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The Gettier counterexamples to Justified True Belief as knowledge

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18 minutes ago, New Buddha said:

Fair enough.  I wasn't able to understand from your brief post what you were driving at.

Measurement omission is actually implicit/inferred measurement inclusion here per both Ayn Rand and clarifications by Harry Binswanger, as I am able to grasp it.

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14 minutes ago, dream_weaver said:

Measurement omission is actually implicit/inferred measurement inclusion here per both Ayn Rand and clarifications by Harry Binswanger, as I am able to grasp it.

But even with the examples that you gave, (donuts, eggs, hot dog buns) the suppliers of those products all have established quality and weight standards (and tolerance levels) as to what constitutes an acceptable product.  No two of the egss, donuts, hot dog buns are "exactly" the same in terms of weight, quality, etc.

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16 minutes ago, New Buddha said:

But even with the examples that you gave, (donuts, eggs, hot dog buns) the suppliers of those products all have established quality and weight standards (and tolerance levels) as to what constitutes an acceptable product.  No two of the egss, donuts, hot dog buns are "exactly" the same in terms of weight, quality, etc.

This fails to identify the measurement(s) that is(are) exact, blending them (instead) with the measurements that necessarily require (a) range(s) for quantification. [stolen concept fallacy?]

Edited by dream_weaver
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1 hour ago, New Buddha said:

 Just because Rand does not use the word "approximation" doesn't some how make what I say false.  

You were using "approximation" in the sense that I said isn't valid, while you were not using it in the sense Rand did and the sense I think is fine. Then I explained why your idea is wrong. I mentioned Rand since you brought up her view being like yours. You specifically mentioned "good enough" and workability as standards, no?

1 hour ago, New Buddha said:

It is perfectly objective to say that something is approximately 7-5/8" long.   Do you also have a similar issue with an "average" or "range of values" for tensile strength of lumber, such as Douglas Fir No. 2?  Or using statistical based sampling for quality control?

It's okay to say that, but it's an estimation for "good enough" and limited time, -not- a basis for definite knowledge or certainty. A range of values is not an estimation, it is absolute and exact, a -range- of exact measures. Statistical based sampling, if you mean whether a measurement is within a specific range, is not an approximation. But if you mean something like you want, p < 5%, that's an approximation and not the greatest way to develop knowledge except as an initial analysis.

The method may be objective, doesn't mean it promises the truth, or that resulting measurements allow you to find the truth directtly.

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7 minutes ago, Eiuol said:

It's okay to say that, but it's an estimation for "good enough" and limited time, -not- a basis for definite knowledge or certainty.

This makes no sense, and borders on Rationalism.  If a brick is 7-5/8" long (and not 7-59/96" or 7-61/96"), it's dimensions will still vary over time due to thermal expansion, moisture absorption, etc.  That's why we design expansion joints in masonry walls, because we know that materials expand and contract through out the day and seasonally.  We also specify established, professional standards (ASTM) that fabricators must follow in the manufacture of bricks.  But we don't assume that the quality of all materials used in construction is "exactly" the same.

I don't know about you, but I use math and mechanics as tools to build things.  Why do you use it?

18 minutes ago, Eiuol said:

A range of values is not an estimation, it is absolute and exact, a -range- of exact measures.

And I said this same thing.  But, again, I use math and mechanics to build things.  I don't confuse mathematics or mechanics with the fact that no two pieces of lumber or no two bricks are "exactly" the same.  If my geotechnical engineer provides me with a report that the soil on a site has a bearing capacity of 3,500 psf. and that the water level is (at the time the samples were taken) on average 3 feet below the surface, I know that all this is inferred from 6 or 7 sparse samples distributed over a couple of acres of the site at a certain time of the year (it rains a lot in the Pacific Northwest).   But what I don't do is mistake the report for "reality", and have still hire him to be on site during construction taking additional measurements.

The difference between you and me in this post is that you are playing word games with things that you don't really understand while I actually use math and mechanics in my job and understand the limits of what I know and what I don't know - i.e. I understand the context in which this information is put to work.

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34 minutes ago, New Buddha said:

I understand the context in which this information is put to work.

What does this have to do with acquiring knowledge or JTBs or the Gettier case? I'm not talking about making stuff... It's just more examples of "truth is that which is useful".

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24 minutes ago, Eiuol said:

What does this have to do with acquiring knowledge or JTBs or the Gettier case? I'm not talking about making stuff... It's just more examples of "truth is that which is useful".

Inductive reasoning (which forms the basis of all knowledge - including science) is not about creating propositions which you must justify in order to believe them to be true.

All swans are white.

This propostion is not a "belief" that needs be be justified.  It is, as McCaskey, notes the incorrect  importation of the Uniformity Principle into induction.  From McCaskey:

For them, classification, and therefore induction, comes before uniformity, not the other way around. It’s not that you must presume uniformity in order to classify. It’s that you classify to find uniformities. For Whately, uniformity is primary. For Aristotle’s followers, classification is primary.

For them, you don’t need a uniformity principle to obtain inductive knowledge, even certain inductive knowledge. You just need the ability to identify similarities and differences, the ability to classify well, and—if you want certainty—the ability to obtain essentialized definitions.

Plasmatic correctly touched upon this in an above post.

Edit:  As an example of the Uniformity Principle and incorrect inductive reasoning:

All kiln dried Douglas Fur No.2 2x12 beams, with a moisture content of 12%, will break under a point load of 500 lbs.

Edited by New Buddha
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On 1/22/2017 at 3:49 AM, Grames said:

But correspondence can often be a matter of degree.  How much correspondence is enough?  According to Rand perception is essentially measurement, and measurements are always and only to within a certain range of precision.   So then even our automatic and infallible perceptions do not correspond perfectly with reality.  In Objectivist epistemology concepts omit measurements completely, so the remaining correspondence of a concept to reality takes an entire book to explain.  Yet knowledge is still possible to finite and fallible human consciousness because the degree of correspondence required is not perfect correspondence but the lesser standard of usefulness.  There is a useful and justifying degree of correspondence when our knowledge can explain without contradiction, can predict reliably, and ultimately serves the practical end-in-itself of living.

Added this for my above post.

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1 hour ago, New Buddha said:

This propostion is not a "belief" that needs be be justified.  It is, as McCaskey, notes the incorrect  importation of the Uniformity Principle into induction.

I don't follow - all knowledge needs to be validated, which is the same as justified.

Do you think truth IS that which is useful?

"How much correspondence" seems more related to my claims of "true as far as one knows", rather than "approximately true". But I'm not sure. @Grames, could you clarify?

Edited by Eiuol
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1 hour ago, Eiuol said:

What does this have to do with acquiring knowledge or JTBs or the Gettier case? I'm not talking about making stuff... It's just more examples of "truth is that which is useful".

Now there's a question that could only be asked by a Rationalist.  Knowledge is really only ever about "making stuff".  That's what keeps you fed, dry, gets you to and fro the places you need to be.  It is the ultimate justification of all knowledge because it enables living, and in the modern era of the 2000's it is living in pretty high style compared to all that went before.

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21 minutes ago, Eiuol said:

I don't follow - all knowledge needs to be validated, which is the same as justified.

Reality justifies knowledge, not converting propositions into symbols and manipulating them according to syntactical rules.

I gave an example of the Medieval discovery of 3-crop rotation.  Does the fact that their "justification" of why it worked (which was wrong) mean that 3-crop rotation does not work?

I gave an example of how the Wright Brothers flew a heavier-than-air airplane with no knowledge of aerodynamics.  Does this mean that the air plane did not really fly?  And, by the way, the field of aerodynamics is still learning about how flight works.  Should we ground all planes until we are "certain" that we can "justify" that flight is "possible"? 

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21 minutes ago, Grames said:

Knowledge is really only ever about "making stuff".  

Yes.  There is a reason that Rand opposed Stadler to Galt.  Stadler was the arch-Rationalist who couldn't understand why Galt would waste his time on engines and not concentrate on the pursuit of "pure" knowledge.

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27 minutes ago, Grames said:

Now there's a question that could only be asked by a Rationalist.  Knowledge is really only ever about "making stuff".  That's what keeps you fed, dry, gets you to and fro the places you need to be.  It is the ultimate justification of all knowledge because it enables living, and in the modern era of the 2000's it is living in pretty high style compared to all that went before.

I mean, it isn't that knowledge isn't useful, just that usefulness is not a "truth maker". I am saying that in the context "what makes a statement true?" Although I take your point that usefulness is a justification for knowledge - useless knowledge would be a contradiction. I see how the question was Rationalist.

But that's different than using approximated measurements to build a house in a week. That wouldn't itself be sufficient to say why the measurements worked. It's only one step to acquiring knowledge, sort of "initial evidence" so to speak. 

NB, at no point did I suggest "don't act until certain about why something worked", I actually said that a justified belief doesn't need to be certain. Approximations are a good start to developing theories. I don't want to call an approximation the truth.

Edited by Eiuol
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It is a broadest possible lesson of the industrial revolution, which Ayn Rand pointed out and I'm sure others as well because its such a basic point, is that philosophy is a practical tool for living not merely a distraction for the rich to show off their high class and social status, or merely an exercise in rhetoric for political gain, or to be a consolation or distraction from life.  

The real distinction is between mere opinion and knowledge, which is the distinction that Plato made in the excerpt from the Meno Spooky used above.  Opinion and knowledge can both be useful, but knowledge is superior because it is opinion that is caused by perception and logic.   Better perception and better logic is always welcome, but what was at one time opinion with cause ( knowledge ) does not retroactively become demoted to baseless opinion without cause when better perception and better logic appears.   

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28 minutes ago, Eiuol said:

But that's different than using approximated measurements to build a house in a week. That wouldn't itself be sufficient to say why the measurements worked. It's only one step to acquiring knowledge, sort of "initial evidence" so to speak. 

Think of it this way.

A blueprint is not the building.  A blueprint is an abstraction.  I can draw straight walls, 90 deg. corners, etc.  But, having worked in both General Contracting and Architecture, I know from first hand experience that walls are not built true, corners are never 90 degrees, a wall that is 12 feet on a blueprint is not "really" 12 feet when built. There will be however, as Grames notes, a useful degree of correspondence.

A Rationalist would regard the blueprint as an a priori or analytic knowledge, and the actual building as a a posteriori or synthetic knowldge.   To the Rationalist, the blueprint would be "more true" than the actual building.  The drawing of the blueprint is guided by "theoretic" knowledge while the actual construction of the building is done by "practical" knowledge.

Of course, Objectivism completely rejects this type of dichotomy.

This is also true for the calculations that a structural engineer uses to size wood beams.  The Mechanics (Classical Mechanics) used by the engineer are abstractions, just like the blueprints.  But the actual wood beams are all existentially different.  Some are warped, some have higher moisture content, different shear and moment values, different dimensions, etc.

To a Rationalist, this means that all knowledge is subjective.

To understand Kant (to the degree that he can be understood at all) you have to understand how powerful the influence of Newton was on the age.  Hume "woke" Kant from his slumber because Hume dared to suggest that knowledge gained via the senses was not "analytic" and therefore all "synthetic" knowledge gained by the senses was subjective.  This disturbed him.

Kant posited that our mind's innate categories were a priori truths in the same way that he regarded Newtonian Laws as a priori truths.

Kant saw Hume as assaulting knowledge, and believed that he had the answer.

Kant's dialectic between the a prior and a posteriori  was actually an attempt to revert knowledge back to Scholasticism and Aristotelianism (not Aristotle!) where there was a difference between Divine Substance and Accident.  This break from Substance/Accident was in part Berkeley's critique of Locke's Primary and Secondary qualities.  Berkeley thought that Locke would lead back to a type of Scholastic dualism.  Newton was also wrestling with Form as causation - which was a hold over of Aristotelian Metaphysics, while Leibniz was developing his Monadology which actually lead to Einstein's Relativity.  The Protestant British Empiricists were the arch-nemesis of the Protestant German Idealists - and both were the arch-nemesis of the Roman Catholic Church.

I don't know if this will add clarity (or confusion!) to the topic, but humor me for the long post.  I think while I write....

 

 

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I have little time to deal with the many things I dissagree with in the recent posts but just wanted to point something out quickly:

That is one of the reasons that Measurement is covered so heavily in the book. Kant (and the German Idealist in general) wanted omniscient, a priori knowledge, and not synthetic knowledge "distorted" by the mind.  So they introduced a dialectic method based on the flawed assumption of an unbridgeable, ontological dichotomy.

I dont know why your claims about Kant are so far off sometimes but this is demonstrably false. Kant believed in the "synthetic apriori". 

Also, Rand actually believed that one can know what properties belong to "things in themselves" through the special sciences....

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I think people here need to learn why Rand called it "omitting measurements" and not "omitting quantities"....why Rand called perception the arithmetic of knowledge and concepts the algebra.... 

There is absolutely nothing approximate about 1+1=2 and the metaphysical "base" of that undeniable fact is given in perception.....

 

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5 hours ago, Plasmatic said:

I dont know why your claims about Kant are so far off sometimes but this is demonstrably false. Kant believed in the "synthetic apriori". 

I don't disagree with this.  I was giving a very generalized (and historical) outline of Kant in the context of Eiuol's understanding of the issue of inductive propositions versus McCaskey's position.  The fundamental flaw of Kant was to divide knowledge into analytic and synthetic propositions.  All subsequent errors of his arise from this flawed premise.  He did so in order to defend Religion from that atheist Hume.  But all Kant really did was put a quasi-scientific "modern" veneer onto the Substance/Accident dichotomy of Scholasticism.

From C.S. Peirce's The Probability of Induction:

Late in the last century, Immanuel Kant asked the question, "How are synthetical judgments a priori possible?" By synthetical judgments he meant such as assert positive fact and are not mere affairs of arrangement; in short, judgments of the kind which synthetical reasoning produces, and which analytic reasoning cannot yield. By a priori judgments he meant such as that all outward objects are in space, every event has a cause, etc., propositions which according to him can never be inferred from experience. Not so much by his answer to this question as by the mere asking of it, the current philosophy of that time was shattered and destroyed, and a new epoch in its history was begun. But before asking that question he ought to have asked the more general one, "How are any synthetical judgments at all possible?" How is it that a man can observe one fact and straightway pronounce judgment concerning another different fact not involved in the first? Such reasoning, as we have seen, has, at least in the usual sense of the phrase, no definite probability; how, then, can it add to our knowledge? This is a strange paradox; the Abbé Gratry says it is a miracle, and that every true induction is an immediate inspiration from on high.[3] I respect this explanation far more than many a pedantic attempt to solve the question by some juggle with probabilities, with the forms of syllogism, or what not. I respect it because it shows an appreciation of the depth of the problem, because it assigns an adequate cause, and because it is intimately connected—as the true account should be—with a general philosophy of the universe. At the same time, I do not accept this explanation, because an explanation should tell how a thing is done, and to assert a perpetual miracle seems to be an abandonment of all hope of doing that, without sufficient justification.

Edited by New Buddha
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10 hours ago, New Buddha said:

But the actual wood beams are all existentially different.  Some are warped, some have higher moisture content, different shear and moment values, different dimensions, etc.

To a Rationalist, this means that all knowledge is subjective.

I think that if the person were whole-hog Kantian, this would only mean that knowledge is unattainable via perception or measurement.

But don't forget that Empiricism is a type of error as is Rationalism. "Wow, look at the sheer number of possible measurements and variations! I have to say what one knows as true is only approximate, there's just too much to be exact. After all, it works, who needs an exact answer?"

There are of course degrees of correspondence as to -precision-, but as far as accuracy, knowledge is exact. If it isn't exact, you would say something like: "This theory works well, but I'm unsure about why it works, so I don't know much about it yet". 

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But, respectfully Euiol, this is where an understanding of Mechanics would benefit you.  Mechanics [roughly, models of systems] are approximate solutions.  This is especially true where there are large degrees of freedom and many parameters.

You hear the words "approximate" and think, "He's a skeptic!" "He's a Pragmatists!" "He's an Empiricists!"  "He believes knowledge isn't possible!"

The difference is that I'm using the term approximate differently than you are.

When analyzing complex systems, we break large complex unsolvable problems down into smaller, manageable sized problems with fewer degrees of freedom that can each be solved.  But there is a price to doing so in the sense that we are only modeling those variables that we consider important to obtaining a workable solution to a problem - which is measured against empirical testing and observation.

When a structural engineer models a building, he starts with the roof deck and some assumptions about live and dead loads, joist spacing, etc.  One he sized the deck, he then calculates the tributary area of loads that falls on each individual joists.  The he takes these loads and applies them to columns and then to footings.  After this, he the analyzes lateral loads such as wind or seismic acceleration, etc.

This is an abstract - and managable - modeling how forces and stress propagate through a building's structure.  It is an idealization of the problem (and no, I'm not an Idealist!).  It is entirely objective, but the actual forces and stress that might present themselves during an actual seismic event when the wind is blowing and it's snowing is not what is being modeled by the engineer.  Buildings are constantly moving in complex, dynamic ways that vary from moment to moment.

It would be impossible to model the range of actual, continual changes because the math would break down due to the complexity.  Computers can help, but there are still limits.  The goal of modeling is not to model for the sake of modeling so that you can have a 1 to 1 correspondence with "reality".  The goal is to build a building that is safe and will last for it's projected life expectancy, meet a budget, be easily constructable, etc.

There is a funny story attributed to the physicist Freeman Dyson.  (And it explains much of what is wrong with General Circulation Models (GCM's) used in Global Warming.  Dyson is a skeptic of Global Warming):

Why von Neumann's elephants? Derek was referring to a great piece by Freeman Dyson (who I have had the privilege of having lunch with a few times) published in Nature a few years back in which Dyson reminisced about a meeting with Enrico Fermi in Chicago. Dyson had taken the Greyhound bus from Cornell to tell Fermi about his latest results concerning meson-proton scattering. Fermi took one look at Dyson's graph and basically demolished the thinking that had permeated Dyson and his students' research for several years. The problem, as Fermi pointed out, was that Dyson's premise was based on fitting a curve to some data using four parameters. But, quipped Fermi, you can get a better fit to the data if you add more parameters. Fermi quoted his friend, the great mathematician John von Neumann - "With four parameters you can fit an elephant to a curve; with five you can make him wiggle his trunk". The conversation lasted about ten minutes. Dyson took the next bus back to Ithaca.

Edited by New Buddha
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The term approximation seems to have been used incorrectly here a few times now.  An approximation is not the same thing as a range.  Measurements are scales based on a delimited range. All of which are reducible back to perception.  An inch is an inch is a fact, not an approximation.  When you measure in inches, you are measuring within a range:  Within the range of an inch.  When we measure we are not looking for exactness, we are looking for preciseness. How precise? Within an inch, within a meter, within a nanometer.  This does not imply subjectivity in knowledge just because we cannot measure something exactly.  It gives us the knowledge that measurements are not exact; they are precise.  Remember, measurements are relationships, not exactness in a void.

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What is the range of answers to 1+1 ?

Why is quantity the one thing one must assume while measuring magnitudes?

From Mathematics is About the World:

Quote

In my view, Ayn Rand's characterization of mathematics gets to the heart of the subject. I maintain, in this book, that to understand how mathematics relates to the world, one must understand how mathematics relates to measurement. Indeed, the key to a full understanding and appreciation of mathematics, from both a philosophical and mathematical perspective and on all levels of mathematical abstraction, is to understand its concepts, propositions, and demonstrations in relation to measurement. In this chapter I apply that perspective to Euclid's Elements.         What is Measurement? 


 In Ayn Rand’s definition,  “Measurement is the identification of a relationship—a quantitative relationship established by means of a standard that serves  as a unit."5—‘1  The purpose of measurement is to extend and objectify our grasp of the world beyond what we can directly perceive by identifying quantitative relationships to what we can directly perceive. One of those means is the application of a universal standard a universal reference point to which all quantities of a particular kind relate.  Establishing quantitative relationships, however, is something more general than measurement in Rand’s sense and establishing a quantitative relationship between two quantities is possible without reference to a standard. For example, “This pencil is longer than that pencil,” identifies a quantitative relationship but makes no reference to a standard and is not, in this sense, a measurement according to Ayn Rand's definition.   On the other hand, a determination that, “This board is 5 feet long,” counts as a measurement because it relates the length of the board to a standard, namely to a foot.  So what does geometry measure? It measures shapes and spatial relationships. In particular, geometry measures triangles, distances, directions, areas, and volumes.  

Edited by Plasmatic
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5 hours ago, New Buddha said:

It would be impossible to model the range of actual, continual changes because the math would break down due to the complexity.  Computers can help, but there are still limits.  The goal of modeling is not to model for the sake of modeling so that you can have a 1 to 1 correspondence with "reality".  The goal is to build a building that is safe and will last for it's projected life expectancy, meet a budget, be easily constructable, etc.

You never did say if you think truth is "that which is useful".  I was disputing you saying if NM and QM give you the same answer, who cares past that? I'm saying great, build that stuff! But it doesn't mean approximation is knowledge.

" That a length falls between 1 and 2 isn't approximate as in "the True length is 1.52501109258mm at nm scale, so between 1mm and 2mm is our best guess", it's only approximate as in "it is absolutely within this range of our standard, and this is definite". "

I tweaked this slightly from earlier to make it clear that I'm disputing the first sense and claim it's your basis to say as long as you attain a goal, then the theory is good enough. If you agree about ranges, I don't understand your replies to SK.

By the way, not very related, but I am inclined to think in a practical engineering way, so it's not as if I don't understand practicality or utility. I like psychology most, where many overemphasize p-values. As justified as they are, they aren't good for saying alone if the theory is true on the whole.

 

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1 hour ago, Eiuol said:

I tweaked this slightly from earlier to make it clear that I'm disputing the first sense and claim it's your basis to say as long as you attain a goal, then the theory is good enough.

In my opinion, we differ on this post as to the nature of inductive propositions.  I agree with McCaskey.  What is your opinion on JM?  Do you understand how it differs from JTB?

As to what is in bold above, I never claimed that and that's not the issue.

Let's approach the issue this way.

I mentioned the Medieval discovery of 3-crop rotation.  Whatever belief that they might have had about why 3-crop rotation works, it would necessarily have be wrong.  They new nothing about fixing nitrates back into the soil, etc.

Did they have true knowledge ? Or only an unjustified belief?

Regarding P-values, it's been coming under fire lately.

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