A Pre-emptive Dialectic (to weed out the weaker objections)

The Battle between Bayesia and Aristotelia (or "Randia" - if preferred)

Aristotelian: When paper money is damaged (such as when a dollar bill tears) there must be a rule for acceptable exchange that will allow for new replacement bills to enter the market. A bank, for example, should exchange some partially torn bills, but not others. I declare that I know the rules that will work and the rules that will fail, before even running an experiment and using further perception - ie. with no new, special empirical knowledge.

Bayesian: That's impossible. How can you know - with certainty - what will work and what will fail, before you've seen any results.

Aristotelian: I have a mechanistic understanding of the entire system (the entire context).

Bayesian: What? An "understanding?" "Understandings" can't help you achieve certainty - all knowledge is empirical.

Aristotelian: Correction: Knowledge originates in perception (empirically), but does not terminate there - man is not limited by sensory powers alone, man has intellectual powers as well.

Bayesian: Speak for yourself - I can't stand when you generalize, telling me what does - and does not - have "universality" regarding human nature.

Aristotelian: Fine. Speaking for myself then, I stand by my original claim - I can still make the correct prediction with 100% certainty.

Bayesian: Well, I will have to run a probability analysis on that; run several others on certain competing hypotheses; obtain their likelihood ratios; and ...

Aristotelian: Spare yourself from the work, my old adversary. You speak of hypotheses, or "educated guesses," but this is not a "guess" of mine, it is a fact of reality that can be known with certainty.

Bayesian: Well alright then, what is YOUR PREDICTION, my reverent Swamy Guru with these mysterious intellectual powers "as well?!"

Aristotelian: I predict - with 100% confidence - that all those systems which accept less than half of one dollar bill as if it were a whole dollar (replacing the torn bill with a new one) will go bankrupt.

Bayesian: Even if they make the cut-off for replacing all torn dollars that still retain a third of the original paper they were printed on?

Aristotelian: Bankrupt.

Bayesian: Even if they make the cut-off for replacing all torn dollars that still retain two-fifths of the original paper?

Aristotelian: Bankrupt.

Bayesian: How in the heck can you be so certain of this - and especially without more empirical knowledge?

Aristotelian: Mechanistic understanding.

Bayesian: Sounds like a cool trick, I'll have to look into it - when I get time away from my liklihood ratios, that is.

Aristotelian: It's no "trick" - it's the proper use of your mind - you are a conceptual being.

Bayesian: Are you starting-in with that metaphysical stuff again?

Aristotelian: Yes ... I guess I can't help but to base my reasoning solidly in the actuality of reality.

Bayesian: Oh dear, where does all this mumbo-jumbo end?

Aristotelian: Actually, I can tell you that, too. You see, if you just work to understand these axioms here ...

Bayesian: Aaagh! Somebody please come and help me - I being reasoned to death over here!

Ed

Post 1

Saturday, June 5, 2004 - 1:17pm

2 self-corrections (clarifications) of my "objective philosophy"-illustrating dialectic above:

What the man from Aristotelia claims to "know" is actually better denoted as what he "understands." What it is that we "know" are facts, and what it is that we "understand" is how the facts "hang together." Said another way, "understanding" is merely the "knowing" of how facts "hang together," from our basic first principles up to our final ends or purposes.

Also, objections can be made as to the precision involved in implementing (by measuring the partial bills) the stipulation of "not ever accepting less than half a dollar" as a whole. However, critical analysis indicates that the principle - of not ever accepting less than 50% of a dollar bill - stands for whatever level of precision the context imposes.

The straightforward reason that the principle can be known to be right (and not merely "believed" right), is that breaking the principle allows one bill to become two bills, which violates the Law of Identity.

The level of precision in a given context will dictate the amount of allowable error (bills too close to the cut-off to distinguish whether or not they should be accepted). What is certain is the principle, what is contingent is the level of precision/error margin that is acceptable, which will affect the fate of each particular bill - something which cannot be known "a priori" (this lack of omniscience, however, is inconsequential to our productive purpose here).

So the fate of each particular bill is uncertain, but our knowledge/understanding of how to "treat" the bills is not. We can also adjust the level of precision in order to satisfy individual doubts - however, we can never adjust the principle; it is, was, and will be true throughout space and time. And it can be understood by a human mind, once that mind has been "empowered" by the confines/limitations of reason and reality.

Ed
(Edited by Ed Thompson on 6/05, 1:27pm)

(Edited by Ed Thompson on 6/05, 1:29pm)

Post 2

Sunday, June 6, 2004 - 2:55am

Entertaining Ed, thanks. Sounds like a clear win to the Bayesian to me ;)

Here's a good link:

http://www.sl4.org/bin/wiki.pl?UntanglingCognition/BayesianProbability

Marc puts on his Darth Vader voice:

"You don't know the power of the Bayes side..." ;)

Post 3

Sunday, June 6, 2004 - 9:43am

Marc,

I'll attempt to provide the clearest exposition of Bayes Theorem to date (available anywhere), but before I do this, please answer the following:

Are you - or are you not - certain that A is A?

Ed

Post 4

Wednesday, June 9, 2004 - 11:02pm

Ed,

Stock Randroid slogans like 'A is A' are meaningless until you try to say exactly what they mean. And then as soon as you do so you will inevitably be drawing on concepts that were formed on the basis of empirical data from which uncertainty cannot be removed. I presume you're referring here to one of the three basic laws of logic, the law of identity. As I said in earlier thread, Rand (and Aristotle) were probably right about the 3 laws of logic. Most probably they are indeed implicit in all our thought processes. But this fact has not (and cannot ever be) established with certainty. As far as we can tell we need the laws of logic to reason. What does that prove? That we probably need the laws of logic to reason. That's all. It does not prove that these laws are absolutes; it does not prove that these laws are certain truths. It just means that as far as we can tell, we humans need these laws to reason.

When I tried to explain this, Objectivists immediately accused me of 'denying the laws of logic'. No I don't deny them at all. I accept them. Just not with certainty.

Post 5

Thursday, June 10, 2004 - 9:32am

Ed, if you haven�t already studied it, I think you would find the thread �Reason is an absolute� to be very illuminating with respect to the meaning and implications of Marc�s epistemology. There, for example, he goes into detail about his idea of knowledge, and about accuracy (possible to man, according to Marc) versus certainty (not possible). Everything really essential that can or should be said about his view (and that of the �Bayesroids�) has, in my opinion, been said. (However, I regret I do not now have time to �chew� the issues further to clarify them, as I had a few more observations to make with regard to specific points.)

(Edited by Rodney Rawlings on 6/10, 3:10pm)

Post 6

Friday, June 11, 2004 - 4:56am

Ed, Marc,

If Marc is not certain A is A, it is irrelevant, not to Marc, but to the truth.

The whole of Marc's argument rests on his non-definition of certainty. If he defines certainty as the state of some individual's conviction about some proposition, it is a subjective matter without philosophical relevance. If certainty means, some propositions are logically and absolutely true (whether anyone actually knows any of them or not), about those there can be no uncertainty, only ignorance.

A is A is absolutely certain, even if Marc or anyone else is only 99% convinced of that certainty, and 1% ignorant of it.

In the practical world, I have great sympathy for Marc's view. In the real complex world we live in, we almost never know all the facts, almost every thing has some doubt about it, and there is some risk in every undertaking. Most of the time we operate, if we are reasonable, on the basis, within the scope of what I know, this is what I expect. When I drive to the grocery store, I'm certain I'll find milk there, but know, there is always a chance the power went out overnight and all the milk spoiled. But once I reach the store and see the milk, there is no more uncertainty about the milk being there.

It would be Marc's contention that there is still some uncertainty, and there might be for Marc, but not for anyone else, I do not think. What most people mean by certain is, "what I see I see." What Marc means by certainty is still in question.

(Marc, please excuse my speaking of you in the third person. I do not intend for this to sound like I'm talking about you. I am addressing your ideas, not your person.)

Regi

Post 7

Saturday, June 12, 2004 - 12:07am

Regi,

I thought I made my defintion of certainty very clear:

I define the degree of certainty as :

"as the state of some individual's rational conviction about some proposition"

and I totally disagree that rational conviction: "is a subjective matter without philosophical relevance" You weigh up the evidence and use probability theory to assign an objective figure. This is not a subjective matter.

If course I agree that the truth or falsity of propositions is an absolute matter, independent of whether we believe them or not. But as I clarified above, this is most definitely not what I meant by 'certainty'.

I do agree that the proposition 'A is A' is likely to be true, but I do not hold a degree of rational conviction equal to 100% for this proposition, and I think that if you are being honest with yourself, you don't either.

Rodney said:

Everything really essential that can or should be said about his view (and that of the �Bayesroids�) has, in my opinion, been said.

Not really Rodney. After all, neither side has been convinced yet ;) If Ed has an article or an essay on the matter I'd look forward to seeing it.

Post 8

Saturday, June 12, 2004 - 4:49am

Marc,

I do agree that the proposition 'A is A' is likely to be true , but I do not hold a degree of rational conviction equal to 100% for this proposition.

That is exactly my point. The truth of A is A is not dependent on your degree of rational conviction.

Let's assume A is A is true, absolutely. If you are not convinced A is A is true absolutely, there must be something about the proposition that you do not know, because if you knew it, you would be 100% convinced. The reason for your doubt is ignorance about some aspect of A is A. If you say, even if you knew everything there was to know about A is A, you would still not be certain, your meaning of certainty is irrational. To doubt, there must be a reason.

You may doubt that you really know everything there is to know about A is A, but you are in no position to assume no one else does. Someone who takes the position that they cannot know anything with 100% certainty, cannot be certain about what anyone else does or does not know.

I am willing to accept your argument that you cannot know anything with absolute certainty, including that you do not know that no one else knows anything with absolute certainty.

You can say you are not certain about anything, but if you say I cannot be certain either, you have to doubt what you said.

Regi

Post 9

Saturday, June 12, 2004 - 7:35am

Marc, surely you can guess what my reply would be!

Post 10

Saturday, June 12, 2004 - 8:49pm

Bayesian Reasoning: Strengths & Limitations
by Ed Thompson

Introductory overview (the 2 essentials to Bayesian Reasoning):

Logical Assumption:
Instances of B update the probability that A.

Theorem:
[the Probability of A; given the instance of B] = [the Probability of both A and B] / [the Probability of B]

What is Bayesian Reasoning?
Bayesian Reasoning is a type of reasoning that combines probability estimates of various contingencies in the attempt to provide an evaluative standard by which their various rational justifications can be measured against and therefore hierarchically arranged.

It is a method of updating the estimate of the likelihood of a given contingency, in light of the evidence of another contingency that is taken to be in a conditional relationship with the first (a horizontal justification of propositions - justification via the Coherency theory of Truth).

Where does it fit within the field of Epistemology?
Bayesian Reasoning is appropriate when applied within the classical Humean model of "frequentistic empiricism" (measuring relative frequencies for the purpose of induction).

A prerequisite for utilizing Bayesian Reasoning is that all of the propositions under consideration must be interpreted as contingent (no irrefutable "necessary truths" are allowed in). This can be validated by visual inspection utilizing the equation above ...

Taking the probability-values for "necessary truth" (p = 1.0) and "falsity" (p = 0.0), and substituting these values into the equation, notice how these probability substitutions eradicate the equation's instrumentality as a tool to inform reasoning (note: objectivists may drop the redundant qualifier "necessary" and simply use "truth" for the value of p = 1.0).

This limitation is perhaps illustrated best by a definitive example - converting Reductio Ad Absurdum into probabilities and checking for informative utility:

If B then A ............ p(A; given "B") = 1.0

not A .................... p(A) = 0.0
----------------
Therefore, not B .... p(B) = 0.0

Are there predictable consequences to philosophically championing Bayesian epistemology?
A Bayesian epistemology - by way of being inherently nominalist - precludes any awareness of an objective Metaphysics (no "understanding" of Reality is possible). To marshal support for this indictment, attention can be called to the "reductio" example above.

Reductio is valid under the assumption that the terms are defined properly. Add to this the additional understanding that properly defined terms will capture what is known to be most essential from known attributes (ie. will capture proper factual relations to Identity). It follows then that, within the context of any philosophy claiming objectivity (those acknowledging Identity), the necessity inherent to Identity necessarily invalidates "Bayesian" utility.

In sum then, outside of the arena of new knowledge acquisition, such as that of investigative science, Bayesian Reasoning is essentially a tool of the nominalist (a subjectivist who disbelieves that conceptual thought can give humans a clear and sufficient understanding of Identity; or of "classes" or "kinds"). And this identification, to one who champions objectivist principles, is unsettling.

To illuminate my personal anxiety regarding the championing of Bayesian Reasoning as a viable epistemological method, I must invoke MacIntyrian wit: nominalism is "intractably problematic, and irremediably so." (read on)

Excerpt from Adler's objective invalidation of Nominalism as a viable philosophical position
"If human beings enjoyed the power of conceptual, as opposed to perceptual thought, there would be no difficulty in explaining how words signify generalities or universals. They would derive their significance from concepts that give us our understanding of classes or kinds.

But regarding human beings as deprived of conceptual thought poses a problem for Berkeley and Hume. They are compelled to say that when we use words that appear to have general significance, we are applying them to a number of perceived individuals indifferently: that is, without any difference in the meaning of the word thus applied. This amounts to saying that there is a certain sameness in the individual things that the speaker or writer recognizes.

Are they not contradicting themselves when they offer this explanation of the meaning of general terms or common nouns? If human beings do not have conceptual thought, how can they recognize the sameness that permits the nominalists to say that the same word can be applied indifferently in a number of individuals?

Are they not contradicting themselves? Should not nominalism -- the assertion that names have general significance even though human beings can have no understanding of kinds or classes -- be rejected?"

source for excerpt:
http://www.thegreatideas.org/apd-nomi.html
(Edited by Ed Thompson on 6/12, 9:02pm)

(Edited by Ed Thompson on 6/13, 8:16pm)

Post 11

Sunday, June 13, 2004 - 11:19am

Hi Ed,

I have a question. In your quote by Adler, "If human beings enjoyed the power of conceptual, as opposed to perceptual thought,..." What does he mean by "perceptual thought?" I know he attributes it to the views of Berkeley and Hume, but I don't know what he means by it. Neither Berkeley or Hume denied that we have concepts, they just denied their validity, as far as I know, and both implied perception is also of doubtful. (Kant invalidated everything.)

I am not a student of Adler, though I have read him, and not been impressed, which is the reason I have not studied him more, I suppose. I am probably missing something, which is the reason for my question.

Thanks!

Regi

Post 12

Sunday, June 13, 2004 - 11:37am

I don't have time to involve myself here, but isn't it "Not A, therefore not B" rather than the other way around? (I don't think it affects Ed's discussion though--which I'm too busy to evaluate.)

Post 13

Sunday, June 13, 2004 - 6:31pm

Marc Geddes writes:
>...slogans like 'A is A' are meaningless until you try to say exactly what they mean

I think that this formula is not quite meaningless, but very close to it. The problem with "A=A" is, of course, that it sacrifices its informative content in order to be as true as possible. In other words, it tells you nothing about what "A" actually is, other than it is itself! But then, what else would it be? The price it pays to be so purely true is that it is almost purely empty. Nor does it offer any clues as to *how* we might reliably discover what "A" is, other than with what little information you already possess. To paraphrase a line from Kafka: "They tell us that A is A - but we knew that already!"

It pays to remember that A=A was basically an attempt by Aristotle to solve the fundamental flaw in his definition-based system. That problem is: every term requires a definition. Yet every definition requires an *additonal* term to avoid a tautology. This term in turn needs to be defined, creating the need for an additional term, and so on in an infinite regress. Aristotle realised this, and proposed axioms like "A=A" in an attempt to block the regress. So rather than fundamental building blocks, axioms like "A=A" are really more like stop-gap measures. And rather than the greater precision this process of definition seems to promise, it can in reality only offer the *opposite* of precision - an infinite regress.

Naturally, such a method will produce mostly tautological debates, where one merely plays with the meanings of words in order to manufacture the conclusions one desires in advance, rather than proceed through creative proposals and testable arguments (the Scholastics being the textbook examples here, though this problem thoroughly permeates modern philosophy too ).

So the problem with "A=A" is not so much that it is meaningless; rather that it is useless.

- Daniel

Post 14

Sunday, June 13, 2004 - 8:38pm

Rodney,

Thanks for the heads-up (error has been edited)!

Regi,

Regarding Adler's "powers of perceptual thought," he took the position that it was a catch-all term for perception, imagination, and memory.

As far as imagination goes, the counter-factual objects of imagination present to a human mind - but which have never been perceptually present - such as centaurs and mermaids, require the additional faculty of conceptual thought.

Ed

Post 15

Sunday, June 13, 2004 - 9:07pm

Daniel,

I don't agree with you that "A is A" is useless. "A is A" is not meant to provide new knowledge to man. It is meant as a guide for man to use when understanding reality.

Using the common perceptually illusory "stick in water appears bent" example, primitive man would think that the stick actually IS bent as you put it underneath the water. But A is A, it cannot be a different thing under water (it is one and the same stick). Utilizing A is A here, we can productively search for the real reason it appears bent: refraction of light.

Therefore, A is A can be extremely useful to keep us on target when we are trying to understand values and reality, and this increasing understanding (of values and reality) is the purpose of philosophy.

Ed

Post 16

Monday, June 14, 2004 - 12:24am

Ed: �"A is A" is not meant to provide new knowledge to man. It is meant as a guide for man to use when understanding reality.�

And that�s just where it falls down, Ed. A is A, or A=A, is an identity statement, and is therefore valid for any and all values of A. In that case, �table is table�, �chair is chair�, �unicorn is unicorn�, �God is God�, are all equally valid because they are identity statements of the type A=A. Yet there is a good deal of debate over the truth value of some of these notions.

�Using the common perceptually illusory "stick in water appears bent" example, primitive man would think that the stick actually IS bent as you put it underneath the water. But A is A��

It�s somewhat presumptuous to surmise what �primitive man�, whoever he might be, would have thought about the bent-stick illusion, but this example has nothing to do with identity. The bent-stick illusion is a predicate statement, so A=A has nothing to tell us about it.

Brendan

Post 17

Monday, June 14, 2004 - 1:56am

Ed writes:
>Using the common perceptually illusory "stick in water appears bent" example, primitive man would think that the stick actually IS bent as you put it underneath the water. But A is A, it cannot be a different thing under water (it is one and the same stick). Utilizing A is A here, we can productively search for the real reason it appears bent: refraction of light.

Well, I for one would applaud our primitive man's thoroughly scientific approach: noticing a phenomenon in his environment, then beginning to guess at the reasons for it, and then perhaps testing those guesses with some crude experiments. It is most unfortunate then that this method is so thoroughly un-Aristotelian. For any knowledge our primitive scientist might hope to gain from his guesses and experiments would be, from the Aristotelian perspective, hopelessly flawed from the outset. Why? Because, as far more knowledgeable philosophers might have informed our poor caveman, he should really have focussed his energies on first establishing the correct definition of "stick"...

- Daniel

Post 18

Monday, June 14, 2004 - 2:12am

I used to think "A is A" was useless. But, I think at the time I just didn't know what Rand meant when she said it.

Rand wrote sometimes about what it's like for an infant to see the world for the first time--it must be something like a big blur of colors, changing and appearing and disappearing seemingly at random. But at some point, the infant realizes that there are *objects*--the infant realizes that there are specific, individual things. For example, he recognizes his mother as one thing, and maybe he recognizes the red ball in the corner as another thing. And he realizes that his mother will never randomly blip out of existence, and the red ball will never randomly blip out of existence, and his mother will never randomly melt into a red ball, and things like that. Moreover, the infant recognizes that his mother has certain properties which the red ball doesn't have. For example, his mother is warm, whereas the red ball is cold; his mother smells very good, whereas the red ball doesn't have much of a smell; his mother makes noises that the red ball never makes.

None of this was obvious to the infant at first, because at first the world just seemed like a bewildering flux of colors, or something like that.

In short, the infant at some point recognizes that the world is made of *things*, and the things each have their own separate identities; the things each behave in their own ways; his mother smells one way, the red ball smells another way, and there will never be a time when the red ball all of a sudden smells very nice; his mother is warm, the red ball is cold, and there will never be a time when the red ball is as warm as his mother. This realization--that the world consists of distinct things, and each distinct thing may only behave in its own unique way--this realization is what I think Ayn Rand meant when she said, "A is A".

It's not really the same thing a mathematician or a logician usually means when he states that "A is A."

Of course, I am by no means an expert on Objectivism, but this is how I understand the issue so far.

Post 19

Monday, June 14, 2004 - 2:38am