when we utter the word 'pi' and its definition we are including within the scope of that utterance all things which can ever be known about pi, but this is not knowledge.

There are many ways to calculate the value of pi, one such is with an infinite series (first discovered by Euler); with this method one can get as close as one has time and computing ability for.

See where you depart from your previous use of 'pi'? You said that the value of pi is pi--another way of saying that a thing is what it is--but now you are saying it can be "calculated" when in fact it, as pi qua pi, can only be approximated.

The artificial forcing of numbers into decimal form is actually a form of Platonism.

Wouldn't it be exactly the opposite?

Wouldn't holding that 'the ratio of a circle's diameter to its circumference is a number we shall call pi,' divorced from value, be exactly the kind of abstraction which qualifies as Platonistic?

I.e. a 'frozen abstraction'; the view that in order to know something, it is necessary to know it in a particular concrete form.

But in the case of pi, isn't one of the more important aspects of its nature its numerical value?

Since we are discussing epistemology, what knowledge would we have of pi if we are in possession only of its definition and the symbol?

I can define "the theory of everything" in a rather short paragraph, and symbolize it with TOE. But when I write

TOE

am I imparting any knowledge of what might constitute an actual theory? Any at all?

Knowing the names of things is not the same as having knowledge about them, and defining something is only one step removed from that.

Nathan Hawking

Post 21

Wednesday, May 4, 2005 - 8:30pm

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Nathan, concerning what knowledge is, you asked: "What about justification?" and then you provided an example of a belief that: "There's a pony in my living room."

Taking you on your own terms, this problem of justification is solved when you arrive at a conclusively justified true belief (about a pony in your living room). In order to conclusively justify something, I suggest something that I call a "double-reverse" modus tollens (DRMT)--to be set up with a conditional if/then proposition where the (deniable) consequent is unique to the antecedent:

If there's NOT a pony in my living room, then X (a unique condition that would only be true in the absence of living room ponies).
Not X.
--------------
Therefore, there IS a pony in my living room.

This syllogism (above) provides positive knowledge of the presence of a pony in the living room. The alternative is to run the syllogism without the "double-reverse" aspect:

If there's a pony in my living room, then X (a unique condition that would only be true in the presence of living room ponies).
Not X.
--------------
Therefore, there is NOT a pony in my living room.

In some cases, both MTs may have to be run in order to get conclusive justification of the truth of the matter--but that is a small price to pay for the contextually-absolute certainty that this dual-MT produces.

Ed

Post 22

Wednesday, May 4, 2005 - 8:41pm

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Nathan,
To give you the kind of answers your excellent points genuinely deserve would require more time than I can devote
to them right now. Suffice to say, I'll think about it and get back to you at greater length and greater clarity.

But to address what seems to be the main thrust, in an admittedly less than completely satisfactory way:

The definition you provide is but one way of definining pi (albeit one of the common ways), but not the only way.

Remember as an 'existent' pi (the thing not the 'number' which is conceptual not physical) has all of it's attributes,
not just the ones stated in the definition. (Calling 'pi' an existent, i.e. a real thing not just a concept
that's used as a rule, is potentially misleading and certainly controversial. What I'm trying to express here is that
circles, for example, do exist; they do have diameters and circumfra and those things, suitably quantified,
can be used to calculate a ratio.)

On this basis, we could conclude that the series definition, or the value of the integrals containing it, or the Euler equation,
or any of dozens of other forms is pi. (With the terms suitably expressed, of course.)

Alternatively, one can define pi as the sum of these series, or the limits of suitably chosen bounds,
and use of those limits or sums is practical, and understanding those expressions is real knowledge.

I.e. there's nothing Platonic about any of that.

That's almost certainly too cryptic, of course without additional explanation.

I'll try to address one other point briefly. Since pi appears in so many
different forms and equations, it is possible to use it to get solutions (with exact numerical
values oftentimes) without calculating the decimal equivalent to some
impossibly infinite number of places. (After all, in this sense, it is a transcendental number.)

That means, among other things, that it is knowledge we get when we use pi to perform the calculations.

As just one example, it's possible to do extensive circuit analysis (not my area of expertise), using
equations in which pi appears, without ever knowing the decimal-equivalent numeric value at all. This is surely knowledge.

Similar considerations, and potential difficulties for your view, would apply to the square root of two, and
other trancendentals too, of course.

As I said, more later.

Jeff

Added in editing: P.S. With respect to your question about conceptual content: remember concepts are open ended. What that implies here is that I can know what pi is (i.e. that conceptual content is not empty) without being able to calculate an infinite number of
decimal places. My point was, there is nothing particularly necessary, for the purposes of knowing pi and using it to gain lots of other knowledge, about expressing it in decimal form.

(Edited by Jeff Perren on 5/04, 8:47pm)

Post 23

Wednesday, May 4, 2005 - 10:37pm

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Nathan, as the obvious method of conclusive justification (of the living room pony) would involve direct contact with the living room--I will proceed with my example above (post 21).

What I need are conditions (perceptual experiences are a wonderful candidate) that can only be met by a pony in the room AND/OR conditions (e.g. perceptual experiences) that must not hold should there be a pony in the room.

Or, either jointly or alternatively, I may use conditions (e.g. perceptual experiences) that can only be met by the absence of a pony in the room AND/OR conditions (e.g. perceptual experiences) that must not hold should there be no pony in the room. I have here four semi-exclusive paths to knowledge.

Now, assuming that there are other objects in the room (TV, sofa, and lamp--for instance), I will only need to EFFECTIVELY DISTINGUISH these objects from a pony in order to know, not merely believe truly or believe justifiably, but to conclusively know that the pony is/is not in the room.

Not to beat a dead horse here, but I do not need to know all there is to know about the pony (or say, pony-ness) in order to accomplish this task. I need only be able to conceptually discern ponies from TVs, ponies from sofas, and ponies from lamps.

And I am equipped with powers of awareness that allow me to complete this task with a 100% success rate. With a few additional loose-ends to tie up--I can make it impossible for me to not know whether the pony is in the room, or not.

Ed

Post 24

Wednesday, May 4, 2005 - 10:42pm

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Ed,

LOLOLOLOLOL...

Only you would come up with a disjunctive syllogism for a pony in your fucking living room! That's marvelous!

"Double-reverse" modus tollens (DRMT)???

LOLOLOLOLOL...

Fuck epistemology!

You gotta get yourself into advertising or screenwriting or something. You have THE GIFT.

Michael

Post 25

Wednesday, May 4, 2005 - 11:48pm

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Michael, thanks so much--for such an unmistakable appreciation of my ramblings.

I do speak to be heard (n' ah' 'spect we'all doo) and you have such a knack for completing the "circle of communication" Michael. It's truly refreshing to witness your insightful, rationally-passionate input--whether it's directed at me, or even at others.

That was very kind, how you ended with such high praise for me--but I'm hearing voices off yonder ... I can't quite make it out ... what are they saying? ... [louder now]

[unanimously] Don't encourage him!

{;-P}

Ed

Post 26

Thursday, May 5, 2005 - 12:21am

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Ed writes:

Nathan, concerning what knowledge is, you asked: "What about justification?" and then you provided an example of a belief that: "There's a pony in my living room."

Taking you on your own terms, this problem of justification is solved when you arrive at a conclusively justified true belief (about a pony in your living room).

Correct me if I'm mistaken, but weren't you offering

'knowledge is being able to distinguish something from all other known entities'

as a SUBSTITUTE for

"justified true belief"?

If so, then I'm suggesting that your definition is inadequate. If not, then I'm uncertain as to the point of your article. Would you clarify?

Now you seem to be addressing the "justified" aspect. Does that mean you accept the "true belief" portion of JTB?

Ed writes:

In order to conclusively justify something, I suggest something that I call a "double-reverse" modus tollens (DRMT)--to be set up with a conditional if/then proposition where the (deniable) consequent is unique to the antecedent:

If there's NOT a pony in my living room, then X (a unique condition that would only be true in the absence of living room ponies).
Not X.
--------------
Therefore, there IS a pony in my living room.

This syllogism (above) provides positive knowledge of the presence of a pony in the living room. The alternative is to run the syllogism without the "double-reverse" aspect:

If there's a pony in my living room, then X (a unique condition that would only be true in the presence of living room ponies).
Not X.
--------------
Therefore, there is NOT a pony in my living room.

EXACTLY what would you propose as a "conclusive" (by which I assume you mean assuring certitude) condition or test for the presence of living room ponies?

This stuff sounds easy in the abstract, but the problems become apparent when one attempts a concrete example.

Nathan Hawking

Post 27

Thursday, May 5, 2005 - 1:33am

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Nathan writes:
------------
"Correct me if I'm mistaken, but weren't you offering

'knowledge is being able to distinguish something from all other known entities'

as a SUBSTITUTE for

'justified true belief'?"
------------

I most certainly was (thanks for noticing) Nathan--that is, until you completely ignored the insight of my essay, and proceeded to revert back to the JTB concept after a blithe dismissal of its main theme in an unargued-for appeal to a "common" sense:

------------
"You seem to imply that because knowledge "cannot be false" it belongs in a different category, but I can see no logical or semantic�justification for this distinction.

In the absense of such, I'm forced to honor the prevailing sense of those terms: All knowledge is belief, but not all belief is knowledge. If we agree that knowledge is belief, we have the "B" in JTB.

If you assert�knowledge "cannot be false"--the same as saying "true"--we now have the "TB" portion of the JTB."
------------

And after asking myself "Did this guy even read my essay?" I said: what the hell--I'll take him on on his own home field.

------------
"If so, then I'm suggesting that your definition is inadequate. If not, then I'm uncertain as to the point of your article. Would you clarify?"
------------

My definition WAS inadequate (again, thanks for noticing). The adequate--ie. refined, thanks to your criticisms--definition is "veridical conceptual discernment of existents" (not of entities). You reminded me that we can have concepts of non-entities (concepts about attributes, concepts about properties, concepts about relations, concepts about methods, etc)--and I thank you for that.

The point of my article was to offer a superior conception of what it is that knowledge is--so that humans can make even more progress in dealing with reality than is currently possible with the now-proven-to-be limited conception of JTB.

------------
"Now you seem to be addressing the "justified" aspect. Does that mean you accept the "true belief" portion of JTB?
------------

I'm addressing these aspects because you brought them up (did you expect evasion on my part?). The only conception of JTB that I accept is CJTB (Conclusively-Justified True Belief), which renders the belief aspect a non-integrated floating abstraction. We cannot fail to believe in something that is conclusively justified--just as we cannot conceive of round squares.

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"EXACTLY what would you propose as a "conclusive" (by which I assume you mean assuring certitude) condition or test�for the presence of living room ponies?"
------------

Ponies take up space. They cannot "fail" to take up space (existence exists). Give me 2 yardsticks (one in each hand) to swing around in this room--and I will tell you whether there is something in there (besides the knowable furniture) "taking up space." Is that good enough for you, Nathan, or will you postulate an invisible pony who can see my every move before I make it--and who will jump high enough where I would miss him, each time, with the swinging yardstick (and land light enough where I couldn't hear the thump)? How about a pony who can space-and-time warp?

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This stuff sounds easy in the abstract, but the problems become apparent when one attempts a concrete example.
------------

Oh, man! I'm sorely interested in hearing Jeff's take on this last point (Jeff seems to think that the concretes are the EASY part--and that abstraction is where the action is). The short answer, however, is that context will dictate the parameters for certitude (as I alluded to above).

Ed

Post 28

Thursday, May 5, 2005 - 12:58am

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Ed wrote:

Nathan, as the obvious method of conclusive justification (of the living room pony) would involve direct contact with the living room--I will proceed with my example above (post 21).

What I need are conditions (perceptual experiences are a wonderful candidate) that can only be met by a pony in the room AND/OR conditions (e.g. perceptual experiences) that must not hold should there be a pony in the room.

Perceptions are an excellent way to justify a true belief.

In other words, with JTB, having a mere BELIEF that there's a pony in your living room is insufficient to qualify as knowledge--even if there IS a pony in your living room. If, for example, you imagined it in a fevered state, and coincidentally your pony managed to get into the living room, most JTBers would say that while it was a true belief, it was accidental and not justified, and therefore NOT knowledge.

Hearing the pony, though, or seeing it, would justify the belief if that information actually caused the belief.

And I am equipped with powers of awareness that allow me to complete this task with a 100% success rate. With a few additional loose-ends to tie up--I can make it impossible for me to not know whether the pony is in the room, or not.

I'm afraid this is untrue, Ed. Your powers of awareness are not capable of a 100% success rate. Even mentally sound people are all subject to misperception and being fooled by illusions.

Then there are those who are subject to hallucinations. I once had a vocational rehabilitation client, a schizophrenic, who saw COWS at unusual times and in unusual places. With the proper therapy she became quite functional, but became convinced that cows in her living room were not likely really there--seeing and hearing them was insufficient evidence.

For most of us, most of the time, our general confidence in the reliability of our perceptions can approach 100%, but only asymptotically. To posit certitude on the basis of our senses is to assert an article of faith unjustified by the facts of human existence.

Confidence in human perceptual efficacy is warranted--certitude is dogma.

Nathan Hawking

Post 29

Thursday, May 5, 2005 - 2:27am

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Nice rhetoric, Nathan. Now, I ask you plainly, to please address the issue which you brought up--this blithe dismissal stuff gets old, and fast.

$64,000 question: when you said that "certitude is dogma", where you integrating my final point:

-----------
"The short answer, however, is that context will dictate the parameters for certitude (as I alluded to above)."
-----------

... or were you selectively omitting it (to reduce the cognitive dissonance between it and what your college professors have "dispensed" to your mind)?

Let me ask this another way:
Do you somehow think that it is "impossible" that I could ever make it "impossible" NOT TO KNOW whether or not a pony is currently taking up space in the living room?

I can't wait for your answer,
Ed
(Edited by Ed Thompson
on 5/05, 2:28am)

Post 30

Thursday, May 5, 2005 - 2:41am

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Nathan writes:
------------
"Correct me if I'm mistaken, but weren't you offering

'knowledge is being able to distinguish something from all other known entities'

as a SUBSTITUTE for

'justified true belief'?"
------------

Ed writes:

I most certainly was (thanks for noticing) Nathan--that is, until you completely ignored the insight of my essay...

No, I disagreed with it.

... and proceeded to revert back to the JTB concept after a blithe dismissal of its main theme in an unargued-for appeal to a "common" sense:

Revert? I thought we were discussing JTB vs. your notion. It hardly seems a 'reversion' or 'blithe' to discuss one of the elements of your argument.

------------
"You seem to imply that because knowledge "cannot be false" it belongs in a different category, but I can see no logical or semantic justification for this distinction.

In the absense of such, I'm forced to honor the prevailing sense of those terms: All knowledge is belief, but not all belief is knowledge. If we agree that knowledge is belief, we have the "B" in JTB.

If you assert knowledge "cannot be false"--the same as saying "true"--we now have the "TB" portion of the JTB."
------------

And after asking myself "Did this guy even read my essay?" I said: what the hell--I'll take him on on his own home field.

Let's not get personal.

Clearly I read your essay. JTB was one of the elements of your essay. It is altogether reasonable to ask you what you believe the defects of JTB are.

In fact, you still have not made it clear exactly what you think is wrong with JTB. You simply make the assertion again, later in this post: "the now-proven-to-be limited conception of JTB."

What limitations?

------------
"If so, then I'm suggesting that your definition is inadequate. If not, then I'm uncertain as to the point of your article. Would you clarify?"
------------

My definition WAS inadequate (again, thanks for noticing). The adequate--ie. refined, thanks to your criticisms--definition is "veridical conceptual discernment of existents" (not of entities).

Ed, I'm afraid your definition still has a multitude of problems.

For example, what is the difference between a "conceptual discernment" and a "concept" or a "discernment"?

"Discern" generally denotes differentiation--is it possible to hold a concept without differentiation? Unless you're using discernment in some odd sense, it sounds like a redundancy, subsumed within the meaning of "concept."

Veridical means truthful. Concepts are beliefs.

That translates to: True Beliefs

Further, existents sounds like a weak form of justification. All in all, I think you're saying Justified True Beliefs when you say "veridical concepts of existents" (dropping the 'discernment' as redundant).

I say 'existents' is a weak form of justification because, as I showed in other posts, the FACTUALITY of a True Belief (veridical concept) is insufficient justification if that belief were arbitrarily acquired.

You reminded me that we can have concepts of non-entities (concepts about attributes, concepts about properties, concepts about relations, concepts about methods, etc)--and I thank you for that.

The point of my article was to offer a superior conception of what it is that knowledge is--so that humans can make even more progress in dealing with reality than is currently possible with the now-proven-to-be limited conception of JTB.

Can you show me what you think the limitations of JTB are?

------------
"Now you seem to be addressing the "justified" aspect. Does that mean you accept the "true belief" portion of JTB?
------------

[personal comments snipped]

The only conception of JTB that I accept is CJTB (Conclusively-Justified True Belief), which renders the belief aspect a non-integrated floating abstraction. We cannot fail to believe in something that is conclusively justified--just as we cannot conceive of round squares.

So, you would not consider what we learn from encyclopedias to be "knowledge"?

------------
"EXACTLY what would you propose as a "conclusive" (by which I assume you mean assuring certitude) condition or test for the presence of living room ponies?"
------------

Ponies take up space. They cannot "fail" to take up space (existence exists). Give me 2 yardsticks (one in each hand) to swing around in this room--and I will tell you whether there is something in there (besides the knowable furniture) "taking up space." Is that good enough for you, Nathan, or will you postulate an invisible pony who can see my every move before I make it...

As I discuss in some detail in another post, sensory data does usually provide a high degree of justification for our beliefs--but it does not provide certitude. I won't repeat myself here.

Think about this, Ed: You point out that demanding omniscience before we call something knowledge (your pi example) is a fallacy, and I would point out that demanding certitude (your CJBT) before we call something knowledge is just as fallacious.

It is a fallacy because 1) perceptual certitude is inattainable, and 2) certitude is not requisite for extremely reliable knowledge.

Nathan Hawking

(Edited by Nathan Hawking on 5/05, 6:27pm)

Post 31

Thursday, May 5, 2005 - 10:31am

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Nathan, you've certainly (pun intended) upp-ed the ante here, by coming back with a reasoned reply.

I apologize for taking it personal and reacting in a somewhat impolite manner--I was reacting on emotion / intention that I had "projected" into your words.

This brings up a great negative example, "psychological projection," which is NOT a veridical method. It is not veridical because of its nature (identity). It cannot EVER be veridical, because it cannot ever act in ways contrary to its nature.

Do you see this "veridical" truth about "psychological projection," Nathan? It comes from a conceptual discernment of the type of thing that something is--and we learn about its particularly-limited nature, by distinguishing it from veridical methods (e.g. logical deduction) of knowledge acquisition.

Your reply had many directed questions though, and I'll say more later on that (I'll eventually attempt an answer to all of these questions).

Ed

Post 32

Thursday, May 5, 2005 - 11:08am

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Ed writes:

Nice rhetoric, Nathan. Now, I ask you plainly, to please address the issue which you brought up--this blithe dismissal stuff gets old, and fast.

I'd urge you to drop the personal stuff, Ed. I know of no way I'm engaging in "blithe dismissal" and I see no purpose to your repeating that, beyond inflammatory rhetoric. Can we stick to the issues?

$64,000 question: when you said that "certitude is dogma", where you integrating my final point:

-----------
"The short answer, however, is that context will dictate the parameters for certitude (as I alluded to above)."
-----------

No, I was not integrating it, I was denying it.

... or were you selectively omitting it (to reduce the cognitive dissonance between it and what your college professors have "dispensed" to your mind)?

You're getting personal again, referring to my motives and mindset or my putative education. So far as I know, Nathan Hawking was not the subject of your article. Can we stick to the actual issues?

Let me ask this another way:

Do you somehow think that it is "impossible" that I could ever make it "impossible" NOT TO KNOW whether or not a pony is currently taking up space in the living room?

Be careful with your terms. I never said anything about the impossibility of knowing.

We are discussing the nature of "knowledge" and whether "certitude" is possible and essential to knowledge--two different issues.

I believe that KNOWLEDGE is possible but I've seen no evidence which demonstrates the possibility of perceptual certitude.

I'm not going to be drawn into your triple-negative 'impossible to make it impossible not' question for rather obvious reasons, not the least of which is that certitude is YOUR claim and your burden of proof, not mine.

I'll believe in certitude when you can demonstrate it.

Nathan Hawking

Post 33

Thursday, May 5, 2005 - 1:07pm

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Jeff wrote:

The definition you provide is but one way of definining pi (albeit one of the common ways), but not the only way.

True.

Remember as an 'existent' pi (the thing not the 'number' which is conceptual not physical) has all of it's attributes, not just the ones stated in the definition.

We should be careful not to beg the question, though. Calling something like pi an 'existent' is inviting just that.

Doesn't it seem to you that this is the very question we are trying to approach, or one of them? It does to me.

(Calling 'pi' an existent, i.e. a real thing not just a concept that's used as a rule, is potentially misleading and certainly controversial. ...

Controversial indeed. I think that would be a form of the mathematical Platonism to which I referred earlier.

http://en.wikipedia.org/wiki/Philosophy_of_mathematics

Mathematical realism or Platonism:
Mathematical realism holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same.

... What I'm trying to express here is that circles, for example, do exist; they do have diameters and circumfra and those things, suitably quantified, can be used to calculate a ratio.)

Exactly. That's why I said you were invoking a form of Platonism. (See above.) I don't consider that a philosophical sin, but it can have confusing consequences. I'd be willing to call them "mathematical entities" or "mathematical existents" but doubt I would use an unqualified form.

On this basis, we could conclude that the series definition, or the value of the integrals containing it, or the Euler equation, or any of dozens of other forms is pi. (With the terms suitably expressed, of course.)

That might sound persuasive if it wasn't fairly clear that the same objection applies to the Euler equation et al. You are treating them as "entities" when they are, in fact, equations. Are equations "existents" or "entities"?

This view requires some very careful scrutiny. Step by step:

1. Pi is a Greek letter. As such, it has no inherent mathematical significance.

2. Pi only acquires mathematical significance by definition. Ordinarily, it is defined as the ratio of a circle's diameter to its circumference. (RCDTC)

3. By various means, we acquire some mathematical knowledge about the numerical value of pi-as-RCDTC (3.14159 26535 89793... ) and its nature (irrational ,etc.).

4. Mathematicians discover (or invent, if one rejects mathematical Platonism) various formulae which generate the numerical value of pi. For example, Leibniz' formula:

4 * (1/1 - 1/3 + 1/5 - 1/7 + 1/9 ...) = pi

Now, as I see it, the central question is one of identity. You are saying above that pi IS "4 * (1/1 - 1/3 + 1/5 - 1/7 + 1/9 ...)" as if it had an "instantaneous" identity.

In contrast, I would say that "4 * (1/1 - 1/3 + 1/5 - 1/7 + 1/9 ...)" is an algorithm which, if followed in perpetuity, is numerically equivalent to pi.

To put this into perspective, is the "entity" or "existent" (4 + 1) the same as (3 + 2)? To my philosophical ear, it seems rather silly to see them as anything more than symbolic representations of algorithms which produce the same value.

In other words, I would not say that (4 + 1) IS (3 + 2), but I might say they are (when processed) numerical equals. Similarly, I don't think it's particularly meaningful to say that pi IS "4 * (1/1 - 1/3 + 1/5 - 1/7 + 1/9 ...)."

(Perhaps it's just my mood, but this is beginning to feel like an angels-on-pinheads monologue. I may give the remainder short shrift.)

Alternatively, one can define pi as the sum of these series, or the limits of suitably chosen bounds, and use of those limits or sums is practical, and understanding those expressions is real knowledge.

I.e. there's nothing Platonic about any of that.

I wonder if, after my above discussion and reference, you still feel that way.

...
That means, among other things, that it is knowledge we get when we use pi to perform the calculations.

As just one example, it's possible to do extensive circuit analysis (not my area of expertise), using equations in which pi appears, without ever knowing the decimal-equivalent numeric value at all. This is surely knowledge.

Undoubtedly.

But we should be careful not to confuse this sort of knowledge with what I was discussing. Remember, I was critiquing the statement: "We do, in fact, know 'the last number' of pi. It is: pi."

The sense in which you use "know" there is the problem. You are treating it as a Platonic "entity" or "existent" while Ed was treating it as a string of decimal digits.

If I say "let P be the set of all prime numbers" P "is" in that sense "all prime numbers," but it exceeds the bounds of meaningful discourse to say "I know all prime numbers: P."

Added in editing: P.S. With respect to your question about conceptual content: remember concepts are open ended. What that implies here is that I can know what pi is (i.e. that conceptual content is not empty) without being able to calculate an infinite number of decimal places. My point was, there is nothing particularly necessary, for the purposes of knowing pi and using it to gain lots of other knowledge, about expressing it in decimal form.

Yes, I agree that we can use it in purely symbolic form knowing only its relationship to other symbols and the rules for manipulating those symbols. Computers, of course, do that all the time. (Engineers too.)

In the end, though, we must ask ourselves, as did Bertrand Russell, what are we really talking about--i.e., when is it really knowledge and not just symbol manipulation, and why does it seem to apply to the physical world so well?

Huge questions. I think folks have been debating that for some time.

Nathan Hawking

Post 34

Thursday, May 5, 2005 - 2:00pm

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Ed wrote:

Nathan, you've certainly (pun intended) upp-ed the ante here, by coming back with a reasoned reply.

I apologize for taking it personal and reacting in a somewhat impolite manner--I was reacting on emotion / intention that I had "projected" into your words.

Passion gone astray, perhaps.

This brings up a great negative example, "psychological projection," which is NOT a veridical method. It is not veridical because of its nature (identity). It cannot EVER be veridical, because it cannot ever act in ways contrary to its nature.

Psychological projection is the usually-unconscious assumption that others think as we do. Sometimes we're correct, and sometimes we're not. Its limitation lies in the fact that it IS an assumption and not knowledge based upon fact.

Do you see this "veridical" truth about "psychological projection," Nathan? It comes from a conceptual discernment of the type of thing that something is--and we learn about its particularly-limited nature, by distinguishing it from veridical methods (e.g. logical deduction) of knowledge acquisition.

I'll try to answer that question if you'll try to express it in plain language of ten words or less. I mean no offense.

(What on Earth, for example, is a "'veridical' truth"? As opposed to what, a false truth?)

Nathan

Post 35

Thursday, May 5, 2005 - 3:23pm

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Nathan,
I can't address your questions now, though they are deserving of lengthy,
clear responses. I will, in time.
Also, I erred in starting this discussion -- diverting the thread from discussing
Ed's article. So, when I can take the time (or you can) I'll start a different
thread to discuss this. (Possibly there's already a philosophy of mathematics
thread on the site somewhere.)

Thanks for your cogent responses. I'll respond soon.

Jeff

Post 36

Friday, May 6, 2005 - 1:59am

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Nathan, as promised (thanks for waiting the full 72 hours!) ...

***ALERT***This post is over 1000 words long--read at your own risk.

****
A quick review of the 2 thinking errors blasted by my essay:
-conventionally-unsolved, Humean Problem of Induction--states that we can't know generalities
-Fallacy of Infinite (Absolute; acontextual) Precision--states that we can't know particulars
****

And now, your questions (numbered for reference or refutation):

------------
1. Do you not consider knowledge "belief"?
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No, beliefs can be wrong, knowledge can't.

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2. What about justification?
------------

I'm sympathetic to the Cogency Principle (from Audi's Epistemology): In order to know something, one needs grounds for it from which one can (in principle) argue cogently for it. [Knowing involves either knowing--in principle, but not always in practice--why (ie. noncontradictory integration) it is that you know, or simply knowing--in principle, but not always in practice--how (ie. grounds) it is that you know]

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3. But how does your knowledge as "being able to distinguish something from all other known entities [edit: existents]" definition work here?
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(from OPAR): Knowledge ... is to identify ... Every type of question reduces to: "What is it?" [And we know what a thing is, only in relation to what it is not--knowledge is a relational phenomenon]

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4. The presence or absense of the pony in the living room would seem to be more a state-of-affairs than an "entity." Perhaps that's one limitation of your definition?
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Yes, as orginally stated, it WAS a limitation--now transcended by the edit directly above ("states" are existents).

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5. We do "know" pi in the sense that we know it's�'that numerical value which is the ratio of a circle's diameter to its circumference.' In fact, we know this because it's the�definition of pi.
------------

Yes. We know it, even if we don't, in actuality, know everything about it--such as its trillionth digit, for example (though, we can, in principle and potentially, know as much about it as we yearn for--because we know what it is, and is not, among everything else known). We know it because of its unique place among other known things. We have a veridical conceptual discernment regarding what it is that pi is. Therefore, our knowledge of it cannot ever be false.

------------
6. Correct me if I'm mistaken, but weren't you offering

'knowledge is being able to distinguish something from all other known entities'

as a SUBSTITUTE for

"justified true belief"?

If so, then I'm suggesting that your definition is inadequate.
------------

Yes, I'm offering veridical conceptual discernment (veridical distinguishability) as a substitute for any belief-based definition of knowledge. Can you provide either reasoning, example, or analogy that supports your contention that my definition is inadequate (e.g. Where is it limited?; What is missed?)?

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7. Now you seem to be addressing the "justified" aspect. Does that mean you accept the "true belief" portion of JTB?*
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*Answered earlier: I only accept the "true belief" portion of JTB with the "conclusively-" qualifier--Conclusively-Justified True Belief (CJTB), which renders "belief" an unintegrated floating abstraction (something that can only hinder progress in epistemology).

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8. EXACTLY what would you propose as a "conclusive" (by which I assume you mean assuring certitude) condition or test�for the presence of living room ponies?*
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*Answered earlier: Selective focus on the axiom of existence (material objects take up space) while combing the space in the living room--conclusively justifies certitude in this matter.

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9. Your powers of awareness are not capable of a 100% success rate. Even mentally sound people are all subject to misperception and being fooled by illusions.
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I mentioned 100% success in relation to a limited context. You have simply dropped context here-rearing the ugly head of the untenable bromide that, because man has been wrong (sometime, somewhere), then man cannot ever be right. I retort that instances of "being right" are logically necessary, for the concept of "being wrong" to ever enter a human mind (success is required for failure to be a coherent concept--success serves as the logical genesis, and standard, of what failure is).

------------
10. Then there are those who are subject to hallucinations. I once had a vocational rehabilitation client, a schizophrenic, who saw COWS at unusual times and in unusual places. With the proper therapy she became quite functional, but became convinced that cows in her living room were not likely really there--seeing and hearing them was insufficient evidence.
------------

See #9 reply above.

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11. For most of us, most of the time, our general confidence in the reliability of our perceptions can approach 100%, but only asymptotically.
------------

Our perceptual experience is not true or false, it just is. You are conflating perceptual experiences with conceptual powers (no doubt invoking the pseudo-concept: perceptual judgment). Perceptual experience is a direct pickup of exactly what it is that is in our environment. Conceptual powers (which can err, but can be made not to) identify what it is that the perceptions are about.

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12. To posit certitude on the basis of our senses is to assert an article of faith unjustified by the facts of human existence.
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Between faith and cogency, you pick faith--I pick cogency. I can marshal evidence and reasoning in support of MY choice--can you do the same for YOUR choice? I think not.

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13. Confidence in human perceptual efficacy is warranted--certitude is dogma.
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Only acontextual certitude is dogma--can you think of the last time that you needed to know something--which didn't even have a context to it? I can't.

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14. In fact, you still have not made it�clear exactly what you think is wrong with JTB. You simply make the assertion again, later in this post: "the now-proven-to-be limited conception of JTB."

What limitations?
------------

To be true to knowledge (pardon the wordplay), which is something whose falsification is impossible, JTB needs to be qualified to CJTB; as stated above. Why does this matter? Otherwise, you get legal- and logical-positivists who, not acknowledging knowledge of what is right and good for man on earth, pass laws (and fool folks into supporting programs) that contradict the nature of man. Things with such importance as Individual Rights, become merely currently-justifiable beliefs--possible expendible as our truths (read: beliefs) change. Truth is obscured by the word belief and a social metaphysics ensues, based on the majority belief. But truth is true regardless of (often IN SPITE OF) belief. We must pay homage to the genesis of truth in reality--JTB doesn't.

Thinking of knowledge as effective discernment solves the dilemma of what is known and what is thought to be known (what is merely justiably believed). As an example, I cannot be wrong about the position of Canada (north) in relation to Mexico--but beliefs are things which can, at times, be wrong. Therefore, signifying knowledge as a belief clouds the issue of what cannot be false--VCD doesn't; and is therefore a superior signification of what knowledge is.

------------
15. For example, what is the difference between a "conceptual discernment" and a "concept" or a "discernment"?

"Discern" generally denotes differentiation--is it possible to hold a concept without differentiation? Unless you're using discernment in some odd sense, it sounds like a redundancy, subsumed within the meaning of "concept."
------------

You're right, Nathan. It is not possible to hold a concept without differentiation. It was merely a useful redundancy for me to speak of conceptual discernment--to hammer the point home that correct concept formation automatically yields knowledge.

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16. Veridical means truthful. Concepts are beliefs.
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I'd say that veridical means directly truthful, or something along those lines--to accentuate that it is not possible to err with that which is veridical. Concepts are not beliefs--concepts are that by which we are aware of contrast in the world.

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17. I say�'existents' is�a weak form of justification because, as I showed in other posts, the FACTUALITY of a True Belief (veridical concept) is insufficient justification if that belief were arbitrarily acquired.
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Right! And I say that that which is acquired by the dual-epistemological process appropriate to man (the marriage of perception and reason) is a conclusive justification of things. Something (FACTUALITY) that is only later found to be found factual, or "right"--was always true, but was not always knowledge. On this point, we seem to agree.

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18. So, you would not consider what we learn from encyclopedias to be "knowledge"?
------------

Much of what we learn from encyclopedias is merely expert opinion. Notable exceptions would be axiomatic concepts, empirical falsifications, logical deductions, openly subjective inferences (perspectives that are transparently explained as such), and most relational matters, such as the geological position of one landmark in relation to another.

------------
19. You point out that demanding omniscience before we call something knowledge (your pi example) is a fallacy, and I would point out that demanding certitude (your CJBT) before we call something knowledge is just as fallacious.
------------

Omniscience is not the standard, effective differentiation is. We can be certain (having certitude) of how something relates to other things (Canada north of Mexico, etc).

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20. It is a fallacy because 1) perceptual certitude is inattainable, and 2) certitude is not requisite for extremely reliable knowledge.
------------

Perceptual certitude is a redundancy (I think you are viewing perception--pardon the pun--as: perceptual judgment; but we only judge via our conceptual faculty, not via our perceptual experiences). Regarding point 2, certitude is not requisite for extremely reliable beliefs--to put a nail in this coffin: conflation of knowledge with merely "reliable" beliefs IS THE PROBLEM my essay was aimed at, Nathan.

Ed

Post 37

Friday, May 6, 2005 - 12:09pm

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Nathan, a postscript:

A key underlying theme of my essay is that knowledge is relational (we need only to effectively discern relations--in order to be in possession of knowledge). Expanding on my last example, the Canada-north-of-Mexico example, would make this more clear.

Now, regarding this example, a Humean, Kantian, or, a logical positivist (ie. someone who thinks wrong) would argue that the knowledge of Canada being north of Mexico is not informative (about the external world). They would go on to state that the concept of "being north of" has merely to do with relations of ideas, or with "limited" mental categories whereby we must filter how we see the world.

These wrong-thinkers (WTs) are somewhat right about the patches of land (to be later dubbed Canada) and the patches of land (to be later dubbed Mexico). These patches stand in a certain relation to each other--and, beyond the initial perception of their place in space, it seems a priori to state that one is north of the other [though I'd argue that to even have a grasp of the concept "north"--requires initial a posteriori experience; and an expanding a priori zone].

Where the WTs fail, is when we've conceptually discerned that the north patch needs identification as a something--to differentiate it from all other somethings. In order to keep it separated, we conceive of a name (an identifier) for that land inside its borders--"Canada." We do the same for Mexico. Now we have conceptual discernment (of Canada from Mexico) that goes beyond mere examination of various patches of land--and mathematic calculation of relations between said patches.

The land in Canada was always north of Mexico. Humans, by effectively distinguishing the patches of land as 2 different countries (by proper concept formation), have knowledge of the external world that cannot be false. While, the REASON that the Canada-north-of-Mexico proposition cannot be false (it has certitude) stems from the basic patches of land, the "informative" aspect stems from how we think about the patches (concepts), not from the previously-unintegrated patches themselves.

Nathan, take any of the 4 examples of knowledge in this thread:

1) Morning Star-Evening Star-Venus
2) Helium-Sulfide
3) Living-Room-Ponies
4) Canada-North-of-Mexico

... and see if you can argue against them in a cogent manner--I think you cannot.

Remember, considering the pony, I had to first make it impossible to be wrong about it, and so I selectively utilized the 2 axioms (which limit what can be true of the world): Existence exists and Existence is Identity. This helped me to conceptualize that ponies take up space (and that they cannot ever cease to), and that rooms have limited space.

For clarity, imagine a much smaller room (say, 2-foot by 4-foot by 4-foot); one which could barely accomodate the pony. Now imagine me entering the room (looking for the pony). I am crouched in the room and able to touch all walls simultaneously--in this limited context Nathan, can I be certain or not, regarding the pony's presence in the room?

Ed

Post 38

Friday, May 6, 2005 - 3:16pm

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I would like to point out "one" minor flaw:

'One' is NOT a prime number.

I have some other problems with the article, but I'll have to postpone writing for lack of time.

PS:

***absolutely irrelevant tangent*** (in case someone needs a break)

Puzzle: Ed and Nathan are related by five fives.

Post 39

Friday, May 6, 2005 - 6:31pm

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Ed Thompson wrote:

This post is over 1000 words long--read at your own risk.

Thanks, Ed. If I expire before I complete reading it, try not to feel too guilty.

Your scrupulousness in responding to every point is greatly appreciated, but lest every sentence swawn ten which spawns ten which spawns ten, etc., I will elide much and leave only those things I judge central to the debate.

Feel free to resurrect anything vital you feel I've overlooked.

And now, your questions (numbered for reference or refutation):
Nathan wrote:
------------
1. Do you not consider knowledge "belief"?
------------

No, beliefs can be wrong, knowledge can't.

I asked if you considered knowledge beliefs, not whether you considered beliefs knowledge. There's a vast difference.

That's why there's Knowledge = JBT, too. Not Knowledge = B.

You know, T as in True?

------------
6. Correct me if I'm mistaken, but weren't you offering

'knowledge is being able to distinguish something from all other known entities'

as a SUBSTITUTE for

"justified true belief"?

If so, then I'm suggesting that your definition is inadequate.
------------

Yes, I'm offering veridical conceptual discernment (veridical distinguishability) as a substitute for any belief-based definition of knowledge.

Can you provide either reasoning, example, or analogy that supports your contention that my definition is inadequate (e.g. Where is it limited?; What is missed?)?

Yes.

You say: 'knowledge is being able to distinguish something from all other known entities (existents)'.

(Unknown) knowledge can be invented.

Knowledge integrates as well as distinguishes.

For starters.

------------
7. Now you seem to be addressing the "justified" aspect. Does that mean you accept the "true belief" portion of JTB?*
------------

*Answered earlier: I only accept the "true belief" portion of JTB with the "conclusively-" qualifier--Conclusively-Justified True Belief (CJTB), which renders "belief" an unintegrated floating abstraction (something that can only hinder progress in epistemology).

JTB does NOT render belief "an unintegrated floating abstraction."

Would an "unintegrated floating abstraction" qualify as Justified?

------------
8. EXACTLY what would you propose as a "conclusive" (by which I assume you mean assuring certitude) condition or test for the presence of living room ponies?*
------------

*Answered earlier: Selective focus on the axiom of existence (material objects take up space) while combing the space in the living room--conclusively justifies certitude in this matter.

Yes, yes. We know existence exists. We know that material objects take up space.

We also know that human beings can perceive things which aren't really there.

------------
9. Your powers of awareness are not capable of a 100% success rate. Even mentally sound people are all subject to misperception and being fooled by illusions.
------------

I mentioned 100% success in relation to a limited context. You have simply dropped context here-rearing the ugly head of the untenable bromide that, because man has been wrong (sometime, somewhere), then man cannot ever be right.

No. I'm afraid you are switching contexts and arguments.

Can you point to one place where I said "man cannot ever be right"? No, of course you can't. That's nonsense.

Why? Because I'm arguing that humans CAN and DO have knowledge which meets the criteria of Justified True Belief (as I will eventually refine that concept).

What I deny is that humans are capable of justified CERTITUDE (in its absolute sense). What I deny is that your form of certitude is a requisite for knowledge.

------------
10. Then there are those who are subject to hallucinations. I once had a vocational rehabilitation client, a schizophrenic, who saw COWS at unusual times and in unusual places. With the proper therapy she became quite functional, but became convinced that cows in her living room were not likely really there--seeing and hearing them was insufficient evidence.
------------

See #9 reply above.

Too bad the argument is misguided. I was arguing against certitude, not the ability of humans to hold accurate knowledge.

If you define "knowledge" as entailing certitude, then of course an argument against certitude is an argument against knowledge. But you apparently forget that is YOUR definition and argument, not mine.

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11. For most of us, most of the time, our general confidence in the reliability of our perceptions can approach 100%, but only asymptotically.
------------

Our perceptual experience is not true or false, it just is.

That statement belies a vast body of evidence. Once again you attempt to define your argument into validity.

If you define "perception" as entailing the necessarily existent, then of course a misperception is not really a perception and perceptions are 100% reliable.

But that's nonsense. People regularly sense/perceive "things" which have no basis in reality. You are simply going to be forced to ignore that fact to maintain a certitude dogma.

Are you beginning to see the pattern of circularity in your thinking and definitions?

You are conflating perceptual experiences with conceptual powers (no doubt invoking the pseudo-concept: perceptual judgment). Perceptual experience is a direct pickup of exactly what it is that is in our environment. Conceptual powers (which can err, but can be made not to) identify what it is that the perceptions are about.

We can discuss that in my new thread:

Concepts and Percepts--Are They Different? Are They Certain?

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12. To posit certitude on the basis of our senses is to assert an article of faith unjustified by the facts of human existence.
------------
Between faith and cogency, you pick faith--I pick cogency.

I can marshal evidence and reasoning in support of MY choice--can you do the same for YOUR choice? I think not.

Don't put words in my mouth. I'm stating that YOUR assertion of perceptual certitude is an act of faith, I'm not "picking faith."

"I pick cogency" is just another way of saying "I'm convinced." Which, in the face of contrary evidence, is merely an assertion of faith or dogma that the senses are 100% reliable.

Where is your evidence that the senses are 100% reliable?

To falsify that claim I merely have to produce ONE example of a person sensing or perceiving something which was not actually real. I have done so--illusion and hallucination.

I can do so again. You are doubtless familiar with the phenomena of 'phantom limbs.'

Now, PLEASE, don't try to define these examples out of existence by claiming they are not "really" perception or sensation. The circularity of that would be visible from the moon.

As a reminder, you are claiming that sense/perception is 100% reliable, i.e., permits certitude. The overwhelming evidence is to the contrary.

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13. Confidence in human perceptual efficacy is warranted--certitude is dogma.
------------

Only acontextual certitude is dogma--can you think of the last time that you needed to know something--which didn't even have a context to it? I can't.

I was not defining dogma. I was citing "certitude in human perceptual efficacy" as an INSTANCE of dogma.

Can you see the difference?

In other words, if you believe that "certitude in human perceptual efficacy" is possible, despite all evidence to the contrary, you are being dogmatic.

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14. In fact, you still have not made it clear exactly what you think is wrong with JTB. You simply make the assertion again, later in this post: "the now-proven-to-be limited conception of JTB."

What limitations?
------------

To be true to knowledge (pardon the wordplay), which is something whose falsification is impossible, JTB needs to be qualified to CJTB; as stated above.

If ("conclusive") certitude were possible, something far from demonstrated, and necessary to one's definition of knowledge, which I would also dispute, then "Conclusive Justified True Belief" is merely a redundancy.

If we are saying that "justification" is not really justification, then drop it altogether. If something really is "conclusive," what further justification is required?

If we are saying that a conclusive certitude is a requisite for justification, then simply define "justification" to include this. After all, that is the word in the JBT formulation which evokes debate and requires definition.

[Argument for the 'need' for certitude snipped.]

Reality is what it is. If certitude is possible, fine, we'll put it to good use in ethics and law. If certitude is NOT possible, then we'll make ethical decisions and formulate laws based upon our closest approximations and best judgments.

Claiming we need certitude doesn't make it ours. Let us be realists, not epistemological looters.

Truth is obscured by the word belief and a social metaphysics ensues, based on the majority belief. But truth is true regardless of (often IN SPITE OF) belief. We must pay homage to the genesis of truth in reality--JTB doesn't.

The term "belief" does not obscure the truth in the least.

There are true beliefs.
There are false beliefs.

See how easy that is? Do you find either of those statements obscure? I don't.

"Belief" alone says absolutely NOTHING about the source of the beliefs, social or otherwise.

Merriam-Webster says:

"BELIEF: 3. conviction of the truth of some statement or the reality of some being or phenomenon especially when based on examination of evidence."

http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=belief

Thinking of knowledge as effective discernment solves the dilemma of what is known and what is thought to be known (what is merely justifiably believed).

No, all you are doing is using different words. I don't think you clearly understand all the ramifications of Justified True Belief.

"Effective discernment" is another way to say "true."

JTB has no "dilemma of what is known and what is thought to be known (what is merely justifiably believed)" to be "solved." At least none you've identified.

JTB IS the proposed resolution to the question of "what is known and what is thought to be known." To be knowledge, according to JTB, there must be:

1. A belief;
2. The belief must be true;
3. The belief must not be accidental, i.e., it must be justified.

As an example, I cannot be wrong about the position of Canada (north) in relation to Mexico--but beliefs are things which can, at times, be wrong. Therefore, signifying knowledge as a belief clouds the issue of what cannot be false--VCD doesn't; and is therefore a superior signification of what knowledge is.

You're mixing an argument against the term "belief" with an argument against JBT. And wrong about both.

As you correctly note, "but beliefs are things which can, at times, be wrong." Put another way, beliefs can be RIGHT, TRUE. Calling "knowledge" in part a "belief" clouds nothing at all, because, it fulfills the definition of a belief.

Has anyone claimed "beliefs are knowledge"? I think not.

JBT correctly holds that "knowledge is belief," something quite different, but then QUALIFIES it with "true" and "justified."

[Arguments about the redundancy of your terms and their equivalency to JBT snipped for the sake of focus.]

------------
18. So, you would not consider what we learn from encyclopedias to be "knowledge"?
------------

Much of what we learn from encyclopedias is merely expert opinion. Notable exceptions would be axiomatic concepts, empirical falsifications, logical deductions, openly subjective inferences (perspectives that are transparently explained as such), and most relational matters, such as the geological position of one landmark in relation to another.

I wonder if you have any idea how little of your knowledge would qualify, given those criteria?

------------
19. You point out that demanding omniscience before we call something knowledge (your pi example) is a fallacy, and I would point out that demanding certitude (your CJBT) before we call something knowledge is just as fallacious.
------------

Omniscience is not the standard, effective differentiation is. We can be certain (having certitude) of how something relates to other things (Canada north of Mexico, etc).

Wait just a minute! Have you actually independently VERIFIED that Canada is north of Mexico, or just taken the words of mapmakers?

Have you verified that the Earth is spherical?

That astronauts actually walked on the moon?

That Lincoln died at Ford's Theater?

By what means did you verify any of these?

(See 18 above.)

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20. It is a fallacy because 1) perceptual certitude is inattainable, and 2) certitude is not requisite for extremely reliable knowledge.
------------

Perceptual certitude is a redundancy (I think you are viewing perception--pardon the pun--as: perceptual judgment; but we only judge via our conceptual faculty, not via our perceptual experiences). Regarding point 2, certitude is not requisite for extremely reliable beliefs--to put a nail in this coffin: conflation of knowledge with merely "reliable" beliefs IS THE PROBLEM my essay was aimed at, Nathan.

You apparently hold that unless something is CERTAIN it is not a perception, nor a concept, nor knowledge.

I think this subject significant enough, Ed, that I'm starting a new thread devoted to it:

Concepts and Percepts--Are They Different? Are They Certain?

Why don't you join me there? I'll not respond here and replicate my efforts.

Remember, considering the pony, I had to first make it impossible to be wrong about it, and so I selectively utilized the 2 axioms (which limit what can be true of the world): Existence exists and Existence is Identity. This helped me to conceptualize that ponies take up space (and that they cannot ever cease to), and that rooms have limited space.

You may repeat that "Existence exists and Existence is Identity" all you wish. That doesn't make a delirium-induced belief in a pony a physical-world existent, does it?

You did not make it impossible to be wrong about the pony. You merely made it very unlikely--assuming, of course, that you're sane.

For clarity, imagine a much smaller room (say, 2-foot by 4-foot by 4-foot); one which could barely accomodate the pony. Now imagine me entering the room (looking for the pony). I am crouched in the room and able to touch all walls simultaneously--in this limited context Nathan, can I be certain or not, regarding the pony's presence in the room?

That's the nature of an asymptote, Ed. You may refine your tests all you wish, and all you can do is add decimal places to the 99.9999% likelihood that you are correct. Adding 9s does not convert it to 100%. Certitude is 100%.

Here is an unlikely, though conceivable, scenario:

One month ago I hit you with a tranquilizer dart on your way to work, and spirited you away to my secret laboratory where I study the brains of philosophers. Your brain is now wired to a very large bank of computers which simulate the "reality" you are currently experiencing.

What are the odds against this? 1,000,000,000,000 to 1? Maybe not even that high, though it's impossible to say for certain. (Ahem.)

Remember, we are talking about a quantifiable concept here: CERTITUDE, 100%!

For that, the odds against my scenario would have to be INFINITE. But they aren't. Experiments which stimulate vivid dreams and false perceptions are rather commonplace.

If your theory of knowledge requires certitude, I'm afraid little would qualify.

I believe any valid theory of knowledge and concepts must allow for uncertainty.

Nathan Hawking